Subgroups — C₂₃×#61062 #19208688

Order 5888.

2750 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3278	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3277	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3273	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3272	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3268	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3266	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#577	—	2	8	no	—
29	C₂₃×#575	—	2	8	no	—
30	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
35	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
42	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
47	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
49	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
50	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
52	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#550	C₂²	1	2	yes	—
54	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
55	C₂₃×#548	C₂²	1	2	yes	complemented
56	C₂₃×#548	C₂²	1	2	yes	complemented
57	C₂₃×#547	—	2	2	no	—
58	C₂₃×#547	C₂²	1	2	yes	complemented
59	C₂₃×#546	—	2	2	no	—
60	C₂₃×#546	—	2	2	no	—
61	C₂₃×#546	C₂²	1	2	yes	—
62	C₂₃×#546	C₂²	1	2	yes	complemented
63	D₄²×C₂₃	—	2	2	no	—
64	D₄²×C₂₃	C₂²	1	2	yes	complemented
65	C₂₃×#537	—	2	1	no	—
66	C₂₃×#537	—	2	1	no	—
67	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#536	—	2	1	no	—
70	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#535	—	2	1	no	—
72	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#525	—	2	1	no	—
74	C₂₃×#525	—	2	1	no	—
75	C₂₃×#525	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
77	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₂₃×#121	—	2	1	no	—
79	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
80	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#497	C₂²	1	2	yes	complemented
83	C₂₃×#496	C₂²	1	2	yes	complemented
84	C₂₃×#495	C₂²	1	2	yes	complemented
85	C₂₃×#492	C₂²	1	2	yes	complemented
86	C₂₃×#468	C₂²	1	2	yes	complemented
87	C₂₃×#468	C₂²	1	2	yes	complemented
88	C₂₃×#468	C₂²	1	2	yes	complemented
89	C₂₃×#468	C₂²	1	2	yes	complemented
90	C₂₃×#468	C₂²	1	2	yes	complemented
91	C₂₃×#468	C₂²	1	2	yes	complemented
92	C₂₃×#467	C₂²	1	2	yes	complemented
93	C₂₃×#466	C₂²	1	2	yes	complemented
94	C₂₃×#464	C₂²	1	2	yes	complemented
95	C₂₃×#464	C₂²	1	2	yes	complemented
96	C₂₃×#463	C₂²	1	2	yes	complemented
97	C₂₃×#463	C₂²	1	2	yes	complemented
98	C₂₃×#462	C₂²	1	2	yes	complemented
99	C₂₃×#461	C₂²	1	2	yes	complemented
100	C₂₃×#460	C₂²	1	2	yes	complemented
101	C₂₃×#459	C₂²	1	2	yes	complemented
102	C₂₃×#452	C₂²	1	2	yes	complemented
103	C₂₃×#452	C₂²	1	2	yes	complemented
104	C₂₃×#452	C₂²	1	2	yes	complemented
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#451	C₂²	1	2	yes	complemented
107	C₂₃×#451	C₂²	1	2	yes	complemented
108	C₂₃×#450	C₂²	1	2	yes	complemented
109	C₂₃×#450	C₂²	1	2	yes	complemented
110	C₂₃×#449	C₂²	1	2	yes	complemented
111	C₂₃×#449	C₂²	1	2	yes	complemented
112	C₂₃×#449	C₂²	1	2	yes	complemented
113	C₂₃×#449	C₂²	1	2	yes	complemented
114	C₂₃×#448	C₂²	1	2	yes	complemented
115	C₂₃×#448	C₂²	1	2	yes	complemented
116	C₂₃×#447	C₂²	1	2	yes	complemented
117	C₂₃×#447	C₂²	1	2	yes	complemented
118	C₂₃×#440	C₂²	1	2	yes	complemented
119	C₂₃×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
121	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
122	C₂₃×#436	C₂²	1	2	yes	complemented
123	C₂₃×#436	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₂₃×#435	C₂²	1	2	yes	complemented
126	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
136	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
137	C₂₃×2₋¹⁺⁴	—	2	4	no	—
138	C₂₃×2₋¹⁺⁴	—	4	2	no	—
139	C₂₃×H(5,𝔽₂)	—	2	4	no	—
140	C₂₃×H(5,𝔽₂)	—	4	2	no	—
141	C₂×#41×C₂₃	—	2	1	no	—
142	C₂×#41×C₂₃	—	2	2	no	—
143	C₂×#41×C₂₃	—	2	1	no	—
144	C₂×#41×C₂₃	—	2	1	no	—
145	C₂×#41×C₂₃	—	2	1	no	—
146	C₂×#41×C₂₃	—	2	1	no	—
147	C₂×#41×C₂₃	—	2	1	no	—
148	C₂×#41×C₂₃	—	2	4	no	—
149	C₂×#41×C₂₃	—	2	4	no	—
150	C₂×#41×C₂₃	—	4	2	no	—
151	C₂×#41×C₂₃	—	4	2	no	—
152	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×#41×C₂₃	C₂³	1	2	yes	—
156	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×#41×C₂₃	C₂³	1	2	yes	—
158	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
163	C₂²×Q₈×C₂₃	—	2	1	no	—
164	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₂²×D₄×C₂₃	—	2	1	no	—
169	C₂²×D₄×C₂₃	—	2	1	no	—
170	C₂²×D₄×C₂₃	—	2	1	no	—
171	C₂²×D₄×C₂₃	—	2	1	no	—
172	C₂²×D₄×C₂₃	—	2	2	no	—
173	C₂²×D₄×C₂₃	—	2	2	no	—
174	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
176	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂³×C₄×C₂₃	—	2	1	no	—
179	C₂³×C₄×C₂₃	—	2	1	no	—
180	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂₃×#137	—	2	4	no	—
182	C₂₃×#137	—	2	4	no	—
183	C₂₃×#137	—	2	4	no	—
184	C₂₃×#137	—	2	8	no	—
185	C₂₃×#137	—	2	4	no	—
186	C₂₃×#137	—	2	4	no	—
187	C₂₃×#137	—	4	2	no	—
188	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
189	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
190	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
191	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
192	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
193	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
194	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
195	C₂₃×#135	—	2	4	no	—
196	C₂₃×#135	—	2	4	no	—
197	C₂₃×#135	—	2	8	no	—
198	C₂₃×#135	—	2	4	no	—
199	C₂₃×#135	D₄	1	8	yes	complemented
200	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
203	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
205	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×SD₁₆×C₂₃	—	2	8	no	—
207	C₂×SD₁₆×C₂₃	—	2	4	no	—
208	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
209	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
210	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
211	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
212	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
219	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
220	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
222	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×D₈×C₂₃	C₂³	1	2	yes	—
224	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×D₈×C₂₃	C₂³	1	2	yes	—
227	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
228	C₂₃×#131	—	2	4	no	—
229	C₂×M₁₆×C₂₃	—	2	4	no	—
230	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
231	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
236	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
237	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
239	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₂₃×C₄⋊Q₈	—	2	2	no	—
241	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
242	C₂₃×#127	—	2	2	no	—
243	C₂₃×#127	C₂³	1	2	yes	—
244	C₂₃×#124	—	2	2	no	—
245	C₂₃×#124	—	2	2	no	—
246	C₂₃×#124	C₂³	1	2	yes	—
247	C₂₃×#124	C₂³	1	2	yes	—
248	C₂₃×#123	—	2	2	no	—
249	C₂₃×#123	—	2	2	no	—
250	C₂₃×#123	—	2	2	no	—
251	C₂₃×#123	—	2	2	no	—
252	C₂₃×#123	—	2	2	no	—
253	C₂₃×#123	D₄	1	2	yes	—
254	C₂₃×C₂²⋊Q₈	—	2	1	no	—
255	C₂₃×C₂²⋊Q₈	—	2	1	no	—
256	C₂₃×C₂²⋊Q₈	—	2	1	no	—
257	C₂₃×C₂²⋊Q₈	—	2	1	no	—
258	C₂₃×C₂²⋊Q₈	—	2	2	no	—
259	C₂₃×C₂²⋊Q₈	—	2	2	no	—
260	C₂₃×C₂²⋊Q₈	—	2	1	no	—
261	C₂₃×C₂²⋊Q₈	—	2	1	no	—
262	C₂₃×C₂²⋊Q₈	—	2	2	no	—
263	C₂₃×C₂²⋊Q₈	—	2	2	no	—
264	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
265	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
266	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
267	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
268	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
269	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
270	C₂₃×#121	—	2	2	no	—
271	C₂₃×#121	—	2	2	no	—
272	C₂₃×#121	—	2	2	no	—
273	C₂₃×#121	—	2	2	no	—
274	C₂₃×#121	—	2	1	no	—
275	C₂₃×#121	—	2	1	no	—
276	C₂₃×#121	—	2	2	no	—
277	C₂₃×#121	—	2	1	no	—
278	C₂₃×#121	—	2	1	no	—
279	C₂₃×#121	—	2	1	no	—
280	C₂₃×#121	—	2	1	no	—
281	C₂₃×#121	—	2	2	no	—
282	C₂₃×#121	—	2	2	no	—
283	C₂₃×#121	—	2	2	no	—
284	C₂₃×#121	—	2	2	no	—
285	C₂₃×#121	—	2	2	no	—
286	C₂₃×#121	D₄	1	1	yes	characteristic
287	C₂₃×#121	D₄	1	1	yes	characteristic
288	C₂₃×#121	C₂³	1	2	yes	—
289	C₂₃×#121	C₂³	1	2	yes	—
290	C₂₃×#121	C₂³	1	2	yes	—
291	C₂₃×#121	C₂³	1	2	yes	—
292	C₂₃×#120	—	2	2	no	—
293	C₂₃×#120	—	2	2	no	—
294	C₂₃×#120	—	2	2	no	—
295	C₂₃×#120	—	2	2	no	—
296	C₂₃×#120	—	2	2	no	—
297	C₂₃×#120	D₄	1	2	yes	—
298	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
299	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
300	C₄×D₄×C₂₃	—	2	2	no	—
301	C₄×D₄×C₂₃	—	2	2	no	—
302	C₄×D₄×C₂₃	—	2	2	no	—
303	C₄×D₄×C₂₃	—	2	2	no	—
304	C₄×D₄×C₂₃	—	2	2	no	—
305	C₄×D₄×C₂₃	—	2	2	no	—
306	C₄×D₄×C₂₃	C₂³	1	2	yes	—
307	C₄×D₄×C₂₃	C₂³	1	2	yes	—
308	C₄×D₄×C₂₃	C₂³	1	2	yes	—
309	C₄×D₄×C₂₃	C₂³	1	2	yes	—
310	C₂₃×#117	—	2	1	no	—
311	C₂₃×#117	—	2	1	no	—
312	C₂₃×#117	C₂³	1	1	yes	characteristic
313	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
314	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
316	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
317	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
320	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
321	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂₃×#107	C₂³	1	2	yes	—
324	C₂₃×#107	C₂³	1	2	yes	—
325	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
326	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
327	C₂₃×#103	C₂³	1	2	yes	—
328	C₂₃×#103	C₂³	1	2	yes	—
329	C₂₃×#103	C₂³	1	2	yes	—
330	C₂₃×#103	C₂³	1	2	yes	—
331	C₂₃×#103	C₂³	1	2	yes	—
332	C₂₃×#103	C₂³	1	2	yes	—
333	C₂₃×#102	C₂³	1	2	yes	—
334	C₂₃×#102	C₂³	1	2	yes	—
335	C₂₃×#102	C₂³	1	2	yes	—
336	C₂₃×#102	C₂³	1	2	yes	—
337	C₂₃×#102	C₂³	1	2	yes	—
338	C₂₃×#102	C₂³	1	2	yes	—
339	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₂₃×#97	C₂³	1	2	yes	—
344	C₄×C₈×C₂₃	C₂³	1	2	yes	—
345	C₂⁴×C₂₃	—	2	1	no	—
346	C₂⁴×C₂₃	—	2	1	no	—
347	C₂⁴×C₂₃	—	2	2	no	—
348	C₂⁴×C₂₃	—	2	1	no	—
349	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
350	#41×C₂₃	—	2	2	no	—
351	#41×C₂₃	—	2	2	no	—
352	#41×C₂₃	—	2	2	no	—
353	#41×C₂₃	—	2	2	no	—
354	#41×C₂₃	—	2	4	no	—
355	#41×C₂₃	—	2	2	no	—
356	#41×C₂₃	—	2	2	no	—
357	#41×C₂₃	—	2	4	no	—
358	#41×C₂₃	—	2	2	no	—
359	#41×C₂₃	—	2	2	no	—
360	#41×C₂₃	—	2	2	no	—
361	#41×C₂₃	—	2	2	no	—
362	#41×C₂₃	—	2	2	no	—
363	#41×C₂₃	—	2	2	no	—
364	#41×C₂₃	—	4	4	no	—
365	#41×C₂₃	—	4	4	no	—
366	#41×C₂₃	—	4	1	no	—
367	#41×C₂₃	—	4	1	no	—
368	#41×C₂₃	—	4	1	no	—
369	#41×C₂₃	—	4	1	no	—
370	#41×C₂₃	—	4	2	no	—
371	#41×C₂₃	—	4	2	no	—
372	#41×C₂₃	—	4	4	no	—
373	#41×C₂₃	—	4	4	no	—
374	#41×C₂₃	—	4	4	no	—
375	#41×C₂₃	—	4	4	no	—
376	#41×C₂₃	—	4	8	no	—
377	#41×C₂₃	C₂×D₄	1	4	yes	—
378	#41×C₂₃	C₂×D₄	1	4	yes	complemented
379	C₂×Q₈×C₂₃	—	2	1	no	—
380	C₂×Q₈×C₂₃	—	2	1	no	—
381	C₂×Q₈×C₂₃	—	2	2	no	—
382	C₂×Q₈×C₂₃	—	2	1	no	—
383	C₂×Q₈×C₂₃	—	2	4	no	—
384	C₂×Q₈×C₂₃	—	2	2	no	—
385	C₂×Q₈×C₂₃	—	2	2	no	—
386	C₂×Q₈×C₂₃	—	2	2	no	—
387	C₂×Q₈×C₂₃	—	2	2	no	—
388	C₂×Q₈×C₂₃	—	4	1	no	—
389	C₂×Q₈×C₂₃	—	4	1	no	—
390	C₂×Q₈×C₂₃	—	4	2	no	—
391	C₂×Q₈×C₂₃	—	4	4	no	—
392	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
394	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
395	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₂₃	—	2	1	no	—
399	C₂×D₄×C₂₃	—	2	1	no	—
400	C₂×D₄×C₂₃	—	2	4	no	—
401	C₂×D₄×C₂₃	—	2	2	no	—
402	C₂×D₄×C₂₃	—	2	2	no	—
403	C₂×D₄×C₂₃	—	2	2	no	—
404	C₂×D₄×C₂₃	—	2	1	no	—
405	C₂×D₄×C₂₃	—	2	1	no	—
406	C₂×D₄×C₂₃	—	2	2	no	—
407	C₂×D₄×C₂₃	—	2	1	no	—
408	C₂×D₄×C₂₃	—	2	1	no	—
409	C₂×D₄×C₂₃	—	2	1	no	—
410	C₂×D₄×C₂₃	—	2	2	no	—
411	C₂×D₄×C₂₃	—	2	1	no	—
412	C₂×D₄×C₂₃	—	2	2	no	—
413	C₂×D₄×C₂₃	—	2	2	no	—
414	C₂×D₄×C₂₃	—	2	2	no	—
415	C₂×D₄×C₂₃	—	2	2	no	—
416	C₂×D₄×C₂₃	—	2	1	no	—
417	C₂×D₄×C₂₃	—	2	2	no	—
418	C₂×D₄×C₂₃	—	2	1	no	—
419	C₂×D₄×C₂₃	—	2	1	no	—
420	C₂×D₄×C₂₃	—	2	2	no	—
421	C₂×D₄×C₂₃	—	2	2	no	—
422	C₂×D₄×C₂₃	—	2	2	no	—
423	C₂×D₄×C₂₃	—	4	1	no	—
424	C₂×D₄×C₂₃	—	4	1	no	—
425	C₂×D₄×C₂₃	—	4	2	no	—
426	C₂×D₄×C₂₃	—	4	4	no	—
427	C₂×D₄×C₂₃	—	4	8	no	—
428	C₂×D₄×C₂₃	—	4	4	no	—
429	C₂×D₄×C₂₃	—	4	4	no	—
430	C₂×D₄×C₂₃	—	8	4	no	—
431	C₂×D₄×C₂₃	—	8	2	no	—
432	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
434	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
438	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
439	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₂₃	—	2	1	no	—
442	C₂²×C₄×C₂₃	—	2	1	no	—
443	C₂²×C₄×C₂₃	—	2	2	no	—
444	C₂²×C₄×C₂₃	—	2	2	no	—
445	C₂²×C₄×C₂₃	—	2	1	no	—
446	C₂²×C₄×C₂₃	—	2	1	no	—
447	C₂²×C₄×C₂₃	—	2	2	no	—
448	C₂²×C₄×C₂₃	—	2	1	no	—
449	C₂²×C₄×C₂₃	—	2	1	no	—
450	C₂²×C₄×C₂₃	—	2	1	no	—
451	C₂²×C₄×C₂₃	—	2	1	no	—
452	C₂²×C₄×C₂₃	—	2	2	no	—
453	C₂²×C₄×C₂₃	—	2	1	no	—
454	C₂²×C₄×C₂₃	—	2	1	no	—
455	C₂²×C₄×C₂₃	—	2	2	no	—
456	C₂²×C₄×C₂₃	—	2	1	no	—
457	C₂²×C₄×C₂₃	—	2	1	no	—
458	C₂²×C₄×C₂₃	—	2	1	no	—
459	C₂²×C₄×C₂₃	—	2	2	no	—
460	C₂²×C₄×C₂₃	—	2	2	no	—
461	C₂²×C₄×C₂₃	—	4	4	no	—
462	C₂²×C₄×C₂₃	—	4	4	no	—
463	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
464	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
465	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
466	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
467	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
470	Q₁₆×C₂₃	—	2	4	no	—
471	Q₁₆×C₂₃	—	2	2	no	—
472	Q₁₆×C₂₃	—	2	2	no	—
473	Q₁₆×C₂₃	—	2	2	no	—
474	Q₁₆×C₂₃	—	4	2	no	—
475	Q₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
476	SD₁₆×C₂₃	—	2	4	no	—
477	SD₁₆×C₂₃	—	2	2	no	—
478	SD₁₆×C₂₃	—	2	2	no	—
479	SD₁₆×C₂₃	—	2	4	no	—
480	SD₁₆×C₂₃	—	2	2	no	—
481	SD₁₆×C₂₃	—	2	2	no	—
482	SD₁₆×C₂₃	—	2	4	no	—
483	SD₁₆×C₂₃	—	2	4	no	—
484	SD₁₆×C₂₃	—	2	2	no	—
485	SD₁₆×C₂₃	—	2	2	no	—
486	SD₁₆×C₂₃	—	4	2	no	—
487	SD₁₆×C₂₃	—	4	2	no	—
488	SD₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
489	SD₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
490	D₈×C₂₃	—	2	2	no	—
491	D₈×C₂₃	—	2	2	no	—
492	D₈×C₂₃	—	2	4	no	—
493	D₈×C₂₃	—	2	2	no	—
494	D₈×C₂₃	—	4	2	no	—
495	D₈×C₂₃	C₂×D₄	1	4	yes	complemented
496	M₁₆×C₂₃	—	2	2	no	—
497	M₁₆×C₂₃	—	2	2	no	—
498	M₁₆×C₂₃	—	2	2	no	—
499	M₁₆×C₂₃	—	2	2	no	—
500	M₁₆×C₂₃	—	2	2	no	—
501	M₁₆×C₂₃	—	2	2	no	—
502	M₁₆×C₂₃	—	2	4	no	—
503	C₂×C₈×C₂₃	—	2	2	no	—
504	C₂×C₈×C₂₃	—	2	4	no	—
505	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
506	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
507	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
508	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
509	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
510	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
511	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
512	C₄⋊C₄×C₂₃	—	2	2	no	—
513	C₄⋊C₄×C₂₃	—	2	1	no	—
514	C₄⋊C₄×C₂₃	—	2	1	no	—
515	C₄⋊C₄×C₂₃	—	2	2	no	—
516	C₄⋊C₄×C₂₃	—	2	2	no	—
517	C₄⋊C₄×C₂₃	—	2	2	no	—
518	C₄⋊C₄×C₂₃	—	2	2	no	—
519	C₄⋊C₄×C₂₃	—	2	2	no	—
520	C₄⋊C₄×C₂₃	—	2	2	no	—
521	C₄⋊C₄×C₂₃	—	2	2	no	—
522	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
523	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
524	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
525	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
526	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
527	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
528	C₂²⋊C₄×C₂₃	—	2	2	no	—
529	C₂²⋊C₄×C₂₃	—	2	2	no	—
530	C₂²⋊C₄×C₂₃	—	2	2	no	—
531	C₂²⋊C₄×C₂₃	—	2	2	no	—
532	C₂²⋊C₄×C₂₃	—	2	2	no	—
533	C₂²⋊C₄×C₂₃	—	2	2	no	—
534	C₂²⋊C₄×C₂₃	—	2	2	no	—
535	C₂²⋊C₄×C₂₃	—	2	2	no	—
536	C₂²⋊C₄×C₂₃	—	2	2	no	—
537	C₂²⋊C₄×C₂₃	—	2	2	no	—
538	C₂²⋊C₄×C₂₃	—	2	2	no	—
539	C₂²⋊C₄×C₂₃	—	2	2	no	—
540	C₂²⋊C₄×C₂₃	—	2	2	no	—
541	C₂²⋊C₄×C₂₃	—	2	2	no	—
542	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
543	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
544	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
545	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
546	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
547	C₄²×C₂₃	—	2	2	no	—
548	C₄²×C₂₃	—	2	2	no	—
549	C₄²×C₂₃	C₂⁴	1	2	yes	—
550	#61062	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
551	C₂³×C₂₃	—	2	1	no	—
552	C₂³×C₂₃	—	2	1	no	—
553	C₂³×C₂₃	—	2	2	no	—
554	C₂³×C₂₃	—	2	1	no	—
555	C₂³×C₂₃	—	2	2	no	—
556	C₂³×C₂₃	—	2	1	no	—
557	C₂³×C₂₃	—	4	1	no	—
558	C₂³×C₂₃	—	4	1	no	—
559	C₂³×C₂₃	—	4	2	no	—
560	C₂³×C₂₃	—	4	2	no	—
561	C₂³×C₂₃	—	4	4	no	—
562	C₂³×C₂₃	—	4	2	no	—
563	C₂³×C₂₃	—	4	2	no	—
564	C₂³×C₂₃	—	4	2	no	—
565	C₂³×C₂₃	—	8	1	no	—
566	C₂³×C₂₃	—	8	1	no	—
567	C₂³×C₂₃	—	8	1	no	—
568	C₂³×C₂₃	—	8	2	no	—
569	C₂³×C₂₃	—	8	1	no	—
570	C₂³×C₂₃	—	8	2	no	—
571	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
573	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
574	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
575	Q₈×C₂₃	—	2	2	no	—
576	Q₈×C₂₃	—	2	1	no	—
577	Q₈×C₂₃	—	2	1	no	—
578	Q₈×C₂₃	—	2	2	no	—
579	Q₈×C₂₃	—	2	1	no	—
580	Q₈×C₂₃	—	2	1	no	—
581	Q₈×C₂₃	—	2	1	no	—
582	Q₈×C₂₃	—	2	2	no	—
583	Q₈×C₂₃	—	2	1	no	—
584	Q₈×C₂₃	—	4	4	no	—
585	Q₈×C₂₃	—	4	2	no	—
586	Q₈×C₂₃	—	4	2	no	—
587	Q₈×C₂₃	—	4	2	no	—
588	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
589	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
590	D₄×C₂₃	—	2	4	no	—
591	D₄×C₂₃	—	2	4	no	—
592	D₄×C₂₃	—	2	4	no	—
593	D₄×C₂₃	—	2	2	no	—
594	D₄×C₂₃	—	2	1	no	—
595	D₄×C₂₃	—	2	1	no	—
596	D₄×C₂₃	—	2	2	no	—
597	D₄×C₂₃	—	2	1	no	—
598	D₄×C₂₃	—	2	1	no	—
599	D₄×C₂₃	—	2	1	no	—
600	D₄×C₂₃	—	2	2	no	—
601	D₄×C₂₃	—	2	1	no	—
602	D₄×C₂₃	—	4	2	no	—
603	D₄×C₂₃	—	4	2	no	—
604	D₄×C₂₃	—	4	4	no	—
605	D₄×C₂₃	—	4	2	no	—
606	D₄×C₂₃	—	4	2	no	—
607	D₄×C₂₃	—	4	4	no	—
608	D₄×C₂₃	—	4	2	no	—
609	D₄×C₂₃	—	4	2	no	—
610	D₄×C₂₃	—	4	2	no	—
611	D₄×C₂₃	—	4	2	no	—
612	D₄×C₂₃	—	4	4	no	—
613	D₄×C₂₃	—	4	4	no	—
614	D₄×C₂₃	—	4	2	no	—
615	D₄×C₂₃	—	4	2	no	—
616	D₄×C₂₃	—	4	2	no	—
617	D₄×C₂₃	—	8	2	no	—
618	D₄×C₂₃	—	8	2	no	—
619	D₄×C₂₃	—	8	2	no	—
620	D₄×C₂₃	—	8	2	no	—
621	D₄×C₂₃	—	8	2	no	—
622	D₄×C₂₃	C₂²×D₄	1	2	yes	—
623	D₄×C₂₃	C₂²×D₄	1	2	yes	—
624	C₂×C₄×C₂₃	—	2	2	no	—
625	C₂×C₄×C₂₃	—	2	1	no	—
626	C₂×C₄×C₂₃	—	2	1	no	—
627	C₂×C₄×C₂₃	—	2	2	no	—
628	C₂×C₄×C₂₃	—	2	2	no	—
629	C₂×C₄×C₂₃	—	2	4	no	—
630	C₂×C₄×C₂₃	—	2	4	no	—
631	C₂×C₄×C₂₃	—	2	2	no	—
632	C₂×C₄×C₂₃	—	2	1	no	—
633	C₂×C₄×C₂₃	—	2	1	no	—
634	C₂×C₄×C₂₃	—	2	1	no	—
635	C₂×C₄×C₂₃	—	2	1	no	—
636	C₂×C₄×C₂₃	—	2	2	no	—
637	C₂×C₄×C₂₃	—	2	2	no	—
638	C₂×C₄×C₂₃	—	2	2	no	—
639	C₂×C₄×C₂₃	—	2	1	no	—
640	C₂×C₄×C₂₃	—	2	2	no	—
641	C₂×C₄×C₂₃	—	2	1	no	—
642	C₂×C₄×C₂₃	—	4	2	no	—
643	C₂×C₄×C₂₃	—	4	2	no	—
644	C₂×C₄×C₂₃	—	4	4	no	—
645	C₂×C₄×C₂₃	—	4	2	no	—
646	C₂×C₄×C₂₃	—	4	2	no	—
647	C₂×C₄×C₂₃	—	4	2	no	—
648	C₂×C₄×C₂₃	—	4	2	no	—
649	C₂×C₄×C₂₃	—	4	4	no	—
650	C₂×C₄×C₂₃	—	4	4	no	—
651	C₂×C₄×C₂₃	—	4	2	no	—
652	C₂×C₄×C₂₃	—	4	2	no	—
653	C₂×C₄×C₂₃	—	4	2	no	—
654	C₂×C₄×C₂₃	—	8	2	no	—
655	C₂×C₄×C₂₃	—	8	2	no	—
656	C₂×C₄×C₂₃	—	8	1	no	—
657	C₂×C₄×C₂₃	—	8	1	no	—
658	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
659	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
660	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
663	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
664	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
665	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
666	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
667	C₈×C₂₃	—	2	1	no	—
668	C₈×C₂₃	—	2	1	no	—
669	C₈×C₂₃	—	2	2	no	—
670	C₈×C₂₃	—	2	2	no	—
671	C₈×C₂₃	C₂²×D₄	1	2	yes	—
672	C₈×C₂₃	C₂²×D₄	1	2	yes	—
673	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
674	C₂×#575	C₂×C₂₃	1	1	yes	characteristic, complemented
675	#3489	C₂×C₂₃	1	1	yes	characteristic, complemented
676	#3488	C₂×C₂₃	1	1	yes	characteristic, complemented
677	#3278	C₂×C₂₃	1	2	yes	complemented
678	#3277	C₂×C₂₃	1	2	yes	complemented
679	#3273	C₂×C₂₃	1	2	yes	complemented
680	#3272	C₂×C₂₃	1	2	yes	complemented
681	#3269	C₂×C₂₃	1	2	yes	complemented
682	#3268	C₂×C₂₃	1	2	yes	complemented
683	#3266	C₂×C₂₃	1	2	yes	complemented
684	#3265	C₂×C₂₃	1	2	yes	complemented
685	#3154	C₂×C₂₃	1	1	yes	characteristic, complemented
686	#3061	C₂×C₂₃	1	1	yes	characteristic, complemented
687	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
688	#3046	C₂×C₂₃	1	1	yes	characteristic, complemented
689	#3045	C₂×C₂₃	1	1	yes	characteristic, complemented
690	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
691	#3012	C₂×C₂₃	1	1	yes	characteristic, complemented
692	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
693	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
694	#2951	C₂×C₂₃	1	1	yes	characteristic, complemented
695	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
696	C₂²×C₂₃	—	2	1	no	—
697	C₂²×C₂₃	—	2	1	no	—
698	C₂²×C₂₃	—	2	1	no	—
699	C₂²×C₂₃	—	2	2	no	—
700	C₂²×C₂₃	—	2	1	no	—
701	C₂²×C₂₃	—	2	1	no	—
702	C₂²×C₂₃	—	2	2	no	—
703	C₂²×C₂₃	—	2	1	no	—
704	C₂²×C₂₃	—	2	1	no	—
705	C₂²×C₂₃	—	2	1	no	—
706	C₂²×C₂₃	—	2	2	no	—
707	C₂²×C₂₃	—	2	2	no	—
708	C₂²×C₂₃	—	2	2	no	—
709	C₂²×C₂₃	—	4	1	no	—
710	C₂²×C₂₃	—	4	1	no	—
711	C₂²×C₂₃	—	4	1	no	—
712	C₂²×C₂₃	—	4	1	no	—
713	C₂²×C₂₃	—	4	2	no	—
714	C₂²×C₂₃	—	4	1	no	—
715	C₂²×C₂₃	—	4	1	no	—
716	C₂²×C₂₃	—	4	1	no	—
717	C₂²×C₂₃	—	4	2	no	—
718	C₂²×C₂₃	—	4	1	no	—
719	C₂²×C₂₃	—	4	1	no	—
720	C₂²×C₂₃	—	4	1	no	—
721	C₂²×C₂₃	—	4	2	no	—
722	C₂²×C₂₃	—	8	2	no	—
723	C₂²×C₂₃	—	8	4	no	—
724	C₂²×C₂₃	—	8	4	no	—
725	C₂²×C₂₃	—	16	2	no	—
726	C₂²×C₂₃	—	16	4	no	—
727	C₂²×C₂₃	D₄²	1	2	yes	—
728	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
729	C₄×C₂₃	—	2	2	no	—
730	C₄×C₂₃	—	2	2	no	—
731	C₄×C₂₃	—	2	1	no	—
732	C₄×C₂₃	—	2	1	no	—
733	C₄×C₂₃	—	2	2	no	—
734	C₄×C₂₃	—	2	2	no	—
735	C₄×C₂₃	—	2	2	no	—
736	C₄×C₂₃	—	4	2	no	—
737	C₄×C₂₃	—	4	2	no	—
738	C₄×C₂₃	—	4	1	no	—
739	C₄×C₂₃	—	4	1	no	—
740	C₄×C₂₃	—	4	2	no	—
741	C₄×C₂₃	D₄²	1	2	yes	—
742	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
743	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
744	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
746	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
747	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
748	#577	—	2	8	no	—
749	#575	—	2	8	no	—
750	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
751	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
752	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
753	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
754	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
755	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
756	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
757	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
758	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
759	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
760	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
762	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
763	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
764	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
765	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
766	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
767	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
768	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
769	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
770	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
771	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
772	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
773	#550	C₂²×C₂₃	1	2	yes	—
774	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
775	#548	C₂²×C₂₃	1	2	yes	complemented
776	#548	C₂²×C₂₃	1	2	yes	complemented
777	#547	—	2	2	no	—
778	#547	C₂²×C₂₃	1	2	yes	complemented
779	#546	—	2	2	no	—
780	#546	—	2	2	no	—
781	#546	C₂²×C₂₃	1	2	yes	—
782	#546	C₂²×C₂₃	1	2	yes	complemented
783	D₄²	—	2	2	no	—
784	D₄²	C₂²×C₂₃	1	2	yes	complemented
785	#537	—	2	1	no	—
786	#537	—	2	1	no	—
787	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
788	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
789	#536	—	2	1	no	—
790	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
791	#535	—	2	1	no	—
792	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
793	#525	—	2	1	no	—
794	#525	—	2	1	no	—
795	#525	C₂²×C₂₃	1	1	yes	characteristic
796	C₂×C₂²⋊Q₈	—	2	1	no	—
797	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
798	C₂×#121	—	2	1	no	—
799	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
800	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
801	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
802	#497	C₂²×C₂₃	1	2	yes	complemented
803	#496	C₂²×C₂₃	1	2	yes	complemented
804	#495	C₂²×C₂₃	1	2	yes	complemented
805	#492	C₂²×C₂₃	1	2	yes	complemented
806	#468	C₂²×C₂₃	1	2	yes	complemented
807	#468	C₂²×C₂₃	1	2	yes	complemented
808	#468	C₂²×C₂₃	1	2	yes	complemented
809	#468	C₂²×C₂₃	1	2	yes	complemented
810	#468	C₂²×C₂₃	1	2	yes	complemented
811	#468	C₂²×C₂₃	1	2	yes	complemented
812	#467	C₂²×C₂₃	1	2	yes	complemented
813	#466	C₂²×C₂₃	1	2	yes	complemented
814	#464	C₂²×C₂₃	1	2	yes	complemented
815	#464	C₂²×C₂₃	1	2	yes	complemented
816	#463	C₂²×C₂₃	1	2	yes	complemented
817	#463	C₂²×C₂₃	1	2	yes	complemented
818	#462	C₂²×C₂₃	1	2	yes	complemented
819	#461	C₂²×C₂₃	1	2	yes	complemented
820	#460	C₂²×C₂₃	1	2	yes	complemented
821	#459	C₂²×C₂₃	1	2	yes	complemented
822	#452	C₂²×C₂₃	1	2	yes	complemented
823	#452	C₂²×C₂₃	1	2	yes	complemented
824	#452	C₂²×C₂₃	1	2	yes	complemented
825	#452	C₂²×C₂₃	1	2	yes	complemented
826	#451	C₂²×C₂₃	1	2	yes	complemented
827	#451	C₂²×C₂₃	1	2	yes	complemented
828	#450	C₂²×C₂₃	1	2	yes	complemented
829	#450	C₂²×C₂₃	1	2	yes	complemented
830	#449	C₂²×C₂₃	1	2	yes	complemented
831	#449	C₂²×C₂₃	1	2	yes	complemented
832	#449	C₂²×C₂₃	1	2	yes	complemented
833	#449	C₂²×C₂₃	1	2	yes	complemented
834	#448	C₂²×C₂₃	1	2	yes	complemented
835	#448	C₂²×C₂₃	1	2	yes	complemented
836	#447	C₂²×C₂₃	1	2	yes	complemented
837	#447	C₂²×C₂₃	1	2	yes	complemented
838	#440	C₂²×C₂₃	1	2	yes	complemented
839	#440	C₂²×C₂₃	1	2	yes	complemented
840	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
841	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
842	#436	C₂²×C₂₃	1	2	yes	complemented
843	#436	C₂²×C₂₃	1	2	yes	complemented
844	#435	C₂²×C₂₃	1	2	yes	complemented
845	#435	C₂²×C₂₃	1	2	yes	complemented
846	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
847	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
848	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
849	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
850	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
851	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
852	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
853	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
854	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
855	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
856	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
857	C₂×C₂₃	—	2	2	no	—
858	C₂×C₂₃	—	4	1	no	—
859	C₂×C₂₃	—	4	1	no	—
860	C₂×C₂₃	—	4	2	no	—
861	C₂×C₂₃	—	4	2	no	—
862	C₂×C₂₃	—	4	2	no	—
863	C₂×C₂₃	—	8	1	no	—
864	C₂×C₂₃	—	8	1	no	—
865	C₂×C₂₃	—	8	2	no	—
866	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
867	C₂×C₂₃	#3585	1	1	yes	characteristic
868	C₂×C₂₃	#3586	1	1	yes	characteristic
869	2₋¹⁺⁴	—	2	4	no	—
870	2₋¹⁺⁴	—	4	2	no	—
871	H(5,𝔽₂)	—	2	4	no	—
872	H(5,𝔽₂)	—	4	2	no	—
873	C₂×#41	—	2	1	no	—
874	C₂×#41	—	2	1	no	—
875	C₂×#41	—	2	2	no	—
876	C₂×#41	—	2	1	no	—
877	C₂×#41	—	2	1	no	—
878	C₂×#41	—	2	1	no	—
879	C₂×#41	—	2	1	no	—
880	C₂×#41	—	2	4	no	—
881	C₂×#41	—	2	4	no	—
882	C₂×#41	—	4	2	no	—
883	C₂×#41	—	4	2	no	—
884	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
885	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
886	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
887	C₂×#41	C₂³×C₂₃	1	2	yes	—
888	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
889	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
890	C₂×#41	C₂³×C₂₃	1	2	yes	—
891	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
892	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
893	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
894	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
895	C₂²×Q₈	—	2	1	no	—
896	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
897	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
898	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
899	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
900	C₂²×D₄	—	2	1	no	—
901	C₂²×D₄	—	2	1	no	—
902	C₂²×D₄	—	2	1	no	—
903	C₂²×D₄	—	2	1	no	—
904	C₂²×D₄	—	2	2	no	—
905	C₂²×D₄	—	2	2	no	—
906	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
907	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
908	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
909	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
910	C₂³×C₄	—	2	1	no	—
911	C₂³×C₄	—	2	1	no	—
912	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
913	#137	—	2	4	no	—
914	#137	—	2	4	no	—
915	#137	—	2	4	no	—
916	#137	—	2	8	no	—
917	#137	—	2	4	no	—
918	#137	—	2	4	no	—
919	#137	—	4	2	no	—
920	AGL(1,ℤ/8)	—	2	4	no	—
921	AGL(1,ℤ/8)	—	2	4	no	—
922	AGL(1,ℤ/8)	—	2	4	no	—
923	AGL(1,ℤ/8)	—	2	4	no	—
924	AGL(1,ℤ/8)	—	2	4	no	—
925	AGL(1,ℤ/8)	—	2	8	no	—
926	AGL(1,ℤ/8)	—	4	2	no	—
927	#135	—	2	4	no	—
928	#135	—	2	4	no	—
929	#135	—	2	8	no	—
930	#135	—	2	4	no	—
931	#135	D₄×C₂₃	1	8	yes	complemented
932	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
933	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
934	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
935	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
936	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
937	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
938	C₂×SD₁₆	—	2	8	no	—
939	C₂×SD₁₆	—	2	4	no	—
940	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
941	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
942	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
943	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
944	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
945	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
946	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
947	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
948	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
949	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
950	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
951	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
952	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
953	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
954	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
955	C₂×D₈	C₂³×C₂₃	1	2	yes	—
956	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
957	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
958	C₂×D₈	C₂³×C₂₃	1	2	yes	—
959	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
960	#131	—	2	4	no	—
961	C₂×M₁₆	—	2	4	no	—
962	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
963	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
964	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
965	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
966	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
967	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
968	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
969	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
970	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
971	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
972	C₄⋊Q₈	—	2	2	no	—
973	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
974	#127	—	2	2	no	—
975	#127	C₂³×C₂₃	1	2	yes	—
976	#124	—	2	2	no	—
977	#124	—	2	2	no	—
978	#124	C₂³×C₂₃	1	2	yes	—
979	#124	C₂³×C₂₃	1	2	yes	—
980	#123	—	2	2	no	—
981	#123	—	2	2	no	—
982	#123	—	2	2	no	—
983	#123	—	2	2	no	—
984	#123	—	2	2	no	—
985	#123	D₄×C₂₃	1	2	yes	—
986	C₂²⋊Q₈	—	2	1	no	—
987	C₂²⋊Q₈	—	2	1	no	—
988	C₂²⋊Q₈	—	2	1	no	—
989	C₂²⋊Q₈	—	2	1	no	—
990	C₂²⋊Q₈	—	2	1	no	—
991	C₂²⋊Q₈	—	2	2	no	—
992	C₂²⋊Q₈	—	2	1	no	—
993	C₂²⋊Q₈	—	2	2	no	—
994	C₂²⋊Q₈	—	2	2	no	—
995	C₂²⋊Q₈	—	2	2	no	—
996	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
997	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
998	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
999	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1000	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1001	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
1002	#121	—	2	1	no	—
1003	#121	—	2	2	no	—
1004	#121	—	2	1	no	—
1005	#121	—	2	2	no	—
1006	#121	—	2	2	no	—
1007	#121	—	2	2	no	—
1008	#121	—	2	2	no	—
1009	#121	—	2	1	no	—
1010	#121	—	2	1	no	—
1011	#121	—	2	1	no	—
1012	#121	—	2	1	no	—
1013	#121	—	2	2	no	—
1014	#121	—	2	2	no	—
1015	#121	—	2	2	no	—
1016	#121	—	2	2	no	—
1017	#121	—	2	2	no	—
1018	#121	D₄×C₂₃	1	1	yes	characteristic
1019	#121	D₄×C₂₃	1	1	yes	characteristic
1020	#121	C₂³×C₂₃	1	2	yes	—
1021	#121	C₂³×C₂₃	1	2	yes	—
1022	#121	C₂³×C₂₃	1	2	yes	—
1023	#121	C₂³×C₂₃	1	2	yes	—
1024	#120	—	2	2	no	—
1025	#120	—	2	2	no	—
1026	#120	—	2	2	no	—
1027	#120	—	2	2	no	—
1028	#120	—	2	2	no	—
1029	#120	D₄×C₂₃	1	2	yes	—
1030	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
1031	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
1032	C₄×D₄	—	2	2	no	—
1033	C₄×D₄	—	2	2	no	—
1034	C₄×D₄	—	2	2	no	—
1035	C₄×D₄	—	2	2	no	—
1036	C₄×D₄	—	2	2	no	—
1037	C₄×D₄	—	2	2	no	—
1038	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1039	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1040	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1041	C₄×D₄	C₂³×C₂₃	1	2	yes	—
1042	#117	—	2	1	no	—
1043	#117	—	2	1	no	—
1044	#117	C₂³×C₂₃	1	1	yes	characteristic
1045	C₂×C₄⋊C₄	—	2	1	no	—
1046	C₂×C₄⋊C₄	—	2	1	no	—
1047	C₂×C₄⋊C₄	—	2	1	no	—
1048	C₂×C₄⋊C₄	—	2	2	no	—
1049	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	—	2	1	no	—
1052	C₂×C₂²⋊C₄	—	2	1	no	—
1053	C₂×C₂²⋊C₄	—	2	2	no	—
1054	C₂×C₂²⋊C₄	—	2	2	no	—
1055	#107	C₂³×C₂₃	1	2	yes	—
1056	#107	C₂³×C₂₃	1	2	yes	—
1057	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
1058	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
1059	#103	C₂³×C₂₃	1	2	yes	—
1060	#103	C₂³×C₂₃	1	2	yes	—
1061	#103	C₂³×C₂₃	1	2	yes	—
1062	#103	C₂³×C₂₃	1	2	yes	—
1063	#103	C₂³×C₂₃	1	2	yes	—
1064	#103	C₂³×C₂₃	1	2	yes	—
1065	#102	C₂³×C₂₃	1	2	yes	—
1066	#102	C₂³×C₂₃	1	2	yes	—
1067	#102	C₂³×C₂₃	1	2	yes	—
1068	#102	C₂³×C₂₃	1	2	yes	—
1069	#102	C₂³×C₂₃	1	2	yes	—
1070	#102	C₂³×C₂₃	1	2	yes	—
1071	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1072	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1073	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1074	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1075	#97	C₂³×C₂₃	1	2	yes	—
1076	C₄×C₈	C₂³×C₂₃	1	2	yes	—
1077	C₂₃	#61062	1	1	yes	characteristic, direct product factor, Sylow
1078	C₂⁴	—	2	1	no	—
1079	C₂⁴	—	2	1	no	—
1080	C₂⁴	—	2	2	no	—
1081	C₂⁴	—	2	1	no	—
1082	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1083	#41	—	2	2	no	—
1084	#41	—	2	2	no	—
1085	#41	—	2	2	no	—
1086	#41	—	2	2	no	—
1087	#41	—	2	4	no	—
1088	#41	—	2	2	no	—
1089	#41	—	2	2	no	—
1090	#41	—	2	4	no	—
1091	#41	—	2	2	no	—
1092	#41	—	2	2	no	—
1093	#41	—	2	2	no	—
1094	#41	—	2	2	no	—
1095	#41	—	2	2	no	—
1096	#41	—	2	2	no	—
1097	#41	—	4	4	no	—
1098	#41	—	4	4	no	—
1099	#41	—	4	1	no	—
1100	#41	—	4	1	no	—
1101	#41	—	4	1	no	—
1102	#41	—	4	1	no	—
1103	#41	—	4	2	no	—
1104	#41	—	4	2	no	—
1105	#41	—	4	4	no	—
1106	#41	—	4	4	no	—
1107	#41	—	4	4	no	—
1108	#41	—	4	4	no	—
1109	#41	—	4	8	no	—
1110	#41	C₂×D₄×C₂₃	1	4	yes	—
1111	#41	C₂×D₄×C₂₃	1	4	yes	complemented
1112	C₂×Q₈	—	2	1	no	—
1113	C₂×Q₈	—	2	1	no	—
1114	C₂×Q₈	—	2	2	no	—
1115	C₂×Q₈	—	2	1	no	—
1116	C₂×Q₈	—	2	4	no	—
1117	C₂×Q₈	—	2	2	no	—
1118	C₂×Q₈	—	2	2	no	—
1119	C₂×Q₈	—	2	2	no	—
1120	C₂×Q₈	—	2	2	no	—
1121	C₂×Q₈	—	4	1	no	—
1122	C₂×Q₈	—	4	1	no	—
1123	C₂×Q₈	—	4	2	no	—
1124	C₂×Q₈	—	4	4	no	—
1125	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1126	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1127	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1128	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1129	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1130	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1131	C₂×D₄	—	2	1	no	—
1132	C₂×D₄	—	2	1	no	—
1133	C₂×D₄	—	2	4	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	2	2	no	—
1136	C₂×D₄	—	2	2	no	—
1137	C₂×D₄	—	2	1	no	—
1138	C₂×D₄	—	2	1	no	—
1139	C₂×D₄	—	2	2	no	—
1140	C₂×D₄	—	2	1	no	—
1141	C₂×D₄	—	2	1	no	—
1142	C₂×D₄	—	2	1	no	—
1143	C₂×D₄	—	2	2	no	—
1144	C₂×D₄	—	2	1	no	—
1145	C₂×D₄	—	2	2	no	—
1146	C₂×D₄	—	2	2	no	—
1147	C₂×D₄	—	2	2	no	—
1148	C₂×D₄	—	2	2	no	—
1149	C₂×D₄	—	2	1	no	—
1150	C₂×D₄	—	2	2	no	—
1151	C₂×D₄	—	2	1	no	—
1152	C₂×D₄	—	2	1	no	—
1153	C₂×D₄	—	2	2	no	—
1154	C₂×D₄	—	2	2	no	—
1155	C₂×D₄	—	2	2	no	—
1156	C₂×D₄	—	4	1	no	—
1157	C₂×D₄	—	4	1	no	—
1158	C₂×D₄	—	4	2	no	—
1159	C₂×D₄	—	4	4	no	—
1160	C₂×D₄	—	4	8	no	—
1161	C₂×D₄	—	4	4	no	—
1162	C₂×D₄	—	4	4	no	—
1163	C₂×D₄	—	8	4	no	—
1164	C₂×D₄	—	8	2	no	—
1165	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1166	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1167	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1168	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1169	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1170	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1171	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1172	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1173	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1174	C₂²×C₄	—	2	1	no	—
1175	C₂²×C₄	—	2	1	no	—
1176	C₂²×C₄	—	2	2	no	—
1177	C₂²×C₄	—	2	2	no	—
1178	C₂²×C₄	—	2	1	no	—
1179	C₂²×C₄	—	2	1	no	—
1180	C₂²×C₄	—	2	2	no	—
1181	C₂²×C₄	—	2	1	no	—
1182	C₂²×C₄	—	2	1	no	—
1183	C₂²×C₄	—	2	1	no	—
1184	C₂²×C₄	—	2	1	no	—
1185	C₂²×C₄	—	2	2	no	—
1186	C₂²×C₄	—	2	1	no	—
1187	C₂²×C₄	—	2	1	no	—
1188	C₂²×C₄	—	2	2	no	—
1189	C₂²×C₄	—	2	1	no	—
1190	C₂²×C₄	—	2	1	no	—
1191	C₂²×C₄	—	2	1	no	—
1192	C₂²×C₄	—	2	2	no	—
1193	C₂²×C₄	—	2	2	no	—
1194	C₂²×C₄	—	4	4	no	—
1195	C₂²×C₄	—	4	4	no	—
1196	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1200	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1202	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1203	Q₁₆	—	2	4	no	—
1204	Q₁₆	—	2	2	no	—
1205	Q₁₆	—	2	2	no	—
1206	Q₁₆	—	2	2	no	—
1207	Q₁₆	—	4	2	no	—
1208	Q₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
1209	SD₁₆	—	2	4	no	—
1210	SD₁₆	—	2	2	no	—
1211	SD₁₆	—	2	2	no	—
1212	SD₁₆	—	2	4	no	—
1213	SD₁₆	—	2	2	no	—
1214	SD₁₆	—	2	2	no	—
1215	SD₁₆	—	2	4	no	—
1216	SD₁₆	—	2	4	no	—
1217	SD₁₆	—	2	2	no	—
1218	SD₁₆	—	2	2	no	—
1219	SD₁₆	—	4	2	no	—
1220	SD₁₆	—	4	2	no	—
1221	SD₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
1222	SD₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
1223	D₈	—	2	2	no	—
1224	D₈	—	2	2	no	—
1225	D₈	—	2	4	no	—
1226	D₈	—	2	2	no	—
1227	D₈	—	4	2	no	—
1228	D₈	C₂×D₄×C₂₃	1	4	yes	complemented
1229	M₁₆	—	2	2	no	—
1230	M₁₆	—	2	2	no	—
1231	M₁₆	—	2	2	no	—
1232	M₁₆	—	2	2	no	—
1233	M₁₆	—	2	2	no	—
1234	M₁₆	—	2	2	no	—
1235	M₁₆	—	2	4	no	—
1236	C₂×C₈	—	2	2	no	—
1237	C₂×C₈	—	2	4	no	—
1238	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
1239	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1240	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1241	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1242	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1243	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1244	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1245	C₄⋊C₄	—	2	2	no	—
1246	C₄⋊C₄	—	2	1	no	—
1247	C₄⋊C₄	—	2	1	no	—
1248	C₄⋊C₄	—	2	2	no	—
1249	C₄⋊C₄	—	2	2	no	—
1250	C₄⋊C₄	—	2	2	no	—
1251	C₄⋊C₄	—	2	2	no	—
1252	C₄⋊C₄	—	2	2	no	—
1253	C₄⋊C₄	—	2	2	no	—
1254	C₄⋊C₄	—	2	2	no	—
1255	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1256	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1257	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1258	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1259	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1260	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	2	2	no	—
1265	C₂²⋊C₄	—	2	2	no	—
1266	C₂²⋊C₄	—	2	2	no	—
1267	C₂²⋊C₄	—	2	2	no	—
1268	C₂²⋊C₄	—	2	2	no	—
1269	C₂²⋊C₄	—	2	2	no	—
1270	C₂²⋊C₄	—	2	2	no	—
1271	C₂²⋊C₄	—	2	2	no	—
1272	C₂²⋊C₄	—	2	2	no	—
1273	C₂²⋊C₄	—	2	2	no	—
1274	C₂²⋊C₄	—	2	2	no	—
1275	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1276	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1277	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1278	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1279	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1280	C₄²	—	2	2	no	—
1281	C₄²	—	2	2	no	—
1282	C₄²	C₂⁴×C₂₃	1	2	yes	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	2	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	2	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	4	1	no	—
1290	C₂³	—	4	1	no	—
1291	C₂³	—	4	2	no	—
1292	C₂³	—	4	2	no	—
1293	C₂³	—	4	4	no	—
1294	C₂³	—	4	2	no	—
1295	C₂³	—	4	2	no	—
1296	C₂³	—	4	2	no	—
1297	C₂³	—	8	1	no	—
1298	C₂³	—	8	1	no	—
1299	C₂³	—	8	1	no	—
1300	C₂³	—	8	2	no	—
1301	C₂³	—	8	1	no	—
1302	C₂³	—	8	2	no	—
1303	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1304	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1305	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1306	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1307	Q₈	—	2	1	no	—
1308	Q₈	—	2	1	no	—
1309	Q₈	—	2	2	no	—
1310	Q₈	—	2	2	no	—
1311	Q₈	—	2	1	no	—
1312	Q₈	—	2	1	no	—
1313	Q₈	—	2	1	no	—
1314	Q₈	—	2	2	no	—
1315	Q₈	—	2	1	no	—
1316	Q₈	—	4	4	no	—
1317	Q₈	—	4	2	no	—
1318	Q₈	—	4	2	no	—
1319	Q₈	—	4	2	no	—
1320	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1321	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1322	D₄	—	2	4	no	—
1323	D₄	—	2	4	no	—
1324	D₄	—	2	4	no	—
1325	D₄	—	2	1	no	—
1326	D₄	—	2	1	no	—
1327	D₄	—	2	2	no	—
1328	D₄	—	2	1	no	—
1329	D₄	—	2	1	no	—
1330	D₄	—	2	1	no	—
1331	D₄	—	2	2	no	—
1332	D₄	—	2	1	no	—
1333	D₄	—	2	2	no	—
1334	D₄	—	4	2	no	—
1335	D₄	—	4	2	no	—
1336	D₄	—	4	4	no	—
1337	D₄	—	4	2	no	—
1338	D₄	—	4	2	no	—
1339	D₄	—	4	4	no	—
1340	D₄	—	4	2	no	—
1341	D₄	—	4	2	no	—
1342	D₄	—	4	2	no	—
1343	D₄	—	4	2	no	—
1344	D₄	—	4	4	no	—
1345	D₄	—	4	4	no	—
1346	D₄	—	4	2	no	—
1347	D₄	—	4	2	no	—
1348	D₄	—	4	2	no	—
1349	D₄	—	8	2	no	—
1350	D₄	—	8	2	no	—
1351	D₄	—	8	2	no	—
1352	D₄	—	8	2	no	—
1353	D₄	—	8	2	no	—
1354	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1355	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	2	no	—
1359	C₂×C₄	—	2	2	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	2	no	—
1365	C₂×C₄	—	2	2	no	—
1366	C₂×C₄	—	2	2	no	—
1367	C₂×C₄	—	2	4	no	—
1368	C₂×C₄	—	2	4	no	—
1369	C₂×C₄	—	2	2	no	—
1370	C₂×C₄	—	2	2	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	2	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	4	2	no	—
1375	C₂×C₄	—	4	2	no	—
1376	C₂×C₄	—	4	4	no	—
1377	C₂×C₄	—	4	2	no	—
1378	C₂×C₄	—	4	2	no	—
1379	C₂×C₄	—	4	2	no	—
1380	C₂×C₄	—	4	2	no	—
1381	C₂×C₄	—	4	4	no	—
1382	C₂×C₄	—	4	4	no	—
1383	C₂×C₄	—	4	2	no	—
1384	C₂×C₄	—	4	2	no	—
1385	C₂×C₄	—	4	2	no	—
1386	C₂×C₄	—	8	2	no	—
1387	C₂×C₄	—	8	2	no	—
1388	C₂×C₄	—	8	1	no	—
1389	C₂×C₄	—	8	1	no	—
1390	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1391	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1392	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1393	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1394	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1395	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1396	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1397	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1398	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1399	C₈	—	2	1	no	—
1400	C₈	—	2	1	no	—
1401	C₈	—	2	2	no	—
1402	C₈	—	2	2	no	—
1403	C₈	C₂²×D₄×C₂₃	1	2	yes	—
1404	C₈	C₂²×D₄×C₂₃	1	2	yes	—
1405	C₂²	—	2	1	no	—
1406	C₂²	—	2	1	no	—
1407	C₂²	—	2	1	no	—
1408	C₂²	—	2	1	no	—
1409	C₂²	—	2	2	no	—
1410	C₂²	—	2	2	no	—
1411	C₂²	—	2	2	no	—
1412	C₂²	—	2	1	no	—
1413	C₂²	—	2	2	no	—
1414	C₂²	—	2	1	no	—
1415	C₂²	—	2	1	no	—
1416	C₂²	—	2	2	no	—
1417	C₂²	—	2	1	no	—
1418	C₂²	—	4	1	no	—
1419	C₂²	—	4	1	no	—
1420	C₂²	—	4	1	no	—
1421	C₂²	—	4	1	no	—
1422	C₂²	—	4	1	no	—
1423	C₂²	—	4	1	no	—
1424	C₂²	—	4	2	no	—
1425	C₂²	—	4	2	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	4	1	no	—
1428	C₂²	—	4	1	no	—
1429	C₂²	—	4	2	no	—
1430	C₂²	—	4	1	no	—
1431	C₂²	—	8	2	no	—
1432	C₂²	—	8	4	no	—
1433	C₂²	—	8	4	no	—
1434	C₂²	—	16	2	no	—
1435	C₂²	—	16	4	no	—
1436	C₂²	D₄²×C₂₃	1	2	yes	—
1437	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1438	C₄	—	2	1	no	—
1439	C₄	—	2	1	no	—
1440	C₄	—	2	2	no	—
1441	C₄	—	2	2	no	—
1442	C₄	—	2	2	no	—
1443	C₄	—	2	2	no	—
1444	C₄	—	2	2	no	—
1445	C₄	—	4	1	no	—
1446	C₄	—	4	1	no	—
1447	C₄	—	4	2	no	—
1448	C₄	—	4	2	no	—
1449	C₄	—	4	2	no	—
1450	C₄	D₄²×C₂₃	1	2	yes	—
1451	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1452	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1453	C₂	—	2	2	no	—
1454	C₂	—	4	1	no	—
1455	C₂	—	4	1	no	—
1456	C₂	—	4	2	no	—
1457	C₂	—	4	2	no	—
1458	C₂	—	4	2	no	—
1459	C₂	—	8	1	no	—
1460	C₂	—	8	1	no	—
1461	C₂	—	8	2	no	—
1462	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1463	C₂	C₂₃×#3585	1	1	yes	characteristic
1464	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₂₃×#577	C₂	semidirect
2. C₂×C₂₃×#575	C₂	semidirect
3. C₂₃×#3489	C₂	semidirect
4. C₂₃×#3488	C₂	semidirect
5. C₂₃×#3278	C₂	semidirect
6. C₂₃×#3277	C₂	semidirect
7. C₂₃×#3273	C₂	semidirect
8. C₂₃×#3272	C₂	semidirect
9. C₂₃×#3269	C₂	semidirect
10. C₂₃×#3268	C₂	semidirect
11. C₂₃×#3266	C₂	semidirect
12. C₂₃×#3265	C₂	semidirect
13. C₂₃×#3154	C₂	semidirect
14. C₂₃×#3061	C₂	semidirect
15. C₂×C₂₃×#468	C₂	semidirect
16. C₂₃×#3046	C₂	semidirect
17. C₂₃×#3045	C₂	semidirect
18. C₂₃×#3013	C₂	semidirect
19. C₂₃×#3012	C₂	semidirect
20. C₂₃×#3007	C₂	semidirect
21. C₂₃×#3006	C₂	semidirect
22. C₂₃×#2951	C₂	semidirect
23. C₂₃×#2930	C₂	semidirect
24. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
25. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
27. C₂²×#41×C₂₃	C₂²	semidirect
30. C₂×C₂₃×#137	C₂²	semidirect
31. C₂×C₂₃×#137	C₂²	semidirect
32. C₂×C₂₃×#137	C₂²	semidirect
33. C₂×C₂₃×#137	C₂²	semidirect
34. C₂×C₂₃×#137	C₂²	semidirect
35. C₂×C₂₃×#137	C₂²	semidirect
36. C₂×C₂₃×#137	C₂²	semidirect
37. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
38. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
39. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
40. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
41. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
42. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
43. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
46. C₂×C₂₃×#135	C₂²	semidirect
47. C₂×C₂₃×#135	C₂²	semidirect
48. C₂×C₂₃×#135	C₂²	semidirect
49. C₂²×SD₁₆×C₂₃	C₂²	semidirect
50. C₂²×SD₁₆×C₂₃	C₂²	semidirect
51. C₂×C₂₃×#131	C₂²	semidirect
52. C₂²×M₁₆×C₂₃	C₂²	semidirect
54. D₄×Q₈×C₂₃	C₂²	semidirect
55. C₂₃×#548	C₂²	semidirect
56. C₂₃×#548	C₂²	semidirect
58. C₂₃×#547	C₂²	semidirect
62. C₂₃×#546	C₂²	semidirect
64. D₄²×C₂₃	C₂²	semidirect
67. C₂₃×#537	C₂²	semidirect
68. C₂₃×#537	C₂²	semidirect
70. C₂₃×#536	C₂²	semidirect
72. C₂₃×#535	C₂²	semidirect
77. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
80. C₂₃×#520	C₂²	semidirect
81. C₂₃×#520	C₂²	semidirect
82. C₂₃×#497	C₂²	semidirect
83. C₂₃×#496	C₂²	semidirect
84. C₂₃×#495	C₂²	semidirect
85. C₂₃×#492	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#468	C₂²	semidirect
88. C₂₃×#468	C₂²	semidirect
89. C₂₃×#468	C₂²	semidirect
90. C₂₃×#468	C₂²	semidirect
91. C₂₃×#468	C₂²	semidirect
92. C₂₃×#467	C₂²	semidirect
93. C₂₃×#466	C₂²	semidirect
94. C₂₃×#464	C₂²	semidirect
95. C₂₃×#464	C₂²	semidirect
96. C₂₃×#463	C₂²	semidirect
97. C₂₃×#463	C₂²	semidirect
98. C₂₃×#462	C₂²	semidirect
99. C₂₃×#461	C₂²	semidirect
100. C₂₃×#460	C₂²	semidirect
101. C₂₃×#459	C₂²	semidirect
102. C₂₃×#452	C₂²	semidirect
103. C₂₃×#452	C₂²	semidirect
104. C₂₃×#452	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#451	C₂²	semidirect
107. C₂₃×#451	C₂²	semidirect
108. C₂₃×#450	C₂²	semidirect
109. C₂₃×#450	C₂²	semidirect
110. C₂₃×#449	C₂²	semidirect
111. C₂₃×#449	C₂²	semidirect
112. C₂₃×#449	C₂²	semidirect
113. C₂₃×#449	C₂²	semidirect
114. C₂₃×#448	C₂²	semidirect
115. C₂₃×#448	C₂²	semidirect
116. C₂₃×#447	C₂²	semidirect
117. C₂₃×#447	C₂²	semidirect
118. C₂₃×#440	C₂²	semidirect
119. C₂₃×#440	C₂²	semidirect
120. C₄×Q₁₆×C₂₃	C₂²	semidirect
121. C₄×D₈×C₂₃	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#436	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₂₃×#435	C₂²	semidirect
126. C₂×C₂₃×#107	C₂²	semidirect
127. C₂₃×#424	C₂²	semidirect
128. C₂₃×#417	C₂²	semidirect
129. C₂₃×#417	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂₃×#417	C₂²	semidirect
132. C₂×C₂₃×#103	C₂²	semidirect
133. C₂×C₂₃×#102	C₂²	semidirect
134. C₂₃×#408	C₂²	semidirect
135. C₂₃×#407	C₂²	semidirect
136. C₂₃×#405	C₂²	semidirect
199. C₂₃×#135	D₄	semidirect
378. #41×C₂₃	C₂×D₄	semidirect
475. Q₁₆×C₂₃	C₂×D₄	semidirect
488. SD₁₆×C₂₃	C₂×D₄	semidirect
489. SD₁₆×C₂₃	C₂×D₄	semidirect
495. D₈×C₂₃	C₂×D₄	semidirect
505. C₂×C₈×C₂₃	C₂×D₄	semidirect
550. #61062	C₂₃	direct (N × H)
673. C₂×#577	C₂×C₂₃	semidirect
674. C₂×#575	C₂×C₂₃	semidirect
675. #3489	C₂×C₂₃	semidirect
676. #3488	C₂×C₂₃	semidirect
677. #3278	C₂×C₂₃	semidirect
678. #3277	C₂×C₂₃	semidirect
679. #3273	C₂×C₂₃	semidirect
680. #3272	C₂×C₂₃	semidirect
681. #3269	C₂×C₂₃	semidirect
682. #3268	C₂×C₂₃	semidirect
683. #3266	C₂×C₂₃	semidirect
684. #3265	C₂×C₂₃	semidirect
685. #3154	C₂×C₂₃	semidirect
686. #3061	C₂×C₂₃	semidirect
687. C₂×#468	C₂×C₂₃	semidirect
688. #3046	C₂×C₂₃	semidirect
689. #3045	C₂×C₂₃	semidirect
690. #3013	C₂×C₂₃	semidirect
691. #3012	C₂×C₂₃	semidirect
692. #3007	C₂×C₂₃	semidirect
693. #3006	C₂×C₂₃	semidirect
694. #2951	C₂×C₂₃	semidirect
695. #2930	C₂×C₂₃	semidirect
744. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
745. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
747. C₂²×#41	C₂²×C₂₃	semidirect
750. C₂×#137	C₂²×C₂₃	semidirect
751. C₂×#137	C₂²×C₂₃	semidirect
752. C₂×#137	C₂²×C₂₃	semidirect
753. C₂×#137	C₂²×C₂₃	semidirect
754. C₂×#137	C₂²×C₂₃	semidirect
755. C₂×#137	C₂²×C₂₃	semidirect
756. C₂×#137	C₂²×C₂₃	semidirect
757. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
758. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
759. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
760. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
761. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
762. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
763. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
766. C₂×#135	C₂²×C₂₃	semidirect
767. C₂×#135	C₂²×C₂₃	semidirect
768. C₂×#135	C₂²×C₂₃	semidirect
769. C₂²×SD₁₆	C₂²×C₂₃	semidirect
770. C₂²×SD₁₆	C₂²×C₂₃	semidirect
771. C₂×#131	C₂²×C₂₃	semidirect
772. C₂²×M₁₆	C₂²×C₂₃	semidirect
774. D₄×Q₈	C₂²×C₂₃	semidirect
775. #548	C₂²×C₂₃	semidirect
776. #548	C₂²×C₂₃	semidirect
778. #547	C₂²×C₂₃	semidirect
782. #546	C₂²×C₂₃	semidirect
784. D₄²	C₂²×C₂₃	semidirect
787. #537	C₂²×C₂₃	semidirect
788. #537	C₂²×C₂₃	semidirect
790. #536	C₂²×C₂₃	semidirect
792. #535	C₂²×C₂₃	semidirect
797. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
800. #520	C₂²×C₂₃	semidirect
801. #520	C₂²×C₂₃	semidirect
802. #497	C₂²×C₂₃	semidirect
803. #496	C₂²×C₂₃	semidirect
804. #495	C₂²×C₂₃	semidirect
805. #492	C₂²×C₂₃	semidirect
806. #468	C₂²×C₂₃	semidirect
807. #468	C₂²×C₂₃	semidirect
808. #468	C₂²×C₂₃	semidirect
809. #468	C₂²×C₂₃	semidirect
810. #468	C₂²×C₂₃	semidirect
811. #468	C₂²×C₂₃	semidirect
812. #467	C₂²×C₂₃	semidirect
813. #466	C₂²×C₂₃	semidirect
814. #464	C₂²×C₂₃	semidirect
815. #464	C₂²×C₂₃	semidirect
816. #463	C₂²×C₂₃	semidirect
817. #463	C₂²×C₂₃	semidirect
818. #462	C₂²×C₂₃	semidirect
819. #461	C₂²×C₂₃	semidirect
820. #460	C₂²×C₂₃	semidirect
821. #459	C₂²×C₂₃	semidirect
822. #452	C₂²×C₂₃	semidirect
823. #452	C₂²×C₂₃	semidirect
824. #452	C₂²×C₂₃	semidirect
825. #452	C₂²×C₂₃	semidirect
826. #451	C₂²×C₂₃	semidirect
827. #451	C₂²×C₂₃	semidirect
828. #450	C₂²×C₂₃	semidirect
829. #450	C₂²×C₂₃	semidirect
830. #449	C₂²×C₂₃	semidirect
831. #449	C₂²×C₂₃	semidirect
832. #449	C₂²×C₂₃	semidirect
833. #449	C₂²×C₂₃	semidirect
834. #448	C₂²×C₂₃	semidirect
835. #448	C₂²×C₂₃	semidirect
836. #447	C₂²×C₂₃	semidirect
837. #447	C₂²×C₂₃	semidirect
838. #440	C₂²×C₂₃	semidirect
839. #440	C₂²×C₂₃	semidirect
840. C₄×Q₁₆	C₂²×C₂₃	semidirect
841. C₄×D₈	C₂²×C₂₃	semidirect
842. #436	C₂²×C₂₃	semidirect
843. #436	C₂²×C₂₃	semidirect
844. #435	C₂²×C₂₃	semidirect
845. #435	C₂²×C₂₃	semidirect
846. C₂×#107	C₂²×C₂₃	semidirect
847. #424	C₂²×C₂₃	semidirect
848. #417	C₂²×C₂₃	semidirect
849. #417	C₂²×C₂₃	semidirect
850. #417	C₂²×C₂₃	semidirect
851. #417	C₂²×C₂₃	semidirect
852. C₂×#103	C₂²×C₂₃	semidirect
853. C₂×#102	C₂²×C₂₃	semidirect
854. #408	C₂²×C₂₃	semidirect
855. #407	C₂²×C₂₃	semidirect
856. #405	C₂²×C₂₃	semidirect
931. #135	D₄×C₂₃	semidirect
1077. C₂₃	#61062	direct (N × H)
1111. #41	C₂×D₄×C₂₃	semidirect
1208. Q₁₆	C₂×D₄×C₂₃	semidirect
1221. SD₁₆	C₂×D₄×C₂₃	semidirect
1222. SD₁₆	C₂×D₄×C₂₃	semidirect
1228. D₈	C₂×D₄×C₂₃	semidirect
1238. C₂×C₈	C₂×D₄×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#577	2
C₂×C₂₃×#575	2
C₂₃×#3489	2
C₂₃×#3488	2
C₂₃×#3278	2
C₂₃×#3277	2
C₂₃×#3273	2
C₂₃×#3272	2
C₂₃×#3269	2
C₂₃×#3268	2
C₂₃×#3266	2
C₂₃×#3265	2
C₂₃×#3154	2
C₂₃×#3061	2
C₂×C₂₃×#468	2
C₂₃×#3046	2
C₂₃×#3045	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂₃×#3007	2
C₂₃×#3006	2
C₂₃×#2951	2
C₂₃×#2930	2
#61062	23

Subgroups — C23×#61062 #19208688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61062 #19208688