Subgroups — C₂₃×#61092 #19208718

Order 5888.

2770 conjugacy classes of subgroups.

The subgroup lattice has 1400 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×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3282	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3280	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3275	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3273	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3267	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3264	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#463	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×#3009	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2935	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
26	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#577	—	2	8	no	—
29	C₂₃×#576	—	2	8	no	—
30	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
31	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
35	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
36	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	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×#135	C₂²	1	2	yes	complemented
40	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
43	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
45	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
47	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#548	C₂²	1	2	yes	complemented
50	C₂₃×#548	C₂²	1	2	yes	complemented
51	C₂₃×#547	—	2	1	no	—
52	C₂₃×#547	C₂²	1	2	yes	complemented
53	C₂₃×#546	—	2	1	no	—
54	C₂₃×#546	—	2	1	no	—
55	C₂₃×#546	—	2	2	no	—
56	C₂₃×#546	—	2	2	no	—
57	C₂₃×#546	C₂²	1	2	yes	complemented
58	C₂₃×#546	C₂²	1	2	yes	complemented
59	C₂₃×#546	C₂²	1	2	yes	complemented
60	C₂₃×#546	C₂²	1	2	yes	complemented
61	D₄²×C₂₃	—	2	1	no	—
62	D₄²×C₂₃	C₂²	1	2	yes	complemented
63	C₂₃×#537	C₂²	1	1	yes	characteristic
64	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#536	—	2	1	no	—
66	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#535	—	2	1	no	—
68	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#534	—	2	2	no	—
70	C₂₃×#532	—	2	1	no	—
71	C₂₃×#532	C₂²	1	1	yes	characteristic
72	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₂₃×#124	—	2	1	no	—
74	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₂₃×#121	—	2	2	no	—
76	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#497	C₂²	1	2	yes	complemented
79	C₂₃×#496	C₂²	1	2	yes	complemented
80	C₂₃×#495	C₂²	1	2	yes	complemented
81	C₂₃×#495	C₂²	1	2	yes	complemented
82	C₂₃×#470	C₂²	1	2	yes	complemented
83	C₂₃×#469	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#468	C₂²	1	2	yes	complemented
86	C₂₃×#467	C₂²	1	2	yes	complemented
87	C₂₃×#466	C₂²	1	2	yes	complemented
88	C₂₃×#465	C₂²	1	2	yes	complemented
89	C₂₃×#465	C₂²	1	2	yes	complemented
90	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#463	C₂²	1	2	yes	complemented
93	C₂₃×#463	C₂²	1	2	yes	complemented
94	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#463	C₂²	1	2	yes	complemented
96	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#463	C₂²	1	2	yes	complemented
98	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#459	C₂²	1	1	yes	characteristic, 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×#450	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×#447	C₂²	1	2	yes	complemented
116	C₂₃×#447	C₂²	1	2	yes	complemented
117	C₂₃×#447	C₂²	1	2	yes	complemented
118	C₂₃×#442	C₂²	1	2	yes	complemented
119	C₂₃×#440	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×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×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
126	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
131	C₂₃×#416	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×#408	C₂²	1	1	yes	characteristic, complemented
136	C₄×M₁₆×C₂₃	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)	—	2	4	no	—
141	C₂₃×H(5,𝔽₂)	—	2	4	no	—
142	C₂₃×H(5,𝔽₂)	—	4	2	no	—
143	C₂₃×H(5,𝔽₂)	—	4	2	no	—
144	C₂₃×H(5,𝔽₂)	—	4	2	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	1	no	—
149	C₂×#41×C₂₃	—	2	2	no	—
150	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×#41×C₂₃	C₂³	1	2	yes	—
153	C₂×#41×C₂₃	C₂³	1	2	yes	—
154	C₂×#41×C₂₃	C₂³	1	2	yes	—
155	C₂×#41×C₂₃	C₂³	1	2	yes	—
156	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₂₃	—	2	1	no	—
160	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₂²×D₄×C₂₃	—	2	2	no	—
163	C₂²×D₄×C₂₃	—	2	1	no	—
164	C₂²×D₄×C₂₃	—	2	2	no	—
165	C₂²×D₄×C₂₃	—	2	1	no	—
166	C₂²×D₄×C₂₃	—	2	1	no	—
167	C₂²×D₄×C₂₃	—	2	2	no	—
168	C₂²×D₄×C₂₃	—	2	2	no	—
169	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
171	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
172	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
173	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₂₃	—	2	1	no	—
175	C₂₃×#137	—	2	8	no	—
176	C₂₃×#137	—	2	4	no	—
177	C₂₃×#137	—	4	2	no	—
178	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
179	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
180	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
181	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
182	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
183	C₂₃×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
184	C₂₃×#135	—	2	4	no	—
185	C₂₃×#135	—	2	4	no	—
186	C₂₃×#135	—	2	8	no	—
187	C₂₃×#135	—	2	8	no	—
188	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
191	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
192	C₂×SD₁₆×C₂₃	—	2	4	no	—
193	C₂×SD₁₆×C₂₃	—	2	8	no	—
194	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
196	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
197	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
198	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
200	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
202	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
203	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
205	C₂×D₈×C₂₃	—	2	4	no	—
206	C₂×D₈×C₂₃	—	2	8	no	—
207	C₂×D₈×C₂₃	C₂³	1	2	yes	—
208	C₂×D₈×C₂₃	C₂³	1	2	yes	—
209	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×D₈×C₂₃	C₂³	1	2	yes	—
211	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×D₈×C₂₃	C₂³	1	2	yes	—
213	C₂×D₈×C₂₃	C₂³	1	2	yes	—
214	C₂₃×#131	—	2	4	no	—
215	C₂₃×#131	—	2	4	no	—
216	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
217	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
218	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
220	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
222	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
224	C₂₃×C₄⋊Q₈	—	2	1	no	—
225	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
226	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂₃×#127	—	2	1	no	—
228	C₂₃×#127	D₄	1	1	yes	characteristic
229	C₂₃×#127	C₂³	1	1	yes	characteristic
230	C₂₃×#124	—	2	1	no	—
231	C₂₃×#124	—	2	1	no	—
232	C₂₃×#124	—	2	2	no	—
233	C₂₃×#124	—	2	2	no	—
234	C₂₃×#124	—	2	1	no	—
235	C₂₃×#124	—	2	1	no	—
236	C₂₃×#124	D₄	1	1	yes	characteristic
237	C₂₃×#124	D₄	1	1	yes	characteristic
238	C₂₃×#124	C₂³	1	2	yes	—
239	C₂₃×#124	C₂³	1	2	yes	—
240	C₂₃×#124	C₂³	1	1	yes	characteristic
241	C₂₃×#124	C₂³	1	1	yes	characteristic
242	C₂₃×#123	—	2	2	no	—
243	C₂₃×#123	—	2	2	no	—
244	C₂₃×#123	—	2	2	no	—
245	C₂₃×#123	—	2	2	no	—
246	C₂₃×#123	—	2	2	no	—
247	C₂₃×#123	—	2	2	no	—
248	C₂₃×#123	—	2	2	no	—
249	C₂₃×C₂²⋊Q₈	—	2	1	no	—
250	C₂₃×C₂²⋊Q₈	—	2	1	no	—
251	C₂₃×C₂²⋊Q₈	—	2	2	no	—
252	C₂₃×C₂²⋊Q₈	—	2	2	no	—
253	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
254	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
255	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
257	C₂₃×#121	—	2	2	no	—
258	C₂₃×#121	—	2	2	no	—
259	C₂₃×#121	—	2	2	no	—
260	C₂₃×#121	—	2	2	no	—
261	C₂₃×#121	—	2	2	no	—
262	C₂₃×#121	—	2	1	no	—
263	C₂₃×#121	—	2	1	no	—
264	C₂₃×#121	—	2	1	no	—
265	C₂₃×#121	—	2	1	no	—
266	C₂₃×#121	—	2	2	no	—
267	C₂₃×#121	—	2	2	no	—
268	C₂₃×#121	—	2	2	no	—
269	C₂₃×#121	—	2	2	no	—
270	C₂₃×#121	—	2	2	no	—
271	C₂₃×#121	D₄	1	2	yes	—
272	C₂₃×#121	D₄	1	2	yes	—
273	C₂₃×#121	C₂³	1	2	yes	—
274	C₂₃×#121	C₂³	1	2	yes	—
275	C₂₃×#121	C₂³	1	2	yes	—
276	C₂₃×#121	C₂³	1	2	yes	—
277	C₂₃×#120	—	2	2	no	—
278	C₂₃×#120	—	2	2	no	—
279	C₂₃×#120	—	2	2	no	—
280	C₂₃×#120	—	2	2	no	—
281	C₂₃×#120	—	2	2	no	—
282	C₂₃×#120	—	2	2	no	—
283	C₂₃×#120	—	2	2	no	—
284	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₂₃	—	2	1	no	—
287	C₄×D₄×C₂₃	—	2	1	no	—
288	C₄×D₄×C₂₃	—	2	2	no	—
289	C₄×D₄×C₂₃	—	2	2	no	—
290	C₄×D₄×C₂₃	—	2	1	no	—
291	C₄×D₄×C₂₃	—	2	1	no	—
292	C₄×D₄×C₂₃	—	2	1	no	—
293	C₄×D₄×C₂₃	—	2	1	no	—
294	C₄×D₄×C₂₃	C₂³	1	2	yes	—
295	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₂₃	C₂³	1	2	yes	—
297	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₂₃	C₂³	1	2	yes	—
299	C₄×D₄×C₂₃	C₂³	1	2	yes	—
300	C₂₃×#117	—	2	1	no	—
301	C₂₃×#117	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂×C₄²×C₂₃	—	2	1	no	—
312	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
313	C₂₃×#107	C₂³	1	2	yes	—
314	C₂₃×#106	C₂³	1	2	yes	—
315	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
318	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
319	C₂₃×#103	C₂³	1	2	yes	—
320	C₂₃×#103	C₂³	1	2	yes	—
321	C₂₃×#103	C₂³	1	1	yes	characteristic
322	C₂₃×#103	C₂³	1	1	yes	characteristic
323	C₂₃×#103	C₂³	1	1	yes	characteristic
324	C₂₃×#103	C₂³	1	1	yes	characteristic
325	C₂₃×#103	C₂³	1	2	yes	—
326	C₂₃×#102	C₂³	1	2	yes	—
327	C₂₃×#102	C₂³	1	2	yes	—
328	C₂₃×#102	C₂³	1	1	yes	characteristic
329	C₂₃×#102	C₂³	1	1	yes	characteristic
330	C₂₃×#102	C₂³	1	1	yes	characteristic
331	C₂₃×#102	C₂³	1	1	yes	characteristic
332	C₂₃×#102	C₂³	1	2	yes	—
333	C₂₃×#102	C₂³	1	2	yes	—
334	C₂₃×#102	C₂³	1	2	yes	—
335	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₂₃×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₂₃	C₂³	1	2	yes	—
341	C₂⁴×C₂₃	—	2	1	no	—
342	C₂⁴×C₂₃	—	2	2	no	—
343	C₂⁴×C₂₃	—	2	1	no	—
344	C₂⁴×C₂₃	—	2	2	no	—
345	C₂⁴×C₂₃	—	2	2	no	—
346	#41×C₂₃	—	2	2	no	—
347	#41×C₂₃	—	2	2	no	—
348	#41×C₂₃	—	2	2	no	—
349	#41×C₂₃	—	2	2	no	—
350	#41×C₂₃	—	2	2	no	—
351	#41×C₂₃	—	2	4	no	—
352	#41×C₂₃	—	2	4	no	—
353	#41×C₂₃	—	2	4	no	—
354	#41×C₂₃	—	2	4	no	—
355	#41×C₂₃	—	2	2	no	—
356	#41×C₂₃	—	2	2	no	—
357	#41×C₂₃	—	2	2	no	—
358	#41×C₂₃	—	2	2	no	—
359	#41×C₂₃	—	4	2	no	—
360	#41×C₂₃	—	4	2	no	—
361	#41×C₂₃	—	4	2	no	—
362	#41×C₂₃	—	4	2	no	—
363	#41×C₂₃	—	4	4	no	—
364	#41×C₂₃	—	4	4	no	—
365	#41×C₂₃	—	4	8	no	—
366	#41×C₂₃	—	4	4	no	—
367	#41×C₂₃	—	4	4	no	—
368	#41×C₂₃	C₂×D₄	1	4	yes	complemented
369	C₂×Q₈×C₂₃	—	2	2	no	—
370	C₂×Q₈×C₂₃	—	2	1	no	—
371	C₂×Q₈×C₂₃	—	2	4	no	—
372	C₂×Q₈×C₂₃	—	2	2	no	—
373	C₂×Q₈×C₂₃	—	2	2	no	—
374	C₂×Q₈×C₂₃	—	4	2	no	—
375	C₂×Q₈×C₂₃	—	4	4	no	—
376	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
379	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₂₃	—	2	1	no	—
383	C₂×D₄×C₂₃	—	2	4	no	—
384	C₂×D₄×C₂₃	—	2	4	no	—
385	C₂×D₄×C₂₃	—	2	4	no	—
386	C₂×D₄×C₂₃	—	2	2	no	—
387	C₂×D₄×C₂₃	—	2	2	no	—
388	C₂×D₄×C₂₃	—	2	2	no	—
389	C₂×D₄×C₂₃	—	2	1	no	—
390	C₂×D₄×C₂₃	—	2	1	no	—
391	C₂×D₄×C₂₃	—	2	2	no	—
392	C₂×D₄×C₂₃	—	2	2	no	—
393	C₂×D₄×C₂₃	—	2	2	no	—
394	C₂×D₄×C₂₃	—	2	2	no	—
395	C₂×D₄×C₂₃	—	2	2	no	—
396	C₂×D₄×C₂₃	—	2	1	no	—
397	C₂×D₄×C₂₃	—	2	2	no	—
398	C₂×D₄×C₂₃	—	2	1	no	—
399	C₂×D₄×C₂₃	—	2	2	no	—
400	C₂×D₄×C₂₃	—	2	2	no	—
401	C₂×D₄×C₂₃	—	2	2	no	—
402	C₂×D₄×C₂₃	—	2	1	no	—
403	C₂×D₄×C₂₃	—	2	1	no	—
404	C₂×D₄×C₂₃	—	2	2	no	—
405	C₂×D₄×C₂₃	—	2	2	no	—
406	C₂×D₄×C₂₃	—	4	2	no	—
407	C₂×D₄×C₂₃	—	4	2	no	—
408	C₂×D₄×C₂₃	—	4	2	no	—
409	C₂×D₄×C₂₃	—	4	4	no	—
410	C₂×D₄×C₂₃	—	4	8	no	—
411	C₂×D₄×C₂₃	—	4	4	no	—
412	C₂×D₄×C₂₃	—	4	4	no	—
413	C₂×D₄×C₂₃	—	4	8	no	—
414	C₂×D₄×C₂₃	—	4	8	no	—
415	C₂×D₄×C₂₃	—	8	4	no	—
416	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
417	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
418	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
419	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
420	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
421	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
423	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
424	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
425	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
426	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
427	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
428	C₂²×C₄×C₂₃	—	2	1	no	—
429	C₂²×C₄×C₂₃	—	2	1	no	—
430	C₂²×C₄×C₂₃	—	2	2	no	—
431	C₂²×C₄×C₂₃	—	2	1	no	—
432	C₂²×C₄×C₂₃	—	2	2	no	—
433	C₂²×C₄×C₂₃	—	2	2	no	—
434	C₂²×C₄×C₂₃	—	2	2	no	—
435	C₂²×C₄×C₂₃	—	2	2	no	—
436	C₂²×C₄×C₂₃	—	2	1	no	—
437	C₂²×C₄×C₂₃	—	2	1	no	—
438	C₂²×C₄×C₂₃	—	2	2	no	—
439	C₂²×C₄×C₂₃	—	2	1	no	—
440	C₂²×C₄×C₂₃	—	2	1	no	—
441	C₂²×C₄×C₂₃	—	2	2	no	—
442	C₂²×C₄×C₂₃	—	8	2	no	—
443	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
446	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
447	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	Q₁₆×C₂₃	—	2	2	no	—
449	Q₁₆×C₂₃	—	2	2	no	—
450	Q₁₆×C₂₃	—	2	4	no	—
451	Q₁₆×C₂₃	—	4	2	no	—
452	SD₁₆×C₂₃	—	2	2	no	—
453	SD₁₆×C₂₃	—	2	2	no	—
454	SD₁₆×C₂₃	—	2	4	no	—
455	SD₁₆×C₂₃	—	2	4	no	—
456	SD₁₆×C₂₃	—	2	2	no	—
457	SD₁₆×C₂₃	—	2	2	no	—
458	SD₁₆×C₂₃	—	2	4	no	—
459	SD₁₆×C₂₃	—	2	4	no	—
460	SD₁₆×C₂₃	—	4	2	no	—
461	SD₁₆×C₂₃	—	4	2	no	—
462	SD₁₆×C₂₃	C₂×D₄	1	8	yes	complemented
463	D₈×C₂₃	—	2	2	no	—
464	D₈×C₂₃	—	2	4	no	—
465	D₈×C₂₃	—	2	4	no	—
466	D₈×C₂₃	—	2	2	no	—
467	D₈×C₂₃	—	2	4	no	—
468	D₈×C₂₃	—	4	2	no	—
469	D₈×C₂₃	C₂×D₄	1	8	yes	complemented
470	M₁₆×C₂₃	—	2	2	no	—
471	M₁₆×C₂₃	—	2	4	no	—
472	M₁₆×C₂₃	—	2	4	no	—
473	M₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
474	C₂×C₈×C₂₃	—	2	2	no	—
475	C₂×C₈×C₂₃	—	2	2	no	—
476	C₂×C₈×C₂₃	—	2	4	no	—
477	C₂×C₈×C₂₃	—	2	4	no	—
478	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
479	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
480	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
481	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
482	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
483	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
484	C₄⋊C₄×C₂₃	—	2	1	no	—
485	C₄⋊C₄×C₂₃	—	2	2	no	—
486	C₄⋊C₄×C₂₃	—	2	2	no	—
487	C₄⋊C₄×C₂₃	—	2	1	no	—
488	C₄⋊C₄×C₂₃	—	2	1	no	—
489	C₄⋊C₄×C₂₃	—	2	1	no	—
490	C₄⋊C₄×C₂₃	—	2	2	no	—
491	C₄⋊C₄×C₂₃	—	2	2	no	—
492	C₄⋊C₄×C₂₃	—	2	1	no	—
493	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
494	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
495	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
496	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
497	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
498	C₂²⋊C₄×C₂₃	—	2	2	no	—
499	C₂²⋊C₄×C₂₃	—	2	2	no	—
500	C₂²⋊C₄×C₂₃	—	2	2	no	—
501	C₂²⋊C₄×C₂₃	—	2	2	no	—
502	C₂²⋊C₄×C₂₃	—	2	1	no	—
503	C₂²⋊C₄×C₂₃	—	2	1	no	—
504	C₂²⋊C₄×C₂₃	—	2	1	no	—
505	C₂²⋊C₄×C₂₃	—	2	2	no	—
506	C₂²⋊C₄×C₂₃	—	2	2	no	—
507	C₂²⋊C₄×C₂₃	—	2	2	no	—
508	C₂²⋊C₄×C₂₃	—	2	2	no	—
509	C₂²⋊C₄×C₂₃	—	2	2	no	—
510	C₂²⋊C₄×C₂₃	—	2	2	no	—
511	C₂²⋊C₄×C₂₃	—	2	2	no	—
512	C₂²⋊C₄×C₂₃	—	2	2	no	—
513	C₂²⋊C₄×C₂₃	—	2	2	no	—
514	C₂²⋊C₄×C₂₃	—	2	2	no	—
515	C₂²⋊C₄×C₂₃	—	2	1	no	—
516	C₂²⋊C₄×C₂₃	—	2	1	no	—
517	C₂²⋊C₄×C₂₃	—	2	1	no	—
518	C₂²⋊C₄×C₂₃	—	2	1	no	—
519	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
520	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
521	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
522	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
523	C₄²×C₂₃	—	2	1	no	—
524	C₄²×C₂₃	—	2	1	no	—
525	C₄²×C₂₃	—	2	1	no	—
526	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
527	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
528	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
529	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
530	#61092	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
531	C₂³×C₂₃	—	2	1	no	—
532	C₂³×C₂₃	—	2	2	no	—
533	C₂³×C₂₃	—	2	4	no	—
534	C₂³×C₂₃	—	2	2	no	—
535	C₂³×C₂₃	—	2	1	no	—
536	C₂³×C₂₃	—	2	1	no	—
537	C₂³×C₂₃	—	4	4	no	—
538	C₂³×C₂₃	—	4	4	no	—
539	C₂³×C₂₃	—	4	4	no	—
540	C₂³×C₂₃	—	4	2	no	—
541	C₂³×C₂₃	—	8	1	no	—
542	C₂³×C₂₃	—	8	1	no	—
543	C₂³×C₂₃	—	8	2	no	—
544	C₂³×C₂₃	—	8	2	no	—
545	C₂³×C₂₃	—	8	1	no	—
546	C₂³×C₂₃	—	8	1	no	—
547	C₂³×C₂₃	—	8	2	no	—
548	C₂³×C₂₃	—	8	2	no	—
549	C₂³×C₂₃	—	8	2	no	—
550	C₂³×C₂₃	—	8	2	no	—
551	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
552	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
553	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
554	Q₈×C₂₃	—	2	2	no	—
555	Q₈×C₂₃	—	2	2	no	—
556	Q₈×C₂₃	—	2	1	no	—
557	Q₈×C₂₃	—	2	2	no	—
558	Q₈×C₂₃	—	2	1	no	—
559	Q₈×C₂₃	—	2	1	no	—
560	Q₈×C₂₃	—	2	1	no	—
561	Q₈×C₂₃	—	2	2	no	—
562	Q₈×C₂₃	—	2	1	no	—
563	Q₈×C₂₃	—	4	4	no	—
564	Q₈×C₂₃	—	4	2	no	—
565	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
566	D₄×C₂₃	—	2	4	no	—
567	D₄×C₂₃	—	2	4	no	—
568	D₄×C₂₃	—	2	4	no	—
569	D₄×C₂₃	—	2	4	no	—
570	D₄×C₂₃	—	2	2	no	—
571	D₄×C₂₃	—	2	2	no	—
572	D₄×C₂₃	—	2	2	no	—
573	D₄×C₂₃	—	2	1	no	—
574	D₄×C₂₃	—	2	1	no	—
575	D₄×C₂₃	—	2	2	no	—
576	D₄×C₂₃	—	2	1	no	—
577	D₄×C₂₃	—	2	1	no	—
578	D₄×C₂₃	—	2	2	no	—
579	D₄×C₂₃	—	2	1	no	—
580	D₄×C₂₃	—	4	2	no	—
581	D₄×C₂₃	—	4	2	no	—
582	D₄×C₂₃	—	4	4	no	—
583	D₄×C₂₃	—	4	4	no	—
584	D₄×C₂₃	—	4	4	no	—
585	D₄×C₂₃	—	4	4	no	—
586	D₄×C₂₃	—	4	2	no	—
587	D₄×C₂₃	—	4	4	no	—
588	D₄×C₂₃	—	4	4	no	—
589	D₄×C₂₃	—	4	4	no	—
590	D₄×C₂₃	—	4	2	no	—
591	D₄×C₂₃	—	4	2	no	—
592	D₄×C₂₃	—	4	2	no	—
593	D₄×C₂₃	—	8	1	no	—
594	D₄×C₂₃	—	8	2	no	—
595	D₄×C₂₃	—	8	2	no	—
596	D₄×C₂₃	—	8	2	no	—
597	D₄×C₂₃	—	8	2	no	—
598	D₄×C₂₃	C₂²×D₄	1	2	yes	—
599	D₄×C₂₃	C₂²×D₄	1	4	yes	—
600	C₂×C₄×C₂₃	—	2	1	no	—
601	C₂×C₄×C₂₃	—	2	4	no	—
602	C₂×C₄×C₂₃	—	2	2	no	—
603	C₂×C₄×C₂₃	—	2	2	no	—
604	C₂×C₄×C₂₃	—	2	2	no	—
605	C₂×C₄×C₂₃	—	2	2	no	—
606	C₂×C₄×C₂₃	—	2	1	no	—
607	C₂×C₄×C₂₃	—	2	1	no	—
608	C₂×C₄×C₂₃	—	2	2	no	—
609	C₂×C₄×C₂₃	—	2	2	no	—
610	C₂×C₄×C₂₃	—	2	1	no	—
611	C₂×C₄×C₂₃	—	2	1	no	—
612	C₂×C₄×C₂₃	—	4	1	no	—
613	C₂×C₄×C₂₃	—	4	1	no	—
614	C₂×C₄×C₂₃	—	4	4	no	—
615	C₂×C₄×C₂₃	—	4	4	no	—
616	C₂×C₄×C₂₃	—	4	4	no	—
617	C₂×C₄×C₂₃	—	4	4	no	—
618	C₂×C₄×C₂₃	—	4	4	no	—
619	C₂×C₄×C₂₃	—	4	4	no	—
620	C₂×C₄×C₂₃	—	4	2	no	—
621	C₂×C₄×C₂₃	—	4	2	no	—
622	C₂×C₄×C₂₃	—	4	2	no	—
623	C₂×C₄×C₂₃	—	8	1	no	—
624	C₂×C₄×C₂₃	—	8	1	no	—
625	C₂×C₄×C₂₃	—	8	2	no	—
626	C₂×C₄×C₂₃	—	8	1	no	—
627	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
629	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
632	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
633	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
635	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
636	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
637	C₈×C₂₃	—	2	1	no	—
638	C₈×C₂₃	—	2	1	no	—
639	C₈×C₂₃	—	2	1	no	—
640	C₈×C₂₃	—	2	1	no	—
641	C₈×C₂₃	—	2	2	no	—
642	C₈×C₂₃	C₂²×D₄	1	4	yes	—
643	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
644	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
645	#3500	C₂×C₂₃	1	1	yes	characteristic, complemented
646	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
647	#3282	C₂×C₂₃	1	2	yes	complemented
648	#3280	C₂×C₂₃	1	2	yes	complemented
649	#3275	C₂×C₂₃	1	2	yes	complemented
650	#3273	C₂×C₂₃	1	2	yes	complemented
651	#3269	C₂×C₂₃	1	2	yes	complemented
652	#3267	C₂×C₂₃	1	2	yes	complemented
653	#3265	C₂×C₂₃	1	2	yes	complemented
654	#3264	C₂×C₂₃	1	2	yes	complemented
655	#3153	C₂×C₂₃	1	1	yes	characteristic, complemented
656	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
657	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
658	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
659	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
660	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
661	#3012	C₂×C₂₃	1	1	yes	characteristic, complemented
662	#3009	C₂×C₂₃	1	1	yes	characteristic, complemented
663	#3008	C₂×C₂₃	1	1	yes	characteristic, complemented
664	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
665	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
666	C₂²×C₂₃	—	2	1	no	—
667	C₂²×C₂₃	—	2	1	no	—
668	C₂²×C₂₃	—	2	2	no	—
669	C₂²×C₂₃	—	2	2	no	—
670	C₂²×C₂₃	—	2	2	no	—
671	C₂²×C₂₃	—	2	2	no	—
672	C₂²×C₂₃	—	2	2	no	—
673	C₂²×C₂₃	—	2	2	no	—
674	C₂²×C₂₃	—	2	2	no	—
675	C₂²×C₂₃	—	2	4	no	—
676	C₂²×C₂₃	—	4	1	no	—
677	C₂²×C₂₃	—	4	2	no	—
678	C₂²×C₂₃	—	4	2	no	—
679	C₂²×C₂₃	—	4	1	no	—
680	C₂²×C₂₃	—	4	1	no	—
681	C₂²×C₂₃	—	4	1	no	—
682	C₂²×C₂₃	—	4	2	no	—
683	C₂²×C₂₃	—	4	1	no	—
684	C₂²×C₂₃	—	4	1	no	—
685	C₂²×C₂₃	—	4	2	no	—
686	C₂²×C₂₃	—	4	2	no	—
687	C₂²×C₂₃	—	4	1	no	—
688	C₂²×C₂₃	—	4	1	no	—
689	C₂²×C₂₃	—	8	4	no	—
690	C₂²×C₂₃	—	16	2	no	—
691	C₂²×C₂₃	—	16	4	no	—
692	C₂²×C₂₃	—	16	4	no	—
693	C₂²×C₂₃	—	16	4	no	—
694	C₂²×C₂₃	D₄²	1	2	yes	—
695	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
696	C₄×C₂₃	—	2	1	no	—
697	C₄×C₂₃	—	2	1	no	—
698	C₄×C₂₃	—	2	1	no	—
699	C₄×C₂₃	—	2	1	no	—
700	C₄×C₂₃	—	2	2	no	—
701	C₄×C₂₃	—	2	2	no	—
702	C₄×C₂₃	—	2	2	no	—
703	C₄×C₂₃	—	4	1	no	—
704	C₄×C₂₃	—	4	2	no	—
705	C₄×C₂₃	—	4	1	no	—
706	C₄×C₂₃	—	4	1	no	—
707	C₄×C₂₃	—	4	1	no	—
708	C₄×C₂₃	—	4	2	no	—
709	C₄×C₂₃	D₄²	1	2	yes	—
710	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
711	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
712	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
714	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
715	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
716	#577	—	2	8	no	—
717	#576	—	2	8	no	—
718	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
720	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
721	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
722	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
723	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
724	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
725	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
726	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
727	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
728	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
729	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
730	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
731	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
732	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
733	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
734	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
735	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
736	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
737	#548	C₂²×C₂₃	1	2	yes	complemented
738	#548	C₂²×C₂₃	1	2	yes	complemented
739	#547	—	2	1	no	—
740	#547	C₂²×C₂₃	1	2	yes	complemented
741	#546	—	2	1	no	—
742	#546	—	2	1	no	—
743	#546	—	2	2	no	—
744	#546	—	2	2	no	—
745	#546	C₂²×C₂₃	1	2	yes	complemented
746	#546	C₂²×C₂₃	1	2	yes	complemented
747	#546	C₂²×C₂₃	1	2	yes	complemented
748	#546	C₂²×C₂₃	1	2	yes	complemented
749	D₄²	—	2	1	no	—
750	D₄²	C₂²×C₂₃	1	2	yes	complemented
751	#537	C₂²×C₂₃	1	1	yes	characteristic
752	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
753	#536	—	2	1	no	—
754	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
755	#535	—	2	1	no	—
756	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
757	#534	—	2	2	no	—
758	#532	—	2	1	no	—
759	#532	C₂²×C₂₃	1	1	yes	characteristic
760	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	C₂×#124	—	2	1	no	—
762	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
763	C₂×#121	—	2	2	no	—
764	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
765	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
766	#497	C₂²×C₂₃	1	2	yes	complemented
767	#496	C₂²×C₂₃	1	2	yes	complemented
768	#495	C₂²×C₂₃	1	2	yes	complemented
769	#495	C₂²×C₂₃	1	2	yes	complemented
770	#470	C₂²×C₂₃	1	2	yes	complemented
771	#469	C₂²×C₂₃	1	2	yes	complemented
772	#468	C₂²×C₂₃	1	2	yes	complemented
773	#468	C₂²×C₂₃	1	2	yes	complemented
774	#467	C₂²×C₂₃	1	2	yes	complemented
775	#466	C₂²×C₂₃	1	2	yes	complemented
776	#465	C₂²×C₂₃	1	2	yes	complemented
777	#465	C₂²×C₂₃	1	2	yes	complemented
778	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
779	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
780	#463	C₂²×C₂₃	1	2	yes	complemented
781	#463	C₂²×C₂₃	1	2	yes	complemented
782	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
783	#463	C₂²×C₂₃	1	2	yes	complemented
784	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
785	#463	C₂²×C₂₃	1	2	yes	complemented
786	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
787	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
788	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
789	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
790	#452	C₂²×C₂₃	1	2	yes	complemented
791	#452	C₂²×C₂₃	1	2	yes	complemented
792	#452	C₂²×C₂₃	1	2	yes	complemented
793	#452	C₂²×C₂₃	1	2	yes	complemented
794	#451	C₂²×C₂₃	1	2	yes	complemented
795	#450	C₂²×C₂₃	1	2	yes	complemented
796	#450	C₂²×C₂₃	1	2	yes	complemented
797	#450	C₂²×C₂₃	1	2	yes	complemented
798	#449	C₂²×C₂₃	1	2	yes	complemented
799	#449	C₂²×C₂₃	1	2	yes	complemented
800	#449	C₂²×C₂₃	1	2	yes	complemented
801	#449	C₂²×C₂₃	1	2	yes	complemented
802	#448	C₂²×C₂₃	1	2	yes	complemented
803	#447	C₂²×C₂₃	1	2	yes	complemented
804	#447	C₂²×C₂₃	1	2	yes	complemented
805	#447	C₂²×C₂₃	1	2	yes	complemented
806	#442	C₂²×C₂₃	1	2	yes	complemented
807	#440	C₂²×C₂₃	1	2	yes	complemented
808	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
809	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
810	#436	C₂²×C₂₃	1	2	yes	complemented
811	#435	C₂²×C₂₃	1	2	yes	complemented
812	#435	C₂²×C₂₃	1	2	yes	complemented
813	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
814	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
815	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
816	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
817	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
818	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
819	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
820	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
821	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
822	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
823	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
824	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
825	C₂×C₂₃	—	2	2	no	—
826	C₂×C₂₃	—	4	2	no	—
827	C₂×C₂₃	—	4	2	no	—
828	C₂×C₂₃	—	4	4	no	—
829	C₂×C₂₃	—	4	2	no	—
830	C₂×C₂₃	—	8	1	no	—
831	C₂×C₂₃	—	8	1	no	—
832	C₂×C₂₃	—	8	2	no	—
833	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
834	C₂×C₂₃	#3584	1	1	yes	characteristic
835	C₂×C₂₃	#3585	1	1	yes	characteristic
836	2₋¹⁺⁴	—	2	4	no	—
837	2₋¹⁺⁴	—	4	2	no	—
838	H(5,𝔽₂)	—	2	4	no	—
839	H(5,𝔽₂)	—	2	4	no	—
840	H(5,𝔽₂)	—	2	4	no	—
841	H(5,𝔽₂)	—	4	2	no	—
842	H(5,𝔽₂)	—	4	2	no	—
843	H(5,𝔽₂)	—	4	2	no	—
844	C₂×#41	—	2	1	no	—
845	C₂×#41	—	2	1	no	—
846	C₂×#41	—	2	1	no	—
847	C₂×#41	—	2	1	no	—
848	C₂×#41	—	2	2	no	—
849	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
850	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
851	C₂×#41	C₂³×C₂₃	1	2	yes	—
852	C₂×#41	C₂³×C₂₃	1	2	yes	—
853	C₂×#41	C₂³×C₂₃	1	2	yes	—
854	C₂×#41	C₂³×C₂₃	1	2	yes	—
855	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
856	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
857	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
858	C₂²×Q₈	—	2	1	no	—
859	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
861	C₂²×D₄	—	2	2	no	—
862	C₂²×D₄	—	2	2	no	—
863	C₂²×D₄	—	2	1	no	—
864	C₂²×D₄	—	2	1	no	—
865	C₂²×D₄	—	2	1	no	—
866	C₂²×D₄	—	2	2	no	—
867	C₂²×D₄	—	2	2	no	—
868	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
869	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
870	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
871	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
872	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
873	C₂³×C₄	—	2	1	no	—
874	#137	—	2	8	no	—
875	#137	—	2	4	no	—
876	#137	—	4	2	no	—
877	AGL(1,ℤ/8)	—	2	8	no	—
878	AGL(1,ℤ/8)	—	2	8	no	—
879	AGL(1,ℤ/8)	—	2	8	no	—
880	AGL(1,ℤ/8)	—	2	4	no	—
881	AGL(1,ℤ/8)	—	4	2	no	—
882	AGL(1,ℤ/8)	D₄×C₂₃	1	8	yes	complemented
883	#135	—	2	4	no	—
884	#135	—	2	4	no	—
885	#135	—	2	8	no	—
886	#135	—	2	8	no	—
887	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
888	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
889	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
890	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
891	C₂×SD₁₆	—	2	4	no	—
892	C₂×SD₁₆	—	2	8	no	—
893	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
894	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
895	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
896	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
897	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
898	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
899	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
900	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
901	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
902	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
903	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
904	C₂×D₈	—	2	4	no	—
905	C₂×D₈	—	2	8	no	—
906	C₂×D₈	C₂³×C₂₃	1	2	yes	—
907	C₂×D₈	C₂³×C₂₃	1	2	yes	—
908	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
909	C₂×D₈	C₂³×C₂₃	1	2	yes	—
910	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
911	C₂×D₈	C₂³×C₂₃	1	2	yes	—
912	C₂×D₈	C₂³×C₂₃	1	2	yes	—
913	#131	—	2	4	no	—
914	#131	—	2	4	no	—
915	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
916	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
917	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
918	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
919	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
920	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
921	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
922	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
923	C₄⋊Q₈	—	2	1	no	—
924	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
925	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
926	#127	—	2	1	no	—
927	#127	D₄×C₂₃	1	1	yes	characteristic
928	#127	C₂³×C₂₃	1	1	yes	characteristic
929	#124	—	2	1	no	—
930	#124	—	2	1	no	—
931	#124	—	2	2	no	—
932	#124	—	2	2	no	—
933	#124	—	2	1	no	—
934	#124	—	2	1	no	—
935	#124	D₄×C₂₃	1	1	yes	characteristic
936	#124	D₄×C₂₃	1	1	yes	characteristic
937	#124	C₂³×C₂₃	1	2	yes	—
938	#124	C₂³×C₂₃	1	2	yes	—
939	#124	C₂³×C₂₃	1	1	yes	characteristic
940	#124	C₂³×C₂₃	1	1	yes	characteristic
941	#123	—	2	2	no	—
942	#123	—	2	2	no	—
943	#123	—	2	2	no	—
944	#123	—	2	2	no	—
945	#123	—	2	2	no	—
946	#123	—	2	2	no	—
947	#123	—	2	2	no	—
948	C₂²⋊Q₈	—	2	1	no	—
949	C₂²⋊Q₈	—	2	1	no	—
950	C₂²⋊Q₈	—	2	2	no	—
951	C₂²⋊Q₈	—	2	2	no	—
952	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
953	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
954	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
955	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
956	#121	—	2	2	no	—
957	#121	—	2	2	no	—
958	#121	—	2	2	no	—
959	#121	—	2	2	no	—
960	#121	—	2	2	no	—
961	#121	—	2	1	no	—
962	#121	—	2	1	no	—
963	#121	—	2	1	no	—
964	#121	—	2	1	no	—
965	#121	—	2	2	no	—
966	#121	—	2	2	no	—
967	#121	—	2	2	no	—
968	#121	—	2	2	no	—
969	#121	—	2	2	no	—
970	#121	D₄×C₂₃	1	2	yes	—
971	#121	D₄×C₂₃	1	2	yes	—
972	#121	C₂³×C₂₃	1	2	yes	—
973	#121	C₂³×C₂₃	1	2	yes	—
974	#121	C₂³×C₂₃	1	2	yes	—
975	#121	C₂³×C₂₃	1	2	yes	—
976	#120	—	2	2	no	—
977	#120	—	2	2	no	—
978	#120	—	2	2	no	—
979	#120	—	2	2	no	—
980	#120	—	2	2	no	—
981	#120	—	2	2	no	—
982	#120	—	2	2	no	—
983	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
984	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
985	C₄×D₄	—	2	1	no	—
986	C₄×D₄	—	2	1	no	—
987	C₄×D₄	—	2	2	no	—
988	C₄×D₄	—	2	2	no	—
989	C₄×D₄	—	2	1	no	—
990	C₄×D₄	—	2	1	no	—
991	C₄×D₄	—	2	1	no	—
992	C₄×D₄	—	2	1	no	—
993	C₄×D₄	C₂³×C₂₃	1	2	yes	—
994	C₄×D₄	C₂³×C₂₃	1	2	yes	—
995	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
996	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
997	C₄×D₄	C₂³×C₂₃	1	2	yes	—
998	C₄×D₄	C₂³×C₂₃	1	2	yes	—
999	#117	—	2	1	no	—
1000	#117	C₂³×C₂₃	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	—	2	2	no	—
1002	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	—	2	1	no	—
1004	C₂×C₂²⋊C₄	—	2	1	no	—
1005	C₂×C₂²⋊C₄	—	2	1	no	—
1006	C₂×C₂²⋊C₄	—	2	2	no	—
1007	C₂×C₂²⋊C₄	—	2	2	no	—
1008	C₂×C₂²⋊C₄	—	2	2	no	—
1009	C₂×C₂²⋊C₄	—	2	2	no	—
1010	C₂×C₄²	—	2	1	no	—
1011	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1012	#107	C₂³×C₂₃	1	2	yes	—
1013	#106	C₂³×C₂₃	1	2	yes	—
1014	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1015	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1016	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1017	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1018	#103	C₂³×C₂₃	1	2	yes	—
1019	#103	C₂³×C₂₃	1	2	yes	—
1020	#103	C₂³×C₂₃	1	1	yes	characteristic
1021	#103	C₂³×C₂₃	1	1	yes	characteristic
1022	#103	C₂³×C₂₃	1	1	yes	characteristic
1023	#103	C₂³×C₂₃	1	1	yes	characteristic
1024	#103	C₂³×C₂₃	1	2	yes	—
1025	#102	C₂³×C₂₃	1	2	yes	—
1026	#102	C₂³×C₂₃	1	2	yes	—
1027	#102	C₂³×C₂₃	1	1	yes	characteristic
1028	#102	C₂³×C₂₃	1	1	yes	characteristic
1029	#102	C₂³×C₂₃	1	1	yes	characteristic
1030	#102	C₂³×C₂₃	1	1	yes	characteristic
1031	#102	C₂³×C₂₃	1	2	yes	—
1032	#102	C₂³×C₂₃	1	2	yes	—
1033	#102	C₂³×C₂₃	1	2	yes	—
1034	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1035	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1036	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1037	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1038	#97	C₂³×C₂₃	1	2	yes	—
1039	C₄×C₈	C₂³×C₂₃	1	2	yes	—
1040	C₂₃	#61092	1	1	yes	characteristic, direct product factor, Sylow
1041	C₂⁴	—	2	1	no	—
1042	C₂⁴	—	2	2	no	—
1043	C₂⁴	—	2	1	no	—
1044	C₂⁴	—	2	2	no	—
1045	C₂⁴	—	2	2	no	—
1046	#41	—	2	2	no	—
1047	#41	—	2	2	no	—
1048	#41	—	2	2	no	—
1049	#41	—	2	2	no	—
1050	#41	—	2	2	no	—
1051	#41	—	2	4	no	—
1052	#41	—	2	4	no	—
1053	#41	—	2	4	no	—
1054	#41	—	2	4	no	—
1055	#41	—	2	2	no	—
1056	#41	—	2	2	no	—
1057	#41	—	2	2	no	—
1058	#41	—	2	2	no	—
1059	#41	—	4	2	no	—
1060	#41	—	4	2	no	—
1061	#41	—	4	2	no	—
1062	#41	—	4	2	no	—
1063	#41	—	4	4	no	—
1064	#41	—	4	4	no	—
1065	#41	—	4	8	no	—
1066	#41	—	4	4	no	—
1067	#41	—	4	4	no	—
1068	#41	C₂×D₄×C₂₃	1	4	yes	complemented
1069	C₂×Q₈	—	2	2	no	—
1070	C₂×Q₈	—	2	1	no	—
1071	C₂×Q₈	—	2	4	no	—
1072	C₂×Q₈	—	2	2	no	—
1073	C₂×Q₈	—	2	2	no	—
1074	C₂×Q₈	—	4	2	no	—
1075	C₂×Q₈	—	4	4	no	—
1076	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1077	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1078	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1079	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1080	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1081	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1082	C₂×D₄	—	2	1	no	—
1083	C₂×D₄	—	2	4	no	—
1084	C₂×D₄	—	2	4	no	—
1085	C₂×D₄	—	2	4	no	—
1086	C₂×D₄	—	2	2	no	—
1087	C₂×D₄	—	2	2	no	—
1088	C₂×D₄	—	2	2	no	—
1089	C₂×D₄	—	2	1	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	2	no	—
1092	C₂×D₄	—	2	2	no	—
1093	C₂×D₄	—	2	2	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	2	2	no	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	2	2	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	2	no	—
1100	C₂×D₄	—	2	2	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	1	no	—
1104	C₂×D₄	—	2	2	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	4	2	no	—
1107	C₂×D₄	—	4	2	no	—
1108	C₂×D₄	—	4	2	no	—
1109	C₂×D₄	—	4	4	no	—
1110	C₂×D₄	—	4	8	no	—
1111	C₂×D₄	—	4	4	no	—
1112	C₂×D₄	—	4	4	no	—
1113	C₂×D₄	—	4	8	no	—
1114	C₂×D₄	—	4	8	no	—
1115	C₂×D₄	—	8	4	no	—
1116	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1117	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1118	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1119	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1120	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
1121	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1122	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1123	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1124	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1125	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1126	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1127	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	2	no	—
1131	C₂²×C₄	—	2	1	no	—
1132	C₂²×C₄	—	2	2	no	—
1133	C₂²×C₄	—	2	2	no	—
1134	C₂²×C₄	—	2	2	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	1	no	—
1138	C₂²×C₄	—	2	2	no	—
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	8	2	no	—
1143	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1146	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1147	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1148	Q₁₆	—	2	2	no	—
1149	Q₁₆	—	2	2	no	—
1150	Q₁₆	—	2	4	no	—
1151	Q₁₆	—	4	2	no	—
1152	SD₁₆	—	2	2	no	—
1153	SD₁₆	—	2	2	no	—
1154	SD₁₆	—	2	4	no	—
1155	SD₁₆	—	2	4	no	—
1156	SD₁₆	—	2	2	no	—
1157	SD₁₆	—	2	2	no	—
1158	SD₁₆	—	2	4	no	—
1159	SD₁₆	—	2	4	no	—
1160	SD₁₆	—	4	2	no	—
1161	SD₁₆	—	4	2	no	—
1162	SD₁₆	C₂×D₄×C₂₃	1	8	yes	complemented
1163	D₈	—	2	2	no	—
1164	D₈	—	2	4	no	—
1165	D₈	—	2	4	no	—
1166	D₈	—	2	2	no	—
1167	D₈	—	2	4	no	—
1168	D₈	—	4	2	no	—
1169	D₈	C₂×D₄×C₂₃	1	8	yes	complemented
1170	M₁₆	—	2	2	no	—
1171	M₁₆	—	2	4	no	—
1172	M₁₆	—	2	4	no	—
1173	M₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
1174	C₂×C₈	—	2	2	no	—
1175	C₂×C₈	—	2	2	no	—
1176	C₂×C₈	—	2	4	no	—
1177	C₂×C₈	—	2	4	no	—
1178	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1179	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1180	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1181	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1182	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1183	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1184	C₄⋊C₄	—	2	1	no	—
1185	C₄⋊C₄	—	2	2	no	—
1186	C₄⋊C₄	—	2	2	no	—
1187	C₄⋊C₄	—	2	1	no	—
1188	C₄⋊C₄	—	2	1	no	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	2	no	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	1	no	—
1193	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1194	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1195	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1196	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	2	no	—
1201	C₂²⋊C₄	—	2	2	no	—
1202	C₂²⋊C₄	—	2	1	no	—
1203	C₂²⋊C₄	—	2	1	no	—
1204	C₂²⋊C₄	—	2	1	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	2	2	no	—
1214	C₂²⋊C₄	—	2	2	no	—
1215	C₂²⋊C₄	—	2	1	no	—
1216	C₂²⋊C₄	—	2	1	no	—
1217	C₂²⋊C₄	—	2	1	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1220	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1221	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1222	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1223	C₄²	—	2	1	no	—
1224	C₄²	—	2	1	no	—
1225	C₄²	—	2	1	no	—
1226	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1227	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1228	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1229	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1230	C₂³	—	2	1	no	—
1231	C₂³	—	2	2	no	—
1232	C₂³	—	2	4	no	—
1233	C₂³	—	2	2	no	—
1234	C₂³	—	2	1	no	—
1235	C₂³	—	2	1	no	—
1236	C₂³	—	4	4	no	—
1237	C₂³	—	4	4	no	—
1238	C₂³	—	4	4	no	—
1239	C₂³	—	4	2	no	—
1240	C₂³	—	8	1	no	—
1241	C₂³	—	8	1	no	—
1242	C₂³	—	8	2	no	—
1243	C₂³	—	8	2	no	—
1244	C₂³	—	8	1	no	—
1245	C₂³	—	8	1	no	—
1246	C₂³	—	8	2	no	—
1247	C₂³	—	8	2	no	—
1248	C₂³	—	8	2	no	—
1249	C₂³	—	8	2	no	—
1250	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1251	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1252	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1253	Q₈	—	2	1	no	—
1254	Q₈	—	2	2	no	—
1255	Q₈	—	2	2	no	—
1256	Q₈	—	2	2	no	—
1257	Q₈	—	2	1	no	—
1258	Q₈	—	2	1	no	—
1259	Q₈	—	2	1	no	—
1260	Q₈	—	2	2	no	—
1261	Q₈	—	2	1	no	—
1262	Q₈	—	4	4	no	—
1263	Q₈	—	4	2	no	—
1264	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1265	D₄	—	2	4	no	—
1266	D₄	—	2	4	no	—
1267	D₄	—	2	4	no	—
1268	D₄	—	2	2	no	—
1269	D₄	—	2	1	no	—
1270	D₄	—	2	1	no	—
1271	D₄	—	2	2	no	—
1272	D₄	—	2	1	no	—
1273	D₄	—	2	1	no	—
1274	D₄	—	2	2	no	—
1275	D₄	—	2	1	no	—
1276	D₄	—	2	4	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	2	2	no	—
1279	D₄	—	4	2	no	—
1280	D₄	—	4	2	no	—
1281	D₄	—	4	4	no	—
1282	D₄	—	4	4	no	—
1283	D₄	—	4	4	no	—
1284	D₄	—	4	4	no	—
1285	D₄	—	4	2	no	—
1286	D₄	—	4	4	no	—
1287	D₄	—	4	4	no	—
1288	D₄	—	4	4	no	—
1289	D₄	—	4	2	no	—
1290	D₄	—	4	2	no	—
1291	D₄	—	4	2	no	—
1292	D₄	—	8	1	no	—
1293	D₄	—	8	2	no	—
1294	D₄	—	8	2	no	—
1295	D₄	—	8	2	no	—
1296	D₄	—	8	2	no	—
1297	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1298	D₄	C₂²×D₄×C₂₃	1	4	yes	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	2	no	—
1301	C₂×C₄	—	2	2	no	—
1302	C₂×C₄	—	2	2	no	—
1303	C₂×C₄	—	2	2	no	—
1304	C₂×C₄	—	2	4	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	2	no	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	4	1	no	—
1312	C₂×C₄	—	4	1	no	—
1313	C₂×C₄	—	4	4	no	—
1314	C₂×C₄	—	4	4	no	—
1315	C₂×C₄	—	4	4	no	—
1316	C₂×C₄	—	4	4	no	—
1317	C₂×C₄	—	4	4	no	—
1318	C₂×C₄	—	4	4	no	—
1319	C₂×C₄	—	4	2	no	—
1320	C₂×C₄	—	4	2	no	—
1321	C₂×C₄	—	4	2	no	—
1322	C₂×C₄	—	8	2	no	—
1323	C₂×C₄	—	8	1	no	—
1324	C₂×C₄	—	8	1	no	—
1325	C₂×C₄	—	8	1	no	—
1326	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1327	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1328	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1329	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1330	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1331	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1332	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1333	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1334	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1335	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1336	C₈	—	2	1	no	—
1337	C₈	—	2	1	no	—
1338	C₈	—	2	1	no	—
1339	C₈	—	2	1	no	—
1340	C₈	—	2	2	no	—
1341	C₈	C₂²×D₄×C₂₃	1	4	yes	—
1342	C₂²	—	2	1	no	—
1343	C₂²	—	2	1	no	—
1344	C₂²	—	2	2	no	—
1345	C₂²	—	2	2	no	—
1346	C₂²	—	2	2	no	—
1347	C₂²	—	2	4	no	—
1348	C₂²	—	2	2	no	—
1349	C₂²	—	2	2	no	—
1350	C₂²	—	2	2	no	—
1351	C₂²	—	2	2	no	—
1352	C₂²	—	4	1	no	—
1353	C₂²	—	4	2	no	—
1354	C₂²	—	4	2	no	—
1355	C₂²	—	4	1	no	—
1356	C₂²	—	4	2	no	—
1357	C₂²	—	4	1	no	—
1358	C₂²	—	4	1	no	—
1359	C₂²	—	4	1	no	—
1360	C₂²	—	4	1	no	—
1361	C₂²	—	4	2	no	—
1362	C₂²	—	4	1	no	—
1363	C₂²	—	4	1	no	—
1364	C₂²	—	4	2	no	—
1365	C₂²	—	8	4	no	—
1366	C₂²	—	16	2	no	—
1367	C₂²	—	16	4	no	—
1368	C₂²	—	16	4	no	—
1369	C₂²	—	16	4	no	—
1370	C₂²	D₄²×C₂₃	1	2	yes	—
1371	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1372	C₄	—	2	2	no	—
1373	C₄	—	2	2	no	—
1374	C₄	—	2	2	no	—
1375	C₄	—	2	1	no	—
1376	C₄	—	2	1	no	—
1377	C₄	—	2	1	no	—
1378	C₄	—	2	1	no	—
1379	C₄	—	4	1	no	—
1380	C₄	—	4	1	no	—
1381	C₄	—	4	2	no	—
1382	C₄	—	4	1	no	—
1383	C₄	—	4	2	no	—
1384	C₄	—	4	1	no	—
1385	C₄	D₄²×C₂₃	1	2	yes	—
1386	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1387	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1388	C₂	—	2	2	no	—
1389	C₂	—	4	2	no	—
1390	C₂	—	4	2	no	—
1391	C₂	—	4	4	no	—
1392	C₂	—	4	2	no	—
1393	C₂	—	8	1	no	—
1394	C₂	—	8	1	no	—
1395	C₂	—	8	2	no	—
1396	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1397	C₂	C₂₃×#3584	1	1	yes	characteristic
1398	C₂	C₂₃×#3585	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×#532 ◁ 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×#576	C₂	semidirect
3. C₂₃×#3500	C₂	semidirect
4. C₂₃×#3496	C₂	semidirect
5. C₂₃×#3282	C₂	semidirect
6. C₂₃×#3280	C₂	semidirect
7. C₂₃×#3275	C₂	semidirect
8. C₂₃×#3273	C₂	semidirect
9. C₂₃×#3269	C₂	semidirect
10. C₂₃×#3267	C₂	semidirect
11. C₂₃×#3265	C₂	semidirect
12. C₂₃×#3264	C₂	semidirect
13. C₂₃×#3153	C₂	semidirect
14. C₂₃×#3063	C₂	semidirect
15. C₂₃×#3062	C₂	semidirect
16. C₂₃×#3035	C₂	semidirect
17. C₂×C₂₃×#463	C₂	semidirect
18. C₂₃×#3013	C₂	semidirect
19. C₂₃×#3012	C₂	semidirect
20. C₂₃×#3009	C₂	semidirect
21. C₂₃×#3008	C₂	semidirect
22. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₂₃×#2935	C₂	semidirect
24. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
26. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
27. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
30. C₂×C₂₃×#137	C₂²	semidirect
31. C₂×C₂₃×#137	C₂²	semidirect
32. C₂×C₂₃×#137	C₂²	semidirect
34. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
37. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
38. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
39. C₂×C₂₃×#135	C₂²	semidirect
40. C₂×C₂₃×#135	C₂²	semidirect
41. C₂×C₂₃×#135	C₂²	semidirect
42. C₂×C₂₃×#135	C₂²	semidirect
43. C₂²×SD₁₆×C₂₃	C₂²	semidirect
44. C₂²×SD₁₆×C₂₃	C₂²	semidirect
46. C₂²×D₈×C₂₃	C₂²	semidirect
47. C₂×C₂₃×#131	C₂²	semidirect
48. C₂×C₂₃×#131	C₂²	semidirect
49. C₂₃×#548	C₂²	semidirect
50. C₂₃×#548	C₂²	semidirect
52. C₂₃×#547	C₂²	semidirect
57. C₂₃×#546	C₂²	semidirect
58. C₂₃×#546	C₂²	semidirect
59. C₂₃×#546	C₂²	semidirect
60. C₂₃×#546	C₂²	semidirect
62. D₄²×C₂₃	C₂²	semidirect
64. C₂₃×#537	C₂²	semidirect
66. C₂₃×#536	C₂²	semidirect
68. C₂₃×#535	C₂²	semidirect
72. C₂₃×#532	C₂²	semidirect
74. C₂×C₂₃×#124	C₂²	semidirect
76. C₄×#41×C₂₃	C₂²	semidirect
77. C₂×C₄×D₄×C₂₃	C₂²	semidirect
78. C₂₃×#497	C₂²	semidirect
79. C₂₃×#496	C₂²	semidirect
80. C₂₃×#495	C₂²	semidirect
81. C₂₃×#495	C₂²	semidirect
82. C₂₃×#470	C₂²	semidirect
83. C₂₃×#469	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#467	C₂²	semidirect
87. C₂₃×#466	C₂²	semidirect
88. C₂₃×#465	C₂²	semidirect
89. C₂₃×#465	C₂²	semidirect
90. C₂₃×#464	C₂²	semidirect
91. C₂₃×#464	C₂²	semidirect
92. C₂₃×#463	C₂²	semidirect
93. C₂₃×#463	C₂²	semidirect
94. C₂₃×#463	C₂²	semidirect
95. C₂₃×#463	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×#450	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×#447	C₂²	semidirect
116. C₂₃×#447	C₂²	semidirect
117. C₂₃×#447	C₂²	semidirect
118. C₂₃×#442	C₂²	semidirect
119. C₂₃×#440	C₂²	semidirect
120. C₄×SD₁₆×C₂₃	C₂²	semidirect
121. C₄×D₈×C₂₃	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₈×D₄×C₂₃	C₂²	semidirect
126. C₂₃×#428	C₂²	semidirect
127. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
128. C₂₃×#418	C₂²	semidirect
129. C₂₃×#417	C₂²	semidirect
130. C₂₃×#416	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂×C₂₃×#103	C₂²	semidirect
133. C₂×C₂₃×#102	C₂²	semidirect
134. C₂₃×#408	C₂²	semidirect
135. C₂₃×#408	C₂²	semidirect
136. C₄×M₁₆×C₂₃	C₂²	semidirect
183. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
368. #41×C₂₃	C₂×D₄	semidirect
462. SD₁₆×C₂₃	C₂×D₄	semidirect
469. D₈×C₂₃	C₂×D₄	semidirect
473. M₁₆×C₂₃	C₂×D₄	semidirect
530. #61092	C₂₃	direct (N × H)
643. C₂×#577	C₂×C₂₃	semidirect
644. C₂×#576	C₂×C₂₃	semidirect
645. #3500	C₂×C₂₃	semidirect
646. #3496	C₂×C₂₃	semidirect
647. #3282	C₂×C₂₃	semidirect
648. #3280	C₂×C₂₃	semidirect
649. #3275	C₂×C₂₃	semidirect
650. #3273	C₂×C₂₃	semidirect
651. #3269	C₂×C₂₃	semidirect
652. #3267	C₂×C₂₃	semidirect
653. #3265	C₂×C₂₃	semidirect
654. #3264	C₂×C₂₃	semidirect
655. #3153	C₂×C₂₃	semidirect
656. #3063	C₂×C₂₃	semidirect
657. #3062	C₂×C₂₃	semidirect
658. #3035	C₂×C₂₃	semidirect
659. C₂×#463	C₂×C₂₃	semidirect
660. #3013	C₂×C₂₃	semidirect
661. #3012	C₂×C₂₃	semidirect
662. #3009	C₂×C₂₃	semidirect
663. #3008	C₂×C₂₃	semidirect
664. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
665. #2935	C₂×C₂₃	semidirect
712. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
714. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
715. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
718. C₂×#137	C₂²×C₂₃	semidirect
719. C₂×#137	C₂²×C₂₃	semidirect
720. C₂×#137	C₂²×C₂₃	semidirect
722. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
723. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
724. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
725. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
726. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
727. C₂×#135	C₂²×C₂₃	semidirect
728. C₂×#135	C₂²×C₂₃	semidirect
729. C₂×#135	C₂²×C₂₃	semidirect
730. C₂×#135	C₂²×C₂₃	semidirect
731. C₂²×SD₁₆	C₂²×C₂₃	semidirect
732. C₂²×SD₁₆	C₂²×C₂₃	semidirect
734. C₂²×D₈	C₂²×C₂₃	semidirect
735. C₂×#131	C₂²×C₂₃	semidirect
736. C₂×#131	C₂²×C₂₃	semidirect
737. #548	C₂²×C₂₃	semidirect
738. #548	C₂²×C₂₃	semidirect
740. #547	C₂²×C₂₃	semidirect
745. #546	C₂²×C₂₃	semidirect
746. #546	C₂²×C₂₃	semidirect
747. #546	C₂²×C₂₃	semidirect
748. #546	C₂²×C₂₃	semidirect
750. D₄²	C₂²×C₂₃	semidirect
752. #537	C₂²×C₂₃	semidirect
754. #536	C₂²×C₂₃	semidirect
756. #535	C₂²×C₂₃	semidirect
760. #532	C₂²×C₂₃	semidirect
762. C₂×#124	C₂²×C₂₃	semidirect
764. C₄×#41	C₂²×C₂₃	semidirect
765. C₂×C₄×D₄	C₂²×C₂₃	semidirect
766. #497	C₂²×C₂₃	semidirect
767. #496	C₂²×C₂₃	semidirect
768. #495	C₂²×C₂₃	semidirect
769. #495	C₂²×C₂₃	semidirect
770. #470	C₂²×C₂₃	semidirect
771. #469	C₂²×C₂₃	semidirect
772. #468	C₂²×C₂₃	semidirect
773. #468	C₂²×C₂₃	semidirect
774. #467	C₂²×C₂₃	semidirect
775. #466	C₂²×C₂₃	semidirect
776. #465	C₂²×C₂₃	semidirect
777. #465	C₂²×C₂₃	semidirect
778. #464	C₂²×C₂₃	semidirect
779. #464	C₂²×C₂₃	semidirect
780. #463	C₂²×C₂₃	semidirect
781. #463	C₂²×C₂₃	semidirect
782. #463	C₂²×C₂₃	semidirect
783. #463	C₂²×C₂₃	semidirect
784. #463	C₂²×C₂₃	semidirect
785. #463	C₂²×C₂₃	semidirect
786. #462	C₂²×C₂₃	semidirect
787. #461	C₂²×C₂₃	semidirect
788. #460	C₂²×C₂₃	semidirect
789. #459	C₂²×C₂₃	semidirect
790. #452	C₂²×C₂₃	semidirect
791. #452	C₂²×C₂₃	semidirect
792. #452	C₂²×C₂₃	semidirect
793. #452	C₂²×C₂₃	semidirect
794. #451	C₂²×C₂₃	semidirect
795. #450	C₂²×C₂₃	semidirect
796. #450	C₂²×C₂₃	semidirect
797. #450	C₂²×C₂₃	semidirect
798. #449	C₂²×C₂₃	semidirect
799. #449	C₂²×C₂₃	semidirect
800. #449	C₂²×C₂₃	semidirect
801. #449	C₂²×C₂₃	semidirect
802. #448	C₂²×C₂₃	semidirect
803. #447	C₂²×C₂₃	semidirect
804. #447	C₂²×C₂₃	semidirect
805. #447	C₂²×C₂₃	semidirect
806. #442	C₂²×C₂₃	semidirect
807. #440	C₂²×C₂₃	semidirect
808. C₄×SD₁₆	C₂²×C₂₃	semidirect
809. C₄×D₈	C₂²×C₂₃	semidirect
810. #436	C₂²×C₂₃	semidirect
811. #435	C₂²×C₂₃	semidirect
812. #435	C₂²×C₂₃	semidirect
813. C₈×D₄	C₂²×C₂₃	semidirect
814. #428	C₂²×C₂₃	semidirect
815. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
816. #418	C₂²×C₂₃	semidirect
817. #417	C₂²×C₂₃	semidirect
818. #416	C₂²×C₂₃	semidirect
819. #416	C₂²×C₂₃	semidirect
820. C₂×#103	C₂²×C₂₃	semidirect
821. C₂×#102	C₂²×C₂₃	semidirect
822. #408	C₂²×C₂₃	semidirect
823. #408	C₂²×C₂₃	semidirect
824. C₄×M₁₆	C₂²×C₂₃	semidirect
882. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
1040. C₂₃	#61092	direct (N × H)
1068. #41	C₂×D₄×C₂₃	semidirect
1162. SD₁₆	C₂×D₄×C₂₃	semidirect
1169. D₈	C₂×D₄×C₂₃	semidirect
1173. M₁₆	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×#576	2
C₂₃×#3500	2
C₂₃×#3496	2
C₂₃×#3282	2
C₂₃×#3280	2
C₂₃×#3275	2
C₂₃×#3273	2
C₂₃×#3269	2
C₂₃×#3267	2
C₂₃×#3265	2
C₂₃×#3264	2
C₂₃×#3153	2
C₂₃×#3063	2
C₂₃×#3062	2
C₂₃×#3035	2
C₂×C₂₃×#463	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂₃×#3009	2
C₂₃×#3008	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#2935	2
#61092	23

Subgroups — C23×#61092 #19208718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61092 #19208718