Subgroups — C₂₃×#61646 #19209272

Order 5888.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3328	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3313	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×#3270	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3266	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3225	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3200	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3197	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3121	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3004	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×#137	C₂²	1	2	yes	—
23	C₂×C₂₃×#137	C₂²	1	2	yes	—
24	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×H(3,𝔽₄)	—	2	1	no	—
29	C₂₃×#560	—	2	1	no	—
30	C₂₃×#559	—	2	1	no	—
31	C₂₃×#556	C₂²	1	2	yes	—
32	C₂₃×#555	C₂²	1	2	yes	—
33	C₂₃×#551	—	2	1	no	—
34	D₄×Q₈×C₂₃	—	2	2	no	—
35	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
36	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
37	C₂₃×#548	—	2	2	no	—
38	C₂₃×#548	C₂²	1	2	yes	—
39	C₂₃×#548	C₂²	1	2	yes	—
40	C₂₃×#548	C₂²	1	2	yes	complemented
41	C₂₃×#546	C₂²	1	2	yes	—
42	C₂₃×#542	—	2	2	no	—
43	C₂₃×#542	C₂²	1	2	yes	—
44	C₂₃×#538	—	2	2	no	—
45	C₂₃×#536	—	2	1	no	—
46	C₂₃×#536	—	2	1	no	—
47	C₂₃×#536	C₂²	1	1	yes	characteristic
48	C₂₃×#536	C₂²	1	1	yes	characteristic
49	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#535	C₂²	1	1	yes	characteristic
51	C₂₃×#525	—	2	1	no	—
52	C₂₃×#525	—	2	1	no	—
53	C₂₃×#525	C₂²	1	2	yes	—
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#497	C₂²	1	2	yes	complemented
58	C₂₃×#495	C₂²	1	2	yes	complemented
59	C₂₃×#489	C₂²	1	2	yes	complemented
60	C₂₃×#487	C₂²	1	2	yes	complemented
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#485	C₂²	1	2	yes	complemented
63	C₂₃×#485	C₂²	1	2	yes	complemented
64	C₂₃×#485	C₂²	1	2	yes	complemented
65	C₂₃×#482	C₂²	1	2	yes	—
66	C₂₃×#482	C₂²	1	2	yes	complemented
67	C₂₃×#477	C₂²	1	2	yes	complemented
68	C₂₃×#475	C₂²	1	2	yes	complemented
69	C₂₃×#470	C₂²	1	2	yes	complemented
70	C₂₃×#470	C₂²	1	2	yes	complemented
71	C₂₃×#469	C₂²	1	2	yes	—
72	C₂₃×#468	C₂²	1	2	yes	—
73	C₂₃×#468	C₂²	1	2	yes	complemented
74	C₂₃×#468	C₂²	1	2	yes	complemented
75	C₂₃×#467	C₂²	1	2	yes	complemented
76	C₂₃×#465	C₂²	1	2	yes	complemented
77	C₂₃×#464	C₂²	1	2	yes	complemented
78	C₂₃×#464	C₂²	1	2	yes	complemented
79	C₂₃×#464	C₂²	1	2	yes	complemented
80	C₂₃×#463	C₂²	1	2	yes	complemented
81	C₂₃×#462	C₂²	1	2	yes	complemented
82	C₂₃×#461	C₂²	1	2	yes	complemented
83	C₂₃×#452	C₂²	1	2	yes	—
84	C₂₃×#452	C₂²	1	2	yes	complemented
85	C₂₃×#452	C₂²	1	2	yes	complemented
86	C₂₃×#451	C₂²	1	2	yes	complemented
87	C₂₃×#451	C₂²	1	2	yes	complemented
88	C₂₃×#451	C₂²	1	2	yes	complemented
89	C₂₃×#451	C₂²	1	2	yes	complemented
90	C₂₃×#451	C₂²	1	2	yes	complemented
91	C₂₃×#451	C₂²	1	2	yes	complemented
92	C₂₃×#450	C₂²	1	2	yes	complemented
93	C₂₃×#449	C₂²	1	2	yes	—
94	C₂₃×#449	C₂²	1	2	yes	—
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#448	C₂²	1	2	yes	—
97	C₂₃×#448	C₂²	1	2	yes	—
98	C₂₃×#448	C₂²	1	2	yes	—
99	C₂₃×#448	C₂²	1	2	yes	—
100	C₂₃×#448	C₂²	1	2	yes	complemented
101	C₂₃×#441	C₂²	1	2	yes	complemented
102	C₂₃×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#436	C₂²	1	2	yes	—
106	C₂₃×#436	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	—
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₂₃×#433	C₂²	1	2	yes	complemented
110	C₂₃×#419	C₂²	1	2	yes	complemented
111	C₂₃×#419	C₂²	1	2	yes	complemented
112	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#408	C₂²	1	1	yes	characteristic
117	C₂₃×#408	C₂²	1	1	yes	characteristic
118	C₂₃×#407	C₂²	1	2	yes	complemented
119	C₂₃×2₋¹⁺⁴	—	4	2	no	—
120	C₂₃×2₋¹⁺⁴	—	4	2	no	—
121	C₂×#41×C₂₃	—	2	1	no	—
122	C₂×#41×C₂₃	—	2	1	no	—
123	C₂×#41×C₂₃	—	2	1	no	—
124	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×#41×C₂₃	C₂³	1	2	yes	—
127	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₂₃	—	2	1	no	—
130	C₂²×Q₈×C₂₃	—	2	2	no	—
131	C₂²×Q₈×C₂₃	—	2	1	no	—
132	C₂²×Q₈×C₂₃	—	4	2	no	—
133	C₂²×Q₈×C₂₃	—	4	2	no	—
134	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
136	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₂₃	—	2	1	no	—
143	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂₃×#137	—	4	4	no	—
145	C₂₃×#137	—	4	4	no	—
146	C₂₃×#137	—	4	2	no	—
147	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
148	C₂×Q₁₆×C₂₃	—	4	2	no	—
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	—	4	2	no	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×D₈×C₂₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₂₃×C₄⋊Q₈	—	2	1	no	—
169	C₂₃×C₄⋊Q₈	—	2	1	no	—
170	C₂₃×C₄⋊Q₈	—	2	2	no	—
171	C₂₃×C₄⋊Q₈	—	2	2	no	—
172	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₂₃×#127	—	2	1	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	2	no	—
178	C₂₃×#124	—	2	1	no	—
179	C₂₃×#124	—	2	1	no	—
180	C₂₃×#124	—	2	1	no	—
181	C₂₃×#124	—	2	2	no	—
182	C₂₃×#124	—	2	2	no	—
183	C₂₃×#124	—	2	2	no	—
184	C₂₃×#124	—	2	2	no	—
185	C₂₃×#124	—	2	2	no	—
186	C₂₃×#124	—	2	2	no	—
187	C₂₃×#124	—	2	2	no	—
188	C₂₃×#124	C₂³	1	2	yes	—
189	C₂₃×#124	C₂³	1	2	yes	—
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	1	no	—
192	C₂₃×#123	—	2	1	no	—
193	C₂₃×#123	—	2	1	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	1	no	—
199	C₂₃×#123	—	2	1	no	—
200	C₂₃×#123	D₄	1	1	yes	characteristic
201	C₂₃×#123	D₄	1	1	yes	characteristic
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	D₄	1	2	yes	—
224	C₂₃×#121	C₂³	1	2	yes	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#120	—	2	2	no	—
229	C₂₃×#120	—	2	1	no	—
230	C₂₃×#120	—	2	1	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	1	no	—
233	C₂₃×#120	D₄	1	1	yes	characteristic
234	C₂₃×#120	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₂₃	—	2	2	no	—
236	C₄×Q₈×C₂₃	—	2	2	no	—
237	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	2	no	—
248	C₄×D₄×C₂₃	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	2	yes	—
250	C₄×D₄×C₂₃	C₂³	1	2	yes	—
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	1	no	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	C₂³	1	1	yes	characteristic
255	C₂₃×#117	C₂³	1	2	yes	—
256	C₂₃×#117	C₂³	1	1	yes	characteristic
257	C₂₃×#117	C₂³	1	1	yes	characteristic
258	C₂₃×#117	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂₃×#107	C₂³	1	2	yes	—
261	C₂₃×#107	C₂³	1	2	yes	—
262	C₂₃×#106	C₂³	1	2	yes	—
263	C₂₃×#106	C₂³	1	2	yes	—
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#103	C₂³	1	2	yes	—
268	C₂₃×#103	C₂³	1	2	yes	—
269	C₂₃×#103	C₂³	1	2	yes	—
270	C₂₃×#103	C₂³	1	2	yes	—
271	C₂₃×#103	C₂³	1	2	yes	—
272	C₂₃×#103	C₂³	1	2	yes	—
273	C₂₃×#103	C₂³	1	2	yes	—
274	C₂₃×#103	C₂³	1	2	yes	—
275	C₂₃×#103	C₂³	1	2	yes	—
276	C₂₃×#103	C₂³	1	2	yes	—
277	C₂₃×#103	C₂³	1	2	yes	—
278	C₂₃×#102	C₂³	1	2	yes	—
279	C₂₃×#102	C₂³	1	2	yes	—
280	C₂₃×#102	C₂³	1	2	yes	—
281	C₂₃×#102	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂₃×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₂₃	C₂³	1	2	yes	—
290	C₂⁴×C₂₃	—	2	1	no	—
291	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
292	#41×C₂₃	—	2	2	no	—
293	#41×C₂₃	—	2	2	no	—
294	#41×C₂₃	—	4	1	no	—
295	#41×C₂₃	—	4	1	no	—
296	#41×C₂₃	—	4	1	no	—
297	#41×C₂₃	—	4	1	no	—
298	#41×C₂₃	—	4	1	no	—
299	#41×C₂₃	—	4	1	no	—
300	#41×C₂₃	—	4	4	no	—
301	#41×C₂₃	—	4	4	no	—
302	#41×C₂₃	—	4	2	no	—
303	#41×C₂₃	—	4	2	no	—
304	#41×C₂₃	—	4	4	no	—
305	C₂×Q₈×C₂₃	—	2	2	no	—
306	C₂×Q₈×C₂₃	—	2	2	no	—
307	C₂×Q₈×C₂₃	—	2	1	no	—
308	C₂×Q₈×C₂₃	—	2	2	no	—
309	C₂×Q₈×C₂₃	—	2	2	no	—
310	C₂×Q₈×C₂₃	—	2	1	no	—
311	C₂×Q₈×C₂₃	—	2	1	no	—
312	C₂×Q₈×C₂₃	—	2	1	no	—
313	C₂×Q₈×C₂₃	—	2	2	no	—
314	C₂×Q₈×C₂₃	—	2	1	no	—
315	C₂×Q₈×C₂₃	—	2	2	no	—
316	C₂×Q₈×C₂₃	—	2	2	no	—
317	C₂×Q₈×C₂₃	—	2	4	no	—
318	C₂×Q₈×C₂₃	—	2	4	no	—
319	C₂×Q₈×C₂₃	—	4	2	no	—
320	C₂×Q₈×C₂₃	—	4	2	no	—
321	C₂×Q₈×C₂₃	—	4	1	no	—
322	C₂×Q₈×C₂₃	—	4	1	no	—
323	C₂×Q₈×C₂₃	—	4	1	no	—
324	C₂×Q₈×C₂₃	—	4	1	no	—
325	C₂×Q₈×C₂₃	—	4	4	no	—
326	C₂×Q₈×C₂₃	—	4	1	no	—
327	C₂×Q₈×C₂₃	—	4	1	no	—
328	C₂×Q₈×C₂₃	—	4	8	no	—
329	C₂×Q₈×C₂₃	—	4	4	no	—
330	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	1	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	2	1	no	—
340	C₂×D₄×C₂₃	—	2	2	no	—
341	C₂×D₄×C₂₃	—	2	2	no	—
342	C₂×D₄×C₂₃	—	2	2	no	—
343	C₂×D₄×C₂₃	—	2	2	no	—
344	C₂×D₄×C₂₃	—	2	1	no	—
345	C₂×D₄×C₂₃	—	4	1	no	—
346	C₂×D₄×C₂₃	—	4	1	no	—
347	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	2	1	no	—
358	C₂²×C₄×C₂₃	—	2	1	no	—
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	1	no	—
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	—	2	2	no	—
366	C₂²×C₄×C₂₃	—	4	1	no	—
367	C₂²×C₄×C₂₃	—	4	1	no	—
368	C₂²×C₄×C₂₃	—	4	4	no	—
369	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	Q₁₆×C₂₃	—	2	4	no	—
376	Q₁₆×C₂₃	—	2	4	no	—
377	Q₁₆×C₂₃	—	4	2	no	—
378	Q₁₆×C₂₃	—	4	2	no	—
379	Q₁₆×C₂₃	—	4	2	no	—
380	SD₁₆×C₂₃	—	2	4	no	—
381	SD₁₆×C₂₃	—	2	4	no	—
382	SD₁₆×C₂₃	—	4	2	no	—
383	SD₁₆×C₂₃	—	4	2	no	—
384	SD₁₆×C₂₃	—	4	2	no	—
385	SD₁₆×C₂₃	—	4	2	no	—
386	D₈×C₂₃	—	4	2	no	—
387	M₁₆×C₂₃	—	4	1	no	—
388	M₁₆×C₂₃	—	4	2	no	—
389	M₁₆×C₂₃	—	4	2	no	—
390	M₁₆×C₂₃	—	4	1	no	—
391	C₂×C₈×C₂₃	—	4	1	no	—
392	C₂×C₈×C₂₃	—	4	1	no	—
393	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
395	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
396	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	2	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	—	2	2	no	—
408	C₄⋊C₄×C₂₃	—	2	2	no	—
409	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	1	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	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	2	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	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	2	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	—	2	1	no	—
445	C₄²×C₂₃	—	2	1	no	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	C₂⁴	1	2	yes	—
448	#61646	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	—	2	2	no	—
451	C₂³×C₂₃	—	4	1	no	—
452	C₂³×C₂₃	—	4	2	no	—
453	C₂³×C₂₃	—	8	1	no	—
454	C₂³×C₂₃	—	8	2	no	—
455	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
456	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
457	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₂₃	—	2	4	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	2	1	no	—
462	Q₈×C₂₃	—	2	1	no	—
463	Q₈×C₂₃	—	2	2	no	—
464	Q₈×C₂₃	—	2	2	no	—
465	Q₈×C₂₃	—	2	2	no	—
466	Q₈×C₂₃	—	2	2	no	—
467	Q₈×C₂₃	—	2	1	no	—
468	Q₈×C₂₃	—	4	1	no	—
469	Q₈×C₂₃	—	4	4	no	—
470	Q₈×C₂₃	—	4	4	no	—
471	Q₈×C₂₃	—	4	2	no	—
472	Q₈×C₂₃	—	4	2	no	—
473	Q₈×C₂₃	—	4	2	no	—
474	Q₈×C₂₃	—	8	2	no	—
475	Q₈×C₂₃	—	8	1	no	—
476	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
477	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₂₃	—	2	1	no	—
479	D₄×C₂₃	—	2	2	no	—
480	D₄×C₂₃	—	2	2	no	—
481	D₄×C₂₃	—	2	1	no	—
482	D₄×C₂₃	—	4	2	no	—
483	D₄×C₂₃	—	4	2	no	—
484	D₄×C₂₃	—	4	1	no	—
485	D₄×C₂₃	—	4	1	no	—
486	D₄×C₂₃	—	4	1	no	—
487	D₄×C₂₃	—	4	2	no	—
488	D₄×C₂₃	—	4	2	no	—
489	D₄×C₂₃	—	4	4	no	—
490	D₄×C₂₃	—	4	2	no	—
491	D₄×C₂₃	—	8	1	no	—
492	D₄×C₂₃	—	8	2	no	—
493	D₄×C₂₃	—	8	2	no	—
494	D₄×C₂₃	—	8	2	no	—
495	D₄×C₂₃	—	8	2	no	—
496	C₂×C₄×C₂₃	—	2	4	no	—
497	C₂×C₄×C₂₃	—	2	1	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	1	no	—
500	C₂×C₄×C₂₃	—	2	1	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	2	2	no	—
503	C₂×C₄×C₂₃	—	2	1	no	—
504	C₂×C₄×C₂₃	—	2	1	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	2	no	—
508	C₂×C₄×C₂₃	—	2	2	no	—
509	C₂×C₄×C₂₃	—	2	2	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	2	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	4	2	no	—
514	C₂×C₄×C₂₃	—	4	1	no	—
515	C₂×C₄×C₂₃	—	4	2	no	—
516	C₂×C₄×C₂₃	—	4	2	no	—
517	C₂×C₄×C₂₃	—	4	4	no	—
518	C₂×C₄×C₂₃	—	4	4	no	—
519	C₂×C₄×C₂₃	—	4	2	no	—
520	C₂×C₄×C₂₃	—	4	2	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	2	no	—
523	C₂×C₄×C₂₃	—	8	2	no	—
524	C₂×C₄×C₂₃	—	8	2	no	—
525	C₂×C₄×C₂₃	—	8	1	no	—
526	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
533	C₈×C₂₃	—	2	2	no	—
534	C₈×C₂₃	—	2	2	no	—
535	C₈×C₂₃	—	2	2	no	—
536	C₈×C₂₃	—	2	2	no	—
537	#3540	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3486	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3329	C₂×C₂₃	1	2	yes	complemented
540	#3328	C₂×C₂₃	1	2	yes	complemented
541	#3321	C₂×C₂₃	1	2	yes	complemented
542	#3313	C₂×C₂₃	1	2	yes	complemented
543	#3277	C₂×C₂₃	1	2	yes	complemented
544	#3275	C₂×C₂₃	1	2	yes	complemented
545	#3270	C₂×C₂₃	1	2	yes	complemented
546	#3266	C₂×C₂₃	1	2	yes	complemented
547	#3225	C₂×C₂₃	1	2	yes	complemented
548	#3202	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3200	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#3197	C₂×C₂₃	1	2	yes	complemented
551	#3121	C₂×C₂₃	1	2	yes	complemented
552	#3011	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#3010	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#3004	C₂×C₂₃	1	2	yes	complemented
555	#2978	C₂×C₂₃	1	1	yes	characteristic, complemented
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	2	no	—
559	C₂²×C₂₃	—	2	2	no	—
560	C₂²×C₂₃	—	2	2	no	—
561	C₂²×C₂₃	—	2	1	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	1	no	—
564	C₂²×C₂₃	—	2	1	no	—
565	C₂²×C₂₃	—	4	4	no	—
566	C₂²×C₂₃	—	4	2	no	—
567	C₂²×C₂₃	—	4	2	no	—
568	C₂²×C₂₃	—	4	2	no	—
569	C₂²×C₂₃	—	4	1	no	—
570	C₂²×C₂₃	—	4	2	no	—
571	C₂²×C₂₃	—	16	2	no	—
572	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₂₃	—	2	2	no	—
574	C₄×C₂₃	—	2	2	no	—
575	C₄×C₂₃	—	2	2	no	—
576	C₄×C₂₃	—	2	2	no	—
577	C₄×C₂₃	—	2	1	no	—
578	C₄×C₂₃	—	2	2	no	—
579	C₄×C₂₃	—	2	1	no	—
580	C₄×C₂₃	—	2	1	no	—
581	C₄×C₂₃	—	4	2	no	—
582	C₄×C₂₃	—	4	2	no	—
583	C₄×C₂₃	—	4	2	no	—
584	C₄×C₂₃	—	4	1	no	—
585	C₄×C₂₃	—	4	2	no	—
586	C₄×C₂₃	—	4	2	no	—
587	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
588	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
590	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
591	C₂×#137	C₂²×C₂₃	1	2	yes	—
592	C₂×#137	C₂²×C₂₃	1	2	yes	—
593	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
594	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
595	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
596	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
597	H(3,𝔽₄)	—	2	1	no	—
598	#560	—	2	1	no	—
599	#559	—	2	1	no	—
600	#556	C₂²×C₂₃	1	2	yes	—
601	#555	C₂²×C₂₃	1	2	yes	—
602	#551	—	2	1	no	—
603	D₄×Q₈	—	2	2	no	—
604	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
605	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
606	#548	—	2	2	no	—
607	#548	C₂²×C₂₃	1	2	yes	—
608	#548	C₂²×C₂₃	1	2	yes	—
609	#548	C₂²×C₂₃	1	2	yes	complemented
610	#546	C₂²×C₂₃	1	2	yes	—
611	#542	—	2	2	no	—
612	#542	C₂²×C₂₃	1	2	yes	—
613	#538	—	2	2	no	—
614	#536	—	2	1	no	—
615	#536	—	2	1	no	—
616	#536	C₂²×C₂₃	1	1	yes	characteristic
617	#536	C₂²×C₂₃	1	1	yes	characteristic
618	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	#535	C₂²×C₂₃	1	1	yes	characteristic
620	#525	—	2	1	no	—
621	#525	—	2	1	no	—
622	#525	C₂²×C₂₃	1	2	yes	—
623	#525	C₂²×C₂₃	1	1	yes	characteristic
624	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#497	C₂²×C₂₃	1	2	yes	complemented
627	#495	C₂²×C₂₃	1	2	yes	complemented
628	#489	C₂²×C₂₃	1	2	yes	complemented
629	#487	C₂²×C₂₃	1	2	yes	complemented
630	#485	C₂²×C₂₃	1	2	yes	complemented
631	#485	C₂²×C₂₃	1	2	yes	complemented
632	#485	C₂²×C₂₃	1	2	yes	complemented
633	#485	C₂²×C₂₃	1	2	yes	complemented
634	#482	C₂²×C₂₃	1	2	yes	—
635	#482	C₂²×C₂₃	1	2	yes	complemented
636	#477	C₂²×C₂₃	1	2	yes	complemented
637	#475	C₂²×C₂₃	1	2	yes	complemented
638	#470	C₂²×C₂₃	1	2	yes	complemented
639	#470	C₂²×C₂₃	1	2	yes	complemented
640	#469	C₂²×C₂₃	1	2	yes	—
641	#468	C₂²×C₂₃	1	2	yes	—
642	#468	C₂²×C₂₃	1	2	yes	complemented
643	#468	C₂²×C₂₃	1	2	yes	complemented
644	#467	C₂²×C₂₃	1	2	yes	complemented
645	#465	C₂²×C₂₃	1	2	yes	complemented
646	#464	C₂²×C₂₃	1	2	yes	complemented
647	#464	C₂²×C₂₃	1	2	yes	complemented
648	#464	C₂²×C₂₃	1	2	yes	complemented
649	#463	C₂²×C₂₃	1	2	yes	complemented
650	#462	C₂²×C₂₃	1	2	yes	complemented
651	#461	C₂²×C₂₃	1	2	yes	complemented
652	#452	C₂²×C₂₃	1	2	yes	—
653	#452	C₂²×C₂₃	1	2	yes	complemented
654	#452	C₂²×C₂₃	1	2	yes	complemented
655	#451	C₂²×C₂₃	1	2	yes	complemented
656	#451	C₂²×C₂₃	1	2	yes	complemented
657	#451	C₂²×C₂₃	1	2	yes	complemented
658	#451	C₂²×C₂₃	1	2	yes	complemented
659	#451	C₂²×C₂₃	1	2	yes	complemented
660	#451	C₂²×C₂₃	1	2	yes	complemented
661	#450	C₂²×C₂₃	1	2	yes	complemented
662	#449	C₂²×C₂₃	1	2	yes	—
663	#449	C₂²×C₂₃	1	2	yes	—
664	#449	C₂²×C₂₃	1	2	yes	complemented
665	#448	C₂²×C₂₃	1	2	yes	—
666	#448	C₂²×C₂₃	1	2	yes	—
667	#448	C₂²×C₂₃	1	2	yes	—
668	#448	C₂²×C₂₃	1	2	yes	—
669	#448	C₂²×C₂₃	1	2	yes	complemented
670	#441	C₂²×C₂₃	1	2	yes	complemented
671	#440	C₂²×C₂₃	1	2	yes	complemented
672	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
673	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
674	#436	C₂²×C₂₃	1	2	yes	—
675	#436	C₂²×C₂₃	1	2	yes	complemented
676	#435	C₂²×C₂₃	1	2	yes	—
677	#435	C₂²×C₂₃	1	2	yes	complemented
678	#433	C₂²×C₂₃	1	2	yes	complemented
679	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	#419	C₂²×C₂₃	1	2	yes	complemented
681	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#419	C₂²×C₂₃	1	2	yes	complemented
683	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	#408	C₂²×C₂₃	1	1	yes	characteristic
686	#408	C₂²×C₂₃	1	1	yes	characteristic
687	#407	C₂²×C₂₃	1	2	yes	complemented
688	C₂×C₂₃	—	4	1	no	—
689	C₂×C₂₃	—	4	2	no	—
690	C₂×C₂₃	—	4	1	no	—
691	C₂×C₂₃	—	4	1	no	—
692	C₂×C₂₃	—	8	1	no	—
693	C₂×C₂₃	—	8	2	no	—
694	C₂×C₂₃	#3484	1	1	yes	characteristic
695	C₂×C₂₃	#3586	1	2	yes	—
696	2₋¹⁺⁴	—	4	2	no	—
697	2₋¹⁺⁴	—	4	2	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₂₃	1	2	yes	—
704	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
706	C₂²×Q₈	—	2	1	no	—
707	C₂²×Q₈	—	2	1	no	—
708	C₂²×Q₈	—	2	2	no	—
709	C₂²×Q₈	—	4	2	no	—
710	C₂²×Q₈	—	4	2	no	—
711	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
712	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
713	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
714	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
715	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
716	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
718	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
719	C₂³×C₄	—	2	1	no	—
720	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
721	#137	—	4	4	no	—
722	#137	—	4	4	no	—
723	#137	—	4	2	no	—
724	AGL(1,ℤ/8)	—	4	2	no	—
725	C₂×Q₁₆	—	4	2	no	—
726	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
731	C₂×SD₁₆	—	4	2	no	—
732	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
738	C₂×D₈	C₂³×C₂₃	1	2	yes	—
739	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
741	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
742	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
743	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
744	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	2	no	—
748	C₄⋊Q₈	—	2	2	no	—
749	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
751	#127	—	2	1	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	C₂³×C₂₃	1	2	yes	—
766	#124	C₂³×C₂₃	1	2	yes	—
767	#123	—	2	1	no	—
768	#123	—	2	1	no	—
769	#123	—	2	1	no	—
770	#123	—	2	1	no	—
771	#123	—	2	2	no	—
772	#123	—	2	1	no	—
773	#123	—	2	2	no	—
774	#123	—	2	1	no	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	D₄×C₂₃	1	1	yes	characteristic
778	#123	D₄×C₂₃	1	1	yes	characteristic
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	D₄×C₂₃	1	2	yes	—
801	#121	C₂³×C₂₃	1	2	yes	—
802	#121	C₂³×C₂₃	1	2	yes	—
803	#121	C₂³×C₂₃	1	2	yes	—
804	#121	C₂³×C₂₃	1	2	yes	—
805	#120	—	2	1	no	—
806	#120	—	2	2	no	—
807	#120	—	2	1	no	—
808	#120	—	2	1	no	—
809	#120	—	2	2	no	—
810	#120	D₄×C₂₃	1	1	yes	characteristic
811	#120	D₄×C₂₃	1	1	yes	characteristic
812	C₄×Q₈	—	2	2	no	—
813	C₄×Q₈	—	2	2	no	—
814	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
815	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
816	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	C₂³×C₂₃	1	2	yes	—
826	C₄×D₄	C₂³×C₂₃	1	2	yes	—
827	C₄×D₄	C₂³×C₂₃	1	2	yes	—
828	#117	—	2	2	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	C₂³×C₂₃	1	1	yes	characteristic
832	#117	C₂³×C₂₃	1	2	yes	—
833	#117	C₂³×C₂₃	1	1	yes	characteristic
834	#117	C₂³×C₂₃	1	1	yes	characteristic
835	#117	C₂³×C₂₃	1	1	yes	characteristic
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	#107	C₂³×C₂₃	1	2	yes	—
838	#107	C₂³×C₂₃	1	2	yes	—
839	#106	C₂³×C₂₃	1	2	yes	—
840	#106	C₂³×C₂₃	1	2	yes	—
841	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
842	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
843	#103	C₂³×C₂₃	1	2	yes	—
844	#103	C₂³×C₂₃	1	2	yes	—
845	#103	C₂³×C₂₃	1	2	yes	—
846	#103	C₂³×C₂₃	1	2	yes	—
847	#103	C₂³×C₂₃	1	2	yes	—
848	#103	C₂³×C₂₃	1	2	yes	—
849	#103	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	2	yes	—
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	2	yes	—
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	2	yes	—
855	#102	C₂³×C₂₃	1	2	yes	—
856	#102	C₂³×C₂₃	1	2	yes	—
857	#102	C₂³×C₂₃	1	2	yes	—
858	#102	C₂³×C₂₃	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
865	#97	C₂³×C₂₃	1	2	yes	—
866	C₄×C₈	C₂³×C₂₃	1	2	yes	—
867	C₂₃	#61646	1	1	yes	characteristic, direct product factor, Sylow
868	C₂⁴	—	2	1	no	—
869	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	4	1	no	—
873	#41	—	4	1	no	—
874	#41	—	4	1	no	—
875	#41	—	4	1	no	—
876	#41	—	4	1	no	—
877	#41	—	4	1	no	—
878	#41	—	4	4	no	—
879	#41	—	4	4	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	4	4	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	4	no	—
896	C₂×Q₈	—	2	4	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	4	1	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	—	4	1	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	—	4	4	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	—	4	8	no	—
907	C₂×Q₈	—	4	4	no	—
908	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	4	1	no	—
924	C₂×D₄	—	4	1	no	—
925	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
927	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
929	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
930	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	4	1	no	—
945	C₂²×C₄	—	4	1	no	—
946	C₂²×C₄	—	4	4	no	—
947	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
948	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
953	Q₁₆	—	2	4	no	—
954	Q₁₆	—	2	4	no	—
955	Q₁₆	—	4	2	no	—
956	Q₁₆	—	4	2	no	—
957	Q₁₆	—	4	2	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	2	4	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	SD₁₆	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	1	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	2	no	—
968	M₁₆	—	4	1	no	—
969	C₂×C₈	—	4	1	no	—
970	C₂×C₈	—	4	1	no	—
971	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
972	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
973	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
974	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1015	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	C₂⁴×C₂₃	1	2	yes	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1033	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1034	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1035	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1036	Q₈	—	2	4	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	2	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	4	1	no	—
1046	Q₈	—	4	4	no	—
1047	Q₈	—	4	4	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	8	1	no	—
1052	Q₈	—	8	2	no	—
1053	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1054	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	4	1	no	—
1060	D₄	—	4	1	no	—
1061	D₄	—	4	1	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	C₂×C₄	—	2	4	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1109	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	2	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	4	4	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	16	2	no	—
1130	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1146	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1147	C₂	—	4	1	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	4	1	no	—
1150	C₂	—	4	1	no	—
1151	C₂	—	8	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	C₂₃×#3484	1	1	yes	characteristic
1154	C₂	C₂₃×#3586	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3540	C₂	semidirect
2. C₂₃×#3486	C₂	semidirect
3. C₂₃×#3329	C₂	semidirect
4. C₂₃×#3328	C₂	semidirect
5. C₂₃×#3321	C₂	semidirect
6. C₂₃×#3313	C₂	semidirect
7. C₂₃×#3277	C₂	semidirect
8. C₂₃×#3275	C₂	semidirect
9. C₂₃×#3270	C₂	semidirect
10. C₂₃×#3266	C₂	semidirect
11. C₂₃×#3225	C₂	semidirect
12. C₂₃×#3202	C₂	semidirect
13. C₂₃×#3200	C₂	semidirect
14. C₂₃×#3197	C₂	semidirect
15. C₂₃×#3121	C₂	semidirect
16. C₂₃×#3011	C₂	semidirect
17. C₂₃×#3010	C₂	semidirect
18. C₂₃×#3004	C₂	semidirect
19. C₂₃×#2978	C₂	semidirect
21. C₂³×Q₈×C₂₃	C₂²	semidirect
24. C₂×C₂₃×#137	C₂²	semidirect
25. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×Q₁₆×C₂₃	C₂²	semidirect
27. C₂²×SD₁₆×C₂₃	C₂²	semidirect
36. D₄×Q₈×C₂₃	C₂²	semidirect
40. C₂₃×#548	C₂²	semidirect
49. C₂₃×#536	C₂²	semidirect
55. C₂₃×#525	C₂²	semidirect
56. C₂₃×#519	C₂²	semidirect
57. C₂₃×#497	C₂²	semidirect
58. C₂₃×#495	C₂²	semidirect
59. C₂₃×#489	C₂²	semidirect
60. C₂₃×#487	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#485	C₂²	semidirect
63. C₂₃×#485	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
66. C₂₃×#482	C₂²	semidirect
67. C₂₃×#477	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#470	C₂²	semidirect
70. C₂₃×#470	C₂²	semidirect
73. C₂₃×#468	C₂²	semidirect
74. C₂₃×#468	C₂²	semidirect
75. C₂₃×#467	C₂²	semidirect
76. C₂₃×#465	C₂²	semidirect
77. C₂₃×#464	C₂²	semidirect
78. C₂₃×#464	C₂²	semidirect
79. C₂₃×#464	C₂²	semidirect
80. C₂₃×#463	C₂²	semidirect
81. C₂₃×#462	C₂²	semidirect
82. C₂₃×#461	C₂²	semidirect
84. C₂₃×#452	C₂²	semidirect
85. C₂₃×#452	C₂²	semidirect
86. C₂₃×#451	C₂²	semidirect
87. C₂₃×#451	C₂²	semidirect
88. C₂₃×#451	C₂²	semidirect
89. C₂₃×#451	C₂²	semidirect
90. C₂₃×#451	C₂²	semidirect
91. C₂₃×#451	C₂²	semidirect
92. C₂₃×#450	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
100. C₂₃×#448	C₂²	semidirect
101. C₂₃×#441	C₂²	semidirect
102. C₂₃×#440	C₂²	semidirect
103. C₄×Q₁₆×C₂₃	C₂²	semidirect
104. C₄×SD₁₆×C₂₃	C₂²	semidirect
106. C₂₃×#436	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₂₃×#433	C₂²	semidirect
110. C₂₃×#419	C₂²	semidirect
111. C₂₃×#419	C₂²	semidirect
112. C₂₃×#419	C₂²	semidirect
113. C₂₃×#419	C₂²	semidirect
114. C₂₃×#416	C₂²	semidirect
115. C₂₃×#416	C₂²	semidirect
118. C₂₃×#407	C₂²	semidirect
448. #61646	C₂₃	direct (N × H)
537. #3540	C₂×C₂₃	semidirect
538. #3486	C₂×C₂₃	semidirect
539. #3329	C₂×C₂₃	semidirect
540. #3328	C₂×C₂₃	semidirect
541. #3321	C₂×C₂₃	semidirect
542. #3313	C₂×C₂₃	semidirect
543. #3277	C₂×C₂₃	semidirect
544. #3275	C₂×C₂₃	semidirect
545. #3270	C₂×C₂₃	semidirect
546. #3266	C₂×C₂₃	semidirect
547. #3225	C₂×C₂₃	semidirect
548. #3202	C₂×C₂₃	semidirect
549. #3200	C₂×C₂₃	semidirect
550. #3197	C₂×C₂₃	semidirect
551. #3121	C₂×C₂₃	semidirect
552. #3011	C₂×C₂₃	semidirect
553. #3010	C₂×C₂₃	semidirect
554. #3004	C₂×C₂₃	semidirect
555. #2978	C₂×C₂₃	semidirect
590. C₂³×Q₈	C₂²×C₂₃	semidirect
593. C₂×#137	C₂²×C₂₃	semidirect
594. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
595. C₂²×Q₁₆	C₂²×C₂₃	semidirect
596. C₂²×SD₁₆	C₂²×C₂₃	semidirect
605. D₄×Q₈	C₂²×C₂₃	semidirect
609. #548	C₂²×C₂₃	semidirect
618. #536	C₂²×C₂₃	semidirect
624. #525	C₂²×C₂₃	semidirect
625. #519	C₂²×C₂₃	semidirect
626. #497	C₂²×C₂₃	semidirect
627. #495	C₂²×C₂₃	semidirect
628. #489	C₂²×C₂₃	semidirect
629. #487	C₂²×C₂₃	semidirect
630. #485	C₂²×C₂₃	semidirect
631. #485	C₂²×C₂₃	semidirect
632. #485	C₂²×C₂₃	semidirect
633. #485	C₂²×C₂₃	semidirect
635. #482	C₂²×C₂₃	semidirect
636. #477	C₂²×C₂₃	semidirect
637. #475	C₂²×C₂₃	semidirect
638. #470	C₂²×C₂₃	semidirect
639. #470	C₂²×C₂₃	semidirect
642. #468	C₂²×C₂₃	semidirect
643. #468	C₂²×C₂₃	semidirect
644. #467	C₂²×C₂₃	semidirect
645. #465	C₂²×C₂₃	semidirect
646. #464	C₂²×C₂₃	semidirect
647. #464	C₂²×C₂₃	semidirect
648. #464	C₂²×C₂₃	semidirect
649. #463	C₂²×C₂₃	semidirect
650. #462	C₂²×C₂₃	semidirect
651. #461	C₂²×C₂₃	semidirect
653. #452	C₂²×C₂₃	semidirect
654. #452	C₂²×C₂₃	semidirect
655. #451	C₂²×C₂₃	semidirect
656. #451	C₂²×C₂₃	semidirect
657. #451	C₂²×C₂₃	semidirect
658. #451	C₂²×C₂₃	semidirect
659. #451	C₂²×C₂₃	semidirect
660. #451	C₂²×C₂₃	semidirect
661. #450	C₂²×C₂₃	semidirect
664. #449	C₂²×C₂₃	semidirect
669. #448	C₂²×C₂₃	semidirect
670. #441	C₂²×C₂₃	semidirect
671. #440	C₂²×C₂₃	semidirect
672. C₄×Q₁₆	C₂²×C₂₃	semidirect
673. C₄×SD₁₆	C₂²×C₂₃	semidirect
675. #436	C₂²×C₂₃	semidirect
677. #435	C₂²×C₂₃	semidirect
678. #433	C₂²×C₂₃	semidirect
679. #419	C₂²×C₂₃	semidirect
680. #419	C₂²×C₂₃	semidirect
681. #419	C₂²×C₂₃	semidirect
682. #419	C₂²×C₂₃	semidirect
683. #416	C₂²×C₂₃	semidirect
684. #416	C₂²×C₂₃	semidirect
687. #407	C₂²×C₂₃	semidirect
867. C₂₃	#61646	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3540	2
C₂₃×#3486	2
C₂₃×#3329	2
C₂₃×#3328	2
C₂₃×#3321	2
C₂₃×#3313	2
C₂₃×#3277	2
C₂₃×#3275	2
C₂₃×#3270	2
C₂₃×#3266	2
C₂₃×#3225	2
C₂₃×#3202	2
C₂₃×#3200	2
C₂₃×#3197	2
C₂₃×#3121	2
C₂₃×#3011	2
C₂₃×#3010	2
C₂₃×#3004	2
C₂₃×#2978	2
#61646	23

Subgroups — C23×#61646 #19209272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61646 #19209272