Subgroups — C₂₃×#61928 #19209554

Order 5888.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3401	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3394	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3376	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3360	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3225	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3221	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
21	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#562	—	2	2	no	—
25	C₂₃×#559	C₂²	1	1	yes	characteristic
26	C₂₃×#559	C₂²	1	1	yes	characteristic
27	C₂₃×#559	C₂²	1	2	yes	—
28	C₂₃×#559	C₂²	1	1	yes	characteristic
29	C₂₃×#557	C₂²	1	1	yes	characteristic
30	C₂₃×#557	C₂²	1	1	yes	characteristic
31	C₂₃×#557	C₂²	1	1	yes	characteristic
32	C₂₃×#556	—	2	1	no	—
33	C₂₃×#556	C₂²	1	2	yes	—
34	C₂₃×#556	C₂²	1	2	yes	—
35	C₂₃×#554	—	2	1	no	—
36	C₂₃×#554	C₂²	1	2	yes	—
37	C₂₃×#552	—	2	2	no	—
38	C₂₃×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#548	—	2	1	no	—
41	C₂₃×#547	—	2	1	no	—
42	C₂₃×#542	—	2	1	no	—
43	C₂₃×#542	C₂²	1	2	yes	—
44	C₂₃×#540	C₂²	1	2	yes	—
45	C₂₃×#539	—	2	2	no	—
46	C₂₃×#539	—	2	2	no	—
47	C₂₃×#536	—	2	1	no	—
48	C₂₃×#536	C₂²	1	2	yes	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic
50	C₂₃×#532	C₂²	1	1	yes	characteristic
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#529	—	2	1	no	—
54	C₂₃×#529	C₂²	1	1	yes	characteristic
55	C₂₃×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#497	C₂²	1	2	yes	—
58	C₂₃×#496	C₂²	1	2	yes	—
59	C₂₃×#495	C₂²	1	2	yes	—
60	C₂₃×#495	C₂²	1	2	yes	—
61	C₂₃×#493	C₂²	1	1	yes	characteristic
62	C₂₃×#492	C₂²	1	1	yes	characteristic
63	C₂₃×#492	C₂²	1	2	yes	—
64	C₂₃×#491	C₂²	1	2	yes	—
65	C₂₃×#489	C₂²	1	2	yes	—
66	C₂₃×#488	C₂²	1	2	yes	—
67	C₂₃×#488	C₂²	1	2	yes	—
68	C₂₃×#487	C₂²	1	1	yes	characteristic
69	C₂₃×#487	C₂²	1	2	yes	—
70	C₂₃×#486	C₂²	1	1	yes	characteristic
71	C₂₃×#483	C₂²	1	1	yes	characteristic
72	C₂₃×#481	C₂²	1	2	yes	—
73	C₂₃×#480	C₂²	1	1	yes	characteristic
74	C₂₃×#479	C₂²	1	1	yes	characteristic
75	C₂₃×#479	C₂²	1	2	yes	—
76	C₂₃×#479	C₂²	1	1	yes	characteristic
77	C₂₃×#478	C₂²	1	2	yes	—
78	C₂₃×#476	C₂²	1	2	yes	—
79	C₂₃×#475	C₂²	1	1	yes	characteristic
80	C₂₃×#475	C₂²	1	1	yes	characteristic
81	C₂₃×#475	C₂²	1	2	yes	—
82	C₂₃×#464	C₂²	1	2	yes	—
83	C₂₃×#464	C₂²	1	1	yes	characteristic
84	C₂₃×#464	C₂²	1	1	yes	characteristic
85	C₂₃×#464	C₂²	1	2	yes	—
86	C₂₃×#463	C₂²	1	2	yes	—
87	C₂₃×#463	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	—
89	C₂₃×#463	C₂²	1	2	yes	—
90	C₂₃×#463	C₂²	1	2	yes	—
91	C₂₃×#463	C₂²	1	2	yes	—
92	C₂₃×#462	C₂²	1	1	yes	characteristic
93	C₂₃×#462	C₂²	1	2	yes	—
94	C₂₃×#461	C₂²	1	1	yes	characteristic
95	C₂₃×#461	C₂²	1	2	yes	—
96	C₂₃×#461	C₂²	1	2	yes	—
97	C₂₃×#461	C₂²	1	2	yes	—
98	C₂₃×#460	C₂²	1	1	yes	characteristic
99	C₂₃×#460	C₂²	1	1	yes	characteristic
100	C₂₃×#460	C₂²	1	1	yes	characteristic
101	C₂₃×#460	C₂²	1	2	yes	—
102	C₂₃×#459	C₂²	1	1	yes	characteristic
103	C₂₃×#459	C₂²	1	2	yes	—
104	C₂₃×#452	C₂²	1	2	yes	—
105	C₂₃×#451	C₂²	1	1	yes	characteristic
106	C₂₃×#449	C₂²	1	2	yes	—
107	C₂₃×#449	C₂²	1	2	yes	—
108	C₂₃×#449	C₂²	1	2	yes	—
109	C₂₃×#448	C₂²	1	1	yes	characteristic
110	C₂₃×#448	C₂²	1	2	yes	—
111	C₂₃×#446	C₂²	1	1	yes	characteristic
112	C₂₃×#446	C₂²	1	1	yes	characteristic
113	C₂₃×#446	C₂²	1	2	yes	—
114	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
116	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
117	C₂₃×#442	C₂²	1	2	yes	—
118	C₂₃×#442	C₂²	1	2	yes	—
119	C₂₃×#441	C₂²	1	2	yes	—
120	C₂₃×#440	C₂²	1	2	yes	—
121	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
122	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
130	C₄×D₈×C₂₃	C₂²	1	2	yes	—
131	C₂₃×#433	C₂²	1	2	yes	—
132	C₂₃×#433	C₂²	1	2	yes	—
133	C₂₃×#431	C₂²	1	1	yes	characteristic
134	C₂₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₃	—	2	1	no	—
139	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×D₈×C₂₃	C₂³	1	2	yes	—
152	C₂×D₈×C₂₃	C₂³	1	2	yes	—
153	C₂×D₈×C₂₃	C₂³	1	2	yes	—
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×#127	C₂³	1	2	yes	—
163	C₂₃×#127	C₂³	1	1	yes	characteristic
164	C₂₃×#127	C₂³	1	1	yes	characteristic
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	1	no	—
171	C₂₃×#125	—	2	2	no	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	—	2	1	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	—	2	2	no	—
176	C₂₃×#125	D₄	1	2	yes	—
177	C₂₃×#125	C₂³	1	1	yes	characteristic
178	C₂₃×#125	C₂³	1	2	yes	—
179	C₂₃×#124	—	2	1	no	—
180	C₂₃×#124	—	2	1	no	—
181	C₂₃×#124	—	2	1	no	—
182	C₂₃×#124	—	2	2	no	—
183	C₂₃×#124	—	2	2	no	—
184	C₂₃×#124	—	2	1	no	—
185	C₂₃×#124	C₂³	1	2	yes	—
186	C₂₃×#124	C₂³	1	2	yes	—
187	C₂₃×#124	C₂³	1	2	yes	—
188	C₂₃×#124	C₂³	1	2	yes	—
189	C₂₃×#124	C₂³	1	1	yes	characteristic
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	2	no	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	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	1	yes	characteristic
212	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×#121	—	2	1	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	1	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	C₂³	1	1	yes	characteristic
223	C₂₃×#121	C₂³	1	2	yes	—
224	C₄×Q₈×C₂₃	—	2	1	no	—
225	C₄×Q₈×C₂₃	—	2	1	no	—
226	C₄×Q₈×C₂₃	—	2	1	no	—
227	C₄×Q₈×C₂₃	—	2	1	no	—
228	C₄×Q₈×C₂₃	—	2	1	no	—
229	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	1	no	—
250	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₂₃	C₂³	1	2	yes	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	2	yes	—
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₂₃×#117	—	2	2	no	—
258	C₂₃×#117	—	2	2	no	—
259	C₂₃×#117	—	2	2	no	—
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	1	yes	characteristic
270	C₂₃×#106	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	1	yes	characteristic
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	1	yes	characteristic
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂₃×#97	C₂³	1	2	yes	—
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₂₃	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	#41×C₂₃	—	4	2	no	—
313	#41×C₂₃	—	4	2	no	—
314	#41×C₂₃	—	8	2	no	—
315	#41×C₂₃	—	8	2	no	—
316	C₂×Q₈×C₂₃	—	2	1	no	—
317	C₂×Q₈×C₂₃	—	2	1	no	—
318	C₂×Q₈×C₂₃	—	2	2	no	—
319	C₂×Q₈×C₂₃	—	4	1	no	—
320	C₂×Q₈×C₂₃	—	4	1	no	—
321	C₂×Q₈×C₂₃	—	8	2	no	—
322	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	1	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
339	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₂₃	—	2	1	no	—
342	C₂²×C₄×C₂₃	—	2	1	no	—
343	C₂²×C₄×C₂₃	—	2	2	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	2	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	Q₁₆×C₂₃	—	4	1	no	—
355	Q₁₆×C₂₃	—	4	2	no	—
356	Q₁₆×C₂₃	—	4	1	no	—
357	SD₁₆×C₂₃	—	4	1	no	—
358	SD₁₆×C₂₃	—	4	2	no	—
359	SD₁₆×C₂₃	—	4	1	no	—
360	SD₁₆×C₂₃	—	4	2	no	—
361	SD₁₆×C₂₃	—	4	2	no	—
362	SD₁₆×C₂₃	—	4	2	no	—
363	SD₁₆×C₂₃	—	4	2	no	—
364	SD₁₆×C₂₃	—	4	2	no	—
365	D₈×C₂₃	—	4	2	no	—
366	D₈×C₂₃	—	4	2	no	—
367	D₈×C₂₃	—	4	2	no	—
368	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₂₃	—	2	1	no	—
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	1	no	—
379	C₄⋊C₄×C₂₃	—	2	1	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	1	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	1	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	1	no	—
396	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	C₂²⋊C₄×C₂₃	—	2	1	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	2	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	1	no	—
418	C₂²⋊C₄×C₂₃	—	2	1	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	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	1	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	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
432	C₄²×C₂₃	—	2	1	no	—
433	C₄²×C₂₃	—	2	1	no	—
434	C₄²×C₂₃	—	2	1	no	—
435	C₄²×C₂₃	—	2	1	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	2	yes	—
445	C₄²×C₂₃	C₂⁴	1	2	yes	—
446	#61928	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	2	no	—
448	C₂³×C₂₃	—	2	2	no	—
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₂₃	—	2	2	no	—
452	Q₈×C₂₃	—	2	2	no	—
453	Q₈×C₂₃	—	2	1	no	—
454	Q₈×C₂₃	—	2	1	no	—
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	2	no	—
457	Q₈×C₂₃	—	2	1	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	2	2	no	—
460	Q₈×C₂₃	—	2	1	no	—
461	Q₈×C₂₃	—	4	2	no	—
462	Q₈×C₂₃	—	4	2	no	—
463	Q₈×C₂₃	—	4	2	no	—
464	Q₈×C₂₃	—	8	2	no	—
465	D₄×C₂₃	—	2	1	no	—
466	D₄×C₂₃	—	2	2	no	—
467	D₄×C₂₃	—	2	2	no	—
468	D₄×C₂₃	—	2	2	no	—
469	D₄×C₂₃	—	2	2	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	4	4	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	8	1	no	—
475	D₄×C₂₃	—	8	1	no	—
476	D₄×C₂₃	—	8	2	no	—
477	D₄×C₂₃	—	8	2	no	—
478	D₄×C₂₃	—	8	1	no	—
479	D₄×C₂₃	—	8	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	4	1	no	—
493	C₂×C₄×C₂₃	—	4	4	no	—
494	C₂×C₄×C₂₃	—	4	2	no	—
495	C₂×C₄×C₂₃	—	4	2	no	—
496	C₂×C₄×C₂₃	—	8	2	no	—
497	C₂×C₄×C₂₃	—	8	2	no	—
498	C₂×C₄×C₂₃	—	8	2	no	—
499	C₂×C₄×C₂₃	—	8	2	no	—
500	C₂×C₄×C₂₃	—	8	2	no	—
501	C₂×C₄×C₂₃	—	8	2	no	—
502	C₂×C₄×C₂₃	—	8	1	no	—
503	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
513	C₈×C₂₃	—	2	1	no	—
514	C₈×C₂₃	—	2	1	no	—
515	C₈×C₂₃	—	2	2	no	—
516	C₈×C₂₃	—	2	2	no	—
517	C₈×C₂₃	—	2	1	no	—
518	C₈×C₂₃	—	2	1	no	—
519	#3554	C₂×C₂₃	1	1	yes	characteristic, complemented
520	#3507	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#3401	C₂×C₂₃	1	2	yes	complemented
522	#3400	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3399	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3396	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3394	C₂×C₂₃	1	2	yes	complemented
526	#3392	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3376	C₂×C₂₃	1	2	yes	complemented
528	#3374	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3365	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3360	C₂×C₂₃	1	2	yes	complemented
532	#3359	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3225	C₂×C₂₃	1	2	yes	complemented
534	#3221	C₂×C₂₃	1	2	yes	complemented
535	#3212	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3125	C₂×C₂₃	1	2	yes	complemented
538	#3119	C₂×C₂₃	1	2	yes	complemented
539	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3103	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
542	C₂²×C₂₃	—	2	1	no	—
543	C₂²×C₂₃	—	2	1	no	—
544	C₂²×C₂₃	—	2	1	no	—
545	C₂²×C₂₃	—	4	2	no	—
546	C₂²×C₂₃	—	4	2	no	—
547	C₂²×C₂₃	—	4	1	no	—
548	C₂²×C₂₃	—	4	2	no	—
549	C₂²×C₂₃	—	4	1	no	—
550	C₂²×C₂₃	—	4	2	no	—
551	C₂²×C₂₃	—	4	1	no	—
552	C₂²×C₂₃	—	4	2	no	—
553	C₂²×C₂₃	—	4	2	no	—
554	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₂₃	—	2	1	no	—
556	C₄×C₂₃	—	2	1	no	—
557	C₄×C₂₃	—	2	2	no	—
558	C₄×C₂₃	—	2	2	no	—
559	C₄×C₂₃	—	2	1	no	—
560	C₄×C₂₃	—	2	1	no	—
561	C₄×C₂₃	—	2	2	no	—
562	C₄×C₂₃	—	2	2	no	—
563	C₄×C₂₃	—	4	1	no	—
564	C₄×C₂₃	—	4	1	no	—
565	C₄×C₂₃	—	4	1	no	—
566	C₄×C₂₃	—	4	2	no	—
567	C₄×C₂₃	—	4	1	no	—
568	C₄×C₂₃	—	4	1	no	—
569	C₄×C₂₃	—	4	1	no	—
570	C₄×C₂₃	—	4	1	no	—
571	C₄×C₂₃	—	4	2	no	—
572	C₄×C₂₃	#577	1	2	yes	—
573	C₄×C₂₃	#585	1	1	yes	characteristic
574	C₄×C₂₃	#585	1	1	yes	characteristic
575	#562	—	2	2	no	—
576	#559	C₂²×C₂₃	1	1	yes	characteristic
577	#559	C₂²×C₂₃	1	1	yes	characteristic
578	#559	C₂²×C₂₃	1	2	yes	—
579	#559	C₂²×C₂₃	1	1	yes	characteristic
580	#557	C₂²×C₂₃	1	1	yes	characteristic
581	#557	C₂²×C₂₃	1	1	yes	characteristic
582	#557	C₂²×C₂₃	1	1	yes	characteristic
583	#556	—	2	1	no	—
584	#556	C₂²×C₂₃	1	2	yes	—
585	#556	C₂²×C₂₃	1	2	yes	—
586	#554	—	2	1	no	—
587	#554	C₂²×C₂₃	1	2	yes	—
588	#552	—	2	2	no	—
589	#550	C₂²×C₂₃	1	1	yes	characteristic
590	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
591	#548	—	2	1	no	—
592	#547	—	2	1	no	—
593	#542	—	2	1	no	—
594	#542	C₂²×C₂₃	1	2	yes	—
595	#540	C₂²×C₂₃	1	2	yes	—
596	#539	—	2	2	no	—
597	#539	—	2	2	no	—
598	#536	—	2	1	no	—
599	#536	C₂²×C₂₃	1	2	yes	—
600	#533	C₂²×C₂₃	1	1	yes	characteristic
601	#532	C₂²×C₂₃	1	1	yes	characteristic
602	#532	C₂²×C₂₃	1	1	yes	characteristic
603	#529	—	2	1	no	—
604	#529	—	2	1	no	—
605	#529	C₂²×C₂₃	1	1	yes	characteristic
606	#520	C₂²×C₂₃	1	2	yes	—
607	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
608	#497	C₂²×C₂₃	1	2	yes	—
609	#496	C₂²×C₂₃	1	2	yes	—
610	#495	C₂²×C₂₃	1	2	yes	—
611	#495	C₂²×C₂₃	1	2	yes	—
612	#493	C₂²×C₂₃	1	1	yes	characteristic
613	#492	C₂²×C₂₃	1	2	yes	—
614	#492	C₂²×C₂₃	1	1	yes	characteristic
615	#491	C₂²×C₂₃	1	2	yes	—
616	#489	C₂²×C₂₃	1	2	yes	—
617	#488	C₂²×C₂₃	1	2	yes	—
618	#488	C₂²×C₂₃	1	2	yes	—
619	#487	C₂²×C₂₃	1	2	yes	—
620	#487	C₂²×C₂₃	1	1	yes	characteristic
621	#486	C₂²×C₂₃	1	1	yes	characteristic
622	#483	C₂²×C₂₃	1	1	yes	characteristic
623	#481	C₂²×C₂₃	1	2	yes	—
624	#480	C₂²×C₂₃	1	1	yes	characteristic
625	#479	C₂²×C₂₃	1	1	yes	characteristic
626	#479	C₂²×C₂₃	1	2	yes	—
627	#479	C₂²×C₂₃	1	1	yes	characteristic
628	#478	C₂²×C₂₃	1	2	yes	—
629	#476	C₂²×C₂₃	1	2	yes	—
630	#475	C₂²×C₂₃	1	1	yes	characteristic
631	#475	C₂²×C₂₃	1	1	yes	characteristic
632	#475	C₂²×C₂₃	1	2	yes	—
633	#464	C₂²×C₂₃	1	1	yes	characteristic
634	#464	C₂²×C₂₃	1	1	yes	characteristic
635	#464	C₂²×C₂₃	1	2	yes	—
636	#464	C₂²×C₂₃	1	2	yes	—
637	#463	C₂²×C₂₃	1	2	yes	—
638	#463	C₂²×C₂₃	1	2	yes	—
639	#463	C₂²×C₂₃	1	2	yes	—
640	#463	C₂²×C₂₃	1	2	yes	—
641	#463	C₂²×C₂₃	1	2	yes	—
642	#463	C₂²×C₂₃	1	2	yes	—
643	#462	C₂²×C₂₃	1	2	yes	—
644	#462	C₂²×C₂₃	1	1	yes	characteristic
645	#461	C₂²×C₂₃	1	1	yes	characteristic
646	#461	C₂²×C₂₃	1	2	yes	—
647	#461	C₂²×C₂₃	1	2	yes	—
648	#461	C₂²×C₂₃	1	2	yes	—
649	#460	C₂²×C₂₃	1	1	yes	characteristic
650	#460	C₂²×C₂₃	1	1	yes	characteristic
651	#460	C₂²×C₂₃	1	1	yes	characteristic
652	#460	C₂²×C₂₃	1	2	yes	—
653	#459	C₂²×C₂₃	1	1	yes	characteristic
654	#459	C₂²×C₂₃	1	2	yes	—
655	#452	C₂²×C₂₃	1	2	yes	—
656	#451	C₂²×C₂₃	1	1	yes	characteristic
657	#449	C₂²×C₂₃	1	2	yes	—
658	#449	C₂²×C₂₃	1	2	yes	—
659	#449	C₂²×C₂₃	1	2	yes	—
660	#448	C₂²×C₂₃	1	2	yes	—
661	#448	C₂²×C₂₃	1	1	yes	characteristic
662	#446	C₂²×C₂₃	1	1	yes	characteristic
663	#446	C₂²×C₂₃	1	1	yes	characteristic
664	#446	C₂²×C₂₃	1	2	yes	—
665	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
666	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
667	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
668	#442	C₂²×C₂₃	1	2	yes	—
669	#442	C₂²×C₂₃	1	2	yes	—
670	#441	C₂²×C₂₃	1	2	yes	—
671	#440	C₂²×C₂₃	1	2	yes	—
672	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
673	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
675	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
676	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
679	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
681	C₄×D₈	C₂²×C₂₃	1	2	yes	—
682	#433	C₂²×C₂₃	1	2	yes	—
683	#433	C₂²×C₂₃	1	2	yes	—
684	#431	C₂²×C₂₃	1	1	yes	characteristic
685	#431	C₂²×C₂₃	1	1	yes	characteristic
686	C₂×C₂₃	—	4	1	no	—
687	C₂×C₂₃	—	8	2	no	—
688	C₂×C₂₃	—	8	2	no	—
689	C₂×C₂₃	—	8	1	no	—
690	C₂×C₂₃	#3487	1	1	yes	characteristic
691	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
692	C₂×C₂₃	#3584	1	1	yes	characteristic
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	2	1	no	—
695	C₂×#41	C₂³×C₂₃	1	2	yes	—
696	C₂²×Q₈	—	2	1	no	—
697	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
699	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
700	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
709	C₂×D₈	C₂³×C₂₃	1	2	yes	—
710	C₂×D₈	C₂³×C₂₃	1	2	yes	—
711	C₂×D₈	C₂³×C₂₃	1	2	yes	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
714	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
720	#127	C₂³×C₂₃	1	1	yes	characteristic
721	#127	C₂³×C₂₃	1	1	yes	characteristic
722	#127	C₂³×C₂₃	1	2	yes	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	D₄×C₂₃	1	2	yes	—
735	#125	C₂³×C₂₃	1	1	yes	characteristic
736	#125	C₂³×C₂₃	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	1	no	—
739	#124	—	2	1	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	1	no	—
743	#124	C₂³×C₂₃	1	1	yes	characteristic
744	#124	C₂³×C₂₃	1	2	yes	—
745	#124	C₂³×C₂₃	1	2	yes	—
746	#124	C₂³×C₂₃	1	2	yes	—
747	#124	C₂³×C₂₃	1	2	yes	—
748	#123	—	2	1	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	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	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	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
770	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
771	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	C₂³×C₂₃	1	1	yes	characteristic
781	#121	C₂³×C₂₃	1	2	yes	—
782	C₄×Q₈	—	2	1	no	—
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	C₂³×C₂₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
792	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
793	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
795	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	C₂³×C₂₃	1	2	yes	—
809	C₄×D₄	C₂³×C₂₃	1	2	yes	—
810	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₂₃	1	2	yes	—
812	C₄×D₄	C₂³×C₂₃	1	2	yes	—
813	C₄×D₄	C₂³×C₂₃	1	2	yes	—
814	C₄×D₄	C₂³×C₂₃	1	2	yes	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	1	no	—
819	#117	C₂³×C₂₃	1	2	yes	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	2	no	—
823	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
826	#107	C₂³×C₂₃	1	1	yes	characteristic
827	#107	C₂³×C₂₃	1	1	yes	characteristic
828	#106	C₂³×C₂₃	1	2	yes	—
829	#106	C₂³×C₂₃	1	1	yes	characteristic
830	#106	C₂³×C₂₃	1	2	yes	—
831	#106	C₂³×C₂₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
837	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
838	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
840	#103	C₂³×C₂₃	1	1	yes	characteristic
841	#103	C₂³×C₂₃	1	2	yes	—
842	#103	C₂³×C₂₃	1	2	yes	—
843	#103	C₂³×C₂₃	1	2	yes	—
844	#103	C₂³×C₂₃	1	1	yes	characteristic
845	#103	C₂³×C₂₃	1	1	yes	characteristic
846	#103	C₂³×C₂₃	1	2	yes	—
847	#103	C₂³×C₂₃	1	1	yes	characteristic
848	#103	C₂³×C₂₃	1	1	yes	characteristic
849	#103	C₂³×C₂₃	1	1	yes	characteristic
850	#103	C₂³×C₂₃	1	2	yes	—
851	#103	C₂³×C₂₃	1	2	yes	—
852	#102	C₂³×C₂₃	1	2	yes	—
853	#102	C₂³×C₂₃	1	2	yes	—
854	#102	C₂³×C₂₃	1	1	yes	characteristic
855	#102	C₂³×C₂₃	1	2	yes	—
856	#102	C₂³×C₂₃	1	1	yes	characteristic
857	#102	C₂³×C₂₃	1	2	yes	—
858	#102	C₂³×C₂₃	1	2	yes	—
859	#102	C₂³×C₂₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
863	#97	C₂³×C₂₃	1	2	yes	—
864	#97	C₂³×C₂₃	1	2	yes	—
865	C₄×C₈	C₂³×C₂₃	1	2	yes	—
866	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₂₃	1	2	yes	—
869	C₄×C₈	C₂³×C₂₃	1	2	yes	—
870	C₂₃	#61928	1	1	yes	characteristic, direct product factor, Sylow
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	8	2	no	—
874	#41	—	8	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	4	1	no	—
879	C₂×Q₈	—	4	1	no	—
880	C₂×Q₈	—	8	2	no	—
881	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
882	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
883	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
884	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
898	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
899	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
911	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
913	Q₁₆	—	4	1	no	—
914	Q₁₆	—	4	2	no	—
915	Q₁₆	—	4	1	no	—
916	SD₁₆	—	4	1	no	—
917	SD₁₆	—	4	2	no	—
918	SD₁₆	—	4	1	no	—
919	SD₁₆	—	4	2	no	—
920	SD₁₆	—	4	2	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	D₈	—	4	2	no	—
925	D₈	—	4	2	no	—
926	D₈	—	4	2	no	—
927	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
928	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
932	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1000	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1002	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₂₃	1	2	yes	—
1004	C₄²	C₂⁴×C₂₃	1	2	yes	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	2	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	8	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	1	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1063	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1064	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1070	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1071	C₈	—	2	1	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	2	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₂²	—	2	1	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	C₂₃×#577	1	2	yes	—
1108	C₄	C₂₃×#585	1	1	yes	characteristic
1109	C₄	C₂₃×#585	1	1	yes	characteristic
1110	C₂	—	4	1	no	—
1111	C₂	—	8	2	no	—
1112	C₂	—	8	1	no	—
1113	C₂	—	8	2	no	—
1114	C₂	C₂₃×#3487	1	1	yes	characteristic
1115	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1116	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3554	C₂	semidirect
2. C₂₃×#3507	C₂	semidirect
3. C₂₃×#3401	C₂	semidirect
4. C₂₃×#3400	C₂	semidirect
5. C₂₃×#3399	C₂	semidirect
6. C₂₃×#3396	C₂	semidirect
7. C₂₃×#3394	C₂	semidirect
8. C₂₃×#3392	C₂	semidirect
9. C₂₃×#3376	C₂	semidirect
10. C₂₃×#3374	C₂	semidirect
11. C₂₃×#3373	C₂	semidirect
12. C₂₃×#3365	C₂	semidirect
13. C₂₃×#3360	C₂	semidirect
14. C₂₃×#3359	C₂	semidirect
15. C₂₃×#3225	C₂	semidirect
16. C₂₃×#3221	C₂	semidirect
17. C₂₃×#3212	C₂	semidirect
18. C₂₃×#3207	C₂	semidirect
19. C₂₃×#3125	C₂	semidirect
20. C₂₃×#3119	C₂	semidirect
21. C₂₃×#3108	C₂	semidirect
22. C₂₃×#3103	C₂	semidirect
23. C₂₃×#2986	C₂	semidirect
446. #61928	C₂₃	direct (N × H)
519. #3554	C₂×C₂₃	semidirect
520. #3507	C₂×C₂₃	semidirect
521. #3401	C₂×C₂₃	semidirect
522. #3400	C₂×C₂₃	semidirect
523. #3399	C₂×C₂₃	semidirect
524. #3396	C₂×C₂₃	semidirect
525. #3394	C₂×C₂₃	semidirect
526. #3392	C₂×C₂₃	semidirect
527. #3376	C₂×C₂₃	semidirect
528. #3374	C₂×C₂₃	semidirect
529. #3373	C₂×C₂₃	semidirect
530. #3365	C₂×C₂₃	semidirect
531. #3360	C₂×C₂₃	semidirect
532. #3359	C₂×C₂₃	semidirect
533. #3225	C₂×C₂₃	semidirect
534. #3221	C₂×C₂₃	semidirect
535. #3212	C₂×C₂₃	semidirect
536. #3207	C₂×C₂₃	semidirect
537. #3125	C₂×C₂₃	semidirect
538. #3119	C₂×C₂₃	semidirect
539. #3108	C₂×C₂₃	semidirect
540. #3103	C₂×C₂₃	semidirect
541. #2986	C₂×C₂₃	semidirect
870. C₂₃	#61928	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×#3554	2
C₂₃×#3507	2
C₂₃×#3401	2
C₂₃×#3400	2
C₂₃×#3399	2
C₂₃×#3396	2
C₂₃×#3394	2
C₂₃×#3392	2
C₂₃×#3376	2
C₂₃×#3374	2
C₂₃×#3373	2
C₂₃×#3365	2
C₂₃×#3360	2
C₂₃×#3359	2
C₂₃×#3225	2
C₂₃×#3221	2
C₂₃×#3212	2
C₂₃×#3207	2
C₂₃×#3125	2
C₂₃×#3119	2
C₂₃×#3108	2
C₂₃×#3103	2
C₂₃×#2986	2
#61928	23

Subgroups — C23×#61928 #19209554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61928 #19209554