Subgroups — C₂₃×#61263 #19208889

Order 5888.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3494	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3340	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3335	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#556	C₂²	1	2	yes	complemented
28	C₂₃×#555	C₂²	1	2	yes	—
29	C₂₃×#554	C₂²	1	2	yes	complemented
30	C₂₃×#553	C₂²	1	2	yes	—
31	C₂₃×#553	C₂²	1	2	yes	—
32	C₂₃×#552	—	2	2	no	—
33	C₂₃×#552	C₂²	1	2	yes	complemented
34	C₂₃×#552	C₂²	1	2	yes	complemented
35	C₂₃×#551	—	2	2	no	—
36	C₂₃×#551	—	2	2	no	—
37	C₂₃×#547	C₂²	1	2	yes	—
38	C₂₃×#546	—	2	2	no	—
39	C₂₃×#544	C₂²	1	1	yes	characteristic
40	C₂₃×#544	C₂²	1	1	yes	characteristic
41	C₂₃×#542	—	2	1	no	—
42	C₂₃×#542	—	2	1	no	—
43	C₂₃×#541	—	2	1	no	—
44	C₂₃×#540	—	2	1	no	—
45	C₂₃×#536	C₂²	1	1	yes	characteristic
46	C₂₃×#535	C₂²	1	1	yes	characteristic
47	C₂₃×#533	—	2	1	no	—
48	C₂₃×#532	—	2	1	no	—
49	C₂₃×#529	—	2	1	no	—
50	C₂₃×#529	—	2	1	no	—
51	C₂₃×#525	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
54	C₂₃×#520	C₂²	1	1	yes	characteristic
55	C₂₃×#520	C₂²	1	1	yes	characteristic
56	C₂₃×#519	C₂²	1	1	yes	characteristic
57	C₂₃×#518	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
60	C₂₃×#501	C₂²	1	2	yes	complemented
61	C₂₃×#501	C₂²	1	2	yes	complemented
62	C₂₃×#499	C₂²	1	2	yes	complemented
63	C₂₃×#498	C₂²	1	2	yes	complemented
64	C₂₃×#485	C₂²	1	2	yes	complemented
65	C₂₃×#485	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#484	C₂²	1	2	yes	complemented
69	C₂₃×#484	C₂²	1	2	yes	complemented
70	C₂₃×#483	C₂²	1	2	yes	complemented
71	C₂₃×#483	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	—
73	C₂₃×#482	C₂²	1	2	yes	—
74	C₂₃×#482	C₂²	1	2	yes	complemented
75	C₂₃×#482	C₂²	1	2	yes	complemented
76	C₂₃×#481	C₂²	1	2	yes	—
77	C₂₃×#481	C₂²	1	2	yes	complemented
78	C₂₃×#480	C₂²	1	2	yes	—
79	C₂₃×#480	C₂²	1	2	yes	complemented
80	C₂₃×#479	C₂²	1	2	yes	complemented
81	C₂₃×#479	C₂²	1	2	yes	complemented
82	C₂₃×#478	C₂²	1	2	yes	complemented
83	C₂₃×#478	C₂²	1	2	yes	complemented
84	C₂₃×#477	C₂²	1	2	yes	complemented
85	C₂₃×#476	C₂²	1	2	yes	complemented
86	C₂₃×#475	C₂²	1	2	yes	complemented
87	C₂₃×#474	C₂²	1	2	yes	complemented
88	C₂₃×#468	C₂²	1	2	yes	complemented
89	C₂₃×#468	C₂²	1	2	yes	complemented
90	C₂₃×#465	C₂²	1	2	yes	—
91	C₂₃×#465	C₂²	1	2	yes	—
92	C₂₃×#465	C₂²	1	2	yes	—
93	C₂₃×#465	C₂²	1	2	yes	—
94	C₂₃×#465	C₂²	1	2	yes	complemented
95	C₂₃×#465	C₂²	1	2	yes	complemented
96	C₂₃×#440	C₂²	1	2	yes	complemented
97	C₂₃×#440	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
99	C₄×SD₁₆×C₂₃	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	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
104	C₂₃×#428	C₂²	1	1	yes	characteristic
105	C₂₃×#428	C₂²	1	1	yes	characteristic
106	C₂₃×#428	C₂²	1	1	yes	characteristic
107	C₂₃×#428	C₂²	1	1	yes	characteristic
108	C₂₃×#428	C₂²	1	2	yes	complemented
109	C₂₃×#428	C₂²	1	2	yes	complemented
110	C₂₃×#427	C₂²	1	1	yes	characteristic
111	C₂₃×#427	C₂²	1	1	yes	characteristic
112	C₂₃×#427	C₂²	1	1	yes	characteristic
113	C₂₃×#427	C₂²	1	1	yes	characteristic
114	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
118	C₂₃×#427	C₂²	1	2	yes	complemented
119	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
122	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
125	C₂₃×#424	C₂²	1	1	yes	characteristic
126	C₂₃×#419	C₂²	1	1	yes	characteristic
127	C₂₃×#419	C₂²	1	1	yes	characteristic
128	C₂₃×#418	C₂²	1	1	yes	characteristic
129	C₂₃×#418	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂₃×#407	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₂₃	—	2	1	no	—
139	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₂₃	—	2	4	no	—
142	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂₃×#131	—	2	4	no	—
145	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₂₃	—	2	4	no	—
149	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×#127	—	2	1	no	—
162	C₂₃×#126	—	2	2	no	—
163	C₂₃×#126	—	2	2	no	—
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#125	—	2	2	no	—
169	C₂₃×#125	—	2	2	no	—
170	C₂₃×#125	—	2	2	no	—
171	C₂₃×#125	—	2	1	no	—
172	C₂₃×#125	—	2	1	no	—
173	C₂₃×#125	C₂³	1	2	yes	—
174	C₂₃×#125	C₂³	1	2	yes	—
175	C₂₃×#124	—	2	1	no	—
176	C₂₃×#124	—	2	2	no	—
177	C₂₃×#124	—	2	1	no	—
178	C₂₃×#124	—	2	2	no	—
179	C₂₃×#124	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	—	2	2	no	—
187	C₂₃×#123	D₄	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	—	2	1	no	—
189	C₂₃×C₂²⋊Q₈	—	2	1	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
196	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
197	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	1	no	—
205	C₂₃×#121	—	2	1	no	—
206	C₂₃×#121	D₄	1	1	yes	characteristic
207	C₂₃×#121	D₄	1	1	yes	characteristic
208	C₂₃×#121	C₂³	1	2	yes	—
209	C₂₃×#121	C₂³	1	2	yes	—
210	C₂₃×#121	C₂³	1	2	yes	—
211	C₂₃×#121	C₂³	1	2	yes	—
212	C₂₃×#120	—	2	2	no	—
213	C₂₃×#120	D₄	1	2	yes	—
214	C₄×Q₈×C₂₃	—	2	1	no	—
215	C₄×Q₈×C₂₃	—	2	1	no	—
216	C₄×Q₈×C₂₃	—	2	2	no	—
217	C₄×Q₈×C₂₃	—	2	1	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
221	C₄×D₄×C₂₃	—	2	2	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	—	2	1	no	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	1	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	C₂³	1	2	yes	—
231	C₄×D₄×C₂₃	C₂³	1	2	yes	—
232	C₄×D₄×C₂₃	C₂³	1	2	yes	—
233	C₄×D₄×C₂₃	C₂³	1	2	yes	—
234	C₂₃×#117	—	2	1	no	—
235	C₂₃×#117	—	2	1	no	—
236	C₂₃×#117	—	2	1	no	—
237	C₂₃×#117	—	2	1	no	—
238	C₂₃×#117	—	2	2	no	—
239	C₂₃×#117	—	2	2	no	—
240	C₂₃×#117	—	2	2	no	—
241	C₂₃×#117	—	2	2	no	—
242	C₂₃×#117	C₂³	1	1	yes	characteristic
243	C₂₃×#117	C₂³	1	2	yes	—
244	C₂₃×#117	C₂³	1	1	yes	characteristic
245	C₂₃×#117	C₂³	1	2	yes	—
246	C₂₃×#117	C₂³	1	1	yes	characteristic
247	C₂₃×#117	C₂³	1	1	yes	characteristic
248	C₂₃×#117	C₂³	1	1	yes	characteristic
249	C₂₃×#117	C₂³	1	1	yes	characteristic
250	C₂₃×#117	C₂³	1	1	yes	characteristic
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂×C₄²×C₂₃	—	2	1	no	—
268	C₂×C₄²×C₂₃	—	2	1	no	—
269	C₂₃×#107	C₂³	1	1	yes	characteristic
270	C₂₃×#107	C₂³	1	1	yes	characteristic
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	1	yes	characteristic
273	C₂₃×#107	C₂³	1	1	yes	characteristic
274	C₂₃×#107	C₂³	1	1	yes	characteristic
275	C₂₃×#107	C₂³	1	1	yes	characteristic
276	C₂₃×#107	C₂³	1	1	yes	characteristic
277	C₂₃×#107	C₂³	1	2	yes	—
278	C₂₃×#107	C₂³	1	2	yes	—
279	C₂₃×#107	C₂³	1	2	yes	—
280	C₂₃×#107	C₂³	1	2	yes	—
281	C₂₃×#106	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	1	yes	characteristic
284	C₂₃×#106	C₂³	1	1	yes	characteristic
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	1	yes	characteristic
287	C₂₃×#106	C₂³	1	1	yes	characteristic
288	C₂₃×#106	C₂³	1	1	yes	characteristic
289	C₂₃×#106	C₂³	1	1	yes	characteristic
290	C₂₃×#106	C₂³	1	1	yes	characteristic
291	C₂₃×#106	C₂³	1	2	yes	—
292	C₂₃×#106	C₂³	1	2	yes	—
293	C₂₃×#106	C₂³	1	2	yes	—
294	C₂₃×#106	C₂³	1	2	yes	—
295	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
296	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#103	C₂³	1	2	yes	—
300	C₂₃×#103	C₂³	1	2	yes	—
301	C₂₃×#103	C₂³	1	2	yes	—
302	C₂₃×#103	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₂⁴×C₂₃	—	2	1	no	—
316	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
317	#41×C₂₃	—	2	2	no	—
318	#41×C₂₃	—	2	2	no	—
319	#41×C₂₃	—	8	4	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	2	no	—
322	C₂×Q₈×C₂₃	—	2	2	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	—	2	2	no	—
325	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	2	no	—
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	2	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	8	2	no	—
335	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₂₃	—	2	2	no	—
341	C₂²×C₄×C₂₃	—	2	2	no	—
342	C₂²×C₄×C₂₃	—	2	1	no	—
343	C₂²×C₄×C₂₃	—	2	1	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	1	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	1	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	SD₁₆×C₂₃	—	2	4	no	—
361	SD₁₆×C₂₃	—	2	4	no	—
362	M₁₆×C₂₃	—	2	2	no	—
363	M₁₆×C₂₃	—	2	2	no	—
364	M₁₆×C₂₃	—	2	4	no	—
365	C₂×C₈×C₂₃	—	2	2	no	—
366	C₂×C₈×C₂₃	—	2	2	no	—
367	C₂×C₈×C₂₃	—	2	2	no	—
368	C₂×C₈×C₂₃	—	2	2	no	—
369	C₂×C₈×C₂₃	—	2	2	no	—
370	C₂×C₈×C₂₃	—	2	4	no	—
371	C₂×C₈×C₂₃	#41	1	4	yes	complemented
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
376	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	1	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	2	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	1	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	1	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	1	no	—
418	C₂²⋊C₄×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
437	C₄²×C₂₃	—	2	1	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	1	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	—	2	1	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	—	2	2	no	—
448	C₄²×C₂₃	—	2	2	no	—
449	C₄²×C₂₃	C₂⁴	1	2	yes	—
450	#61263	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂³×C₂₃	—	2	2	no	—
452	C₂³×C₂₃	—	2	2	no	—
453	C₂³×C₂₃	—	2	2	no	—
454	C₂³×C₂₃	—	4	1	no	—
455	C₂³×C₂₃	—	4	2	no	—
456	C₂³×C₂₃	—	8	1	no	—
457	C₂³×C₂₃	—	8	1	no	—
458	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
460	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₂₃	—	2	2	no	—
463	Q₈×C₂₃	—	2	2	no	—
464	Q₈×C₂₃	—	2	2	no	—
465	Q₈×C₂₃	—	4	2	no	—
466	Q₈×C₂₃	—	8	2	no	—
467	Q₈×C₂₃	—	8	2	no	—
468	D₄×C₂₃	—	2	4	no	—
469	D₄×C₂₃	—	2	4	no	—
470	D₄×C₂₃	—	2	2	no	—
471	D₄×C₂₃	—	2	2	no	—
472	D₄×C₂₃	—	2	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	4	4	no	—
475	D₄×C₂₃	—	4	2	no	—
476	D₄×C₂₃	—	8	2	no	—
477	D₄×C₂₃	—	8	2	no	—
478	D₄×C₂₃	—	8	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	2	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	2	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	1	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	2	no	—
499	C₂×C₄×C₂₃	—	4	2	no	—
500	C₂×C₄×C₂₃	—	4	2	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	8	2	no	—
503	C₂×C₄×C₂₃	—	8	2	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	—	8	1	no	—
506	C₂×C₄×C₂₃	—	8	1	no	—
507	C₂×C₄×C₂₃	—	8	1	no	—
508	C₂×C₄×C₂₃	—	8	1	no	—
509	C₂×C₄×C₂₃	—	8	2	no	—
510	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
517	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
518	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
519	C₈×C₂₃	—	2	1	no	—
520	C₈×C₂₃	—	2	1	no	—
521	C₈×C₂₃	—	2	2	no	—
522	C₈×C₂₃	—	2	2	no	—
523	C₈×C₂₃	C₂×#41	1	2	yes	—
524	C₈×C₂₃	C₂×#41	1	2	yes	—
525	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3494	C₂×C₂₃	1	1	yes	characteristic
527	#3350	C₂×C₂₃	1	2	yes	complemented
528	#3348	C₂×C₂₃	1	2	yes	complemented
529	#3346	C₂×C₂₃	1	2	yes	complemented
530	#3343	C₂×C₂₃	1	2	yes	complemented
531	#3340	C₂×C₂₃	1	2	yes	complemented
532	#3337	C₂×C₂₃	1	2	yes	complemented
533	#3337	C₂×C₂₃	1	2	yes	complemented
534	#3335	C₂×C₂₃	1	2	yes	complemented
535	#3163	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3096	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3082	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3081	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3057	C₂×C₂₃	1	1	yes	characteristic, complemented
543	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#2949	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#2912	C₂×C₂₃	1	1	yes	characteristic, complemented
547	C₂×#427	C₂×C₂₃	1	1	yes	characteristic, complemented
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	1	no	—
550	C₂²×C₂₃	—	2	1	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	2	no	—
553	C₂²×C₂₃	—	2	1	no	—
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	2	no	—
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	2	1	no	—
558	C₂²×C₂₃	—	4	4	no	—
559	C₂²×C₂₃	—	4	2	no	—
560	C₂²×C₂₃	—	4	2	no	—
561	C₂²×C₂₃	—	4	2	no	—
562	C₂²×C₂₃	—	16	2	no	—
563	C₂²×C₂₃	#547	1	2	yes	—
564	C₂²×C₂₃	#577	1	2	yes	—
565	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₂₃	—	2	2	no	—
567	C₄×C₂₃	—	2	1	no	—
568	C₄×C₂₃	—	2	1	no	—
569	C₄×C₂₃	—	2	2	no	—
570	C₄×C₂₃	—	2	2	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	2	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	1	no	—
576	C₄×C₂₃	—	4	2	no	—
577	C₄×C₂₃	—	4	1	no	—
578	C₄×C₂₃	—	4	1	no	—
579	C₄×C₂₃	—	4	1	no	—
580	C₄×C₂₃	—	4	1	no	—
581	C₄×C₂₃	—	4	2	no	—
582	C₄×C₂₃	#547	1	2	yes	—
583	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
584	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
585	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
586	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
587	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
588	#556	C₂²×C₂₃	1	2	yes	complemented
589	#555	C₂²×C₂₃	1	2	yes	—
590	#554	C₂²×C₂₃	1	2	yes	complemented
591	#553	C₂²×C₂₃	1	2	yes	—
592	#553	C₂²×C₂₃	1	2	yes	—
593	#552	—	2	2	no	—
594	#552	C₂²×C₂₃	1	2	yes	complemented
595	#552	C₂²×C₂₃	1	2	yes	complemented
596	#551	—	2	2	no	—
597	#551	—	2	2	no	—
598	#547	C₂²×C₂₃	1	2	yes	—
599	#546	—	2	2	no	—
600	#544	C₂²×C₂₃	1	1	yes	characteristic
601	#544	C₂²×C₂₃	1	1	yes	characteristic
602	#542	—	2	1	no	—
603	#542	—	2	1	no	—
604	#541	—	2	1	no	—
605	#540	—	2	1	no	—
606	#536	C₂²×C₂₃	1	1	yes	characteristic
607	#535	C₂²×C₂₃	1	1	yes	characteristic
608	#533	—	2	1	no	—
609	#532	—	2	1	no	—
610	#529	—	2	1	no	—
611	#529	—	2	1	no	—
612	#525	C₂²×C₂₃	1	1	yes	characteristic
613	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
614	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
615	#520	C₂²×C₂₃	1	1	yes	characteristic
616	#520	C₂²×C₂₃	1	1	yes	characteristic
617	#519	C₂²×C₂₃	1	1	yes	characteristic
618	#518	C₂²×C₂₃	1	1	yes	characteristic
619	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
620	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
621	#501	C₂²×C₂₃	1	2	yes	complemented
622	#501	C₂²×C₂₃	1	2	yes	complemented
623	#499	C₂²×C₂₃	1	2	yes	complemented
624	#498	C₂²×C₂₃	1	2	yes	complemented
625	#485	C₂²×C₂₃	1	2	yes	complemented
626	#485	C₂²×C₂₃	1	2	yes	complemented
627	#485	C₂²×C₂₃	1	2	yes	complemented
628	#485	C₂²×C₂₃	1	2	yes	complemented
629	#484	C₂²×C₂₃	1	2	yes	complemented
630	#484	C₂²×C₂₃	1	2	yes	complemented
631	#483	C₂²×C₂₃	1	2	yes	complemented
632	#483	C₂²×C₂₃	1	2	yes	complemented
633	#482	C₂²×C₂₃	1	2	yes	—
634	#482	C₂²×C₂₃	1	2	yes	—
635	#482	C₂²×C₂₃	1	2	yes	complemented
636	#482	C₂²×C₂₃	1	2	yes	complemented
637	#481	C₂²×C₂₃	1	2	yes	—
638	#481	C₂²×C₂₃	1	2	yes	complemented
639	#480	C₂²×C₂₃	1	2	yes	—
640	#480	C₂²×C₂₃	1	2	yes	complemented
641	#479	C₂²×C₂₃	1	2	yes	complemented
642	#479	C₂²×C₂₃	1	2	yes	complemented
643	#478	C₂²×C₂₃	1	2	yes	complemented
644	#478	C₂²×C₂₃	1	2	yes	complemented
645	#477	C₂²×C₂₃	1	2	yes	complemented
646	#476	C₂²×C₂₃	1	2	yes	complemented
647	#475	C₂²×C₂₃	1	2	yes	complemented
648	#474	C₂²×C₂₃	1	2	yes	complemented
649	#468	C₂²×C₂₃	1	2	yes	complemented
650	#468	C₂²×C₂₃	1	2	yes	complemented
651	#465	C₂²×C₂₃	1	2	yes	—
652	#465	C₂²×C₂₃	1	2	yes	—
653	#465	C₂²×C₂₃	1	2	yes	—
654	#465	C₂²×C₂₃	1	2	yes	—
655	#465	C₂²×C₂₃	1	2	yes	complemented
656	#465	C₂²×C₂₃	1	2	yes	complemented
657	#440	C₂²×C₂₃	1	2	yes	complemented
658	#440	C₂²×C₂₃	1	2	yes	complemented
659	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
660	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
661	#435	C₂²×C₂₃	1	2	yes	complemented
662	#435	C₂²×C₂₃	1	2	yes	complemented
663	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
664	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
665	#428	C₂²×C₂₃	1	1	yes	characteristic
666	#428	C₂²×C₂₃	1	1	yes	characteristic
667	#428	C₂²×C₂₃	1	1	yes	characteristic
668	#428	C₂²×C₂₃	1	1	yes	characteristic
669	#428	C₂²×C₂₃	1	2	yes	complemented
670	#428	C₂²×C₂₃	1	2	yes	complemented
671	#427	C₂²×C₂₃	1	1	yes	characteristic
672	#427	C₂²×C₂₃	1	1	yes	characteristic
673	#427	C₂²×C₂₃	1	1	yes	characteristic
674	#427	C₂²×C₂₃	1	1	yes	characteristic
675	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#427	C₂²×C₂₃	1	2	yes	complemented
677	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
683	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
685	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#424	C₂²×C₂₃	1	1	yes	characteristic
687	#419	C₂²×C₂₃	1	1	yes	characteristic
688	#419	C₂²×C₂₃	1	1	yes	characteristic
689	#418	C₂²×C₂₃	1	1	yes	characteristic
690	#418	C₂²×C₂₃	1	1	yes	characteristic
691	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
692	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
693	#408	C₂²×C₂₃	1	1	yes	characteristic
694	#407	C₂²×C₂₃	1	1	yes	characteristic
695	#405	C₂²×C₂₃	1	1	yes	characteristic
696	C₂×C₂₃	—	2	2	no	—
697	C₂×C₂₃	—	2	2	no	—
698	C₂×C₂₃	—	4	2	no	—
699	C₂×C₂₃	—	4	1	no	—
700	C₂×C₂₃	—	8	2	no	—
701	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
702	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
703	C₂×C₂₃	#3584	1	1	yes	characteristic
704	C₂×#41	—	2	2	no	—
705	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
709	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
710	C₂×SD₁₆	—	2	4	no	—
711	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
713	#131	—	2	4	no	—
714	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
715	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
716	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
717	C₂²×C₈	—	2	4	no	—
718	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
722	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
724	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
730	#127	—	2	1	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	C₂³×C₂₃	1	2	yes	—
743	#125	C₂³×C₂₃	1	2	yes	—
744	#124	—	2	1	no	—
745	#124	—	2	1	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	D₄×C₂₃	1	2	yes	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
765	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	D₄×C₂₃	1	1	yes	characteristic
776	#121	D₄×C₂₃	1	1	yes	characteristic
777	#121	C₂³×C₂₃	1	2	yes	—
778	#121	C₂³×C₂₃	1	2	yes	—
779	#121	C₂³×C₂₃	1	2	yes	—
780	#121	C₂³×C₂₃	1	2	yes	—
781	#120	—	2	2	no	—
782	#120	D₄×C₂₃	1	2	yes	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
789	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	C₂³×C₂₃	1	2	yes	—
800	C₄×D₄	C₂³×C₂₃	1	2	yes	—
801	C₄×D₄	C₂³×C₂₃	1	2	yes	—
802	C₄×D₄	C₂³×C₂₃	1	2	yes	—
803	#117	—	2	1	no	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	C₂³×C₂₃	1	1	yes	characteristic
812	#117	C₂³×C₂₃	1	1	yes	characteristic
813	#117	C₂³×C₂₃	1	1	yes	characteristic
814	#117	C₂³×C₂₃	1	1	yes	characteristic
815	#117	C₂³×C₂₃	1	1	yes	characteristic
816	#117	C₂³×C₂₃	1	1	yes	characteristic
817	#117	C₂³×C₂₃	1	1	yes	characteristic
818	#117	C₂³×C₂₃	1	1	yes	characteristic
819	#117	C₂³×C₂₃	1	2	yes	—
820	#117	C₂³×C₂₃	1	2	yes	—
821	#117	C₂³×C₂₃	1	1	yes	characteristic
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
825	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
830	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₂²⋊C₄	—	2	1	no	—
833	C₂×C₂²⋊C₄	—	2	1	no	—
834	C₂×C₂²⋊C₄	—	2	1	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₄²	—	2	1	no	—
837	C₂×C₄²	—	2	1	no	—
838	#107	C₂³×C₂₃	1	1	yes	characteristic
839	#107	C₂³×C₂₃	1	1	yes	characteristic
840	#107	C₂³×C₂₃	1	1	yes	characteristic
841	#107	C₂³×C₂₃	1	1	yes	characteristic
842	#107	C₂³×C₂₃	1	1	yes	characteristic
843	#107	C₂³×C₂₃	1	1	yes	characteristic
844	#107	C₂³×C₂₃	1	1	yes	characteristic
845	#107	C₂³×C₂₃	1	1	yes	characteristic
846	#107	C₂³×C₂₃	1	2	yes	—
847	#107	C₂³×C₂₃	1	2	yes	—
848	#107	C₂³×C₂₃	1	2	yes	—
849	#107	C₂³×C₂₃	1	2	yes	—
850	#106	C₂³×C₂₃	1	2	yes	—
851	#106	C₂³×C₂₃	1	2	yes	—
852	#106	C₂³×C₂₃	1	1	yes	characteristic
853	#106	C₂³×C₂₃	1	1	yes	characteristic
854	#106	C₂³×C₂₃	1	1	yes	characteristic
855	#106	C₂³×C₂₃	1	1	yes	characteristic
856	#106	C₂³×C₂₃	1	1	yes	characteristic
857	#106	C₂³×C₂₃	1	1	yes	characteristic
858	#106	C₂³×C₂₃	1	1	yes	characteristic
859	#106	C₂³×C₂₃	1	1	yes	characteristic
860	#106	C₂³×C₂₃	1	2	yes	—
861	#106	C₂³×C₂₃	1	2	yes	—
862	#106	C₂³×C₂₃	1	2	yes	—
863	#106	C₂³×C₂₃	1	2	yes	—
864	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	2	yes	—
867	#103	C₂³×C₂₃	1	2	yes	—
868	#103	C₂³×C₂₃	1	2	yes	—
869	#103	C₂³×C₂₃	1	2	yes	—
870	#103	C₂³×C₂₃	1	2	yes	—
871	#103	C₂³×C₂₃	1	2	yes	—
872	#102	C₂³×C₂₃	1	2	yes	—
873	#102	C₂³×C₂₃	1	2	yes	—
874	#102	C₂³×C₂₃	1	2	yes	—
875	#102	C₂³×C₂₃	1	2	yes	—
876	#102	C₂³×C₂₃	1	2	yes	—
877	#102	C₂³×C₂₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
882	#97	C₂³×C₂₃	1	2	yes	—
883	C₄×C₈	C₂³×C₂₃	1	2	yes	—
884	C₂₃	#61263	1	1	yes	characteristic, direct product factor, Sylow
885	C₂⁴	—	2	1	no	—
886	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
887	#41	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	8	4	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	8	2	no	—
905	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
906	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
907	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
908	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
909	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
924	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
925	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	4	no	—
932	M₁₆	—	2	2	no	—
933	M₁₆	—	2	2	no	—
934	M₁₆	—	2	4	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	4	no	—
941	C₂×C₈	#41×C₂₃	1	4	yes	complemented
942	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
943	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
945	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₂₃	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂⁴×C₂₃	1	2	yes	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	2	no	—
1025	C₂³	—	8	1	no	—
1026	C₂³	—	8	1	no	—
1027	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1028	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1029	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1030	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	—	8	2	no	—
1037	D₄	—	2	4	no	—
1038	D₄	—	2	4	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1085	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1086	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1087	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	2	no	—
1092	C₈	C₂×#41×C₂₃	1	2	yes	—
1093	C₈	C₂×#41×C₂₃	1	2	yes	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	4	4	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	16	2	no	—
1109	C₂²	C₂₃×#547	1	2	yes	—
1110	C₂²	C₂₃×#577	1	2	yes	—
1111	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	2	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	C₂₃×#547	1	2	yes	—
1129	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1130	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1131	C₂	—	2	2	no	—
1132	C₂	—	2	2	no	—
1133	C₂	—	4	1	no	—
1134	C₂	—	4	2	no	—
1135	C₂	—	8	2	no	—
1136	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
1137	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1138	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3494	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
1. C₂₃×#3495	C₂	semidirect
3. C₂₃×#3350	C₂	semidirect
4. C₂₃×#3348	C₂	semidirect
5. C₂₃×#3346	C₂	semidirect
6. C₂₃×#3343	C₂	semidirect
7. C₂₃×#3340	C₂	semidirect
8. C₂₃×#3337	C₂	semidirect
9. C₂₃×#3337	C₂	semidirect
10. C₂₃×#3335	C₂	semidirect
11. C₂₃×#3163	C₂	semidirect
12. C₂₃×#3097	C₂	semidirect
13. C₂₃×#3096	C₂	semidirect
14. C₂₃×#3095	C₂	semidirect
15. C₂₃×#3094	C₂	semidirect
16. C₂₃×#3082	C₂	semidirect
17. C₂₃×#3081	C₂	semidirect
18. C₂₃×#3057	C₂	semidirect
19. C₂×C₂₃×#465	C₂	semidirect
20. C₂₃×#2949	C₂	semidirect
21. C₂₃×#2929	C₂	semidirect
22. C₂₃×#2912	C₂	semidirect
23. C₂×C₂₃×#427	C₂	semidirect
27. C₂₃×#556	C₂²	semidirect
29. C₂₃×#554	C₂²	semidirect
33. C₂₃×#552	C₂²	semidirect
34. C₂₃×#552	C₂²	semidirect
60. C₂₃×#501	C₂²	semidirect
61. C₂₃×#501	C₂²	semidirect
62. C₂₃×#499	C₂²	semidirect
63. C₂₃×#498	C₂²	semidirect
64. C₂₃×#485	C₂²	semidirect
65. C₂₃×#485	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
69. C₂₃×#484	C₂²	semidirect
70. C₂₃×#483	C₂²	semidirect
71. C₂₃×#483	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
77. C₂₃×#481	C₂²	semidirect
79. C₂₃×#480	C₂²	semidirect
80. C₂₃×#479	C₂²	semidirect
81. C₂₃×#479	C₂²	semidirect
82. C₂₃×#478	C₂²	semidirect
83. C₂₃×#478	C₂²	semidirect
84. C₂₃×#477	C₂²	semidirect
85. C₂₃×#476	C₂²	semidirect
86. C₂₃×#475	C₂²	semidirect
87. C₂₃×#474	C₂²	semidirect
88. C₂₃×#468	C₂²	semidirect
89. C₂₃×#468	C₂²	semidirect
94. C₂₃×#465	C₂²	semidirect
95. C₂₃×#465	C₂²	semidirect
96. C₂₃×#440	C₂²	semidirect
97. C₂₃×#440	C₂²	semidirect
98. C₄×SD₁₆×C₂₃	C₂²	semidirect
99. C₄×SD₁₆×C₂₃	C₂²	semidirect
100. C₂₃×#435	C₂²	semidirect
101. C₂₃×#435	C₂²	semidirect
102. C₈×D₄×C₂₃	C₂²	semidirect
103. C₈×D₄×C₂₃	C₂²	semidirect
108. C₂₃×#428	C₂²	semidirect
109. C₂₃×#428	C₂²	semidirect
114. C₂₃×#427	C₂²	semidirect
115. C₂₃×#427	C₂²	semidirect
116. C₂₃×#427	C₂²	semidirect
117. C₂₃×#427	C₂²	semidirect
118. C₂₃×#427	C₂²	semidirect
119. C₂×C₂₃×#107	C₂²	semidirect
120. C₂×C₂₃×#107	C₂²	semidirect
122. C₂×C₂₃×#106	C₂²	semidirect
123. C₂×C₂₃×#106	C₂²	semidirect
124. C₂×C₂₃×#106	C₂²	semidirect
371. C₂×C₈×C₂₃	#41	semidirect
450. #61263	C₂₃	direct (N × H)
525. #3495	C₂×C₂₃	semidirect
527. #3350	C₂×C₂₃	semidirect
528. #3348	C₂×C₂₃	semidirect
529. #3346	C₂×C₂₃	semidirect
530. #3343	C₂×C₂₃	semidirect
531. #3340	C₂×C₂₃	semidirect
532. #3337	C₂×C₂₃	semidirect
533. #3337	C₂×C₂₃	semidirect
534. #3335	C₂×C₂₃	semidirect
535. #3163	C₂×C₂₃	semidirect
536. #3097	C₂×C₂₃	semidirect
537. #3096	C₂×C₂₃	semidirect
538. #3095	C₂×C₂₃	semidirect
539. #3094	C₂×C₂₃	semidirect
540. #3082	C₂×C₂₃	semidirect
541. #3081	C₂×C₂₃	semidirect
542. #3057	C₂×C₂₃	semidirect
543. C₂×#465	C₂×C₂₃	semidirect
544. #2949	C₂×C₂₃	semidirect
545. #2929	C₂×C₂₃	semidirect
546. #2912	C₂×C₂₃	semidirect
547. C₂×#427	C₂×C₂₃	semidirect
588. #556	C₂²×C₂₃	semidirect
590. #554	C₂²×C₂₃	semidirect
594. #552	C₂²×C₂₃	semidirect
595. #552	C₂²×C₂₃	semidirect
621. #501	C₂²×C₂₃	semidirect
622. #501	C₂²×C₂₃	semidirect
623. #499	C₂²×C₂₃	semidirect
624. #498	C₂²×C₂₃	semidirect
625. #485	C₂²×C₂₃	semidirect
626. #485	C₂²×C₂₃	semidirect
627. #485	C₂²×C₂₃	semidirect
628. #485	C₂²×C₂₃	semidirect
629. #484	C₂²×C₂₃	semidirect
630. #484	C₂²×C₂₃	semidirect
631. #483	C₂²×C₂₃	semidirect
632. #483	C₂²×C₂₃	semidirect
635. #482	C₂²×C₂₃	semidirect
636. #482	C₂²×C₂₃	semidirect
638. #481	C₂²×C₂₃	semidirect
640. #480	C₂²×C₂₃	semidirect
641. #479	C₂²×C₂₃	semidirect
642. #479	C₂²×C₂₃	semidirect
643. #478	C₂²×C₂₃	semidirect
644. #478	C₂²×C₂₃	semidirect
645. #477	C₂²×C₂₃	semidirect
646. #476	C₂²×C₂₃	semidirect
647. #475	C₂²×C₂₃	semidirect
648. #474	C₂²×C₂₃	semidirect
649. #468	C₂²×C₂₃	semidirect
650. #468	C₂²×C₂₃	semidirect
655. #465	C₂²×C₂₃	semidirect
656. #465	C₂²×C₂₃	semidirect
657. #440	C₂²×C₂₃	semidirect
658. #440	C₂²×C₂₃	semidirect
659. C₄×SD₁₆	C₂²×C₂₃	semidirect
660. C₄×SD₁₆	C₂²×C₂₃	semidirect
661. #435	C₂²×C₂₃	semidirect
662. #435	C₂²×C₂₃	semidirect
663. C₈×D₄	C₂²×C₂₃	semidirect
664. C₈×D₄	C₂²×C₂₃	semidirect
669. #428	C₂²×C₂₃	semidirect
670. #428	C₂²×C₂₃	semidirect
675. #427	C₂²×C₂₃	semidirect
676. #427	C₂²×C₂₃	semidirect
677. #427	C₂²×C₂₃	semidirect
678. #427	C₂²×C₂₃	semidirect
679. #427	C₂²×C₂₃	semidirect
680. C₂×#107	C₂²×C₂₃	semidirect
681. C₂×#107	C₂²×C₂₃	semidirect
683. C₂×#106	C₂²×C₂₃	semidirect
684. C₂×#106	C₂²×C₂₃	semidirect
685. C₂×#106	C₂²×C₂₃	semidirect
884. C₂₃	#61263	direct (N × H)
941. C₂×C₈	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3495	2
C₂₃×#3494	2
C₂₃×#3350	2
C₂₃×#3348	2
C₂₃×#3346	2
C₂₃×#3343	2
C₂₃×#3340	2
C₂₃×#3337	2
C₂₃×#3335	2
C₂₃×#3163	2
C₂₃×#3097	2
C₂₃×#3096	2
C₂₃×#3095	2
C₂₃×#3094	2
C₂₃×#3082	2
C₂₃×#3081	2
C₂₃×#3057	2
C₂×C₂₃×#465	2
C₂₃×#2949	2
C₂₃×#2929	2
C₂₃×#2912	2
C₂×C₂₃×#427	2
#61263	23

Subgroups — C23×#61263 #19208889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61263 #19208889