Subgroups — C₂₃×#61756 #19209382

Order 5888.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3537	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3324	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3200	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3126	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#560	—	2	2	no	—
21	C₂₃×#556	C₂²	1	2	yes	complemented
22	C₂₃×#554	C₂²	1	2	yes	complemented
23	C₂₃×#553	C₂²	1	2	yes	—
24	C₂₃×#553	C₂²	1	2	yes	—
25	C₂₃×#552	—	2	2	no	—
26	C₂₃×#552	C₂²	1	2	yes	complemented
27	C₂₃×#552	C₂²	1	2	yes	complemented
28	C₂₃×#551	—	2	2	no	—
29	D₄²×C₂₃	—	2	2	no	—
30	D₄²×C₂₃	C₂²	1	2	yes	—
31	D₄²×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#541	—	2	1	no	—
35	C₂₃×#540	C₂²	1	2	yes	—
36	C₂₃×#538	—	2	1	no	—
37	C₂₃×#538	—	2	1	no	—
38	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#535	C₂²	1	2	yes	—
40	C₂₃×#534	—	2	1	no	—
41	C₂₃×#534	—	2	1	no	—
42	C₂₃×#533	—	2	1	no	—
43	C₂₃×#529	—	2	1	no	—
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
48	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#501	C₂²	1	2	yes	complemented
52	C₂₃×#499	C₂²	1	2	yes	complemented
53	C₂₃×#490	C₂²	1	2	yes	complemented
54	C₂₃×#486	C₂²	1	2	yes	complemented
55	C₂₃×#485	C₂²	1	2	yes	complemented
56	C₂₃×#485	C₂²	1	2	yes	complemented
57	C₂₃×#484	C₂²	1	2	yes	complemented
58	C₂₃×#483	C₂²	1	2	yes	complemented
59	C₂₃×#482	C₂²	1	2	yes	complemented
60	C₂₃×#482	C₂²	1	2	yes	complemented
61	C₂₃×#482	C₂²	1	2	yes	complemented
62	C₂₃×#482	C₂²	1	2	yes	complemented
63	C₂₃×#482	C₂²	1	2	yes	complemented
64	C₂₃×#482	C₂²	1	2	yes	complemented
65	C₂₃×#482	C₂²	1	2	yes	complemented
66	C₂₃×#482	C₂²	1	2	yes	complemented
67	C₂₃×#481	C₂²	1	2	yes	complemented
68	C₂₃×#481	C₂²	1	2	yes	complemented
69	C₂₃×#481	C₂²	1	2	yes	complemented
70	C₂₃×#480	C₂²	1	2	yes	complemented
71	C₂₃×#480	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#478	C₂²	1	2	yes	complemented
76	C₂₃×#478	C₂²	1	2	yes	complemented
77	C₂₃×#476	C₂²	1	2	yes	complemented
78	C₂₃×#474	C₂²	1	2	yes	complemented
79	C₂₃×#468	C₂²	1	2	yes	complemented
80	C₂₃×#468	C₂²	1	2	yes	complemented
81	C₂₃×#468	C₂²	1	2	yes	complemented
82	C₂₃×#468	C₂²	1	2	yes	complemented
83	C₂₃×#465	C₂²	1	2	yes	complemented
84	C₂₃×#465	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#465	C₂²	1	2	yes	complemented
87	C₂₃×#460	C₂²	1	2	yes	complemented
88	C₂₃×#460	C₂²	1	2	yes	complemented
89	C₂₃×#450	C₂²	1	2	yes	complemented
90	C₂₃×#450	C₂²	1	2	yes	complemented
91	C₂₃×#450	C₂²	1	2	yes	complemented
92	C₂₃×#450	C₂²	1	2	yes	complemented
93	C₂₃×#448	C₂²	1	2	yes	complemented
94	C₂₃×#448	C₂²	1	2	yes	complemented
95	C₂₃×#440	C₂²	1	2	yes	complemented
96	C₂₃×#440	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
99	C₂₃×#436	C₂²	1	2	yes	complemented
100	C₂₃×#435	C₂²	1	2	yes	complemented
101	C₂₃×#435	C₂²	1	2	yes	complemented
102	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
103	C₂₃×#433	C₂²	1	2	yes	complemented
104	C₂₃×#428	C₂²	1	2	yes	complemented
105	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#427	C₂²	1	2	yes	complemented
108	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#418	C₂²	1	2	yes	complemented
112	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
115	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#408	C₂²	1	2	yes	complemented
117	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₂₃	—	2	1	no	—
122	C₂²×D₄×C₂₃	—	2	1	no	—
123	C₂²×D₄×C₂₃	—	2	2	no	—
124	C₂²×D₄×C₂₃	—	2	2	no	—
125	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
136	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
139	C₂₃×C₄⋊Q₈	—	2	1	no	—
140	C₂₃×C₄⋊Q₈	—	2	1	no	—
141	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×#127	—	2	2	no	—
143	C₂₃×#127	C₂³	1	2	yes	—
144	C₂₃×#126	—	2	2	no	—
145	C₂₃×#126	—	2	2	no	—
146	C₂₃×#126	—	2	2	no	—
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	—	2	2	no	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#125	—	2	2	no	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	2	no	—
153	C₂₃×#125	—	2	1	no	—
154	C₂₃×#125	C₂³	1	2	yes	—
155	C₂₃×#125	C₂³	1	2	yes	—
156	C₂₃×#124	—	2	2	no	—
157	C₂₃×#124	—	2	2	no	—
158	C₂₃×#124	—	2	1	no	—
159	C₂₃×#123	—	2	2	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×#123	—	2	2	no	—
162	C₂₃×#123	—	2	2	no	—
163	C₂₃×#123	—	2	2	no	—
164	C₂₃×#123	—	2	2	no	—
165	C₂₃×#123	—	2	2	no	—
166	C₂₃×#123	D₄	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	—	2	1	no	—
168	C₂₃×C₂²⋊Q₈	—	2	1	no	—
169	C₂₃×C₂²⋊Q₈	—	2	2	no	—
170	C₂₃×C₂²⋊Q₈	—	2	2	no	—
171	C₂₃×C₂²⋊Q₈	—	2	2	no	—
172	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
173	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
174	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₂₃×#121	—	2	2	no	—
179	C₂₃×#121	—	2	2	no	—
180	C₂₃×#121	—	2	1	no	—
181	C₂₃×#121	—	2	1	no	—
182	C₂₃×#121	—	2	1	no	—
183	C₂₃×#121	—	2	1	no	—
184	C₂₃×#121	—	2	2	no	—
185	C₂₃×#121	—	2	2	no	—
186	C₂₃×#121	—	2	2	no	—
187	C₂₃×#121	—	2	2	no	—
188	C₂₃×#121	D₄	1	1	yes	characteristic
189	C₂₃×#121	D₄	1	1	yes	characteristic
190	C₂₃×#121	C₂³	1	2	yes	—
191	C₂₃×#121	C₂³	1	2	yes	—
192	C₂₃×#121	C₂³	1	2	yes	—
193	C₂₃×#121	C₂³	1	2	yes	—
194	C₂₃×#121	C₂³	1	2	yes	—
195	C₂₃×#121	C₂³	1	2	yes	—
196	C₂₃×#120	—	2	2	no	—
197	C₂₃×#120	—	2	2	no	—
198	C₂₃×#120	—	2	2	no	—
199	C₂₃×#120	—	2	2	no	—
200	C₂₃×#120	—	2	2	no	—
201	C₂₃×#120	—	2	2	no	—
202	C₂₃×#120	D₄	1	2	yes	—
203	C₄×Q₈×C₂₃	—	2	1	no	—
204	C₄×Q₈×C₂₃	—	2	2	no	—
205	C₄×Q₈×C₂₃	—	2	1	no	—
206	C₄×Q₈×C₂₃	—	2	1	no	—
207	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
209	C₄×D₄×C₂₃	—	2	2	no	—
210	C₄×D₄×C₂₃	—	2	2	no	—
211	C₄×D₄×C₂₃	—	2	1	no	—
212	C₄×D₄×C₂₃	—	2	2	no	—
213	C₄×D₄×C₂₃	—	2	2	no	—
214	C₄×D₄×C₂₃	C₂³	1	2	yes	—
215	C₄×D₄×C₂₃	C₂³	1	2	yes	—
216	C₄×D₄×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	C₂³	1	2	yes	—
218	C₂₃×#117	—	2	1	no	—
219	C₂₃×#117	—	2	1	no	—
220	C₂₃×#117	—	2	2	no	—
221	C₂₃×#117	—	2	2	no	—
222	C₂₃×#117	—	2	2	no	—
223	C₂₃×#117	C₂³	1	1	yes	characteristic
224	C₂₃×#117	C₂³	1	2	yes	—
225	C₂₃×#117	C₂³	1	2	yes	—
226	C₂₃×#117	C₂³	1	1	yes	characteristic
227	C₂₃×#117	C₂³	1	1	yes	characteristic
228	C₂₃×#117	C₂³	1	1	yes	characteristic
229	C₂₃×#117	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
241	C₂×C₄²×C₂₃	—	2	1	no	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#107	C₂³	1	2	yes	—
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#107	C₂³	1	2	yes	—
246	C₂₃×#107	C₂³	1	2	yes	—
247	C₂₃×#107	C₂³	1	2	yes	—
248	C₂₃×#106	C₂³	1	2	yes	—
249	C₂₃×#106	C₂³	1	2	yes	—
250	C₂₃×#106	C₂³	1	2	yes	—
251	C₂₃×#106	C₂³	1	2	yes	—
252	C₂₃×#106	C₂³	1	2	yes	—
253	C₂₃×#106	C₂³	1	2	yes	—
254	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#103	C₂³	1	2	yes	—
258	C₂₃×#103	C₂³	1	2	yes	—
259	C₂₃×#103	C₂³	1	2	yes	—
260	C₂₃×#102	C₂³	1	2	yes	—
261	C₂₃×#102	C₂³	1	2	yes	—
262	C₂₃×#102	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×#102	C₂³	1	2	yes	—
271	C₂₃×#102	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₃×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	—	2	1	no	—
281	C₂⁴×C₂₃	—	2	1	no	—
282	C₂⁴×C₂₃	—	2	2	no	—
283	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
284	#41×C₂₃	—	4	1	no	—
285	#41×C₂₃	—	4	1	no	—
286	C₂×Q₈×C₂₃	—	2	1	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	—	4	1	no	—
289	C₂×Q₈×C₂₃	—	4	1	no	—
290	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₂₃	—	2	2	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	2	2	no	—
296	C₂×D₄×C₂₃	—	2	2	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	1	no	—
299	C₂×D₄×C₂₃	—	2	1	no	—
300	C₂×D₄×C₂₃	—	2	2	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	—	2	2	no	—
303	C₂×D₄×C₂₃	—	4	1	no	—
304	C₂×D₄×C₂₃	—	4	1	no	—
305	C₂×D₄×C₂₃	—	4	2	no	—
306	C₂×D₄×C₂₃	—	4	1	no	—
307	C₂×D₄×C₂₃	—	4	1	no	—
308	C₂×D₄×C₂₃	—	4	2	no	—
309	C₂×D₄×C₂₃	—	8	4	no	—
310	C₂×D₄×C₂₃	—	8	2	no	—
311	C₂×D₄×C₂₃	—	8	4	no	—
312	C₂×D₄×C₂₃	—	8	2	no	—
313	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
317	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₂₃	—	2	1	no	—
320	C₂²×C₄×C₂₃	—	2	1	no	—
321	C₂²×C₄×C₂₃	—	2	1	no	—
322	C₂²×C₄×C₂₃	—	2	1	no	—
323	C₂²×C₄×C₂₃	—	2	1	no	—
324	C₂²×C₄×C₂₃	—	2	1	no	—
325	C₂²×C₄×C₂₃	—	2	2	no	—
326	C₂²×C₄×C₂₃	—	2	2	no	—
327	C₂²×C₄×C₂₃	—	2	2	no	—
328	C₂²×C₄×C₂₃	—	4	1	no	—
329	C₂²×C₄×C₂₃	—	4	1	no	—
330	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
337	SD₁₆×C₂₃	—	4	2	no	—
338	SD₁₆×C₂₃	—	4	2	no	—
339	SD₁₆×C₂₃	—	4	2	no	—
340	SD₁₆×C₂₃	—	4	2	no	—
341	M₁₆×C₂₃	—	4	1	no	—
342	M₁₆×C₂₃	—	4	2	no	—
343	M₁₆×C₂₃	—	4	1	no	—
344	C₂×C₈×C₂₃	—	4	1	no	—
345	C₂×C₈×C₂₃	—	4	2	no	—
346	C₂×C₈×C₂₃	—	4	1	no	—
347	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
348	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
349	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
350	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	2	no	—
353	C₄⋊C₄×C₂₃	—	2	1	no	—
354	C₄⋊C₄×C₂₃	—	2	1	no	—
355	C₄⋊C₄×C₂₃	—	2	1	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	1	no	—
358	C₄⋊C₄×C₂₃	—	2	1	no	—
359	C₄⋊C₄×C₂₃	—	2	2	no	—
360	C₄⋊C₄×C₂₃	—	2	2	no	—
361	C₄⋊C₄×C₂₃	—	2	2	no	—
362	C₄⋊C₄×C₂₃	—	2	2	no	—
363	C₄⋊C₄×C₂₃	—	2	2	no	—
364	C₄⋊C₄×C₂₃	—	2	2	no	—
365	C₄⋊C₄×C₂₃	—	2	2	no	—
366	C₄⋊C₄×C₂₃	—	2	2	no	—
367	C₄⋊C₄×C₂₃	—	2	2	no	—
368	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₂₃	—	2	1	no	—
380	C₂²⋊C₄×C₂₃	—	2	1	no	—
381	C₂²⋊C₄×C₂₃	—	2	1	no	—
382	C₂²⋊C₄×C₂₃	—	2	1	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	2	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	—	2	2	no	—
388	C₂²⋊C₄×C₂₃	—	2	2	no	—
389	C₂²⋊C₄×C₂₃	—	2	2	no	—
390	C₂²⋊C₄×C₂₃	—	2	2	no	—
391	C₂²⋊C₄×C₂₃	—	2	2	no	—
392	C₂²⋊C₄×C₂₃	—	2	2	no	—
393	C₂²⋊C₄×C₂₃	—	2	2	no	—
394	C₂²⋊C₄×C₂₃	—	2	2	no	—
395	C₂²⋊C₄×C₂₃	—	2	2	no	—
396	C₂²⋊C₄×C₂₃	—	2	2	no	—
397	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
402	C₄²×C₂₃	—	2	1	no	—
403	C₄²×C₂₃	—	2	1	no	—
404	C₄²×C₂₃	—	2	1	no	—
405	C₄²×C₂₃	—	2	1	no	—
406	C₄²×C₂₃	—	2	2	no	—
407	C₄²×C₂₃	—	2	2	no	—
408	C₄²×C₂₃	—	2	2	no	—
409	C₄²×C₂₃	—	2	2	no	—
410	C₄²×C₂₃	C₂⁴	1	2	yes	—
411	#61756	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂³×C₂₃	—	2	2	no	—
413	C₂³×C₂₃	—	2	2	no	—
414	C₂³×C₂₃	—	2	2	no	—
415	C₂³×C₂₃	—	4	1	no	—
416	C₂³×C₂₃	—	4	1	no	—
417	C₂³×C₂₃	—	4	2	no	—
418	C₂³×C₂₃	—	4	2	no	—
419	C₂³×C₂₃	—	8	1	no	—
420	C₂³×C₂₃	—	8	1	no	—
421	C₂³×C₂₃	—	8	2	no	—
422	C₂³×C₂₃	—	8	1	no	—
423	C₂³×C₂₃	—	8	2	no	—
424	C₂³×C₂₃	—	8	1	no	—
425	C₂³×C₂₃	—	8	2	no	—
426	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
427	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
428	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
429	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
430	Q₈×C₂₃	—	2	2	no	—
431	Q₈×C₂₃	—	2	2	no	—
432	Q₈×C₂₃	—	4	1	no	—
433	Q₈×C₂₃	—	4	2	no	—
434	Q₈×C₂₃	—	8	2	no	—
435	D₄×C₂₃	—	2	4	no	—
436	D₄×C₂₃	—	2	2	no	—
437	D₄×C₂₃	—	2	2	no	—
438	D₄×C₂₃	—	2	2	no	—
439	D₄×C₂₃	—	2	2	no	—
440	D₄×C₂₃	—	4	2	no	—
441	D₄×C₂₃	—	4	1	no	—
442	D₄×C₂₃	—	4	2	no	—
443	D₄×C₂₃	—	4	4	no	—
444	D₄×C₂₃	—	4	4	no	—
445	D₄×C₂₃	—	8	1	no	—
446	D₄×C₂₃	—	8	1	no	—
447	D₄×C₂₃	—	8	2	no	—
448	D₄×C₂₃	—	8	2	no	—
449	D₄×C₂₃	—	8	2	no	—
450	D₄×C₂₃	—	8	2	no	—
451	D₄×C₂₃	—	8	2	no	—
452	D₄×C₂₃	—	8	2	no	—
453	D₄×C₂₃	—	8	2	no	—
454	C₂×C₄×C₂₃	—	2	1	no	—
455	C₂×C₄×C₂₃	—	2	1	no	—
456	C₂×C₄×C₂₃	—	2	2	no	—
457	C₂×C₄×C₂₃	—	2	1	no	—
458	C₂×C₄×C₂₃	—	2	1	no	—
459	C₂×C₄×C₂₃	—	2	2	no	—
460	C₂×C₄×C₂₃	—	2	1	no	—
461	C₂×C₄×C₂₃	—	2	1	no	—
462	C₂×C₄×C₂₃	—	2	1	no	—
463	C₂×C₄×C₂₃	—	2	1	no	—
464	C₂×C₄×C₂₃	—	2	1	no	—
465	C₂×C₄×C₂₃	—	2	2	no	—
466	C₂×C₄×C₂₃	—	2	1	no	—
467	C₂×C₄×C₂₃	—	2	2	no	—
468	C₂×C₄×C₂₃	—	2	2	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	4	1	no	—
471	C₂×C₄×C₂₃	—	4	1	no	—
472	C₂×C₄×C₂₃	—	4	1	no	—
473	C₂×C₄×C₂₃	—	4	2	no	—
474	C₂×C₄×C₂₃	—	4	2	no	—
475	C₂×C₄×C₂₃	—	8	2	no	—
476	C₂×C₄×C₂₃	—	8	2	no	—
477	C₂×C₄×C₂₃	—	8	2	no	—
478	C₂×C₄×C₂₃	—	8	1	no	—
479	C₂×C₄×C₂₃	—	8	1	no	—
480	C₂×C₄×C₂₃	—	8	1	no	—
481	C₂×C₄×C₂₃	—	8	1	no	—
482	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
489	C₈×C₂₃	—	2	2	no	—
490	C₈×C₂₃	—	2	2	no	—
491	C₈×C₂₃	—	2	2	no	—
492	C₈×C₂₃	—	2	2	no	—
493	#3537	C₂×C₂₃	1	1	yes	characteristic
494	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
495	#3351	C₂×C₂₃	1	2	yes	complemented
496	#3350	C₂×C₂₃	1	2	yes	complemented
497	#3346	C₂×C₂₃	1	2	yes	complemented
498	#3337	C₂×C₂₃	1	2	yes	complemented
499	#3324	C₂×C₂₃	1	2	yes	complemented
500	#3310	C₂×C₂₃	1	2	yes	complemented
501	#3310	C₂×C₂₃	1	2	yes	complemented
502	#3295	C₂×C₂₃	1	2	yes	complemented
503	#3241	C₂×C₂₃	1	2	yes	complemented
504	#3200	C₂×C₂₃	1	2	yes	complemented
505	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
506	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
507	#3126	C₂×C₂₃	1	2	yes	complemented
508	#3096	C₂×C₂₃	1	2	yes	complemented
509	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
510	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
511	#2976	C₂×C₂₃	1	1	yes	characteristic, complemented
512	C₂²×C₂₃	—	2	1	no	—
513	C₂²×C₂₃	—	2	1	no	—
514	C₂²×C₂₃	—	2	2	no	—
515	C₂²×C₂₃	—	2	1	no	—
516	C₂²×C₂₃	—	2	1	no	—
517	C₂²×C₂₃	—	2	1	no	—
518	C₂²×C₂₃	—	2	1	no	—
519	C₂²×C₂₃	—	2	2	no	—
520	C₂²×C₂₃	—	2	1	no	—
521	C₂²×C₂₃	—	2	2	no	—
522	C₂²×C₂₃	—	2	1	no	—
523	C₂²×C₂₃	—	4	2	no	—
524	C₂²×C₂₃	—	4	2	no	—
525	C₂²×C₂₃	—	4	2	no	—
526	C₂²×C₂₃	—	4	2	no	—
527	C₂²×C₂₃	—	4	2	no	—
528	C₂²×C₂₃	—	4	2	no	—
529	C₂²×C₂₃	—	8	2	no	—
530	C₂²×C₂₃	—	16	2	no	—
531	C₂²×C₂₃	—	16	2	no	—
532	C₂²×C₂₃	—	16	4	no	—
533	C₂²×C₂₃	#577	1	2	yes	—
534	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₂₃	—	2	2	no	—
536	C₄×C₂₃	—	2	1	no	—
537	C₄×C₂₃	—	2	1	no	—
538	C₄×C₂₃	—	2	1	no	—
539	C₄×C₂₃	—	2	2	no	—
540	C₄×C₂₃	—	2	2	no	—
541	C₄×C₂₃	—	4	1	no	—
542	C₄×C₂₃	—	4	2	no	—
543	C₄×C₂₃	—	4	2	no	—
544	C₄×C₂₃	—	4	1	no	—
545	C₄×C₂₃	—	4	2	no	—
546	C₄×C₂₃	—	4	1	no	—
547	C₄×C₂₃	—	4	1	no	—
548	C₄×C₂₃	—	4	2	no	—
549	C₄×C₂₃	#585	1	1	yes	characteristic
550	C₄×C₂₃	#585	1	1	yes	characteristic
551	#560	—	2	2	no	—
552	#556	C₂²×C₂₃	1	2	yes	complemented
553	#554	C₂²×C₂₃	1	2	yes	complemented
554	#553	C₂²×C₂₃	1	2	yes	—
555	#553	C₂²×C₂₃	1	2	yes	—
556	#552	—	2	2	no	—
557	#552	C₂²×C₂₃	1	2	yes	complemented
558	#552	C₂²×C₂₃	1	2	yes	complemented
559	#551	—	2	2	no	—
560	D₄²	—	2	2	no	—
561	D₄²	C₂²×C₂₃	1	2	yes	—
562	D₄²	C₂²×C₂₃	1	2	yes	—
563	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	#542	—	2	1	no	—
565	#541	—	2	1	no	—
566	#540	C₂²×C₂₃	1	2	yes	—
567	#538	—	2	1	no	—
568	#538	—	2	1	no	—
569	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	#535	C₂²×C₂₃	1	2	yes	—
571	#534	—	2	1	no	—
572	#534	—	2	1	no	—
573	#533	—	2	1	no	—
574	#529	—	2	1	no	—
575	#525	C₂²×C₂₃	1	1	yes	characteristic
576	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
577	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
578	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
579	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
580	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
581	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
582	#501	C₂²×C₂₃	1	2	yes	complemented
583	#499	C₂²×C₂₃	1	2	yes	complemented
584	#490	C₂²×C₂₃	1	2	yes	complemented
585	#486	C₂²×C₂₃	1	2	yes	complemented
586	#485	C₂²×C₂₃	1	2	yes	complemented
587	#485	C₂²×C₂₃	1	2	yes	complemented
588	#484	C₂²×C₂₃	1	2	yes	complemented
589	#483	C₂²×C₂₃	1	2	yes	complemented
590	#482	C₂²×C₂₃	1	2	yes	complemented
591	#482	C₂²×C₂₃	1	2	yes	complemented
592	#482	C₂²×C₂₃	1	2	yes	complemented
593	#482	C₂²×C₂₃	1	2	yes	complemented
594	#482	C₂²×C₂₃	1	2	yes	complemented
595	#482	C₂²×C₂₃	1	2	yes	complemented
596	#482	C₂²×C₂₃	1	2	yes	complemented
597	#482	C₂²×C₂₃	1	2	yes	complemented
598	#481	C₂²×C₂₃	1	2	yes	complemented
599	#481	C₂²×C₂₃	1	2	yes	complemented
600	#481	C₂²×C₂₃	1	2	yes	complemented
601	#480	C₂²×C₂₃	1	2	yes	complemented
602	#480	C₂²×C₂₃	1	2	yes	complemented
603	#480	C₂²×C₂₃	1	2	yes	complemented
604	#479	C₂²×C₂₃	1	2	yes	complemented
605	#479	C₂²×C₂₃	1	2	yes	complemented
606	#478	C₂²×C₂₃	1	2	yes	complemented
607	#478	C₂²×C₂₃	1	2	yes	complemented
608	#476	C₂²×C₂₃	1	2	yes	complemented
609	#474	C₂²×C₂₃	1	2	yes	complemented
610	#468	C₂²×C₂₃	1	2	yes	complemented
611	#468	C₂²×C₂₃	1	2	yes	complemented
612	#468	C₂²×C₂₃	1	2	yes	complemented
613	#468	C₂²×C₂₃	1	2	yes	complemented
614	#465	C₂²×C₂₃	1	2	yes	complemented
615	#465	C₂²×C₂₃	1	2	yes	complemented
616	#465	C₂²×C₂₃	1	2	yes	complemented
617	#465	C₂²×C₂₃	1	2	yes	complemented
618	#460	C₂²×C₂₃	1	2	yes	complemented
619	#460	C₂²×C₂₃	1	2	yes	complemented
620	#450	C₂²×C₂₃	1	2	yes	complemented
621	#450	C₂²×C₂₃	1	2	yes	complemented
622	#450	C₂²×C₂₃	1	2	yes	complemented
623	#450	C₂²×C₂₃	1	2	yes	complemented
624	#448	C₂²×C₂₃	1	2	yes	complemented
625	#448	C₂²×C₂₃	1	2	yes	complemented
626	#440	C₂²×C₂₃	1	2	yes	complemented
627	#440	C₂²×C₂₃	1	2	yes	complemented
628	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
629	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
630	#436	C₂²×C₂₃	1	2	yes	complemented
631	#435	C₂²×C₂₃	1	2	yes	complemented
632	#435	C₂²×C₂₃	1	2	yes	complemented
633	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
634	#433	C₂²×C₂₃	1	2	yes	complemented
635	#428	C₂²×C₂₃	1	2	yes	complemented
636	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
637	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
638	#427	C₂²×C₂₃	1	2	yes	complemented
639	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	#418	C₂²×C₂₃	1	2	yes	complemented
644	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
647	#408	C₂²×C₂₃	1	2	yes	complemented
648	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	C₂×C₂₃	—	2	2	no	—
651	C₂×C₂₃	—	4	1	no	—
652	C₂×C₂₃	—	4	1	no	—
653	C₂×C₂₃	—	4	2	no	—
654	C₂×C₂₃	—	8	2	no	—
655	C₂×C₂₃	—	8	2	no	—
656	C₂×C₂₃	#3485	1	1	yes	characteristic
657	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
658	C₂×C₂₃	#3585	1	1	yes	characteristic
659	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
660	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
661	C₂²×D₄	—	2	1	no	—
662	C₂²×D₄	—	2	1	no	—
663	C₂²×D₄	—	2	2	no	—
664	C₂²×D₄	—	2	2	no	—
665	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
668	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
669	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
671	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
673	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
674	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
675	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
676	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
678	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
682	#127	—	2	2	no	—
683	#127	C₂³×C₂₃	1	2	yes	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#126	—	2	2	no	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#125	—	2	1	no	—
691	#125	—	2	2	no	—
692	#125	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	C₂³×C₂₃	1	2	yes	—
695	#125	C₂³×C₂₃	1	2	yes	—
696	#124	—	2	2	no	—
697	#124	—	2	1	no	—
698	#124	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	D₄×C₂₃	1	2	yes	—
707	C₂²⋊Q₈	—	2	1	no	—
708	C₂²⋊Q₈	—	2	1	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
713	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
714	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
715	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
716	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
717	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	1	no	—
721	#121	—	2	1	no	—
722	#121	—	2	1	no	—
723	#121	—	2	1	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	D₄×C₂₃	1	1	yes	characteristic
729	#121	D₄×C₂₃	1	1	yes	characteristic
730	#121	C₂³×C₂₃	1	2	yes	—
731	#121	C₂³×C₂₃	1	2	yes	—
732	#121	C₂³×C₂₃	1	2	yes	—
733	#121	C₂³×C₂₃	1	2	yes	—
734	#121	C₂³×C₂₃	1	2	yes	—
735	#121	C₂³×C₂₃	1	2	yes	—
736	#120	—	2	2	no	—
737	#120	—	2	2	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	—	2	2	no	—
741	#120	—	2	2	no	—
742	#120	D₄×C₂₃	1	2	yes	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
748	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	C₂³×C₂₃	1	2	yes	—
755	C₄×D₄	C₂³×C₂₃	1	2	yes	—
756	C₄×D₄	C₂³×C₂₃	1	2	yes	—
757	C₄×D₄	C₂³×C₂₃	1	2	yes	—
758	#117	—	2	1	no	—
759	#117	—	2	1	no	—
760	#117	—	2	2	no	—
761	#117	—	2	2	no	—
762	#117	—	2	2	no	—
763	#117	C₂³×C₂₃	1	1	yes	characteristic
764	#117	C₂³×C₂₃	1	1	yes	characteristic
765	#117	C₂³×C₂₃	1	1	yes	characteristic
766	#117	C₂³×C₂₃	1	1	yes	characteristic
767	#117	C₂³×C₂₃	1	2	yes	—
768	#117	C₂³×C₂₃	1	2	yes	—
769	#117	C₂³×C₂₃	1	1	yes	characteristic
770	C₂×C₄⋊C₄	—	2	1	no	—
771	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
774	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	—	2	1	no	—
778	C₂×C₂²⋊C₄	—	2	1	no	—
779	C₂×C₂²⋊C₄	—	2	1	no	—
780	C₂×C₂²⋊C₄	—	2	1	no	—
781	C₂×C₄²	—	2	1	no	—
782	#107	C₂³×C₂₃	1	2	yes	—
783	#107	C₂³×C₂₃	1	2	yes	—
784	#107	C₂³×C₂₃	1	2	yes	—
785	#107	C₂³×C₂₃	1	2	yes	—
786	#107	C₂³×C₂₃	1	2	yes	—
787	#107	C₂³×C₂₃	1	2	yes	—
788	#106	C₂³×C₂₃	1	2	yes	—
789	#106	C₂³×C₂₃	1	2	yes	—
790	#106	C₂³×C₂₃	1	2	yes	—
791	#106	C₂³×C₂₃	1	2	yes	—
792	#106	C₂³×C₂₃	1	2	yes	—
793	#106	C₂³×C₂₃	1	2	yes	—
794	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
795	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
796	#103	C₂³×C₂₃	1	2	yes	—
797	#103	C₂³×C₂₃	1	2	yes	—
798	#103	C₂³×C₂₃	1	2	yes	—
799	#103	C₂³×C₂₃	1	2	yes	—
800	#102	C₂³×C₂₃	1	2	yes	—
801	#102	C₂³×C₂₃	1	2	yes	—
802	#102	C₂³×C₂₃	1	2	yes	—
803	#102	C₂³×C₂₃	1	2	yes	—
804	#102	C₂³×C₂₃	1	2	yes	—
805	#102	C₂³×C₂₃	1	2	yes	—
806	#102	C₂³×C₂₃	1	2	yes	—
807	#102	C₂³×C₂₃	1	2	yes	—
808	#102	C₂³×C₂₃	1	2	yes	—
809	#102	C₂³×C₂₃	1	2	yes	—
810	#102	C₂³×C₂₃	1	2	yes	—
811	#102	C₂³×C₂₃	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
813	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
814	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
815	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
818	#97	C₂³×C₂₃	1	2	yes	—
819	C₄×C₈	C₂³×C₂₃	1	2	yes	—
820	C₂₃	#61756	1	1	yes	characteristic, direct product factor, Sylow
821	C₂⁴	—	2	1	no	—
822	C₂⁴	—	2	1	no	—
823	C₂⁴	—	2	2	no	—
824	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
825	#41	—	4	1	no	—
826	#41	—	4	1	no	—
827	C₂×Q₈	—	2	1	no	—
828	C₂×Q₈	—	2	2	no	—
829	C₂×Q₈	—	4	1	no	—
830	C₂×Q₈	—	4	1	no	—
831	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
832	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	4	1	no	—
845	C₂×D₄	—	4	1	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	1	no	—
848	C₂×D₄	—	4	1	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	8	4	no	—
851	C₂×D₄	—	8	2	no	—
852	C₂×D₄	—	8	4	no	—
853	C₂×D₄	—	8	2	no	—
854	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
855	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
857	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
858	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
859	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	1	no	—
871	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
872	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
873	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
878	SD₁₆	—	4	2	no	—
879	SD₁₆	—	4	2	no	—
880	SD₁₆	—	4	2	no	—
881	SD₁₆	—	4	2	no	—
882	M₁₆	—	4	1	no	—
883	M₁₆	—	4	2	no	—
884	M₁₆	—	4	1	no	—
885	C₂×C₈	—	4	1	no	—
886	C₂×C₈	—	4	2	no	—
887	C₂×C₈	—	4	1	no	—
888	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
889	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
890	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
891	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
910	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
912	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
913	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
914	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
915	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
919	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
920	C₂²⋊C₄	—	2	1	no	—
921	C₂²⋊C₄	—	2	1	no	—
922	C₂²⋊C₄	—	2	1	no	—
923	C₂²⋊C₄	—	2	1	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
939	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
940	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
941	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
942	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
943	C₄²	—	2	1	no	—
944	C₄²	—	2	1	no	—
945	C₄²	—	2	1	no	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	C₂⁴×C₂₃	1	2	yes	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	4	1	no	—
956	C₂³	—	4	1	no	—
957	C₂³	—	4	2	no	—
958	C₂³	—	4	2	no	—
959	C₂³	—	8	1	no	—
960	C₂³	—	8	1	no	—
961	C₂³	—	8	2	no	—
962	C₂³	—	8	1	no	—
963	C₂³	—	8	1	no	—
964	C₂³	—	8	2	no	—
965	C₂³	—	8	2	no	—
966	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
967	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
968	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
969	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	4	1	no	—
973	Q₈	—	4	2	no	—
974	Q₈	—	8	2	no	—
975	D₄	—	2	4	no	—
976	D₄	—	2	2	no	—
977	D₄	—	2	2	no	—
978	D₄	—	2	2	no	—
979	D₄	—	2	2	no	—
980	D₄	—	4	2	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	2	no	—
983	D₄	—	4	4	no	—
984	D₄	—	4	4	no	—
985	D₄	—	8	1	no	—
986	D₄	—	8	1	no	—
987	D₄	—	8	2	no	—
988	D₄	—	8	2	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	2	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	1	no	—
1018	C₂×C₄	—	8	1	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	1	no	—
1022	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1025	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1028	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1029	C₈	—	2	2	no	—
1030	C₈	—	2	2	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	8	2	no	—
1051	C₂²	—	16	2	no	—
1052	C₂²	—	16	2	no	—
1053	C₂²	—	16	4	no	—
1054	C₂²	C₂₃×#577	1	2	yes	—
1055	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	C₂₃×#585	1	1	yes	characteristic
1071	C₄	C₂₃×#585	1	1	yes	characteristic
1072	C₂	—	2	2	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	4	1	no	—
1075	C₂	—	4	2	no	—
1076	C₂	—	8	2	no	—
1077	C₂	—	8	2	no	—
1078	C₂	C₂₃×#3485	1	1	yes	characteristic
1079	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1080	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3537	C₂
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
2. C₂₃×#3495	C₂	semidirect
3. C₂₃×#3351	C₂	semidirect
4. C₂₃×#3350	C₂	semidirect
5. C₂₃×#3346	C₂	semidirect
6. C₂₃×#3337	C₂	semidirect
7. C₂₃×#3324	C₂	semidirect
8. C₂₃×#3310	C₂	semidirect
9. C₂₃×#3310	C₂	semidirect
10. C₂₃×#3295	C₂	semidirect
11. C₂₃×#3241	C₂	semidirect
12. C₂₃×#3200	C₂	semidirect
13. C₂₃×#3193	C₂	semidirect
14. C₂₃×#3187	C₂	semidirect
15. C₂₃×#3126	C₂	semidirect
16. C₂₃×#3096	C₂	semidirect
17. C₂₃×#3094	C₂	semidirect
18. C₂×C₂₃×#482	C₂	semidirect
19. C₂₃×#2976	C₂	semidirect
21. C₂₃×#556	C₂²	semidirect
22. C₂₃×#554	C₂²	semidirect
26. C₂₃×#552	C₂²	semidirect
27. C₂₃×#552	C₂²	semidirect
32. C₂₃×#544	C₂²	semidirect
38. C₂₃×#536	C₂²	semidirect
45. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂₃×#520	C₂²	semidirect
49. C₂₃×#519	C₂²	semidirect
50. C₂×C₂₃×#117	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#499	C₂²	semidirect
53. C₂₃×#490	C₂²	semidirect
54. C₂₃×#486	C₂²	semidirect
55. C₂₃×#485	C₂²	semidirect
56. C₂₃×#485	C₂²	semidirect
57. C₂₃×#484	C₂²	semidirect
58. C₂₃×#483	C₂²	semidirect
59. C₂₃×#482	C₂²	semidirect
60. C₂₃×#482	C₂²	semidirect
61. C₂₃×#482	C₂²	semidirect
62. C₂₃×#482	C₂²	semidirect
63. C₂₃×#482	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#482	C₂²	semidirect
66. C₂₃×#482	C₂²	semidirect
67. C₂₃×#481	C₂²	semidirect
68. C₂₃×#481	C₂²	semidirect
69. C₂₃×#481	C₂²	semidirect
70. C₂₃×#480	C₂²	semidirect
71. C₂₃×#480	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#478	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#474	C₂²	semidirect
79. C₂₃×#468	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
81. C₂₃×#468	C₂²	semidirect
82. C₂₃×#468	C₂²	semidirect
83. C₂₃×#465	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#465	C₂²	semidirect
87. C₂₃×#460	C₂²	semidirect
88. C₂₃×#460	C₂²	semidirect
89. C₂₃×#450	C₂²	semidirect
90. C₂₃×#450	C₂²	semidirect
91. C₂₃×#450	C₂²	semidirect
92. C₂₃×#450	C₂²	semidirect
93. C₂₃×#448	C₂²	semidirect
94. C₂₃×#448	C₂²	semidirect
95. C₂₃×#440	C₂²	semidirect
96. C₂₃×#440	C₂²	semidirect
97. C₄×SD₁₆×C₂₃	C₂²	semidirect
98. C₄×SD₁₆×C₂₃	C₂²	semidirect
99. C₂₃×#436	C₂²	semidirect
100. C₂₃×#435	C₂²	semidirect
101. C₂₃×#435	C₂²	semidirect
102. C₈×D₄×C₂₃	C₂²	semidirect
103. C₂₃×#433	C₂²	semidirect
104. C₂₃×#428	C₂²	semidirect
105. C₂₃×#428	C₂²	semidirect
106. C₂₃×#428	C₂²	semidirect
107. C₂₃×#427	C₂²	semidirect
108. C₂×C₂₃×#107	C₂²	semidirect
109. C₂×C₂₃×#106	C₂²	semidirect
110. C₂₃×#418	C₂²	semidirect
111. C₂₃×#418	C₂²	semidirect
112. C₂₃×#418	C₂²	semidirect
113. C₂×C₂₃×#102	C₂²	semidirect
114. C₂×C₂₃×#102	C₂²	semidirect
115. C₂×C₂₃×#102	C₂²	semidirect
116. C₂₃×#408	C₂²	semidirect
117. C₂₃×#407	C₂²	semidirect
118. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
411. #61756	C₂₃	direct (N × H)
494. #3495	C₂×C₂₃	semidirect
495. #3351	C₂×C₂₃	semidirect
496. #3350	C₂×C₂₃	semidirect
497. #3346	C₂×C₂₃	semidirect
498. #3337	C₂×C₂₃	semidirect
499. #3324	C₂×C₂₃	semidirect
500. #3310	C₂×C₂₃	semidirect
501. #3310	C₂×C₂₃	semidirect
502. #3295	C₂×C₂₃	semidirect
503. #3241	C₂×C₂₃	semidirect
504. #3200	C₂×C₂₃	semidirect
505. #3193	C₂×C₂₃	semidirect
506. #3187	C₂×C₂₃	semidirect
507. #3126	C₂×C₂₃	semidirect
508. #3096	C₂×C₂₃	semidirect
509. #3094	C₂×C₂₃	semidirect
510. C₂×#482	C₂×C₂₃	semidirect
511. #2976	C₂×C₂₃	semidirect
552. #556	C₂²×C₂₃	semidirect
553. #554	C₂²×C₂₃	semidirect
557. #552	C₂²×C₂₃	semidirect
558. #552	C₂²×C₂₃	semidirect
563. #544	C₂²×C₂₃	semidirect
569. #536	C₂²×C₂₃	semidirect
576. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
579. #520	C₂²×C₂₃	semidirect
580. #519	C₂²×C₂₃	semidirect
581. C₂×#117	C₂²×C₂₃	semidirect
582. #501	C₂²×C₂₃	semidirect
583. #499	C₂²×C₂₃	semidirect
584. #490	C₂²×C₂₃	semidirect
585. #486	C₂²×C₂₃	semidirect
586. #485	C₂²×C₂₃	semidirect
587. #485	C₂²×C₂₃	semidirect
588. #484	C₂²×C₂₃	semidirect
589. #483	C₂²×C₂₃	semidirect
590. #482	C₂²×C₂₃	semidirect
591. #482	C₂²×C₂₃	semidirect
592. #482	C₂²×C₂₃	semidirect
593. #482	C₂²×C₂₃	semidirect
594. #482	C₂²×C₂₃	semidirect
595. #482	C₂²×C₂₃	semidirect
596. #482	C₂²×C₂₃	semidirect
597. #482	C₂²×C₂₃	semidirect
598. #481	C₂²×C₂₃	semidirect
599. #481	C₂²×C₂₃	semidirect
600. #481	C₂²×C₂₃	semidirect
601. #480	C₂²×C₂₃	semidirect
602. #480	C₂²×C₂₃	semidirect
603. #480	C₂²×C₂₃	semidirect
604. #479	C₂²×C₂₃	semidirect
605. #479	C₂²×C₂₃	semidirect
606. #478	C₂²×C₂₃	semidirect
607. #478	C₂²×C₂₃	semidirect
608. #476	C₂²×C₂₃	semidirect
609. #474	C₂²×C₂₃	semidirect
610. #468	C₂²×C₂₃	semidirect
611. #468	C₂²×C₂₃	semidirect
612. #468	C₂²×C₂₃	semidirect
613. #468	C₂²×C₂₃	semidirect
614. #465	C₂²×C₂₃	semidirect
615. #465	C₂²×C₂₃	semidirect
616. #465	C₂²×C₂₃	semidirect
617. #465	C₂²×C₂₃	semidirect
618. #460	C₂²×C₂₃	semidirect
619. #460	C₂²×C₂₃	semidirect
620. #450	C₂²×C₂₃	semidirect
621. #450	C₂²×C₂₃	semidirect
622. #450	C₂²×C₂₃	semidirect
623. #450	C₂²×C₂₃	semidirect
624. #448	C₂²×C₂₃	semidirect
625. #448	C₂²×C₂₃	semidirect
626. #440	C₂²×C₂₃	semidirect
627. #440	C₂²×C₂₃	semidirect
628. C₄×SD₁₆	C₂²×C₂₃	semidirect
629. C₄×SD₁₆	C₂²×C₂₃	semidirect
630. #436	C₂²×C₂₃	semidirect
631. #435	C₂²×C₂₃	semidirect
632. #435	C₂²×C₂₃	semidirect
633. C₈×D₄	C₂²×C₂₃	semidirect
634. #433	C₂²×C₂₃	semidirect
635. #428	C₂²×C₂₃	semidirect
636. #428	C₂²×C₂₃	semidirect
637. #428	C₂²×C₂₃	semidirect
638. #427	C₂²×C₂₃	semidirect
639. C₂×#107	C₂²×C₂₃	semidirect
640. C₂×#106	C₂²×C₂₃	semidirect
641. #418	C₂²×C₂₃	semidirect
642. #418	C₂²×C₂₃	semidirect
643. #418	C₂²×C₂₃	semidirect
644. C₂×#102	C₂²×C₂₃	semidirect
645. C₂×#102	C₂²×C₂₃	semidirect
646. C₂×#102	C₂²×C₂₃	semidirect
647. #408	C₂²×C₂₃	semidirect
648. #407	C₂²×C₂₃	semidirect
649. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
820. C₂₃	#61756	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×#3537	2
C₂₃×#3495	2
C₂₃×#3351	2
C₂₃×#3350	2
C₂₃×#3346	2
C₂₃×#3337	2
C₂₃×#3324	2
C₂₃×#3310	2
C₂₃×#3295	2
C₂₃×#3241	2
C₂₃×#3200	2
C₂₃×#3193	2
C₂₃×#3187	2
C₂₃×#3126	2
C₂₃×#3096	2
C₂₃×#3094	2
C₂×C₂₃×#482	2
C₂₃×#2976	2
#61756	23

Subgroups — C23×#61756 #19209382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61756 #19209382