Subgroups — C₂₃×#61096 #19208722

Order 5888.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3285	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3282	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3277	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3270	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3268	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3266	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×#464	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×#3011	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#137	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
25	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
28	C₂₃×#578	—	2	8	no	—
29	C₂₃×#577	—	2	8	no	—
30	C₂×C₂₃×#137	C₂²	1	2	yes	—
31	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
33	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
34	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
37	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#135	C₂²	1	2	yes	—
42	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
43	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
45	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
47	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#550	—	2	1	no	—
50	C₂₃×#550	C₂²	1	2	yes	complemented
51	D₄×Q₈×C₂₃	—	2	1	no	—
52	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
53	C₂₃×#548	—	2	1	no	—
54	C₂₃×#548	—	2	1	no	—
55	C₂₃×#548	C₂²	1	2	yes	—
56	C₂₃×#548	C₂²	1	2	yes	—
57	C₂₃×#548	C₂²	1	2	yes	complemented
58	C₂₃×#548	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	—
63	C₂₃×#537	—	2	2	no	—
64	C₂₃×#537	C₂²	1	1	yes	characteristic
65	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#536	—	2	1	no	—
67	C₂₃×#536	C₂²	1	1	yes	characteristic
68	C₂₃×#535	—	2	1	no	—
69	C₂₃×#535	C₂²	1	1	yes	characteristic
70	C₂₃×#532	—	2	1	no	—
71	C₂₃×#532	—	2	2	no	—
72	C₂₃×#532	C₂²	1	1	yes	characteristic
73	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂₃×#124	—	2	1	no	—
75	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
76	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
77	C₂×C₄×Q₈×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	2	yes	complemented
91	C₂₃×#464	C₂²	1	2	yes	complemented
92	C₂₃×#464	C₂²	1	2	yes	complemented
93	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#464	C₂²	1	2	yes	complemented
95	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#463	C₂²	1	1	yes	characteristic, 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	—
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×#451	C₂²	1	2	yes	complemented
109	C₂₃×#450	C₂²	1	2	yes	—
110	C₂₃×#449	C₂²	1	2	yes	—
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×#448	C₂²	1	2	yes	complemented
117	C₂₃×#447	C₂²	1	2	yes	—
118	C₂₃×#441	C₂²	1	2	yes	complemented
119	C₂₃×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×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×#419	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#417	C₂²	1	1	yes	characteristic
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
134	C₂₃×#408	C₂²	1	1	yes	characteristic
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	—	2	4	no	—
139	C₂₃×2₋¹⁺⁴	—	2	4	no	—
140	C₂₃×2₋¹⁺⁴	—	4	2	no	—
141	C₂₃×2₋¹⁺⁴	—	4	2	no	—
142	C₂₃×2₋¹⁺⁴	—	4	2	no	—
143	C₂₃×H(5,𝔽₂)	—	2	4	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	—	2	2	no	—
151	C₂×#41×C₂₃	—	2	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	2	yes	—
155	C₂×#41×C₂₃	C₂³	1	2	yes	—
156	C₂×#41×C₂₃	C₂³	1	2	yes	—
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	C₂²×Q₈×C₂₃	—	2	1	no	—
162	C₂²×Q₈×C₂₃	—	2	1	no	—
163	C₂²×Q₈×C₂₃	—	2	1	no	—
164	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
166	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₂²×D₄×C₂₃	—	2	1	no	—
170	C₂²×D₄×C₂₃	—	2	2	no	—
171	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
173	C₂₃×#137	—	2	8	no	—
174	C₂₃×#137	—	2	8	no	—
175	C₂₃×#137	—	2	8	no	—
176	C₂₃×#137	—	2	4	no	—
177	C₂₃×#137	—	4	2	no	—
178	C₂₃×#137	D₄	1	8	yes	complemented
179	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
180	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
181	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
182	C₂₃×#135	—	2	4	no	—
183	C₂₃×#135	—	2	4	no	—
184	C₂₃×#135	—	2	8	no	—
185	C₂₃×#135	—	2	8	no	—
186	C₂×Q₁₆×C₂₃	—	2	4	no	—
187	C₂×Q₁₆×C₂₃	—	2	8	no	—
188	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
190	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
191	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
192	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
194	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
195	C₂×SD₁₆×C₂₃	—	2	4	no	—
196	C₂×SD₁₆×C₂₃	—	2	8	no	—
197	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
198	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
201	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
205	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
206	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
208	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
209	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×D₈×C₂₃	C₂³	1	2	yes	—
211	C₂×D₈×C₂₃	C₂³	1	2	yes	—
212	C₂₃×#131	—	2	4	no	—
213	C₂₃×#131	—	2	4	no	—
214	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
215	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
216	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
218	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
220	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
222	C₂₃×C₄⋊Q₈	—	2	1	no	—
223	C₂₃×C₄⋊Q₈	—	2	2	no	—
224	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
225	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂₃×#127	—	2	2	no	—
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	2	no	—
235	C₂₃×#124	—	2	2	no	—
236	C₂₃×#124	—	2	1	no	—
237	C₂₃×#124	—	2	1	no	—
238	C₂₃×#124	D₄	1	1	yes	characteristic
239	C₂₃×#124	D₄	1	1	yes	characteristic
240	C₂₃×#124	C₂³	1	2	yes	—
241	C₂₃×#124	C₂³	1	2	yes	—
242	C₂₃×#124	C₂³	1	1	yes	characteristic
243	C₂₃×#124	C₂³	1	1	yes	characteristic
244	C₂₃×#123	—	2	2	no	—
245	C₂₃×#123	—	2	2	no	—
246	C₂₃×#123	—	2	2	no	—
247	C₂₃×C₂²⋊Q₈	—	2	1	no	—
248	C₂₃×C₂²⋊Q₈	—	2	1	no	—
249	C₂₃×C₂²⋊Q₈	—	2	2	no	—
250	C₂₃×C₂²⋊Q₈	—	2	2	no	—
251	C₂₃×C₂²⋊Q₈	—	2	2	no	—
252	C₂₃×C₂²⋊Q₈	—	2	2	no	—
253	C₂₃×C₂²⋊Q₈	—	2	2	no	—
254	C₂₃×C₂²⋊Q₈	—	2	2	no	—
255	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
258	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
259	C₂₃×#121	—	2	1	no	—
260	C₂₃×#121	—	2	1	no	—
261	C₂₃×#121	—	2	2	no	—
262	C₂₃×#121	—	2	2	no	—
263	C₂₃×#121	—	2	2	no	—
264	C₂₃×#121	—	2	2	no	—
265	C₂₃×#121	—	2	2	no	—
266	C₂₃×#121	—	2	2	no	—
267	C₂₃×#121	—	2	1	no	—
268	C₂₃×#121	—	2	1	no	—
269	C₂₃×#121	—	2	2	no	—
270	C₂₃×#121	—	2	2	no	—
271	C₂₃×#121	—	2	2	no	—
272	C₂₃×#121	—	2	2	no	—
273	C₂₃×#121	D₄	1	2	yes	—
274	C₂₃×#121	D₄	1	2	yes	—
275	C₂₃×#121	C₂³	1	2	yes	—
276	C₂₃×#121	C₂³	1	2	yes	—
277	C₂₃×#121	C₂³	1	2	yes	—
278	C₂₃×#121	C₂³	1	2	yes	—
279	C₂₃×#120	—	2	2	no	—
280	C₂₃×#120	—	2	2	no	—
281	C₂₃×#120	—	2	2	no	—
282	C₄×Q₈×C₂₃	—	2	1	no	—
283	C₄×Q₈×C₂₃	—	2	1	no	—
284	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
287	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
288	C₄×D₄×C₂₃	—	2	2	no	—
289	C₄×D₄×C₂₃	—	2	1	no	—
290	C₄×D₄×C₂₃	—	2	1	no	—
291	C₄×D₄×C₂₃	—	2	2	no	—
292	C₄×D₄×C₂₃	—	2	2	no	—
293	C₄×D₄×C₂₃	—	2	2	no	—
294	C₄×D₄×C₂₃	—	2	2	no	—
295	C₄×D₄×C₂₃	—	2	2	no	—
296	C₄×D₄×C₂₃	—	2	1	no	—
297	C₄×D₄×C₂₃	—	2	1	no	—
298	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₂₃	C₂³	1	2	yes	—
301	C₄×D₄×C₂₃	C₂³	1	2	yes	—
302	C₂₃×#117	—	2	1	no	—
303	C₂₃×#117	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
305	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂×C₄²×C₂₃	—	2	1	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×#103	C₂³	1	2	yes	—
327	C₂₃×#103	C₂³	1	2	yes	—
328	C₂₃×#102	C₂³	1	2	yes	—
329	C₂₃×#102	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	1	yes	characteristic
331	C₂₃×#102	C₂³	1	1	yes	characteristic
332	C₂₃×#102	C₂³	1	1	yes	characteristic
333	C₂₃×#102	C₂³	1	1	yes	characteristic
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	2	no	—
342	C₂⁴×C₂₃	—	2	1	no	—
343	#41×C₂₃	—	2	2	no	—
344	#41×C₂₃	—	2	2	no	—
345	#41×C₂₃	—	2	2	no	—
346	#41×C₂₃	—	2	2	no	—
347	#41×C₂₃	—	2	2	no	—
348	#41×C₂₃	—	2	4	no	—
349	#41×C₂₃	—	2	4	no	—
350	#41×C₂₃	—	2	4	no	—
351	#41×C₂₃	—	2	4	no	—
352	#41×C₂₃	—	2	2	no	—
353	#41×C₂₃	—	2	2	no	—
354	#41×C₂₃	—	2	2	no	—
355	#41×C₂₃	—	2	2	no	—
356	#41×C₂₃	—	4	2	no	—
357	#41×C₂₃	—	4	2	no	—
358	#41×C₂₃	—	4	2	no	—
359	#41×C₂₃	—	4	2	no	—
360	#41×C₂₃	—	4	8	no	—
361	#41×C₂₃	—	4	8	no	—
362	#41×C₂₃	—	4	4	no	—
363	#41×C₂₃	—	4	4	no	—
364	#41×C₂₃	—	4	8	no	—
365	#41×C₂₃	—	4	4	no	—
366	#41×C₂₃	—	4	4	no	—
367	#41×C₂₃	C₂×D₄	1	4	yes	—
368	C₂×Q₈×C₂₃	—	2	1	no	—
369	C₂×Q₈×C₂₃	—	2	2	no	—
370	C₂×Q₈×C₂₃	—	2	2	no	—
371	C₂×Q₈×C₂₃	—	2	2	no	—
372	C₂×Q₈×C₂₃	—	2	1	no	—
373	C₂×Q₈×C₂₃	—	2	2	no	—
374	C₂×Q₈×C₂₃	—	2	4	no	—
375	C₂×Q₈×C₂₃	—	2	4	no	—
376	C₂×Q₈×C₂₃	—	2	4	no	—
377	C₂×Q₈×C₂₃	—	2	2	no	—
378	C₂×Q₈×C₂₃	—	2	2	no	—
379	C₂×Q₈×C₂₃	—	4	2	no	—
380	C₂×Q₈×C₂₃	—	4	2	no	—
381	C₂×Q₈×C₂₃	—	4	2	no	—
382	C₂×Q₈×C₂₃	—	4	4	no	—
383	C₂×Q₈×C₂₃	—	4	4	no	—
384	C₂×Q₈×C₂₃	—	4	4	no	—
385	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
386	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
389	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
392	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₂×D₄×C₂₃	—	2	1	no	—
394	C₂×D₄×C₂₃	—	2	4	no	—
395	C₂×D₄×C₂₃	—	2	2	no	—
396	C₂×D₄×C₂₃	—	2	1	no	—
397	C₂×D₄×C₂₃	—	2	1	no	—
398	C₂×D₄×C₂₃	—	2	2	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	2	no	—
403	C₂×D₄×C₂₃	—	2	2	no	—
404	C₂×D₄×C₂₃	—	2	2	no	—
405	C₂×D₄×C₂₃	—	2	2	no	—
406	C₂×D₄×C₂₃	—	2	1	no	—
407	C₂×D₄×C₂₃	—	2	2	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	—	4	2	no	—
412	C₂×D₄×C₂₃	—	4	4	no	—
413	C₂×D₄×C₂₃	—	4	8	no	—
414	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
415	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
416	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
417	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
418	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
419	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
420	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
421	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
422	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
423	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₂₃	—	2	1	no	—
425	C₂²×C₄×C₂₃	—	2	1	no	—
426	C₂²×C₄×C₂₃	—	2	1	no	—
427	C₂²×C₄×C₂₃	—	2	2	no	—
428	C₂²×C₄×C₂₃	—	2	2	no	—
429	C₂²×C₄×C₂₃	—	2	2	no	—
430	C₂²×C₄×C₂₃	—	2	1	no	—
431	C₂²×C₄×C₂₃	—	2	2	no	—
432	C₂²×C₄×C₂₃	—	2	2	no	—
433	C₂²×C₄×C₂₃	—	2	2	no	—
434	C₂²×C₄×C₂₃	—	2	1	no	—
435	C₂²×C₄×C₂₃	—	2	1	no	—
436	C₂²×C₄×C₂₃	—	2	2	no	—
437	C₂²×C₄×C₂₃	—	2	1	no	—
438	C₂²×C₄×C₂₃	—	2	1	no	—
439	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
442	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
443	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
444	Q₁₆×C₂₃	—	2	4	no	—
445	Q₁₆×C₂₃	—	2	2	no	—
446	Q₁₆×C₂₃	—	2	4	no	—
447	Q₁₆×C₂₃	—	2	2	no	—
448	Q₁₆×C₂₃	—	2	4	no	—
449	Q₁₆×C₂₃	—	4	2	no	—
450	Q₁₆×C₂₃	C₂×D₄	1	8	yes	—
451	SD₁₆×C₂₃	—	2	4	no	—
452	SD₁₆×C₂₃	—	2	4	no	—
453	SD₁₆×C₂₃	—	2	2	no	—
454	SD₁₆×C₂₃	—	2	2	no	—
455	SD₁₆×C₂₃	—	2	2	no	—
456	SD₁₆×C₂₃	—	2	2	no	—
457	SD₁₆×C₂₃	—	2	4	no	—
458	SD₁₆×C₂₃	—	2	4	no	—
459	SD₁₆×C₂₃	—	4	2	no	—
460	SD₁₆×C₂₃	—	4	2	no	—
461	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
462	D₈×C₂₃	—	2	2	no	—
463	D₈×C₂₃	—	2	2	no	—
464	D₈×C₂₃	—	2	4	no	—
465	D₈×C₂₃	—	4	2	no	—
466	M₁₆×C₂₃	—	2	2	no	—
467	M₁₆×C₂₃	—	2	4	no	—
468	M₁₆×C₂₃	—	2	4	no	—
469	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
470	C₂×C₈×C₂₃	—	2	2	no	—
471	C₂×C₈×C₂₃	—	2	2	no	—
472	C₂×C₈×C₂₃	—	2	4	no	—
473	C₂×C₈×C₂₃	—	2	4	no	—
474	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
475	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
476	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
477	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
478	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
479	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
480	C₄⋊C₄×C₂₃	—	2	2	no	—
481	C₄⋊C₄×C₂₃	—	2	2	no	—
482	C₄⋊C₄×C₂₃	—	2	1	no	—
483	C₄⋊C₄×C₂₃	—	2	1	no	—
484	C₄⋊C₄×C₂₃	—	2	1	no	—
485	C₄⋊C₄×C₂₃	—	2	1	no	—
486	C₄⋊C₄×C₂₃	—	2	1	no	—
487	C₄⋊C₄×C₂₃	—	2	2	no	—
488	C₄⋊C₄×C₂₃	—	2	2	no	—
489	C₄⋊C₄×C₂₃	—	2	2	no	—
490	C₄⋊C₄×C₂₃	—	2	2	no	—
491	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
492	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
493	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
494	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
495	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
496	C₂²⋊C₄×C₂₃	—	2	2	no	—
497	C₂²⋊C₄×C₂₃	—	2	2	no	—
498	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
503	C₂²⋊C₄×C₂₃	—	2	2	no	—
504	C₂²⋊C₄×C₂₃	—	2	2	no	—
505	C₂²⋊C₄×C₂₃	—	2	2	no	—
506	C₂²⋊C₄×C₂₃	—	2	2	no	—
507	C₂²⋊C₄×C₂₃	—	2	1	no	—
508	C₂²⋊C₄×C₂₃	—	2	1	no	—
509	C₂²⋊C₄×C₂₃	—	2	1	no	—
510	C₂²⋊C₄×C₂₃	—	2	1	no	—
511	C₂²⋊C₄×C₂₃	—	2	1	no	—
512	C₂²⋊C₄×C₂₃	—	2	1	no	—
513	C₂²⋊C₄×C₂₃	—	2	2	no	—
514	C₂²⋊C₄×C₂₃	—	2	2	no	—
515	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
516	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
517	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
518	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
519	C₄²×C₂₃	—	2	1	no	—
520	C₄²×C₂₃	—	2	1	no	—
521	C₄²×C₂₃	—	2	1	no	—
522	C₄²×C₂₃	—	2	2	no	—
523	C₄²×C₂₃	—	2	2	no	—
524	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
525	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
526	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
527	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
528	#61096	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
529	C₂³×C₂₃	—	2	1	no	—
530	C₂³×C₂₃	—	2	2	no	—
531	C₂³×C₂₃	—	2	1	no	—
532	C₂³×C₂₃	—	2	1	no	—
533	C₂³×C₂₃	—	4	4	no	—
534	C₂³×C₂₃	—	4	2	no	—
535	C₂³×C₂₃	—	8	1	no	—
536	C₂³×C₂₃	—	8	1	no	—
537	C₂³×C₂₃	—	8	2	no	—
538	C₂³×C₂₃	—	8	2	no	—
539	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
540	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
541	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
542	Q₈×C₂₃	—	2	4	no	—
543	Q₈×C₂₃	—	2	2	no	—
544	Q₈×C₂₃	—	2	2	no	—
545	Q₈×C₂₃	—	2	2	no	—
546	Q₈×C₂₃	—	2	1	no	—
547	Q₈×C₂₃	—	2	1	no	—
548	Q₈×C₂₃	—	2	1	no	—
549	Q₈×C₂₃	—	2	2	no	—
550	Q₈×C₂₃	—	2	1	no	—
551	Q₈×C₂₃	—	2	2	no	—
552	Q₈×C₂₃	—	2	1	no	—
553	Q₈×C₂₃	—	4	4	no	—
554	Q₈×C₂₃	—	4	4	no	—
555	Q₈×C₂₃	—	4	4	no	—
556	Q₈×C₂₃	—	4	2	no	—
557	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
558	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
559	D₄×C₂₃	—	2	4	no	—
560	D₄×C₂₃	—	2	4	no	—
561	D₄×C₂₃	—	2	4	no	—
562	D₄×C₂₃	—	2	2	no	—
563	D₄×C₂₃	—	2	2	no	—
564	D₄×C₂₃	—	2	1	no	—
565	D₄×C₂₃	—	2	2	no	—
566	D₄×C₂₃	—	2	1	no	—
567	D₄×C₂₃	—	2	1	no	—
568	D₄×C₂₃	—	2	1	no	—
569	D₄×C₂₃	—	2	2	no	—
570	D₄×C₂₃	—	2	1	no	—
571	D₄×C₂₃	—	4	2	no	—
572	D₄×C₂₃	—	4	2	no	—
573	D₄×C₂₃	—	4	4	no	—
574	D₄×C₂₃	—	4	4	no	—
575	D₄×C₂₃	—	4	4	no	—
576	D₄×C₂₃	—	4	4	no	—
577	D₄×C₂₃	—	4	2	no	—
578	D₄×C₂₃	—	4	4	no	—
579	D₄×C₂₃	—	4	2	no	—
580	D₄×C₂₃	—	4	2	no	—
581	D₄×C₂₃	—	4	2	no	—
582	D₄×C₂₃	—	8	1	no	—
583	D₄×C₂₃	—	8	2	no	—
584	D₄×C₂₃	—	8	2	no	—
585	D₄×C₂₃	—	8	2	no	—
586	D₄×C₂₃	—	8	2	no	—
587	D₄×C₂₃	C₂²×D₄	1	2	yes	—
588	C₂×C₄×C₂₃	—	2	4	no	—
589	C₂×C₄×C₂₃	—	2	1	no	—
590	C₂×C₄×C₂₃	—	2	2	no	—
591	C₂×C₄×C₂₃	—	2	4	no	—
592	C₂×C₄×C₂₃	—	2	2	no	—
593	C₂×C₄×C₂₃	—	2	2	no	—
594	C₂×C₄×C₂₃	—	2	2	no	—
595	C₂×C₄×C₂₃	—	2	2	no	—
596	C₂×C₄×C₂₃	—	2	1	no	—
597	C₂×C₄×C₂₃	—	2	1	no	—
598	C₂×C₄×C₂₃	—	2	2	no	—
599	C₂×C₄×C₂₃	—	2	2	no	—
600	C₂×C₄×C₂₃	—	2	1	no	—
601	C₂×C₄×C₂₃	—	2	1	no	—
602	C₂×C₄×C₂₃	—	4	1	no	—
603	C₂×C₄×C₂₃	—	4	1	no	—
604	C₂×C₄×C₂₃	—	4	4	no	—
605	C₂×C₄×C₂₃	—	4	4	no	—
606	C₂×C₄×C₂₃	—	4	4	no	—
607	C₂×C₄×C₂₃	—	4	4	no	—
608	C₂×C₄×C₂₃	—	4	4	no	—
609	C₂×C₄×C₂₃	—	4	4	no	—
610	C₂×C₄×C₂₃	—	4	4	no	—
611	C₂×C₄×C₂₃	—	4	2	no	—
612	C₂×C₄×C₂₃	—	4	2	no	—
613	C₂×C₄×C₂₃	—	4	2	no	—
614	C₂×C₄×C₂₃	—	8	1	no	—
615	C₂×C₄×C₂₃	—	8	1	no	—
616	C₂×C₄×C₂₃	—	8	1	no	—
617	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
622	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
623	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
624	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
625	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
626	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
627	C₈×C₂₃	—	2	1	no	—
628	C₈×C₂₃	—	2	1	no	—
629	C₈×C₂₃	—	2	1	no	—
630	C₈×C₂₃	—	2	1	no	—
631	C₈×C₂₃	—	2	2	no	—
632	C₈×C₂₃	C₂²×D₄	1	4	yes	—
633	C₂×#578	C₂×C₂₃	1	1	yes	characteristic, complemented
634	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
635	#3500	C₂×C₂₃	1	1	yes	characteristic, complemented
636	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
637	#3285	C₂×C₂₃	1	2	yes	complemented
638	#3282	C₂×C₂₃	1	2	yes	complemented
639	#3277	C₂×C₂₃	1	2	yes	complemented
640	#3275	C₂×C₂₃	1	2	yes	complemented
641	#3271	C₂×C₂₃	1	2	yes	complemented
642	#3270	C₂×C₂₃	1	2	yes	complemented
643	#3268	C₂×C₂₃	1	2	yes	complemented
644	#3266	C₂×C₂₃	1	2	yes	complemented
645	#3153	C₂×C₂₃	1	1	yes	characteristic, complemented
646	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
647	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
648	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
649	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
650	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
651	#3012	C₂×C₂₃	1	1	yes	characteristic, complemented
652	#3011	C₂×C₂₃	1	1	yes	characteristic, complemented
653	#3010	C₂×C₂₃	1	1	yes	characteristic, complemented
654	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
655	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
656	C₂²×C₂₃	—	2	1	no	—
657	C₂²×C₂₃	—	2	1	no	—
658	C₂²×C₂₃	—	2	2	no	—
659	C₂²×C₂₃	—	2	2	no	—
660	C₂²×C₂₃	—	2	2	no	—
661	C₂²×C₂₃	—	2	2	no	—
662	C₂²×C₂₃	—	2	2	no	—
663	C₂²×C₂₃	—	2	2	no	—
664	C₂²×C₂₃	—	2	2	no	—
665	C₂²×C₂₃	—	4	1	no	—
666	C₂²×C₂₃	—	4	1	no	—
667	C₂²×C₂₃	—	4	1	no	—
668	C₂²×C₂₃	—	4	1	no	—
669	C₂²×C₂₃	—	4	2	no	—
670	C₂²×C₂₃	—	4	1	no	—
671	C₂²×C₂₃	—	4	1	no	—
672	C₂²×C₂₃	—	4	2	no	—
673	C₂²×C₂₃	—	4	1	no	—
674	C₂²×C₂₃	—	4	1	no	—
675	C₂²×C₂₃	—	4	2	no	—
676	C₂²×C₂₃	—	16	2	no	—
677	C₂²×C₂₃	—	16	4	no	—
678	C₂²×C₂₃	D₄²	1	2	yes	—
679	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
680	C₄×C₂₃	—	2	1	no	—
681	C₄×C₂₃	—	2	1	no	—
682	C₄×C₂₃	—	2	1	no	—
683	C₄×C₂₃	—	2	1	no	—
684	C₄×C₂₃	—	2	2	no	—
685	C₄×C₂₃	—	2	4	no	—
686	C₄×C₂₃	—	2	2	no	—
687	C₄×C₂₃	—	2	2	no	—
688	C₄×C₂₃	—	4	1	no	—
689	C₄×C₂₃	—	4	2	no	—
690	C₄×C₂₃	—	4	1	no	—
691	C₄×C₂₃	—	4	2	no	—
692	C₄×C₂₃	—	4	1	no	—
693	C₄×C₂₃	—	4	1	no	—
694	C₄×C₂₃	D₄²	1	2	yes	—
695	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
696	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
698	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
699	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
701	#578	—	2	8	no	—
702	#577	—	2	8	no	—
703	C₂×#137	C₂²×C₂₃	1	2	yes	—
704	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
705	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
707	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
708	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
710	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
711	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
712	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
713	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
714	C₂×#135	C₂²×C₂₃	1	2	yes	—
715	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
716	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
717	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
718	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
719	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
720	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
721	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	#550	—	2	1	no	—
723	#550	C₂²×C₂₃	1	2	yes	complemented
724	D₄×Q₈	—	2	1	no	—
725	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
726	#548	—	2	1	no	—
727	#548	—	2	1	no	—
728	#548	C₂²×C₂₃	1	2	yes	—
729	#548	C₂²×C₂₃	1	2	yes	—
730	#548	C₂²×C₂₃	1	2	yes	complemented
731	#548	C₂²×C₂₃	1	2	yes	complemented
732	#546	—	2	2	no	—
733	#546	—	2	2	no	—
734	#546	C₂²×C₂₃	1	2	yes	—
735	#546	C₂²×C₂₃	1	2	yes	—
736	#537	—	2	2	no	—
737	#537	C₂²×C₂₃	1	1	yes	characteristic
738	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
739	#536	—	2	1	no	—
740	#536	C₂²×C₂₃	1	1	yes	characteristic
741	#535	—	2	1	no	—
742	#535	C₂²×C₂₃	1	1	yes	characteristic
743	#532	—	2	1	no	—
744	#532	—	2	2	no	—
745	#532	C₂²×C₂₃	1	1	yes	characteristic
746	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
747	C₂×#124	—	2	1	no	—
748	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
749	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
750	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
751	#497	C₂²×C₂₃	1	2	yes	complemented
752	#496	C₂²×C₂₃	1	2	yes	complemented
753	#495	C₂²×C₂₃	1	2	yes	complemented
754	#495	C₂²×C₂₃	1	2	yes	complemented
755	#470	C₂²×C₂₃	1	2	yes	complemented
756	#469	C₂²×C₂₃	1	2	yes	complemented
757	#468	C₂²×C₂₃	1	2	yes	complemented
758	#468	C₂²×C₂₃	1	2	yes	complemented
759	#467	C₂²×C₂₃	1	2	yes	complemented
760	#466	C₂²×C₂₃	1	2	yes	complemented
761	#465	C₂²×C₂₃	1	2	yes	complemented
762	#465	C₂²×C₂₃	1	2	yes	complemented
763	#464	C₂²×C₂₃	1	2	yes	complemented
764	#464	C₂²×C₂₃	1	2	yes	complemented
765	#464	C₂²×C₂₃	1	2	yes	complemented
766	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
767	#464	C₂²×C₂₃	1	2	yes	complemented
768	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
769	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
770	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
771	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
772	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
773	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
774	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
775	#452	C₂²×C₂₃	1	2	yes	—
776	#452	C₂²×C₂₃	1	2	yes	complemented
777	#452	C₂²×C₂₃	1	2	yes	complemented
778	#452	C₂²×C₂₃	1	2	yes	complemented
779	#451	C₂²×C₂₃	1	2	yes	complemented
780	#451	C₂²×C₂₃	1	2	yes	complemented
781	#451	C₂²×C₂₃	1	2	yes	complemented
782	#450	C₂²×C₂₃	1	2	yes	—
783	#449	C₂²×C₂₃	1	2	yes	—
784	#449	C₂²×C₂₃	1	2	yes	complemented
785	#449	C₂²×C₂₃	1	2	yes	complemented
786	#449	C₂²×C₂₃	1	2	yes	complemented
787	#448	C₂²×C₂₃	1	2	yes	complemented
788	#448	C₂²×C₂₃	1	2	yes	complemented
789	#448	C₂²×C₂₃	1	2	yes	complemented
790	#447	C₂²×C₂₃	1	2	yes	—
791	#441	C₂²×C₂₃	1	2	yes	complemented
792	#440	C₂²×C₂₃	1	2	yes	complemented
793	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
794	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
795	#436	C₂²×C₂₃	1	2	yes	complemented
796	#435	C₂²×C₂₃	1	2	yes	complemented
797	#435	C₂²×C₂₃	1	2	yes	complemented
798	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
799	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
800	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
801	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
802	#417	C₂²×C₂₃	1	1	yes	characteristic
803	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
804	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
805	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
806	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
807	#408	C₂²×C₂₃	1	1	yes	characteristic
808	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
809	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
810	C₂×C₂₃	—	2	2	no	—
811	C₂×C₂₃	—	4	2	no	—
812	C₂×C₂₃	—	4	2	no	—
813	C₂×C₂₃	—	4	2	no	—
814	C₂×C₂₃	—	8	1	no	—
815	C₂×C₂₃	—	8	1	no	—
816	C₂×C₂₃	—	8	2	no	—
817	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
818	C₂×C₂₃	#3584	1	1	yes	characteristic
819	C₂×C₂₃	#3586	1	1	yes	characteristic
820	2₋¹⁺⁴	—	2	4	no	—
821	2₋¹⁺⁴	—	2	4	no	—
822	2₋¹⁺⁴	—	2	4	no	—
823	2₋¹⁺⁴	—	4	2	no	—
824	2₋¹⁺⁴	—	4	2	no	—
825	2₋¹⁺⁴	—	4	2	no	—
826	H(5,𝔽₂)	—	2	4	no	—
827	H(5,𝔽₂)	—	4	2	no	—
828	C₂×#41	—	2	1	no	—
829	C₂×#41	—	2	1	no	—
830	C₂×#41	—	2	2	no	—
831	C₂×#41	—	2	2	no	—
832	C₂×#41	—	2	2	no	—
833	C₂×#41	—	2	1	no	—
834	C₂×#41	—	2	1	no	—
835	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
836	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
837	C₂×#41	C₂³×C₂₃	1	2	yes	—
838	C₂×#41	C₂³×C₂₃	1	2	yes	—
839	C₂×#41	C₂³×C₂₃	1	2	yes	—
840	C₂×#41	C₂³×C₂₃	1	2	yes	—
841	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
842	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
843	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
844	C₂²×Q₈	—	2	1	no	—
845	C₂²×Q₈	—	2	1	no	—
846	C₂²×Q₈	—	2	1	no	—
847	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
849	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
850	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
851	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
852	C₂²×D₄	—	2	1	no	—
853	C₂²×D₄	—	2	2	no	—
854	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
855	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
856	#137	—	2	8	no	—
857	#137	—	2	8	no	—
858	#137	—	2	8	no	—
859	#137	—	2	4	no	—
860	#137	—	4	2	no	—
861	#137	D₄×C₂₃	1	8	yes	complemented
862	AGL(1,ℤ/8)	—	2	8	no	—
863	AGL(1,ℤ/8)	—	2	4	no	—
864	AGL(1,ℤ/8)	—	4	2	no	—
865	#135	—	2	4	no	—
866	#135	—	2	4	no	—
867	#135	—	2	8	no	—
868	#135	—	2	8	no	—
869	C₂×Q₁₆	—	2	4	no	—
870	C₂×Q₁₆	—	2	8	no	—
871	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
872	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
873	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
874	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
875	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
876	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
877	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
878	C₂×SD₁₆	—	2	4	no	—
879	C₂×SD₁₆	—	2	8	no	—
880	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
881	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
882	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
883	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
884	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
885	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
886	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
887	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
888	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
889	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
890	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
891	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
892	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
893	C₂×D₈	C₂³×C₂₃	1	2	yes	—
894	C₂×D₈	C₂³×C₂₃	1	2	yes	—
895	#131	—	2	4	no	—
896	#131	—	2	4	no	—
897	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
898	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
899	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
900	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
901	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
902	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
903	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
904	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
905	C₄⋊Q₈	—	2	1	no	—
906	C₄⋊Q₈	—	2	2	no	—
907	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
908	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
909	#127	—	2	1	no	—
910	#127	—	2	2	no	—
911	#127	D₄×C₂₃	1	1	yes	characteristic
912	#127	C₂³×C₂₃	1	1	yes	characteristic
913	#124	—	2	1	no	—
914	#124	—	2	1	no	—
915	#124	—	2	2	no	—
916	#124	—	2	2	no	—
917	#124	—	2	2	no	—
918	#124	—	2	2	no	—
919	#124	—	2	1	no	—
920	#124	—	2	1	no	—
921	#124	D₄×C₂₃	1	1	yes	characteristic
922	#124	D₄×C₂₃	1	1	yes	characteristic
923	#124	C₂³×C₂₃	1	2	yes	—
924	#124	C₂³×C₂₃	1	2	yes	—
925	#124	C₂³×C₂₃	1	1	yes	characteristic
926	#124	C₂³×C₂₃	1	1	yes	characteristic
927	#123	—	2	2	no	—
928	#123	—	2	2	no	—
929	#123	—	2	2	no	—
930	C₂²⋊Q₈	—	2	1	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	2	no	—
933	C₂²⋊Q₈	—	2	2	no	—
934	C₂²⋊Q₈	—	2	2	no	—
935	C₂²⋊Q₈	—	2	2	no	—
936	C₂²⋊Q₈	—	2	2	no	—
937	C₂²⋊Q₈	—	2	2	no	—
938	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
939	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
940	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
941	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
942	#121	—	2	2	no	—
943	#121	—	2	2	no	—
944	#121	—	2	2	no	—
945	#121	—	2	2	no	—
946	#121	—	2	2	no	—
947	#121	—	2	2	no	—
948	#121	—	2	1	no	—
949	#121	—	2	1	no	—
950	#121	—	2	1	no	—
951	#121	—	2	1	no	—
952	#121	—	2	2	no	—
953	#121	—	2	2	no	—
954	#121	—	2	2	no	—
955	#121	—	2	2	no	—
956	#121	D₄×C₂₃	1	2	yes	—
957	#121	D₄×C₂₃	1	2	yes	—
958	#121	C₂³×C₂₃	1	2	yes	—
959	#121	C₂³×C₂₃	1	2	yes	—
960	#121	C₂³×C₂₃	1	2	yes	—
961	#121	C₂³×C₂₃	1	2	yes	—
962	#120	—	2	2	no	—
963	#120	—	2	2	no	—
964	#120	—	2	2	no	—
965	C₄×Q₈	—	2	1	no	—
966	C₄×Q₈	—	2	1	no	—
967	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
968	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
969	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
970	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
971	C₄×D₄	—	2	2	no	—
972	C₄×D₄	—	2	1	no	—
973	C₄×D₄	—	2	1	no	—
974	C₄×D₄	—	2	2	no	—
975	C₄×D₄	—	2	2	no	—
976	C₄×D₄	—	2	2	no	—
977	C₄×D₄	—	2	2	no	—
978	C₄×D₄	—	2	2	no	—
979	C₄×D₄	—	2	1	no	—
980	C₄×D₄	—	2	1	no	—
981	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
982	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
983	C₄×D₄	C₂³×C₂₃	1	2	yes	—
984	C₄×D₄	C₂³×C₂₃	1	2	yes	—
985	#117	—	2	1	no	—
986	#117	C₂³×C₂₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	—	2	1	no	—
988	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	—	2	1	no	—
990	C₂×C₂²⋊C₄	—	2	1	no	—
991	C₂×C₂²⋊C₄	—	2	2	no	—
992	C₂×C₂²⋊C₄	—	2	2	no	—
993	C₂×C₄²	—	2	1	no	—
994	C₂×C₄²	—	2	1	no	—
995	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
996	#107	C₂³×C₂₃	1	2	yes	—
997	#106	C₂³×C₂₃	1	2	yes	—
998	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
999	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1000	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1001	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1002	#103	C₂³×C₂₃	1	2	yes	—
1003	#103	C₂³×C₂₃	1	2	yes	—
1004	#103	C₂³×C₂₃	1	1	yes	characteristic
1005	#103	C₂³×C₂₃	1	1	yes	characteristic
1006	#103	C₂³×C₂₃	1	1	yes	characteristic
1007	#103	C₂³×C₂₃	1	1	yes	characteristic
1008	#103	C₂³×C₂₃	1	2	yes	—
1009	#103	C₂³×C₂₃	1	2	yes	—
1010	#103	C₂³×C₂₃	1	2	yes	—
1011	#102	C₂³×C₂₃	1	2	yes	—
1012	#102	C₂³×C₂₃	1	2	yes	—
1013	#102	C₂³×C₂₃	1	1	yes	characteristic
1014	#102	C₂³×C₂₃	1	1	yes	characteristic
1015	#102	C₂³×C₂₃	1	1	yes	characteristic
1016	#102	C₂³×C₂₃	1	1	yes	characteristic
1017	#102	C₂³×C₂₃	1	2	yes	—
1018	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1019	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1020	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1021	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1022	#97	C₂³×C₂₃	1	2	yes	—
1023	C₄×C₈	C₂³×C₂₃	1	2	yes	—
1024	C₂₃	#61096	1	1	yes	characteristic, direct product factor, Sylow
1025	C₂⁴	—	2	2	no	—
1026	C₂⁴	—	2	1	no	—
1027	#41	—	2	2	no	—
1028	#41	—	2	2	no	—
1029	#41	—	2	2	no	—
1030	#41	—	2	2	no	—
1031	#41	—	2	2	no	—
1032	#41	—	2	4	no	—
1033	#41	—	2	4	no	—
1034	#41	—	2	4	no	—
1035	#41	—	2	4	no	—
1036	#41	—	2	2	no	—
1037	#41	—	2	2	no	—
1038	#41	—	2	2	no	—
1039	#41	—	2	2	no	—
1040	#41	—	4	2	no	—
1041	#41	—	4	2	no	—
1042	#41	—	4	2	no	—
1043	#41	—	4	2	no	—
1044	#41	—	4	8	no	—
1045	#41	—	4	8	no	—
1046	#41	—	4	4	no	—
1047	#41	—	4	4	no	—
1048	#41	—	4	8	no	—
1049	#41	—	4	4	no	—
1050	#41	—	4	4	no	—
1051	#41	C₂×D₄×C₂₃	1	4	yes	—
1052	C₂×Q₈	—	2	1	no	—
1053	C₂×Q₈	—	2	2	no	—
1054	C₂×Q₈	—	2	2	no	—
1055	C₂×Q₈	—	2	2	no	—
1056	C₂×Q₈	—	2	1	no	—
1057	C₂×Q₈	—	2	2	no	—
1058	C₂×Q₈	—	2	4	no	—
1059	C₂×Q₈	—	2	4	no	—
1060	C₂×Q₈	—	2	4	no	—
1061	C₂×Q₈	—	2	2	no	—
1062	C₂×Q₈	—	2	2	no	—
1063	C₂×Q₈	—	4	2	no	—
1064	C₂×Q₈	—	4	2	no	—
1065	C₂×Q₈	—	4	2	no	—
1066	C₂×Q₈	—	4	4	no	—
1067	C₂×Q₈	—	4	4	no	—
1068	C₂×Q₈	—	4	4	no	—
1069	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
1070	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1071	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1072	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1073	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1074	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1075	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
1076	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1077	C₂×D₄	—	2	1	no	—
1078	C₂×D₄	—	2	4	no	—
1079	C₂×D₄	—	2	2	no	—
1080	C₂×D₄	—	2	1	no	—
1081	C₂×D₄	—	2	1	no	—
1082	C₂×D₄	—	2	2	no	—
1083	C₂×D₄	—	2	2	no	—
1084	C₂×D₄	—	2	2	no	—
1085	C₂×D₄	—	2	2	no	—
1086	C₂×D₄	—	2	2	no	—
1087	C₂×D₄	—	2	2	no	—
1088	C₂×D₄	—	2	2	no	—
1089	C₂×D₄	—	2	2	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	2	no	—
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	1	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	4	2	no	—
1096	C₂×D₄	—	4	4	no	—
1097	C₂×D₄	—	4	8	no	—
1098	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1099	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1100	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1101	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1102	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1103	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1104	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1105	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1106	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1107	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1108	C₂²×C₄	—	2	1	no	—
1109	C₂²×C₄	—	2	1	no	—
1110	C₂²×C₄	—	2	1	no	—
1111	C₂²×C₄	—	2	2	no	—
1112	C₂²×C₄	—	2	2	no	—
1113	C₂²×C₄	—	2	2	no	—
1114	C₂²×C₄	—	2	1	no	—
1115	C₂²×C₄	—	2	2	no	—
1116	C₂²×C₄	—	2	2	no	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	1	no	—
1119	C₂²×C₄	—	2	1	no	—
1120	C₂²×C₄	—	2	2	no	—
1121	C₂²×C₄	—	2	1	no	—
1122	C₂²×C₄	—	2	1	no	—
1123	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1126	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1127	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1128	Q₁₆	—	2	4	no	—
1129	Q₁₆	—	2	2	no	—
1130	Q₁₆	—	2	4	no	—
1131	Q₁₆	—	2	2	no	—
1132	Q₁₆	—	2	4	no	—
1133	Q₁₆	—	4	2	no	—
1134	Q₁₆	C₂×D₄×C₂₃	1	8	yes	—
1135	SD₁₆	—	2	4	no	—
1136	SD₁₆	—	2	4	no	—
1137	SD₁₆	—	2	2	no	—
1138	SD₁₆	—	2	2	no	—
1139	SD₁₆	—	2	2	no	—
1140	SD₁₆	—	2	2	no	—
1141	SD₁₆	—	2	4	no	—
1142	SD₁₆	—	2	4	no	—
1143	SD₁₆	—	4	2	no	—
1144	SD₁₆	—	4	2	no	—
1145	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
1146	D₈	—	2	2	no	—
1147	D₈	—	2	2	no	—
1148	D₈	—	2	4	no	—
1149	D₈	—	4	2	no	—
1150	M₁₆	—	2	2	no	—
1151	M₁₆	—	2	4	no	—
1152	M₁₆	—	2	4	no	—
1153	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
1154	C₂×C₈	—	2	2	no	—
1155	C₂×C₈	—	2	2	no	—
1156	C₂×C₈	—	2	4	no	—
1157	C₂×C₈	—	2	4	no	—
1158	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1159	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1160	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1161	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1162	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1163	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1164	C₄⋊C₄	—	2	2	no	—
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	1	no	—
1167	C₄⋊C₄	—	2	1	no	—
1168	C₄⋊C₄	—	2	1	no	—
1169	C₄⋊C₄	—	2	1	no	—
1170	C₄⋊C₄	—	2	1	no	—
1171	C₄⋊C₄	—	2	2	no	—
1172	C₄⋊C₄	—	2	2	no	—
1173	C₄⋊C₄	—	2	2	no	—
1174	C₄⋊C₄	—	2	2	no	—
1175	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1176	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1177	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1178	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1179	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1180	C₂²⋊C₄	—	2	2	no	—
1181	C₂²⋊C₄	—	2	2	no	—
1182	C₂²⋊C₄	—	2	1	no	—
1183	C₂²⋊C₄	—	2	2	no	—
1184	C₂²⋊C₄	—	2	2	no	—
1185	C₂²⋊C₄	—	2	2	no	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	2	2	no	—
1188	C₂²⋊C₄	—	2	2	no	—
1189	C₂²⋊C₄	—	2	2	no	—
1190	C₂²⋊C₄	—	2	2	no	—
1191	C₂²⋊C₄	—	2	1	no	—
1192	C₂²⋊C₄	—	2	1	no	—
1193	C₂²⋊C₄	—	2	1	no	—
1194	C₂²⋊C₄	—	2	1	no	—
1195	C₂²⋊C₄	—	2	1	no	—
1196	C₂²⋊C₄	—	2	1	no	—
1197	C₂²⋊C₄	—	2	2	no	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1200	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1201	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1202	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1203	C₄²	—	2	1	no	—
1204	C₄²	—	2	1	no	—
1205	C₄²	—	2	1	no	—
1206	C₄²	—	2	2	no	—
1207	C₄²	—	2	2	no	—
1208	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1209	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1210	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1211	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	2	no	—
1214	C₂³	—	2	1	no	—
1215	C₂³	—	2	1	no	—
1216	C₂³	—	4	4	no	—
1217	C₂³	—	4	2	no	—
1218	C₂³	—	8	1	no	—
1219	C₂³	—	8	1	no	—
1220	C₂³	—	8	2	no	—
1221	C₂³	—	8	2	no	—
1222	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1223	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1224	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1225	Q₈	—	2	2	no	—
1226	Q₈	—	2	1	no	—
1227	Q₈	—	2	4	no	—
1228	Q₈	—	2	2	no	—
1229	Q₈	—	2	2	no	—
1230	Q₈	—	2	1	no	—
1231	Q₈	—	2	1	no	—
1232	Q₈	—	2	2	no	—
1233	Q₈	—	2	1	no	—
1234	Q₈	—	2	2	no	—
1235	Q₈	—	2	1	no	—
1236	Q₈	—	4	4	no	—
1237	Q₈	—	4	4	no	—
1238	Q₈	—	4	4	no	—
1239	Q₈	—	4	2	no	—
1240	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
1241	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
1242	D₄	—	2	4	no	—
1243	D₄	—	2	4	no	—
1244	D₄	—	2	4	no	—
1245	D₄	—	2	1	no	—
1246	D₄	—	2	2	no	—
1247	D₄	—	2	1	no	—
1248	D₄	—	2	1	no	—
1249	D₄	—	2	1	no	—
1250	D₄	—	2	2	no	—
1251	D₄	—	2	1	no	—
1252	D₄	—	2	2	no	—
1253	D₄	—	2	2	no	—
1254	D₄	—	4	2	no	—
1255	D₄	—	4	2	no	—
1256	D₄	—	4	4	no	—
1257	D₄	—	4	4	no	—
1258	D₄	—	4	4	no	—
1259	D₄	—	4	4	no	—
1260	D₄	—	4	2	no	—
1261	D₄	—	4	4	no	—
1262	D₄	—	4	2	no	—
1263	D₄	—	4	2	no	—
1264	D₄	—	4	2	no	—
1265	D₄	—	8	1	no	—
1266	D₄	—	8	2	no	—
1267	D₄	—	8	2	no	—
1268	D₄	—	8	2	no	—
1269	D₄	—	8	2	no	—
1270	D₄	C₂²×D₄×C₂₃	1	2	yes	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	2	no	—
1273	C₂×C₄	—	2	4	no	—
1274	C₂×C₄	—	2	2	no	—
1275	C₂×C₄	—	2	2	no	—
1276	C₂×C₄	—	2	2	no	—
1277	C₂×C₄	—	2	2	no	—
1278	C₂×C₄	—	2	4	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	2	no	—
1282	C₂×C₄	—	2	2	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	4	1	no	—
1286	C₂×C₄	—	4	1	no	—
1287	C₂×C₄	—	4	4	no	—
1288	C₂×C₄	—	4	4	no	—
1289	C₂×C₄	—	4	4	no	—
1290	C₂×C₄	—	4	4	no	—
1291	C₂×C₄	—	4	4	no	—
1292	C₂×C₄	—	4	4	no	—
1293	C₂×C₄	—	4	4	no	—
1294	C₂×C₄	—	4	2	no	—
1295	C₂×C₄	—	4	2	no	—
1296	C₂×C₄	—	4	2	no	—
1297	C₂×C₄	—	8	1	no	—
1298	C₂×C₄	—	8	1	no	—
1299	C₂×C₄	—	8	1	no	—
1300	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1301	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1302	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1303	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1304	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1305	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1306	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1307	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1308	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1309	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1310	C₈	—	2	1	no	—
1311	C₈	—	2	1	no	—
1312	C₈	—	2	1	no	—
1313	C₈	—	2	1	no	—
1314	C₈	—	2	2	no	—
1315	C₈	C₂²×D₄×C₂₃	1	4	yes	—
1316	C₂²	—	2	1	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	2	no	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	2	2	no	—
1324	C₂²	—	2	2	no	—
1325	C₂²	—	4	1	no	—
1326	C₂²	—	4	1	no	—
1327	C₂²	—	4	1	no	—
1328	C₂²	—	4	1	no	—
1329	C₂²	—	4	2	no	—
1330	C₂²	—	4	1	no	—
1331	C₂²	—	4	1	no	—
1332	C₂²	—	4	2	no	—
1333	C₂²	—	4	1	no	—
1334	C₂²	—	4	1	no	—
1335	C₂²	—	4	2	no	—
1336	C₂²	—	16	2	no	—
1337	C₂²	—	16	4	no	—
1338	C₂²	D₄²×C₂₃	1	2	yes	—
1339	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1340	C₄	—	2	2	no	—
1341	C₄	—	2	4	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	—	2	1	no	—
1345	C₄	—	2	1	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	1	no	—
1348	C₄	—	4	2	no	—
1349	C₄	—	4	1	no	—
1350	C₄	—	4	1	no	—
1351	C₄	—	4	1	no	—
1352	C₄	—	4	2	no	—
1353	C₄	—	4	1	no	—
1354	C₄	D₄²×C₂₃	1	2	yes	—
1355	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1356	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1357	C₂	—	2	2	no	—
1358	C₂	—	4	2	no	—
1359	C₂	—	4	2	no	—
1360	C₂	—	4	2	no	—
1361	C₂	—	8	2	no	—
1362	C₂	—	8	1	no	—
1363	C₂	—	8	1	no	—
1364	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1365	C₂	C₂₃×#3584	1	1	yes	characteristic
1366	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#578	C₂	semidirect
2. C₂×C₂₃×#577	C₂	semidirect
3. C₂₃×#3500	C₂	semidirect
4. C₂₃×#3497	C₂	semidirect
5. C₂₃×#3285	C₂	semidirect
6. C₂₃×#3282	C₂	semidirect
7. C₂₃×#3277	C₂	semidirect
8. C₂₃×#3275	C₂	semidirect
9. C₂₃×#3271	C₂	semidirect
10. C₂₃×#3270	C₂	semidirect
11. C₂₃×#3268	C₂	semidirect
12. C₂₃×#3266	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×#464	C₂	semidirect
18. C₂₃×#3013	C₂	semidirect
19. C₂₃×#3012	C₂	semidirect
20. C₂₃×#3011	C₂	semidirect
21. C₂₃×#3010	C₂	semidirect
22. C₄×C₂₃×#137	C₂	semidirect
23. C₂₃×#2935	C₂	semidirect
26. C₂×C₂₃×2₋¹⁺⁴	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
42. C₂×C₂₃×#135	C₂²	semidirect
43. C₂²×Q₁₆×C₂₃	C₂²	semidirect
44. C₂²×Q₁₆×C₂₃	C₂²	semidirect
48. C₂×C₂₃×#131	C₂²	semidirect
50. C₂₃×#550	C₂²	semidirect
52. D₄×Q₈×C₂₃	C₂²	semidirect
57. C₂₃×#548	C₂²	semidirect
58. C₂₃×#548	C₂²	semidirect
65. C₂₃×#537	C₂²	semidirect
73. C₂₃×#532	C₂²	semidirect
77. C₂×C₄×Q₈×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×#464	C₂²	semidirect
93. C₂₃×#464	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
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×#451	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×#448	C₂²	semidirect
118. C₂₃×#441	C₂²	semidirect
119. C₂₃×#440	C₂²	semidirect
120. C₄×Q₁₆×C₂₃	C₂²	semidirect
121. C₄×SD₁₆×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×#419	C₂²	semidirect
130. C₂₃×#416	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂×C₂₃×#103	C₂²	semidirect
135. C₂₃×#408	C₂²	semidirect
136. C₄×M₁₆×C₂₃	C₂²	semidirect
178. C₂₃×#137	D₄	semidirect
528. #61096	C₂₃	direct (N × H)
633. C₂×#578	C₂×C₂₃	semidirect
634. C₂×#577	C₂×C₂₃	semidirect
635. #3500	C₂×C₂₃	semidirect
636. #3497	C₂×C₂₃	semidirect
637. #3285	C₂×C₂₃	semidirect
638. #3282	C₂×C₂₃	semidirect
639. #3277	C₂×C₂₃	semidirect
640. #3275	C₂×C₂₃	semidirect
641. #3271	C₂×C₂₃	semidirect
642. #3270	C₂×C₂₃	semidirect
643. #3268	C₂×C₂₃	semidirect
644. #3266	C₂×C₂₃	semidirect
645. #3153	C₂×C₂₃	semidirect
646. #3063	C₂×C₂₃	semidirect
647. #3062	C₂×C₂₃	semidirect
648. #3035	C₂×C₂₃	semidirect
649. C₂×#464	C₂×C₂₃	semidirect
650. #3013	C₂×C₂₃	semidirect
651. #3012	C₂×C₂₃	semidirect
652. #3011	C₂×C₂₃	semidirect
653. #3010	C₂×C₂₃	semidirect
654. C₄×#137	C₂×C₂₃	semidirect
655. #2935	C₂×C₂₃	semidirect
699. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
705. C₂×#137	C₂²×C₂₃	semidirect
706. C₂×#137	C₂²×C₂₃	semidirect
707. C₂×#137	C₂²×C₂₃	semidirect
708. C₂×#137	C₂²×C₂₃	semidirect
715. C₂×#135	C₂²×C₂₃	semidirect
716. C₂²×Q₁₆	C₂²×C₂₃	semidirect
717. C₂²×Q₁₆	C₂²×C₂₃	semidirect
721. C₂×#131	C₂²×C₂₃	semidirect
723. #550	C₂²×C₂₃	semidirect
725. D₄×Q₈	C₂²×C₂₃	semidirect
730. #548	C₂²×C₂₃	semidirect
731. #548	C₂²×C₂₃	semidirect
738. #537	C₂²×C₂₃	semidirect
746. #532	C₂²×C₂₃	semidirect
750. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
751. #497	C₂²×C₂₃	semidirect
752. #496	C₂²×C₂₃	semidirect
753. #495	C₂²×C₂₃	semidirect
754. #495	C₂²×C₂₃	semidirect
755. #470	C₂²×C₂₃	semidirect
756. #469	C₂²×C₂₃	semidirect
757. #468	C₂²×C₂₃	semidirect
758. #468	C₂²×C₂₃	semidirect
759. #467	C₂²×C₂₃	semidirect
760. #466	C₂²×C₂₃	semidirect
761. #465	C₂²×C₂₃	semidirect
762. #465	C₂²×C₂₃	semidirect
763. #464	C₂²×C₂₃	semidirect
764. #464	C₂²×C₂₃	semidirect
765. #464	C₂²×C₂₃	semidirect
766. #464	C₂²×C₂₃	semidirect
767. #464	C₂²×C₂₃	semidirect
768. #464	C₂²×C₂₃	semidirect
769. #463	C₂²×C₂₃	semidirect
770. #463	C₂²×C₂₃	semidirect
771. #462	C₂²×C₂₃	semidirect
772. #461	C₂²×C₂₃	semidirect
773. #460	C₂²×C₂₃	semidirect
774. #459	C₂²×C₂₃	semidirect
776. #452	C₂²×C₂₃	semidirect
777. #452	C₂²×C₂₃	semidirect
778. #452	C₂²×C₂₃	semidirect
779. #451	C₂²×C₂₃	semidirect
780. #451	C₂²×C₂₃	semidirect
781. #451	C₂²×C₂₃	semidirect
784. #449	C₂²×C₂₃	semidirect
785. #449	C₂²×C₂₃	semidirect
786. #449	C₂²×C₂₃	semidirect
787. #448	C₂²×C₂₃	semidirect
788. #448	C₂²×C₂₃	semidirect
789. #448	C₂²×C₂₃	semidirect
791. #441	C₂²×C₂₃	semidirect
792. #440	C₂²×C₂₃	semidirect
793. C₄×Q₁₆	C₂²×C₂₃	semidirect
794. C₄×SD₁₆	C₂²×C₂₃	semidirect
795. #436	C₂²×C₂₃	semidirect
796. #435	C₂²×C₂₃	semidirect
797. #435	C₂²×C₂₃	semidirect
798. C₈×D₄	C₂²×C₂₃	semidirect
799. #428	C₂²×C₂₃	semidirect
800. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
801. #419	C₂²×C₂₃	semidirect
803. #416	C₂²×C₂₃	semidirect
804. #416	C₂²×C₂₃	semidirect
805. C₂×#103	C₂²×C₂₃	semidirect
808. #408	C₂²×C₂₃	semidirect
809. C₄×M₁₆	C₂²×C₂₃	semidirect
861. #137	D₄×C₂₃	semidirect
1024. C₂₃	#61096	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#578	2
C₂×C₂₃×#577	2
C₂₃×#3500	2
C₂₃×#3497	2
C₂₃×#3285	2
C₂₃×#3282	2
C₂₃×#3277	2
C₂₃×#3275	2
C₂₃×#3271	2
C₂₃×#3270	2
C₂₃×#3268	2
C₂₃×#3266	2
C₂₃×#3153	2
C₂₃×#3063	2
C₂₃×#3062	2
C₂₃×#3035	2
C₂×C₂₃×#464	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂₃×#3011	2
C₂₃×#3010	2
C₄×C₂₃×#137	2
C₂₃×#2935	2
#61096	23

Subgroups — C23×#61096 #19208722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61096 #19208722