Subgroups — C₂₃×#61019 #19208645

Order 5888.

1788 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3260	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3259	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3240	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3234	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3217	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3214	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3198	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3180	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3123	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3122	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3119	C₂	1	4	yes	maximal, complemented
15	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#559	—	2	2	no	—
17	C₂₃×#553	—	2	2	no	—
18	C₂₃×#553	—	2	2	no	—
19	C₂₃×#553	—	2	2	no	—
20	C₂₃×#552	—	2	2	no	—
21	C₂₃×#550	—	2	2	no	—
22	C₂₃×#546	—	2	2	no	—
23	C₂₃×#546	—	2	2	no	—
24	C₂₃×#541	C₂²	1	1	yes	characteristic
25	C₂₃×#541	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#540	C₂²	1	2	yes	—
27	C₂₃×#540	C₂²	1	2	yes	—
28	C₂₃×#540	C₂²	1	1	yes	characteristic
29	C₂₃×#540	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#537	C₂²	1	2	yes	—
31	C₂₃×#535	C₂²	1	2	yes	—
32	C₂₃×#533	C₂²	1	1	yes	characteristic
33	C₂₃×#532	C₂²	1	2	yes	—
34	C₂₃×#532	C₂²	1	2	yes	—
35	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#529	C₂²	1	2	yes	complemented
39	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#520	C₂²	1	2	yes	complemented
41	C₂₃×#518	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#501	C₂²	1	2	yes	complemented
44	C₂₃×#501	C₂²	1	2	yes	complemented
45	C₂₃×#496	C₂²	1	2	yes	—
46	C₂₃×#496	C₂²	1	2	yes	—
47	C₂₃×#490	C₂²	1	2	yes	—
48	C₂₃×#490	C₂²	1	2	yes	—
49	C₂₃×#489	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#485	C₂²	1	4	yes	—
52	C₂₃×#482	C₂²	1	4	yes	—
53	C₂₃×#481	C₂²	1	4	yes	complemented
54	C₂₃×#480	C₂²	1	4	yes	complemented
55	C₂₃×#479	C₂²	1	4	yes	complemented
56	C₂₃×#478	C₂²	1	4	yes	complemented
57	C₂₃×#478	C₂²	1	4	yes	complemented
58	C₂₃×#478	C₂²	1	4	yes	complemented
59	C₂₃×#469	C₂²	1	4	yes	complemented
60	C₂₃×#468	C₂²	1	4	yes	complemented
61	C₂₃×#466	C₂²	1	4	yes	complemented
62	C₂₃×#465	C₂²	1	4	yes	complemented
63	C₂₃×#461	C₂²	1	4	yes	complemented
64	C₂₃×#460	C₂²	1	4	yes	—
65	C₂₃×#459	C₂²	1	4	yes	—
66	C₂₃×#459	C₂²	1	4	yes	complemented
67	C₂₃×#450	C₂²	1	4	yes	—
68	C₂₃×#449	C₂²	1	4	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#447	C₂²	1	4	yes	—
71	C₂₃×#442	C₂²	1	4	yes	complemented
72	C₂₃×#440	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
74	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
75	C₂₃×#433	C₂²	1	2	yes	—
76	C₂₃×#433	C₂²	1	2	yes	complemented
77	C₂₃×#432	C₂²	1	2	yes	—
78	C₂₃×#432	C₂²	1	2	yes	complemented
79	C₂₃×#424	C₂²	1	2	yes	complemented
80	C₂₃×#408	C₂²	1	2	yes	—
81	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
83	C₂×#41×C₂₃	—	2	2	no	—
84	C₂×#41×C₂₃	—	2	2	no	—
85	C₂×#41×C₂₃	C₂³	1	2	yes	—
86	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₂₃	—	2	2	no	—
88	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
89	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂×D₈×C₂₃	C₂³	1	4	yes	—
92	C₂×D₈×C₂₃	C₂³	1	4	yes	—
93	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
95	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₂₃×#127	—	2	2	no	—
98	C₂₃×#127	—	2	2	no	—
99	C₂₃×#127	C₂³	1	2	yes	—
100	C₂₃×#127	C₂³	1	1	yes	characteristic
101	C₂₃×#127	C₂³	1	2	yes	—
102	C₂₃×#126	—	2	2	no	—
103	C₂₃×#126	—	2	2	no	—
104	C₂₃×#126	—	2	2	no	—
105	C₂₃×#126	—	2	2	no	—
106	C₂₃×#125	—	2	2	no	—
107	C₂₃×#125	—	2	2	no	—
108	C₂₃×#125	—	2	2	no	—
109	C₂₃×#125	C₂³	1	1	yes	characteristic
110	C₂₃×#125	C₂³	1	1	yes	characteristic
111	C₂₃×#125	C₂³	1	2	yes	—
112	C₂₃×#125	C₂³	1	2	yes	—
113	C₂₃×#124	—	2	2	no	—
114	C₂₃×#124	—	2	2	no	—
115	C₂₃×#124	—	2	2	no	—
116	C₂₃×#124	C₂³	1	2	yes	—
117	C₂₃×#123	—	2	2	no	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	2	no	—
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×#123	—	2	4	no	—
122	C₂₃×#123	—	2	4	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	—	2	2	no	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	2	no	—
129	C₂₃×#121	—	2	2	no	—
130	C₂₃×#121	—	2	2	no	—
131	C₂₃×#121	—	2	2	no	—
132	C₂₃×#121	—	2	2	no	—
133	C₂₃×#121	—	2	4	no	—
134	C₂₃×#121	—	2	4	no	—
135	C₂₃×#121	—	2	2	no	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	C₂³	1	2	yes	—
138	C₂₃×#121	C₂³	1	4	yes	—
139	C₂₃×#121	C₂³	1	4	yes	—
140	C₂₃×#121	C₂³	1	2	yes	—
141	C₂₃×#120	—	2	2	no	—
142	C₂₃×#120	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	D₄	1	2	yes	—
145	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
147	C₄×D₄×C₂₃	—	2	2	no	—
148	C₄×D₄×C₂₃	—	2	2	no	—
149	C₄×D₄×C₂₃	—	2	4	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	2	no	—
152	C₄×D₄×C₂₃	—	2	2	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	2	no	—
155	C₄×D₄×C₂₃	D₄	1	2	yes	—
156	C₄×D₄×C₂₃	D₄	1	2	yes	—
157	C₄×D₄×C₂₃	D₄	1	2	yes	—
158	C₄×D₄×C₂₃	C₂³	1	2	yes	—
159	C₄×D₄×C₂₃	C₂³	1	4	yes	—
160	C₄×D₄×C₂₃	C₂³	1	2	yes	—
161	C₄×D₄×C₂₃	C₂³	1	4	yes	—
162	C₂₃×#117	—	2	2	no	—
163	C₂₃×#117	—	2	2	no	—
164	C₂₃×#117	—	2	2	no	—
165	C₂₃×#117	C₂³	1	2	yes	—
166	C₂₃×#117	C₂³	1	1	yes	characteristic
167	C₂₃×#117	C₂³	1	1	yes	characteristic
168	C₂₃×#117	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
173	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
176	C₂₃×#107	C₂³	1	4	yes	—
177	C₂₃×#107	C₂³	1	4	yes	—
178	C₂₃×#106	C₂³	1	4	yes	—
179	C₂₃×#106	C₂³	1	4	yes	—
180	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
182	C₂₃×#103	C₂³	1	4	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#102	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	4	yes	—
186	C₂₃×#102	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×#102	C₂³	1	4	yes	—
189	C₂₃×#102	C₂³	1	4	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₂₃×#97	C₂³	1	2	yes	—
194	C₂₃×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₂₃	C₂³	1	2	yes	—
196	C₂⁴×C₂₃	—	2	2	no	—
197	#41×C₂₃	—	4	2	no	—
198	#41×C₂₃	—	4	4	no	—
199	#41×C₂₃	—	8	4	no	—
200	#41×C₂₃	—	8	4	no	—
201	C₂×Q₈×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
204	C₂×D₄×C₂₃	—	2	2	no	—
205	C₂×D₄×C₂₃	—	2	2	no	—
206	C₂×D₄×C₂₃	—	2	2	no	—
207	C₂×D₄×C₂₃	—	2	4	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	2	no	—
210	C₂×D₄×C₂₃	—	2	2	no	—
211	C₂×D₄×C₂₃	—	2	2	no	—
212	C₂×D₄×C₂₃	—	2	2	no	—
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	4	4	no	—
215	C₂×D₄×C₂₃	—	8	4	no	—
216	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	2	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	2	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	SD₁₆×C₂₃	—	4	4	no	—
234	SD₁₆×C₂₃	—	4	4	no	—
235	D₈×C₂₃	—	4	4	no	—
236	D₈×C₂₃	—	4	4	no	—
237	M₁₆×C₂₃	—	4	2	no	—
238	C₂×C₈×C₂₃	—	4	2	no	—
239	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
240	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₂₃	—	2	2	no	—
242	C₄⋊C₄×C₂₃	—	2	2	no	—
243	C₄⋊C₄×C₂₃	—	2	2	no	—
244	C₄⋊C₄×C₂₃	—	2	2	no	—
245	C₄⋊C₄×C₂₃	—	2	2	no	—
246	C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	—	2	2	no	—
250	C₄⋊C₄×C₂₃	—	2	2	no	—
251	C₄⋊C₄×C₂₃	—	2	2	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
259	C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂²⋊C₄×C₂₃	—	2	2	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	4	no	—
264	C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	2	no	—
268	C₂²⋊C₄×C₂₃	—	2	2	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₄²×C₂₃	—	2	2	no	—
276	C₄²×C₂₃	—	2	2	no	—
277	C₄²×C₂₃	—	2	2	no	—
278	C₄²×C₂₃	C₂×D₄	1	2	yes	—
279	C₄²×C₂₃	C₂×D₄	1	2	yes	—
280	C₄²×C₂₃	C₂×D₄	1	2	yes	—
281	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
285	#61019	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	2	4	no	—
288	C₂³×C₂₃	—	4	4	no	—
289	C₂³×C₂₃	—	8	4	no	—
290	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
291	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₂₃	—	2	4	no	—
294	Q₈×C₂₃	—	4	1	no	—
295	Q₈×C₂₃	—	4	4	no	—
296	D₄×C₂₃	—	2	4	no	—
297	D₄×C₂₃	—	2	4	no	—
298	D₄×C₂₃	—	2	4	no	—
299	D₄×C₂₃	—	4	1	no	—
300	D₄×C₂₃	—	4	1	no	—
301	D₄×C₂₃	—	4	1	no	—
302	D₄×C₂₃	—	4	4	no	—
303	D₄×C₂₃	—	4	4	no	—
304	D₄×C₂₃	—	4	4	no	—
305	D₄×C₂₃	—	4	4	no	—
306	D₄×C₂₃	—	8	2	no	—
307	D₄×C₂₃	—	8	4	no	—
308	D₄×C₂₃	—	8	2	no	—
309	D₄×C₂₃	—	8	2	no	—
310	D₄×C₂₃	—	8	4	no	—
311	D₄×C₂₃	—	8	4	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	4	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	4	2	no	—
320	C₂×C₄×C₂₃	—	4	2	no	—
321	C₂×C₄×C₂₃	—	4	2	no	—
322	C₂×C₄×C₂₃	—	4	4	no	—
323	C₂×C₄×C₂₃	—	8	2	no	—
324	C₂×C₄×C₂₃	—	8	2	no	—
325	C₂×C₄×C₂₃	—	8	4	no	—
326	C₂×C₄×C₂₃	—	8	4	no	—
327	C₂×C₄×C₂₃	—	8	2	no	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
336	C₈×C₂₃	—	2	4	no	—
337	C₈×C₂₃	—	2	4	no	—
338	#3512	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#3260	C₂×C₂₃	1	2	yes	complemented
341	#3259	C₂×C₂₃	1	2	yes	complemented
342	#3240	C₂×C₂₃	1	2	yes	complemented
343	#3234	C₂×C₂₃	1	2	yes	complemented
344	#3217	C₂×C₂₃	1	2	yes	complemented
345	#3214	C₂×C₂₃	1	2	yes	complemented
346	#3198	C₂×C₂₃	1	4	yes	complemented
347	#3180	C₂×C₂₃	1	2	yes	complemented
348	#3171	C₂×C₂₃	1	2	yes	complemented
349	#3123	C₂×C₂₃	1	2	yes	complemented
350	#3122	C₂×C₂₃	1	2	yes	complemented
351	#3119	C₂×C₂₃	1	4	yes	complemented
352	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	1	no	—
357	C₂²×C₂₃	—	2	1	no	—
358	C₂²×C₂₃	—	2	1	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	4	no	—
361	C₂²×C₂₃	—	4	4	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	4	2	no	—
364	C₂²×C₂₃	—	4	4	no	—
365	C₂²×C₂₃	—	16	4	no	—
366	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	—	2	2	no	—
369	C₄×C₂₃	—	2	2	no	—
370	C₄×C₂₃	—	2	2	no	—
371	C₄×C₂₃	—	2	1	no	—
372	C₄×C₂₃	—	2	1	no	—
373	C₄×C₂₃	—	2	1	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	—	4	2	no	—
376	C₄×C₂₃	—	4	4	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	#585	1	2	yes	—
379	#559	—	2	2	no	—
380	#553	—	2	2	no	—
381	#553	—	2	2	no	—
382	#553	—	2	2	no	—
383	#552	—	2	2	no	—
384	#550	—	2	2	no	—
385	#546	—	2	2	no	—
386	#546	—	2	2	no	—
387	#541	C₂²×C₂₃	1	1	yes	characteristic
388	#541	C₂²×C₂₃	1	1	yes	characteristic, complemented
389	#540	C₂²×C₂₃	1	2	yes	—
390	#540	C₂²×C₂₃	1	1	yes	characteristic
391	#540	C₂²×C₂₃	1	2	yes	—
392	#540	C₂²×C₂₃	1	1	yes	characteristic, complemented
393	#537	C₂²×C₂₃	1	2	yes	—
394	#535	C₂²×C₂₃	1	2	yes	—
395	#533	C₂²×C₂₃	1	1	yes	characteristic
396	#532	C₂²×C₂₃	1	2	yes	—
397	#532	C₂²×C₂₃	1	2	yes	—
398	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
399	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
400	#529	C₂²×C₂₃	1	2	yes	—
401	#529	C₂²×C₂₃	1	2	yes	complemented
402	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
403	#520	C₂²×C₂₃	1	2	yes	complemented
404	#518	C₂²×C₂₃	1	2	yes	—
405	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
406	#501	C₂²×C₂₃	1	2	yes	complemented
407	#501	C₂²×C₂₃	1	2	yes	complemented
408	#496	C₂²×C₂₃	1	2	yes	—
409	#496	C₂²×C₂₃	1	2	yes	—
410	#490	C₂²×C₂₃	1	2	yes	—
411	#490	C₂²×C₂₃	1	2	yes	—
412	#489	C₂²×C₂₃	1	2	yes	complemented
413	#489	C₂²×C₂₃	1	2	yes	complemented
414	#485	C₂²×C₂₃	1	4	yes	—
415	#482	C₂²×C₂₃	1	4	yes	—
416	#481	C₂²×C₂₃	1	4	yes	complemented
417	#480	C₂²×C₂₃	1	4	yes	complemented
418	#479	C₂²×C₂₃	1	4	yes	complemented
419	#478	C₂²×C₂₃	1	4	yes	complemented
420	#478	C₂²×C₂₃	1	4	yes	complemented
421	#478	C₂²×C₂₃	1	4	yes	complemented
422	#469	C₂²×C₂₃	1	4	yes	complemented
423	#468	C₂²×C₂₃	1	4	yes	complemented
424	#466	C₂²×C₂₃	1	4	yes	complemented
425	#465	C₂²×C₂₃	1	4	yes	complemented
426	#461	C₂²×C₂₃	1	4	yes	complemented
427	#460	C₂²×C₂₃	1	4	yes	—
428	#459	C₂²×C₂₃	1	4	yes	—
429	#459	C₂²×C₂₃	1	4	yes	complemented
430	#450	C₂²×C₂₃	1	4	yes	—
431	#449	C₂²×C₂₃	1	4	yes	complemented
432	#449	C₂²×C₂₃	1	4	yes	complemented
433	#447	C₂²×C₂₃	1	4	yes	—
434	#442	C₂²×C₂₃	1	4	yes	complemented
435	#440	C₂²×C₂₃	1	4	yes	complemented
436	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
437	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
438	#433	C₂²×C₂₃	1	2	yes	—
439	#433	C₂²×C₂₃	1	2	yes	complemented
440	#432	C₂²×C₂₃	1	2	yes	—
441	#432	C₂²×C₂₃	1	2	yes	complemented
442	#424	C₂²×C₂₃	1	2	yes	complemented
443	#408	C₂²×C₂₃	1	2	yes	—
444	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	C₂×C₂₃	—	4	1	no	—
447	C₂×C₂₃	—	4	1	no	—
448	C₂×C₂₃	—	4	1	no	—
449	C₂×C₂₃	—	8	2	no	—
450	C₂×C₂₃	—	8	4	no	—
451	C₂×C₂₃	#3449	1	1	yes	characteristic
452	C₂×C₂₃	#3585	1	2	yes	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	C₂³×C₂₃	1	2	yes	—
456	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
457	C₂²×D₄	—	2	2	no	—
458	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
459	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
460	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
461	C₂×D₈	C₂³×C₂₃	1	4	yes	—
462	C₂×D₈	C₂³×C₂₃	1	4	yes	—
463	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
464	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
467	#127	—	2	2	no	—
468	#127	—	2	2	no	—
469	#127	C₂³×C₂₃	1	2	yes	—
470	#127	C₂³×C₂₃	1	2	yes	—
471	#127	C₂³×C₂₃	1	1	yes	characteristic
472	#126	—	2	2	no	—
473	#126	—	2	2	no	—
474	#126	—	2	2	no	—
475	#126	—	2	2	no	—
476	#125	—	2	2	no	—
477	#125	—	2	2	no	—
478	#125	—	2	2	no	—
479	#125	C₂³×C₂₃	1	2	yes	—
480	#125	C₂³×C₂₃	1	1	yes	characteristic
481	#125	C₂³×C₂₃	1	1	yes	characteristic
482	#125	C₂³×C₂₃	1	2	yes	—
483	#124	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	C₂³×C₂₃	1	2	yes	—
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	2	no	—
492	#123	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
496	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	4	no	—
504	#121	—	2	4	no	—
505	#121	—	2	2	no	—
506	#121	—	2	2	no	—
507	#121	C₂³×C₂₃	1	2	yes	—
508	#121	C₂³×C₂₃	1	2	yes	—
509	#121	C₂³×C₂₃	1	4	yes	—
510	#121	C₂³×C₂₃	1	4	yes	—
511	#120	—	2	2	no	—
512	#120	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	D₄×C₂₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
516	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	D₄×C₂₃	1	2	yes	—
526	C₄×D₄	D₄×C₂₃	1	2	yes	—
527	C₄×D₄	D₄×C₂₃	1	2	yes	—
528	C₄×D₄	C₂³×C₂₃	1	4	yes	—
529	C₄×D₄	C₂³×C₂₃	1	4	yes	—
530	C₄×D₄	C₂³×C₂₃	1	2	yes	—
531	C₄×D₄	C₂³×C₂₃	1	2	yes	—
532	#117	—	2	2	no	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	C₂³×C₂₃	1	2	yes	—
536	#117	C₂³×C₂₃	1	1	yes	characteristic
537	#117	C₂³×C₂₃	1	1	yes	characteristic
538	#117	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	—	2	2	no	—
540	C₂×C₄⋊C₄	—	2	2	no	—
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
546	#107	C₂³×C₂₃	1	4	yes	—
547	#107	C₂³×C₂₃	1	4	yes	—
548	#106	C₂³×C₂₃	1	4	yes	—
549	#106	C₂³×C₂₃	1	4	yes	—
550	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
551	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
552	#103	C₂³×C₂₃	1	4	yes	—
553	#103	C₂³×C₂₃	1	4	yes	—
554	#102	C₂³×C₂₃	1	4	yes	—
555	#102	C₂³×C₂₃	1	4	yes	—
556	#102	C₂³×C₂₃	1	4	yes	—
557	#102	C₂³×C₂₃	1	4	yes	—
558	#102	C₂³×C₂₃	1	4	yes	—
559	#102	C₂³×C₂₃	1	4	yes	—
560	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
561	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
562	#97	C₂³×C₂₃	1	2	yes	—
563	#97	C₂³×C₂₃	1	2	yes	—
564	#97	C₂³×C₂₃	1	2	yes	—
565	C₄×C₈	C₂³×C₂₃	1	2	yes	—
566	C₂₃	#61019	1	1	yes	characteristic, direct product factor, Sylow
567	C₂⁴	—	2	2	no	—
568	#41	—	4	2	no	—
569	#41	—	4	4	no	—
570	#41	—	8	4	no	—
571	#41	—	8	4	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	—	8	4	no	—
587	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
588	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
591	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
604	SD₁₆	—	4	4	no	—
605	SD₁₆	—	4	4	no	—
606	D₈	—	4	4	no	—
607	D₈	—	4	4	no	—
608	M₁₆	—	4	2	no	—
609	C₂×C₈	—	4	2	no	—
610	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
611	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂×D₄×C₂₃	1	2	yes	—
650	C₄²	C₂×D₄×C₂₃	1	2	yes	—
651	C₄²	C₂×D₄×C₂₃	1	2	yes	—
652	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
653	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
654	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
655	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	8	4	no	—
660	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
661	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
662	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
663	Q₈	—	2	4	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	4	no	—
668	D₄	—	2	4	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	4	no	—
676	D₄	—	8	4	no	—
677	D₄	—	8	2	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
705	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
706	C₈	—	2	4	no	—
707	C₈	—	2	4	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	16	4	no	—
721	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	4	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	C₂₃×#585	1	2	yes	—
734	C₂	—	4	1	no	—
735	C₂	—	4	1	no	—
736	C₂	—	4	1	no	—
737	C₂	—	8	4	no	—
738	C₂	—	8	2	no	—
739	C₂	C₂₃×#3449	1	1	yes	characteristic
740	C₂	C₂₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3512	C₂	semidirect
2. C₂₃×#3508	C₂	semidirect
3. C₂₃×#3260	C₂	semidirect
4. C₂₃×#3259	C₂	semidirect
5. C₂₃×#3240	C₂	semidirect
6. C₂₃×#3234	C₂	semidirect
7. C₂₃×#3217	C₂	semidirect
8. C₂₃×#3214	C₂	semidirect
9. C₂₃×#3198	C₂	semidirect
10. C₂₃×#3180	C₂	semidirect
11. C₂₃×#3171	C₂	semidirect
12. C₂₃×#3123	C₂	semidirect
13. C₂₃×#3122	C₂	semidirect
14. C₂₃×#3119	C₂	semidirect
15. C₂₃×#2923	C₂	semidirect
25. C₂₃×#541	C₂²	semidirect
29. C₂₃×#540	C₂²	semidirect
35. C₂₃×#532	C₂²	semidirect
38. C₂₃×#529	C₂²	semidirect
39. C₂×C₂₃×#125	C₂²	semidirect
40. C₂₃×#520	C₂²	semidirect
43. C₂₃×#501	C₂²	semidirect
44. C₂₃×#501	C₂²	semidirect
49. C₂₃×#489	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
53. C₂₃×#481	C₂²	semidirect
54. C₂₃×#480	C₂²	semidirect
55. C₂₃×#479	C₂²	semidirect
56. C₂₃×#478	C₂²	semidirect
57. C₂₃×#478	C₂²	semidirect
58. C₂₃×#478	C₂²	semidirect
59. C₂₃×#469	C₂²	semidirect
60. C₂₃×#468	C₂²	semidirect
61. C₂₃×#466	C₂²	semidirect
62. C₂₃×#465	C₂²	semidirect
63. C₂₃×#461	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
68. C₂₃×#449	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
71. C₂₃×#442	C₂²	semidirect
72. C₂₃×#440	C₂²	semidirect
73. C₄×SD₁₆×C₂₃	C₂²	semidirect
74. C₄×D₈×C₂₃	C₂²	semidirect
76. C₂₃×#433	C₂²	semidirect
78. C₂₃×#432	C₂²	semidirect
79. C₂₃×#424	C₂²	semidirect
81. C₄×M₁₆×C₂₃	C₂²	semidirect
82. C₂×C₂₃×#97	C₂²	semidirect
285. #61019	C₂₃	direct (N × H)
338. #3512	C₂×C₂₃	semidirect
339. #3508	C₂×C₂₃	semidirect
340. #3260	C₂×C₂₃	semidirect
341. #3259	C₂×C₂₃	semidirect
342. #3240	C₂×C₂₃	semidirect
343. #3234	C₂×C₂₃	semidirect
344. #3217	C₂×C₂₃	semidirect
345. #3214	C₂×C₂₃	semidirect
346. #3198	C₂×C₂₃	semidirect
347. #3180	C₂×C₂₃	semidirect
348. #3171	C₂×C₂₃	semidirect
349. #3123	C₂×C₂₃	semidirect
350. #3122	C₂×C₂₃	semidirect
351. #3119	C₂×C₂₃	semidirect
352. #2923	C₂×C₂₃	semidirect
388. #541	C₂²×C₂₃	semidirect
392. #540	C₂²×C₂₃	semidirect
398. #532	C₂²×C₂₃	semidirect
401. #529	C₂²×C₂₃	semidirect
402. C₂×#125	C₂²×C₂₃	semidirect
403. #520	C₂²×C₂₃	semidirect
406. #501	C₂²×C₂₃	semidirect
407. #501	C₂²×C₂₃	semidirect
412. #489	C₂²×C₂₃	semidirect
413. #489	C₂²×C₂₃	semidirect
416. #481	C₂²×C₂₃	semidirect
417. #480	C₂²×C₂₃	semidirect
418. #479	C₂²×C₂₃	semidirect
419. #478	C₂²×C₂₃	semidirect
420. #478	C₂²×C₂₃	semidirect
421. #478	C₂²×C₂₃	semidirect
422. #469	C₂²×C₂₃	semidirect
423. #468	C₂²×C₂₃	semidirect
424. #466	C₂²×C₂₃	semidirect
425. #465	C₂²×C₂₃	semidirect
426. #461	C₂²×C₂₃	semidirect
429. #459	C₂²×C₂₃	semidirect
431. #449	C₂²×C₂₃	semidirect
432. #449	C₂²×C₂₃	semidirect
434. #442	C₂²×C₂₃	semidirect
435. #440	C₂²×C₂₃	semidirect
436. C₄×SD₁₆	C₂²×C₂₃	semidirect
437. C₄×D₈	C₂²×C₂₃	semidirect
439. #433	C₂²×C₂₃	semidirect
441. #432	C₂²×C₂₃	semidirect
442. #424	C₂²×C₂₃	semidirect
444. C₄×M₁₆	C₂²×C₂₃	semidirect
445. C₂×#97	C₂²×C₂₃	semidirect
566. C₂₃	#61019	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×#3512	2
C₂₃×#3508	2
C₂₃×#3260	2
C₂₃×#3259	2
C₂₃×#3240	2
C₂₃×#3234	2
C₂₃×#3217	2
C₂₃×#3214	2
C₂₃×#3198	2
C₂₃×#3180	2
C₂₃×#3171	2
C₂₃×#3123	2
C₂₃×#3122	2
C₂₃×#3119	2
C₂₃×#2923	2
#61019	23

Subgroups — C23×#61019 #19208645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61019 #19208645