Subgroups — C₂₃×#60797 #19208423

Order 5888.

2062 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3224	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3223	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3222	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3221	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3035	C₂	1	4	yes	maximal, complemented
14	C₂₃×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	2	yes	—
17	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
18	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
19	C₂₃×#542	C₂²	1	4	yes	complemented
20	C₂₃×#541	C₂²	1	2	yes	complemented
21	C₂₃×#540	C₂²	1	2	yes	complemented
22	C₂₃×#539	—	2	2	no	—
23	C₂₃×#538	—	2	2	no	—
24	C₂₃×#537	—	2	2	no	—
25	C₂₃×#536	C₂²	1	2	yes	—
26	C₂₃×#536	C₂²	1	2	yes	—
27	C₂₃×#535	C₂²	1	2	yes	—
28	C₂₃×#535	C₂²	1	2	yes	—
29	C₂₃×#534	—	2	2	no	—
30	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#532	C₂²	1	2	yes	—
32	C₂₃×#532	C₂²	1	1	yes	characteristic
33	C₂₃×#532	C₂²	1	1	yes	characteristic
34	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#529	—	2	4	no	—
36	C₂₃×#525	—	2	4	no	—
37	C₂₃×#525	C₂²	1	2	yes	—
38	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
39	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
40	C₂₃×#497	C₂²	1	2	yes	complemented
41	C₂₃×#497	C₂²	1	2	yes	complemented
42	C₂₃×#496	C₂²	1	2	yes	complemented
43	C₂₃×#496	C₂²	1	2	yes	complemented
44	C₂₃×#495	C₂²	1	4	yes	complemented
45	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#491	C₂²	1	2	yes	complemented
50	C₂₃×#490	C₂²	1	2	yes	complemented
51	C₂₃×#489	C₂²	1	4	yes	complemented
52	C₂₃×#488	C₂²	1	2	yes	complemented
53	C₂₃×#488	C₂²	1	2	yes	complemented
54	C₂₃×#487	C₂²	1	2	yes	complemented
55	C₂₃×#486	C₂²	1	2	yes	complemented
56	C₂₃×#464	C₂²	1	4	yes	complemented
57	C₂₃×#464	C₂²	1	4	yes	complemented
58	C₂₃×#463	C₂²	1	4	yes	complemented
59	C₂₃×#463	C₂²	1	4	yes	complemented
60	C₂₃×#462	C₂²	1	4	yes	complemented
61	C₂₃×#461	C₂²	1	4	yes	complemented
62	C₂₃×#460	C₂²	1	4	yes	complemented
63	C₂₃×#459	C₂²	1	4	yes	complemented
64	C₂₃×#452	C₂²	1	4	yes	—
65	C₂₃×#452	C₂²	1	4	yes	—
66	C₂₃×#451	C₂²	1	4	yes	complemented
67	C₂₃×#450	C₂²	1	4	yes	complemented
68	C₂₃×#449	C₂²	1	4	yes	—
69	C₂₃×#449	C₂²	1	4	yes	—
70	C₂₃×#448	C₂²	1	4	yes	complemented
71	C₂₃×#447	C₂²	1	4	yes	complemented
72	C₂₃×#433	C₂²	1	2	yes	complemented
73	C₂₃×#433	C₂²	1	2	yes	complemented
74	C₂₃×#433	C₂²	1	4	yes	complemented
75	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
76	C₂₃×#416	C₂²	1	4	yes	complemented
77	C₂₃×#416	C₂²	1	4	yes	complemented
78	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
79	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×#41×C₂₃	—	2	2	no	—
82	C₂×#41×C₂₃	—	2	2	no	—
83	C₂×#41×C₂₃	—	4	8	no	—
84	C₂×#41×C₂₃	C₂³	1	2	yes	—
85	C₂×#41×C₂₃	C₂³	1	2	yes	—
86	C₂×#41×C₂₃	C₂³	1	2	yes	—
87	C₂×#41×C₂₃	C₂³	1	2	yes	—
88	C₂×#41×C₂₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₂₃	—	2	2	no	—
91	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₂₃	—	2	2	no	—
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×#135	—	4	8	no	—
95	C₂₃×#135	—	4	8	no	—
96	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
97	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×D₈×C₂₃	C₂³	1	4	yes	—
103	C₂×D₈×C₂₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
106	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₂₃×#127	C₂³	1	2	yes	—
112	C₂₃×#127	C₂³	1	1	yes	characteristic
113	C₂₃×#127	C₂³	1	1	yes	characteristic
114	C₂₃×#127	C₂³	1	1	yes	characteristic
115	C₂₃×#126	—	2	4	no	—
116	C₂₃×#126	—	2	4	no	—
117	C₂₃×#125	—	2	4	no	—
118	C₂₃×#125	C₂³	1	2	yes	—
119	C₂₃×#124	—	2	4	no	—
120	C₂₃×#124	C₂³	1	2	yes	—
121	C₂₃×#124	C₂³	1	2	yes	—
122	C₂₃×#124	C₂³	1	2	yes	—
123	C₂₃×#124	C₂³	1	2	yes	—
124	C₂₃×#124	C₂³	1	2	yes	—
125	C₂₃×#123	—	2	2	no	—
126	C₂₃×#123	—	2	4	no	—
127	C₂₃×#123	—	2	4	no	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	—	2	4	no	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₂₃×#121	—	2	4	no	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	2	no	—
139	C₂₃×#121	—	2	4	no	—
140	C₂₃×#121	—	2	4	no	—
141	C₂₃×#121	—	2	4	no	—
142	C₂₃×#121	C₂³	1	4	yes	—
143	C₂₃×#120	—	2	2	no	—
144	C₂₃×#120	—	2	4	no	—
145	C₂₃×#120	—	2	4	no	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
148	C₄×D₄×C₂₃	—	2	4	no	—
149	C₄×D₄×C₂₃	—	2	4	no	—
150	C₄×D₄×C₂₃	—	2	4	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	C₂³	1	4	yes	—
155	C₂₃×#117	—	2	2	no	—
156	C₂₃×#117	D₄	1	4	yes	—
157	C₂₃×#117	C₂³	1	2	yes	—
158	C₂₃×#117	C₂³	1	2	yes	—
159	C₂₃×#117	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
162	C₂×C₄²×C₂₃	—	2	2	no	—
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
165	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
166	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
167	C₂₃×#103	C₂³	1	4	yes	—
168	C₂₃×#103	C₂³	1	4	yes	—
169	C₂₃×#103	C₂³	1	4	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#102	C₂³	1	4	yes	—
172	C₂₃×#102	C₂³	1	4	yes	—
173	C₂₃×#102	C₂³	1	4	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₂₃×#97	C₂³	1	2	yes	—
178	C₂₃×#97	C₂³	1	2	yes	—
179	C₄×C₈×C₂₃	C₂³	1	2	yes	—
180	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
182	C₂⁴×C₂₃	—	2	2	no	—
183	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
184	#41×C₂₃	—	2	8	no	—
185	#41×C₂₃	—	2	8	no	—
186	#41×C₂₃	—	2	8	no	—
187	#41×C₂₃	—	4	4	no	—
188	#41×C₂₃	—	4	4	no	—
189	#41×C₂₃	—	4	8	no	—
190	#41×C₂₃	—	4	8	no	—
191	C₂×Q₈×C₂₃	—	2	2	no	—
192	C₂×Q₈×C₂₃	—	2	2	no	—
193	C₂×Q₈×C₂₃	—	4	4	no	—
194	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
195	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	2	2	no	—
199	C₂×D₄×C₂₃	—	2	2	no	—
200	C₂×D₄×C₂₃	—	2	2	no	—
201	C₂×D₄×C₂₃	—	2	2	no	—
202	C₂×D₄×C₂₃	—	2	4	no	—
203	C₂×D₄×C₂₃	—	2	2	no	—
204	C₂×D₄×C₂₃	—	2	4	no	—
205	C₂×D₄×C₂₃	—	2	2	no	—
206	C₂×D₄×C₂₃	—	2	2	no	—
207	C₂×D₄×C₂₃	—	2	2	no	—
208	C₂×D₄×C₂₃	—	4	4	no	—
209	C₂×D₄×C₂₃	—	4	8	no	—
210	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
212	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	2	no	—
217	C₂²×C₄×C₂₃	—	2	2	no	—
218	C₂²×C₄×C₂₃	—	2	2	no	—
219	C₂²×C₄×C₂₃	—	2	2	no	—
220	C₂²×C₄×C₂₃	—	2	4	no	—
221	C₂²×C₄×C₂₃	—	4	8	no	—
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	Q₁₆×C₂₃	—	4	4	no	—
229	Q₁₆×C₂₃	—	4	4	no	—
230	SD₁₆×C₂₃	—	4	4	no	—
231	SD₁₆×C₂₃	—	4	4	no	—
232	SD₁₆×C₂₃	—	4	4	no	—
233	SD₁₆×C₂₃	—	4	4	no	—
234	D₈×C₂₃	—	4	4	no	—
235	D₈×C₂₃	—	4	4	no	—
236	C₂×C₈×C₂₃	—	2	4	no	—
237	C₂×C₈×C₂₃	—	2	4	no	—
238	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
240	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	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	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	4	no	—
255	C₂²⋊C₄×C₂₃	—	2	4	no	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
263	C₄²×C₂₃	—	2	4	no	—
264	C₄²×C₂₃	—	2	2	no	—
265	C₄²×C₂₃	C₂×D₄	1	2	yes	—
266	C₄²×C₂₃	C₂×D₄	1	2	yes	—
267	C₄²×C₂₃	C₂⁴	1	2	yes	—
268	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
270	#60797	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	4	2	no	—
276	C₂³×C₂₃	—	4	4	no	—
277	C₂³×C₂₃	—	8	4	no	—
278	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
279	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₂₃	—	2	4	no	—
281	Q₈×C₂₃	—	2	4	no	—
282	Q₈×C₂₃	—	2	4	no	—
283	Q₈×C₂₃	—	4	4	no	—
284	Q₈×C₂₃	—	8	2	no	—
285	D₄×C₂₃	—	2	4	no	—
286	D₄×C₂₃	—	2	4	no	—
287	D₄×C₂₃	—	2	4	no	—
288	D₄×C₂₃	—	4	4	no	—
289	D₄×C₂₃	—	4	4	no	—
290	D₄×C₂₃	—	4	4	no	—
291	D₄×C₂₃	—	4	4	no	—
292	D₄×C₂₃	—	4	4	no	—
293	D₄×C₂₃	—	4	4	no	—
294	D₄×C₂₃	—	8	4	no	—
295	D₄×C₂₃	—	8	2	no	—
296	D₄×C₂₃	—	8	2	no	—
297	D₄×C₂₃	—	8	2	no	—
298	D₄×C₂₃	—	8	4	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	4	no	—
301	C₂×C₄×C₂₃	—	2	4	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	4	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	4	2	no	—
307	C₂×C₄×C₂₃	—	4	2	no	—
308	C₂×C₄×C₂₃	—	4	4	no	—
309	C₂×C₄×C₂₃	—	4	4	no	—
310	C₂×C₄×C₂₃	—	4	4	no	—
311	C₂×C₄×C₂₃	—	4	4	no	—
312	C₂×C₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	4	4	no	—
314	C₂×C₄×C₂₃	—	8	4	no	—
315	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
321	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
322	C₈×C₂₃	—	2	2	no	—
323	C₈×C₂₃	—	2	4	no	—
324	C₈×C₂₃	—	2	2	no	—
325	#3455	C₂×C₂₃	1	1	yes	characteristic, complemented
326	#3449	C₂×C₂₃	1	1	yes	characteristic, complemented
327	#3225	C₂×C₂₃	1	4	yes	complemented
328	#3224	C₂×C₂₃	1	4	yes	complemented
329	#3223	C₂×C₂₃	1	2	yes	complemented
330	#3222	C₂×C₂₃	1	2	yes	complemented
331	#3221	C₂×C₂₃	1	2	yes	complemented
332	#3220	C₂×C₂₃	1	2	yes	complemented
333	#3150	C₂×C₂₃	1	1	yes	characteristic, complemented
334	#3147	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#3135	C₂×C₂₃	1	1	yes	characteristic, complemented
336	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#3035	C₂×C₂₃	1	4	yes	complemented
338	#3002	C₂×C₂₃	1	4	yes	complemented
339	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂²×C₂₃	—	2	2	no	—
341	C₂²×C₂₃	—	2	4	no	—
342	C₂²×C₂₃	—	2	2	no	—
343	C₂²×C₂₃	—	4	4	no	—
344	C₂²×C₂₃	—	4	4	no	—
345	C₂²×C₂₃	—	4	4	no	—
346	C₂²×C₂₃	—	4	2	no	—
347	C₂²×C₂₃	—	4	2	no	—
348	C₂²×C₂₃	—	4	2	no	—
349	C₂²×C₂₃	—	8	2	no	—
350	C₂²×C₂₃	—	8	8	no	—
351	C₂²×C₂₃	#535	1	2	yes	—
352	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
353	C₄×C₂₃	—	2	4	no	—
354	C₄×C₂₃	—	2	2	no	—
355	C₄×C₂₃	—	2	2	no	—
356	C₄×C₂₃	—	2	2	no	—
357	C₄×C₂₃	—	4	4	no	—
358	C₄×C₂₃	—	4	2	no	—
359	C₄×C₂₃	—	4	2	no	—
360	C₄×C₂₃	—	4	2	no	—
361	C₄×C₂₃	#535	1	2	yes	—
362	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
363	C₂²×#41	C₂²×C₂₃	1	2	yes	—
364	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
365	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
366	#542	C₂²×C₂₃	1	4	yes	complemented
367	#541	C₂²×C₂₃	1	2	yes	complemented
368	#540	C₂²×C₂₃	1	2	yes	complemented
369	#539	—	2	2	no	—
370	#538	—	2	2	no	—
371	#537	—	2	2	no	—
372	#536	C₂²×C₂₃	1	2	yes	—
373	#536	C₂²×C₂₃	1	2	yes	—
374	#535	C₂²×C₂₃	1	2	yes	—
375	#535	C₂²×C₂₃	1	2	yes	—
376	#534	—	2	2	no	—
377	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
378	#532	C₂²×C₂₃	1	1	yes	characteristic
379	#532	C₂²×C₂₃	1	1	yes	characteristic
380	#532	C₂²×C₂₃	1	2	yes	—
381	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
382	#529	—	2	4	no	—
383	#525	—	2	4	no	—
384	#525	C₂²×C₂₃	1	2	yes	—
385	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
386	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
387	#497	C₂²×C₂₃	1	2	yes	complemented
388	#497	C₂²×C₂₃	1	2	yes	complemented
389	#496	C₂²×C₂₃	1	2	yes	complemented
390	#496	C₂²×C₂₃	1	2	yes	complemented
391	#495	C₂²×C₂₃	1	4	yes	complemented
392	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
393	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
394	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
395	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
396	#491	C₂²×C₂₃	1	2	yes	complemented
397	#490	C₂²×C₂₃	1	2	yes	complemented
398	#489	C₂²×C₂₃	1	4	yes	complemented
399	#488	C₂²×C₂₃	1	2	yes	complemented
400	#488	C₂²×C₂₃	1	2	yes	complemented
401	#487	C₂²×C₂₃	1	2	yes	complemented
402	#486	C₂²×C₂₃	1	2	yes	complemented
403	#464	C₂²×C₂₃	1	4	yes	complemented
404	#464	C₂²×C₂₃	1	4	yes	complemented
405	#463	C₂²×C₂₃	1	4	yes	complemented
406	#463	C₂²×C₂₃	1	4	yes	complemented
407	#462	C₂²×C₂₃	1	4	yes	complemented
408	#461	C₂²×C₂₃	1	4	yes	complemented
409	#460	C₂²×C₂₃	1	4	yes	complemented
410	#459	C₂²×C₂₃	1	4	yes	complemented
411	#452	C₂²×C₂₃	1	4	yes	—
412	#452	C₂²×C₂₃	1	4	yes	—
413	#451	C₂²×C₂₃	1	4	yes	complemented
414	#450	C₂²×C₂₃	1	4	yes	complemented
415	#449	C₂²×C₂₃	1	4	yes	—
416	#449	C₂²×C₂₃	1	4	yes	—
417	#448	C₂²×C₂₃	1	4	yes	complemented
418	#447	C₂²×C₂₃	1	4	yes	complemented
419	#433	C₂²×C₂₃	1	2	yes	complemented
420	#433	C₂²×C₂₃	1	2	yes	complemented
421	#433	C₂²×C₂₃	1	4	yes	complemented
422	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
423	#416	C₂²×C₂₃	1	4	yes	complemented
424	#416	C₂²×C₂₃	1	4	yes	complemented
425	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
426	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	C₂×C₂₃	—	2	2	no	—
429	C₂×C₂₃	—	4	2	no	—
430	C₂×C₂₃	—	8	2	no	—
431	C₂×C₂₃	—	8	2	no	—
432	C₂×C₂₃	—	8	2	no	—
433	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
434	C₂×C₂₃	#3584	1	2	yes	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	2	2	no	—
437	C₂×#41	—	4	8	no	—
438	C₂×#41	C₂³×C₂₃	1	2	yes	—
439	C₂×#41	C₂³×C₂₃	1	2	yes	—
440	C₂×#41	C₂³×C₂₃	1	2	yes	—
441	C₂×#41	C₂³×C₂₃	1	2	yes	—
442	C₂×#41	C₂³×C₂₃	1	2	yes	—
443	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
444	C₂²×D₄	—	2	2	no	—
445	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
446	C₂³×C₄	—	2	2	no	—
447	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
448	#135	—	4	8	no	—
449	#135	—	4	8	no	—
450	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
451	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
452	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
453	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
454	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
455	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
456	C₂×D₈	C₂³×C₂₃	1	4	yes	—
457	C₂×D₈	C₂³×C₂₃	1	4	yes	—
458	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
459	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
460	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
461	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
465	#127	C₂³×C₂₃	1	2	yes	—
466	#127	C₂³×C₂₃	1	1	yes	characteristic
467	#127	C₂³×C₂₃	1	1	yes	characteristic
468	#127	C₂³×C₂₃	1	1	yes	characteristic
469	#126	—	2	4	no	—
470	#126	—	2	4	no	—
471	#125	—	2	4	no	—
472	#125	C₂³×C₂₃	1	2	yes	—
473	#124	—	2	4	no	—
474	#124	C₂³×C₂₃	1	2	yes	—
475	#124	C₂³×C₂₃	1	2	yes	—
476	#124	C₂³×C₂₃	1	2	yes	—
477	#124	C₂³×C₂₃	1	2	yes	—
478	#124	C₂³×C₂₃	1	2	yes	—
479	#123	—	2	2	no	—
480	#123	—	2	4	no	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
489	#121	—	2	4	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	4	no	—
494	#121	—	2	4	no	—
495	#121	—	2	4	no	—
496	#121	C₂³×C₂₃	1	4	yes	—
497	#120	—	2	2	no	—
498	#120	—	2	4	no	—
499	#120	—	2	4	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
502	C₄×D₄	—	2	4	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	C₂³×C₂₃	1	4	yes	—
509	#117	—	2	2	no	—
510	#117	D₄×C₂₃	1	4	yes	—
511	#117	C₂³×C₂₃	1	2	yes	—
512	#117	C₂³×C₂₃	1	2	yes	—
513	#117	C₂³×C₂₃	1	2	yes	—
514	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
515	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
516	C₂×C₄²	—	2	2	no	—
517	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
520	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
521	#103	C₂³×C₂₃	1	4	yes	—
522	#103	C₂³×C₂₃	1	4	yes	—
523	#103	C₂³×C₂₃	1	4	yes	—
524	#103	C₂³×C₂₃	1	4	yes	—
525	#102	C₂³×C₂₃	1	4	yes	—
526	#102	C₂³×C₂₃	1	4	yes	—
527	#102	C₂³×C₂₃	1	4	yes	—
528	#102	C₂³×C₂₃	1	4	yes	—
529	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
530	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
531	#97	C₂³×C₂₃	1	2	yes	—
532	#97	C₂³×C₂₃	1	2	yes	—
533	C₄×C₈	C₂³×C₂₃	1	2	yes	—
534	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
535	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
536	C₂₃	#60797	1	1	yes	characteristic, direct product factor, Sylow
537	C₂⁴	—	2	2	no	—
538	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
539	#41	—	2	8	no	—
540	#41	—	2	8	no	—
541	#41	—	2	8	no	—
542	#41	—	4	4	no	—
543	#41	—	4	4	no	—
544	#41	—	4	8	no	—
545	#41	—	4	8	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	4	4	no	—
549	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
550	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
551	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	4	8	no	—
565	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
566	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
567	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	4	8	no	—
577	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
580	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
583	Q₁₆	—	4	4	no	—
584	Q₁₆	—	4	4	no	—
585	SD₁₆	—	4	4	no	—
586	SD₁₆	—	4	4	no	—
587	SD₁₆	—	4	4	no	—
588	SD₁₆	—	4	4	no	—
589	D₈	—	4	4	no	—
590	D₈	—	4	4	no	—
591	C₂×C₈	—	2	4	no	—
592	C₂×C₈	—	2	4	no	—
593	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
594	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
595	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
605	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
606	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
617	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	4	no	—
620	C₄²	C₂×D₄×C₂₃	1	2	yes	—
621	C₄²	C₂×D₄×C₂₃	1	2	yes	—
622	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
623	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
624	C₄²	C₂⁴×C₂₃	1	2	yes	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	4	no	—
631	C₂³	—	8	4	no	—
632	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
633	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
634	Q₈	—	2	4	no	—
635	Q₈	—	2	4	no	—
636	Q₈	—	2	4	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	8	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	4	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	2	no	—
652	D₄	—	8	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
674	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
675	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
676	C₈	—	2	2	no	—
677	C₈	—	2	4	no	—
678	C₈	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	8	no	—
690	C₂²	C₂₃×#535	1	2	yes	—
691	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	4	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	4	no	—
700	C₄	C₂₃×#535	1	2	yes	—
701	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
702	C₂	—	2	2	no	—
703	C₂	—	4	2	no	—
704	C₂	—	8	2	no	—
705	C₂	—	8	2	no	—
706	C₂	—	8	2	no	—
707	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
708	C₂	C₂₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3455	C₂	semidirect
2. C₂₃×#3449	C₂	semidirect
3. C₂₃×#3225	C₂	semidirect
4. C₂₃×#3224	C₂	semidirect
5. C₂₃×#3223	C₂	semidirect
6. C₂₃×#3222	C₂	semidirect
7. C₂₃×#3221	C₂	semidirect
8. C₂₃×#3220	C₂	semidirect
9. C₂₃×#3150	C₂	semidirect
10. C₂₃×#3147	C₂	semidirect
11. C₂₃×#3135	C₂	semidirect
12. C₂₃×#3131	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂₃×#3002	C₂	semidirect
15. C₂×C₂₃×#433	C₂	semidirect
17. C₂×C₂₃×#135	C₂²	semidirect
18. C₂×C₂₃×#135	C₂²	semidirect
19. C₂₃×#542	C₂²	semidirect
20. C₂₃×#541	C₂²	semidirect
21. C₂₃×#540	C₂²	semidirect
30. C₂₃×#533	C₂²	semidirect
34. C₂₃×#532	C₂²	semidirect
38. C₄×#41×C₂₃	C₂²	semidirect
40. C₂₃×#497	C₂²	semidirect
41. C₂₃×#497	C₂²	semidirect
42. C₂₃×#496	C₂²	semidirect
43. C₂₃×#496	C₂²	semidirect
44. C₂₃×#495	C₂²	semidirect
45. C₂₃×#494	C₂²	semidirect
46. C₂₃×#493	C₂²	semidirect
47. C₂₃×#492	C₂²	semidirect
48. C₂₃×#492	C₂²	semidirect
49. C₂₃×#491	C₂²	semidirect
50. C₂₃×#490	C₂²	semidirect
51. C₂₃×#489	C₂²	semidirect
52. C₂₃×#488	C₂²	semidirect
53. C₂₃×#488	C₂²	semidirect
54. C₂₃×#487	C₂²	semidirect
55. C₂₃×#486	C₂²	semidirect
56. C₂₃×#464	C₂²	semidirect
57. C₂₃×#464	C₂²	semidirect
58. C₂₃×#463	C₂²	semidirect
59. C₂₃×#463	C₂²	semidirect
60. C₂₃×#462	C₂²	semidirect
61. C₂₃×#461	C₂²	semidirect
62. C₂₃×#460	C₂²	semidirect
63. C₂₃×#459	C₂²	semidirect
66. C₂₃×#451	C₂²	semidirect
67. C₂₃×#450	C₂²	semidirect
70. C₂₃×#448	C₂²	semidirect
71. C₂₃×#447	C₂²	semidirect
72. C₂₃×#433	C₂²	semidirect
73. C₂₃×#433	C₂²	semidirect
74. C₂₃×#433	C₂²	semidirect
75. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
76. C₂₃×#416	C₂²	semidirect
77. C₂₃×#416	C₂²	semidirect
79. C₂×C₂₃×#97	C₂²	semidirect
80. C₂×C₄×C₈×C₂₃	C₂²	semidirect
270. #60797	C₂₃	direct (N × H)
325. #3455	C₂×C₂₃	semidirect
326. #3449	C₂×C₂₃	semidirect
327. #3225	C₂×C₂₃	semidirect
328. #3224	C₂×C₂₃	semidirect
329. #3223	C₂×C₂₃	semidirect
330. #3222	C₂×C₂₃	semidirect
331. #3221	C₂×C₂₃	semidirect
332. #3220	C₂×C₂₃	semidirect
333. #3150	C₂×C₂₃	semidirect
334. #3147	C₂×C₂₃	semidirect
335. #3135	C₂×C₂₃	semidirect
336. #3131	C₂×C₂₃	semidirect
337. #3035	C₂×C₂₃	semidirect
338. #3002	C₂×C₂₃	semidirect
339. C₂×#433	C₂×C₂₃	semidirect
364. C₂×#135	C₂²×C₂₃	semidirect
365. C₂×#135	C₂²×C₂₃	semidirect
366. #542	C₂²×C₂₃	semidirect
367. #541	C₂²×C₂₃	semidirect
368. #540	C₂²×C₂₃	semidirect
377. #533	C₂²×C₂₃	semidirect
381. #532	C₂²×C₂₃	semidirect
385. C₄×#41	C₂²×C₂₃	semidirect
387. #497	C₂²×C₂₃	semidirect
388. #497	C₂²×C₂₃	semidirect
389. #496	C₂²×C₂₃	semidirect
390. #496	C₂²×C₂₃	semidirect
391. #495	C₂²×C₂₃	semidirect
392. #494	C₂²×C₂₃	semidirect
393. #493	C₂²×C₂₃	semidirect
394. #492	C₂²×C₂₃	semidirect
395. #492	C₂²×C₂₃	semidirect
396. #491	C₂²×C₂₃	semidirect
397. #490	C₂²×C₂₃	semidirect
398. #489	C₂²×C₂₃	semidirect
399. #488	C₂²×C₂₃	semidirect
400. #488	C₂²×C₂₃	semidirect
401. #487	C₂²×C₂₃	semidirect
402. #486	C₂²×C₂₃	semidirect
403. #464	C₂²×C₂₃	semidirect
404. #464	C₂²×C₂₃	semidirect
405. #463	C₂²×C₂₃	semidirect
406. #463	C₂²×C₂₃	semidirect
407. #462	C₂²×C₂₃	semidirect
408. #461	C₂²×C₂₃	semidirect
409. #460	C₂²×C₂₃	semidirect
410. #459	C₂²×C₂₃	semidirect
413. #451	C₂²×C₂₃	semidirect
414. #450	C₂²×C₂₃	semidirect
417. #448	C₂²×C₂₃	semidirect
418. #447	C₂²×C₂₃	semidirect
419. #433	C₂²×C₂₃	semidirect
420. #433	C₂²×C₂₃	semidirect
421. #433	C₂²×C₂₃	semidirect
422. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
423. #416	C₂²×C₂₃	semidirect
424. #416	C₂²×C₂₃	semidirect
426. C₂×#97	C₂²×C₂₃	semidirect
427. C₂×C₄×C₈	C₂²×C₂₃	semidirect
536. C₂₃	#60797	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×#3455	2
C₂₃×#3449	2
C₂₃×#3225	2
C₂₃×#3224	2
C₂₃×#3223	2
C₂₃×#3222	2
C₂₃×#3221	2
C₂₃×#3220	2
C₂₃×#3150	2
C₂₃×#3147	2
C₂₃×#3135	2
C₂₃×#3131	2
C₂₃×#3035	2
C₂₃×#3002	2
C₂×C₂₃×#433	2
#60797	23

Subgroups — C23×#60797 #19208423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60797 #19208423