Subgroups — C₂₃×#62839 #19210465

Order 5888.

6616 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3557	C₂	1	6	yes	maximal, complemented
2	C₂₃×#3551	C₂	1	6	yes	maximal, complemented
3	C₂₃×#3540	C₂	1	6	yes	maximal, complemented
4	C₂₃×#3539	C₂	1	6	yes	maximal, complemented
5	C₂₃×#3524	C₂	1	12	yes	maximal, complemented
6	C₂₃×#3521	C₂	1	12	yes	maximal, complemented
7	C₂₃×#3511	C₂	1	6	yes	maximal, complemented
8	C₂₃×#3509	C₂	1	3	yes	maximal, complemented
9	C₂₃×#3508	C₂	1	3	yes	maximal, complemented
10	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3444	C₂	1	2	yes	maximal, complemented
12	C₂₃×#563	C₂²	1	12	yes	complemented
13	C₂₃×H(3,𝔽₄)	C₂²	1	4	yes	—
14	C₂₃×#560	C₂²	1	12	yes	complemented
15	C₂₃×#560	C₂²	1	4	yes	complemented
16	C₂₃×#559	C₂²	1	12	yes	complemented
17	C₂₃×#559	C₂²	1	12	yes	complemented
18	C₂₃×#557	C₂²	1	12	yes	complemented
19	C₂₃×#556	C₂²	1	12	yes	—
20	C₂₃×#556	C₂²	1	12	yes	complemented
21	C₂₃×#555	C₂²	1	12	yes	complemented
22	C₂₃×#555	C₂²	1	12	yes	complemented
23	C₂₃×#554	C₂²	1	12	yes	complemented
24	C₂₃×#553	C₂²	1	12	yes	complemented
25	C₂₃×#553	C₂²	1	12	yes	complemented
26	C₂₃×#553	C₂²	1	24	yes	complemented
27	C₂₃×#552	C₂²	1	12	yes	complemented
28	C₂₃×#552	C₂²	1	12	yes	complemented
29	C₂₃×#552	C₂²	1	24	yes	complemented
30	C₂₃×#551	C₂²	1	12	yes	—
31	C₂₃×#551	C₂²	1	12	yes	complemented
32	C₂₃×#550	C₂²	1	12	yes	—
33	C₂₃×#548	C₂²	1	12	yes	complemented
34	C₂₃×#548	C₂²	1	12	yes	complemented
35	C₂₃×#547	C₂²	1	12	yes	complemented
36	C₂₃×#546	C₂²	1	12	yes	—
37	C₂₃×#546	C₂²	1	12	yes	complemented
38	C₂₃×#542	C₂²	1	12	yes	complemented
39	C₂₃×#542	C₂²	1	12	yes	complemented
40	C₂₃×#542	C₂²	1	24	yes	complemented
41	C₂₃×#541	C₂²	1	6	yes	complemented
42	C₂₃×#541	C₂²	1	6	yes	complemented
43	C₂₃×#540	C₂²	1	6	yes	—
44	C₂₃×#540	C₂²	1	6	yes	complemented
45	C₂₃×#540	C₂²	1	24	yes	complemented
46	C₂₃×#539	C₂²	1	24	yes	complemented
47	C₂₃×#538	C₂²	1	24	yes	—
48	C₂₃×#537	C₂²	1	12	yes	complemented
49	C₂₃×#536	C₂²	1	6	yes	—
50	C₂₃×#535	C₂²	1	6	yes	—
51	C₂₃×#533	C₂²	1	6	yes	complemented
52	C₂₃×#533	C₂²	1	3	yes	complemented
53	C₂₃×#533	C₂²	1	3	yes	complemented
54	C₂₃×#533	C₂²	1	3	yes	complemented
55	C₂₃×#532	C₂²	1	6	yes	—
56	C₂₃×#532	C₂²	1	3	yes	—
57	C₂₃×#532	C₂²	1	6	yes	complemented
58	C₂×C₂₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
59	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#529	C₂²	1	6	yes	—
61	C₂₃×#529	C₂²	1	12	yes	complemented
62	C₂₃×#529	C₂²	1	6	yes	complemented
63	C₂₃×#529	C₂²	1	12	yes	complemented
64	C₂₃×#529	C₂²	1	24	yes	complemented
65	C₂×C₂₃×#126	C₂²	1	8	yes	complemented
66	C₂₃×#525	C₂²	1	3	yes	—
67	C₂₃×#525	C₂²	1	3	yes	complemented
68	C₂₃×#525	C₂²	1	12	yes	complemented
69	C₂₃×#520	C₂²	1	12	yes	complemented
70	C₂₃×#519	C₂²	1	6	yes	complemented
71	C₂₃×#518	C₂²	1	6	yes	complemented
72	C₄×#41×C₂₃	C₂²	1	3	yes	—
73	C₄×#41×C₂₃	C₂²	1	3	yes	complemented
74	C₄×#41×C₂₃	C₂²	1	12	yes	complemented
75	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#41×C₂₃	C₂³	1	12	yes	—
77	C₂×#41×C₂₃	C₂³	1	12	yes	—
78	C₂×#41×C₂₃	C₂³	1	3	yes	—
79	C₂×#41×C₂₃	C₂³	1	3	yes	—
80	C₂²×Q₈×C₂₃	C₂³	1	6	yes	—
81	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
82	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
83	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
84	C₂₃×C₄⋊Q₈	C₂³	1	12	yes	—
85	C₂₃×C₄⋊Q₈	C₂³	1	12	yes	—
86	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
87	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
88	C₂₃×#127	C₂³	1	6	yes	—
89	C₂₃×#127	C₂³	1	12	yes	—
90	C₂₃×#127	C₂³	1	1	yes	characteristic
91	C₂₃×#127	C₂³	1	2	yes	—
92	C₂₃×#126	C₂³	1	24	yes	—
93	C₂₃×#126	C₂³	1	24	yes	—
94	C₂₃×#126	C₂³	1	24	yes	—
95	C₂₃×#126	C₂³	1	24	yes	—
96	C₂₃×#126	C₂³	1	8	yes	—
97	C₂₃×#126	C₂³	1	2	yes	—
98	C₂₃×#126	C₂³	1	8	yes	—
99	C₂₃×#126	C₂³	1	6	yes	—
100	C₂₃×#125	C₂³	1	6	yes	—
101	C₂₃×#125	C₂³	1	24	yes	—
102	C₂₃×#125	C₂³	1	6	yes	—
103	C₂₃×#125	C₂³	1	24	yes	—
104	C₂₃×#125	C₂³	1	12	yes	—
105	C₂₃×#125	C₂³	1	6	yes	—
106	C₂₃×#124	C₂³	1	24	yes	—
107	C₂₃×#124	C₂³	1	24	yes	—
108	C₂₃×#124	C₂³	1	12	yes	—
109	C₂₃×#124	C₂³	1	12	yes	—
110	C₂₃×#124	C₂³	1	12	yes	—
111	C₂₃×#124	C₂³	1	3	yes	—
112	C₂₃×#124	C₂³	1	3	yes	—
113	C₂₃×#124	C₂³	1	12	yes	—
114	C₂₃×#123	C₂³	1	24	yes	—
115	C₂₃×#123	C₂³	1	24	yes	—
116	C₂₃×#123	C₂³	1	3	yes	—
117	C₂₃×#123	C₂³	1	12	yes	—
118	C₂₃×#123	C₂³	1	12	yes	—
119	C₂₃×#123	C₂³	1	24	yes	—
120	C₂₃×#123	C₂³	1	24	yes	—
121	C₂₃×#123	C₂³	1	6	yes	—
122	C₂₃×#123	C₂³	1	3	yes	—
123	C₂₃×#123	C₂³	1	24	yes	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	24	yes	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	24	yes	—
128	C₂₃×C₂²⋊Q₈	C₂³	1	24	yes	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
130	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
131	C₂₃×C₂²⋊Q₈	C₂³	1	6	yes	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
133	C₂₃×#121	C₂³	1	24	yes	—
134	C₂₃×#121	C₂³	1	12	yes	—
135	C₂₃×#121	C₂³	1	24	yes	—
136	C₂₃×#121	C₂³	1	24	yes	—
137	C₂₃×#121	C₂³	1	12	yes	—
138	C₂₃×#121	C₂³	1	12	yes	—
139	C₂₃×#121	C₂³	1	24	yes	—
140	C₂₃×#121	C₂³	1	24	yes	—
141	C₂₃×#121	C₂³	1	6	yes	—
142	C₂₃×#121	C₂³	1	12	yes	—
143	C₂₃×#121	C₂³	1	6	yes	—
144	C₂₃×#120	C₂³	1	12	yes	—
145	C₂₃×#120	C₂³	1	12	yes	—
146	C₂₃×#120	C₂³	1	3	yes	—
147	C₂₃×#120	C₂³	1	8	yes	—
148	C₂₃×#120	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
150	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
151	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
152	C₄×Q₈×C₂₃	C₂³	1	24	yes	—
153	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
156	C₄×D₄×C₂₃	C₂³	1	6	yes	—
157	C₄×D₄×C₂₃	C₂³	1	12	yes	—
158	C₄×D₄×C₂₃	C₂³	1	6	yes	—
159	C₄×D₄×C₂₃	C₂³	1	6	yes	—
160	C₄×D₄×C₂₃	C₂³	1	24	yes	—
161	C₄×D₄×C₂₃	C₂³	1	24	yes	—
162	C₄×D₄×C₂₃	C₂³	1	6	yes	—
163	C₄×D₄×C₂₃	C₂³	1	24	yes	—
164	C₄×D₄×C₂₃	C₂³	1	24	yes	—
165	C₄×D₄×C₂₃	C₂³	1	6	yes	—
166	C₄×D₄×C₂₃	C₂³	1	12	yes	—
167	C₄×D₄×C₂₃	C₂³	1	12	yes	—
168	C₄×D₄×C₂₃	C₂³	1	6	yes	—
169	C₄×D₄×C₂₃	C₂³	1	12	yes	—
170	C₄×D₄×C₂₃	C₂³	1	24	yes	—
171	C₂₃×#117	C₂³	1	24	yes	—
172	C₂₃×#117	C₂³	1	24	yes	—
173	C₂₃×#117	C₂³	1	24	yes	—
174	C₂₃×#117	C₂³	1	6	yes	—
175	C₂₃×#117	C₂³	1	12	yes	—
176	C₂₃×#117	C₂³	1	6	yes	—
177	C₂₃×#117	C₂³	1	3	yes	—
178	C₂₃×#117	C₂³	1	3	yes	—
179	C₂₃×#117	C₂³	1	3	yes	—
180	C₂₃×#117	C₂³	1	6	yes	—
181	C₂₃×#117	C₂³	1	3	yes	—
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	24	yes	—
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	24	yes	—
185	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
186	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
187	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
188	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
190	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
191	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
192	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
193	#41×C₂₃	—	4	6	no	—
194	#41×C₂₃	—	4	6	no	—
195	#41×C₂₃	—	4	24	no	—
196	#41×C₂₃	—	4	24	no	—
197	C₂×Q₈×C₂₃	—	4	12	no	—
198	C₂×Q₈×C₂₃	C₂⁴	1	12	yes	—
199	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
200	C₂×Q₈×C₂₃	C₂⁴	1	12	yes	—
201	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
202	C₂×D₄×C₂₃	—	4	12	no	—
203	C₂×D₄×C₂₃	C₂⁴	1	12	yes	—
204	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
205	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
206	C₂×D₄×C₂₃	C₂⁴	1	24	yes	—
207	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
208	C₂×D₄×C₂₃	C₂⁴	1	24	yes	—
209	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
210	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
211	C₂×D₄×C₂₃	C₂⁴	1	12	yes	—
212	C₂²×C₄×C₂₃	—	4	6	no	—
213	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	24	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	24	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	12	yes	—
223	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
224	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
225	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
226	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
227	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
228	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
229	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
230	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
231	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
232	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
233	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
234	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
235	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
236	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
237	C₂²⋊C₄×C₂₃	C₂⁴	1	12	yes	—
238	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
239	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
240	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
241	C₂²⋊C₄×C₂₃	C₂⁴	1	12	yes	—
242	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
243	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
244	C₂²⋊C₄×C₂₃	C₂⁴	1	6	yes	—
245	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
246	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
247	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
248	C₂²⋊C₄×C₂₃	C₂⁴	1	3	yes	—
249	C₂²⋊C₄×C₂₃	C₂⁴	1	3	yes	—
250	C₄²×C₂₃	C₂⁴	1	2	yes	—
251	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₄²×C₂₃	C₂⁴	1	3	yes	—
253	C₄²×C₂₃	C₂⁴	1	3	yes	—
254	C₄²×C₂₃	C₂⁴	1	6	yes	—
255	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₄²×C₂₃	C₂⁴	1	24	yes	—
257	C₄²×C₂₃	C₂⁴	1	3	yes	—
258	C₄²×C₂₃	C₂⁴	1	6	yes	—
259	C₄²×C₂₃	C₂⁴	1	3	yes	—
260	C₄²×C₂₃	C₂⁴	1	12	yes	—
261	C₄²×C₂₃	C₂⁴	1	12	yes	—
262	#62839	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂³×C₂₃	—	4	3	no	—
264	C₂³×C₂₃	—	4	12	no	—
265	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
266	C₂³×C₂₃	C₂⁵	1	3	yes	—
267	C₂³×C₂₃	C₂⁵	1	8	yes	—
268	C₂³×C₂₃	C₂⁵	1	3	yes	—
269	Q₈×C₂₃	—	2	24	no	—
270	Q₈×C₂₃	—	4	12	no	—
271	Q₈×C₂₃	—	4	3	no	—
272	Q₈×C₂₃	—	4	3	no	—
273	D₄×C₂₃	—	2	24	no	—
274	D₄×C₂₃	—	4	12	no	—
275	D₄×C₂₃	—	4	6	no	—
276	D₄×C₂₃	—	4	3	no	—
277	D₄×C₂₃	—	4	3	no	—
278	D₄×C₂₃	—	4	3	no	—
279	D₄×C₂₃	—	4	3	no	—
280	D₄×C₂₃	—	4	24	no	—
281	D₄×C₂₃	—	4	24	no	—
282	C₂×C₄×C₂₃	—	2	12	no	—
283	C₂×C₄×C₂₃	—	2	6	no	—
284	C₂×C₄×C₂₃	—	2	6	no	—
285	C₂×C₄×C₂₃	—	2	6	no	—
286	C₂×C₄×C₂₃	—	2	12	no	—
287	C₂×C₄×C₂₃	—	4	3	no	—
288	C₂×C₄×C₂₃	—	4	6	no	—
289	C₂×C₄×C₂₃	—	4	12	no	—
290	C₂×C₄×C₂₃	—	4	24	no	—
291	C₂×C₄×C₂₃	—	4	24	no	—
292	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
293	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
294	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
295	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
296	C₂×C₄×C₂₃	C₂⁵	1	24	yes	—
297	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
298	C₂×C₄×C₂₃	C₂⁵	1	3	yes	—
299	#3557	C₂×C₂₃	1	6	yes	complemented
300	#3551	C₂×C₂₃	1	6	yes	complemented
301	#3540	C₂×C₂₃	1	6	yes	complemented
302	#3539	C₂×C₂₃	1	6	yes	complemented
303	#3524	C₂×C₂₃	1	12	yes	complemented
304	#3521	C₂×C₂₃	1	12	yes	complemented
305	#3511	C₂×C₂₃	1	6	yes	complemented
306	#3509	C₂×C₂₃	1	3	yes	complemented
307	#3508	C₂×C₂₃	1	3	yes	complemented
308	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
309	#3444	C₂×C₂₃	1	2	yes	complemented
310	C₂²×C₂₃	—	2	3	no	—
311	C₂²×C₂₃	—	2	6	no	—
312	C₂²×C₂₃	—	2	3	no	—
313	C₂²×C₂₃	—	2	6	no	—
314	C₂²×C₂₃	—	2	3	no	—
315	C₂²×C₂₃	—	2	24	no	—
316	C₂²×C₂₃	—	4	4	no	—
317	C₂²×C₂₃	—	16	4	no	—
318	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
319	C₄×C₂₃	—	2	6	no	—
320	C₄×C₂₃	—	2	6	no	—
321	C₄×C₂₃	—	2	3	no	—
322	C₄×C₂₃	—	2	3	no	—
323	C₄×C₂₃	—	2	3	no	—
324	C₄×C₂₃	—	2	24	no	—
325	C₄×C₂₃	#585	1	6	yes	—
326	#563	C₂²×C₂₃	1	12	yes	complemented
327	H(3,𝔽₄)	C₂²×C₂₃	1	4	yes	—
328	#560	C₂²×C₂₃	1	12	yes	complemented
329	#560	C₂²×C₂₃	1	4	yes	complemented
330	#559	C₂²×C₂₃	1	12	yes	complemented
331	#559	C₂²×C₂₃	1	12	yes	complemented
332	#557	C₂²×C₂₃	1	12	yes	complemented
333	#556	C₂²×C₂₃	1	12	yes	—
334	#556	C₂²×C₂₃	1	12	yes	complemented
335	#555	C₂²×C₂₃	1	12	yes	complemented
336	#555	C₂²×C₂₃	1	12	yes	complemented
337	#554	C₂²×C₂₃	1	12	yes	complemented
338	#553	C₂²×C₂₃	1	12	yes	complemented
339	#553	C₂²×C₂₃	1	12	yes	complemented
340	#553	C₂²×C₂₃	1	24	yes	complemented
341	#552	C₂²×C₂₃	1	12	yes	complemented
342	#552	C₂²×C₂₃	1	12	yes	complemented
343	#552	C₂²×C₂₃	1	24	yes	complemented
344	#551	C₂²×C₂₃	1	12	yes	—
345	#551	C₂²×C₂₃	1	12	yes	complemented
346	#550	C₂²×C₂₃	1	12	yes	—
347	#548	C₂²×C₂₃	1	12	yes	complemented
348	#548	C₂²×C₂₃	1	12	yes	complemented
349	#547	C₂²×C₂₃	1	12	yes	complemented
350	#546	C₂²×C₂₃	1	12	yes	—
351	#546	C₂²×C₂₃	1	12	yes	complemented
352	#542	C₂²×C₂₃	1	12	yes	complemented
353	#542	C₂²×C₂₃	1	12	yes	complemented
354	#542	C₂²×C₂₃	1	24	yes	complemented
355	#541	C₂²×C₂₃	1	6	yes	complemented
356	#541	C₂²×C₂₃	1	6	yes	complemented
357	#540	C₂²×C₂₃	1	6	yes	—
358	#540	C₂²×C₂₃	1	6	yes	complemented
359	#540	C₂²×C₂₃	1	24	yes	complemented
360	#539	C₂²×C₂₃	1	24	yes	complemented
361	#538	C₂²×C₂₃	1	24	yes	—
362	#537	C₂²×C₂₃	1	12	yes	complemented
363	#536	C₂²×C₂₃	1	6	yes	—
364	#535	C₂²×C₂₃	1	6	yes	—
365	#533	C₂²×C₂₃	1	6	yes	complemented
366	#533	C₂²×C₂₃	1	3	yes	complemented
367	#533	C₂²×C₂₃	1	3	yes	complemented
368	#533	C₂²×C₂₃	1	3	yes	complemented
369	#532	C₂²×C₂₃	1	6	yes	—
370	#532	C₂²×C₂₃	1	3	yes	—
371	#532	C₂²×C₂₃	1	6	yes	complemented
372	C₂×C₄⋊Q₈	C₂²×C₂₃	1	3	yes	complemented
373	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
374	#529	C₂²×C₂₃	1	6	yes	—
375	#529	C₂²×C₂₃	1	12	yes	complemented
376	#529	C₂²×C₂₃	1	6	yes	complemented
377	#529	C₂²×C₂₃	1	12	yes	complemented
378	#529	C₂²×C₂₃	1	24	yes	complemented
379	C₂×#126	C₂²×C₂₃	1	8	yes	complemented
380	#525	C₂²×C₂₃	1	3	yes	—
381	#525	C₂²×C₂₃	1	3	yes	complemented
382	#525	C₂²×C₂₃	1	12	yes	complemented
383	#520	C₂²×C₂₃	1	12	yes	complemented
384	#519	C₂²×C₂₃	1	6	yes	complemented
385	#518	C₂²×C₂₃	1	6	yes	complemented
386	C₄×#41	C₂²×C₂₃	1	3	yes	—
387	C₄×#41	C₂²×C₂₃	1	3	yes	complemented
388	C₄×#41	C₂²×C₂₃	1	12	yes	complemented
389	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
390	C₂×C₂₃	—	4	3	no	—
391	C₂×C₂₃	—	4	3	no	—
392	C₂×C₂₃	—	4	8	no	—
393	C₂×C₂₃	—	4	1	no	—
394	C₂×C₂₃	C₂×#585	1	3	yes	—
395	C₂×#41	C₂³×C₂₃	1	3	yes	—
396	C₂×#41	C₂³×C₂₃	1	3	yes	—
397	C₂×#41	C₂³×C₂₃	1	12	yes	—
398	C₂×#41	C₂³×C₂₃	1	12	yes	—
399	C₂²×Q₈	C₂³×C₂₃	1	6	yes	—
400	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
401	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
402	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
403	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
404	C₄⋊Q₈	C₂³×C₂₃	1	12	yes	—
405	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
406	C₄⋊Q₈	C₂³×C₂₃	1	12	yes	—
407	#127	C₂³×C₂₃	1	2	yes	—
408	#127	C₂³×C₂₃	1	6	yes	—
409	#127	C₂³×C₂₃	1	1	yes	characteristic
410	#127	C₂³×C₂₃	1	12	yes	—
411	#126	C₂³×C₂₃	1	2	yes	—
412	#126	C₂³×C₂₃	1	8	yes	—
413	#126	C₂³×C₂₃	1	24	yes	—
414	#126	C₂³×C₂₃	1	24	yes	—
415	#126	C₂³×C₂₃	1	6	yes	—
416	#126	C₂³×C₂₃	1	8	yes	—
417	#126	C₂³×C₂₃	1	24	yes	—
418	#126	C₂³×C₂₃	1	24	yes	—
419	#125	C₂³×C₂₃	1	6	yes	—
420	#125	C₂³×C₂₃	1	12	yes	—
421	#125	C₂³×C₂₃	1	24	yes	—
422	#125	C₂³×C₂₃	1	6	yes	—
423	#125	C₂³×C₂₃	1	6	yes	—
424	#125	C₂³×C₂₃	1	24	yes	—
425	#124	C₂³×C₂₃	1	3	yes	—
426	#124	C₂³×C₂₃	1	12	yes	—
427	#124	C₂³×C₂₃	1	3	yes	—
428	#124	C₂³×C₂₃	1	24	yes	—
429	#124	C₂³×C₂₃	1	12	yes	—
430	#124	C₂³×C₂₃	1	12	yes	—
431	#124	C₂³×C₂₃	1	12	yes	—
432	#124	C₂³×C₂₃	1	24	yes	—
433	#123	C₂³×C₂₃	1	3	yes	—
434	#123	C₂³×C₂₃	1	3	yes	—
435	#123	C₂³×C₂₃	1	6	yes	—
436	#123	C₂³×C₂₃	1	24	yes	—
437	#123	C₂³×C₂₃	1	24	yes	—
438	#123	C₂³×C₂₃	1	24	yes	—
439	#123	C₂³×C₂₃	1	12	yes	—
440	#123	C₂³×C₂₃	1	12	yes	—
441	#123	C₂³×C₂₃	1	24	yes	—
442	#123	C₂³×C₂₃	1	24	yes	—
443	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
444	C₂²⋊Q₈	C₂³×C₂₃	1	6	yes	—
445	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
446	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
447	C₂²⋊Q₈	C₂³×C₂₃	1	24	yes	—
448	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
449	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
450	C₂²⋊Q₈	C₂³×C₂₃	1	24	yes	—
451	C₂²⋊Q₈	C₂³×C₂₃	1	24	yes	—
452	#121	C₂³×C₂₃	1	6	yes	—
453	#121	C₂³×C₂₃	1	12	yes	—
454	#121	C₂³×C₂₃	1	6	yes	—
455	#121	C₂³×C₂₃	1	12	yes	—
456	#121	C₂³×C₂₃	1	24	yes	—
457	#121	C₂³×C₂₃	1	12	yes	—
458	#121	C₂³×C₂₃	1	12	yes	—
459	#121	C₂³×C₂₃	1	24	yes	—
460	#121	C₂³×C₂₃	1	24	yes	—
461	#121	C₂³×C₂₃	1	24	yes	—
462	#121	C₂³×C₂₃	1	24	yes	—
463	#120	C₂³×C₂₃	1	1	yes	characteristic
464	#120	C₂³×C₂₃	1	3	yes	—
465	#120	C₂³×C₂₃	1	8	yes	—
466	#120	C₂³×C₂₃	1	12	yes	—
467	#120	C₂³×C₂₃	1	12	yes	—
468	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
469	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
470	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
471	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
472	C₄×Q₈	C₂³×C₂₃	1	24	yes	—
473	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
474	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
475	C₄×D₄	C₂³×C₂₃	1	6	yes	—
476	C₄×D₄	C₂³×C₂₃	1	6	yes	—
477	C₄×D₄	C₂³×C₂₃	1	6	yes	—
478	C₄×D₄	C₂³×C₂₃	1	12	yes	—
479	C₄×D₄	C₂³×C₂₃	1	6	yes	—
480	C₄×D₄	C₂³×C₂₃	1	6	yes	—
481	C₄×D₄	C₂³×C₂₃	1	24	yes	—
482	C₄×D₄	C₂³×C₂₃	1	24	yes	—
483	C₄×D₄	C₂³×C₂₃	1	12	yes	—
484	C₄×D₄	C₂³×C₂₃	1	6	yes	—
485	C₄×D₄	C₂³×C₂₃	1	24	yes	—
486	C₄×D₄	C₂³×C₂₃	1	12	yes	—
487	C₄×D₄	C₂³×C₂₃	1	24	yes	—
488	C₄×D₄	C₂³×C₂₃	1	24	yes	—
489	C₄×D₄	C₂³×C₂₃	1	12	yes	—
490	#117	C₂³×C₂₃	1	3	yes	—
491	#117	C₂³×C₂₃	1	3	yes	—
492	#117	C₂³×C₂₃	1	3	yes	—
493	#117	C₂³×C₂₃	1	6	yes	—
494	#117	C₂³×C₂₃	1	3	yes	—
495	#117	C₂³×C₂₃	1	12	yes	—
496	#117	C₂³×C₂₃	1	24	yes	—
497	#117	C₂³×C₂₃	1	6	yes	—
498	#117	C₂³×C₂₃	1	24	yes	—
499	#117	C₂³×C₂₃	1	6	yes	—
500	#117	C₂³×C₂₃	1	24	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	24	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₂₃	1	24	yes	—
504	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
506	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
507	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
508	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
509	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
510	C₂₃	#62839	1	1	yes	characteristic, direct product factor, Sylow
511	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
512	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
513	#41	—	4	6	no	—
514	#41	—	4	6	no	—
515	#41	—	4	24	no	—
516	#41	—	4	24	no	—
517	C₂×Q₈	—	4	12	no	—
518	C₂×Q₈	C₂⁴×C₂₃	1	12	yes	—
519	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
520	C₂×Q₈	C₂⁴×C₂₃	1	12	yes	—
521	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
522	C₂×D₄	—	4	12	no	—
523	C₂×D₄	C₂⁴×C₂₃	1	12	yes	—
524	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
525	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
526	C₂×D₄	C₂⁴×C₂₃	1	24	yes	—
527	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
528	C₂×D₄	C₂⁴×C₂₃	1	24	yes	—
529	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
530	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
531	C₂×D₄	C₂⁴×C₂₃	1	12	yes	—
532	C₂²×C₄	—	4	6	no	—
533	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
534	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
535	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
536	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
537	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
538	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
539	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
540	C₂²×C₄	C₂⁴×C₂₃	1	24	yes	—
541	C₂²×C₄	C₂⁴×C₂₃	1	24	yes	—
542	C₂²×C₄	C₂⁴×C₂₃	1	12	yes	—
543	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
544	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
545	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
546	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
547	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
548	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
549	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
550	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
551	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
552	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
553	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
554	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
555	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
556	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
557	C₂²⋊C₄	C₂⁴×C₂₃	1	12	yes	—
558	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
559	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
560	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
561	C₂²⋊C₄	C₂⁴×C₂₃	1	12	yes	—
562	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
563	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
564	C₂²⋊C₄	C₂⁴×C₂₃	1	6	yes	—
565	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
566	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
567	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
568	C₂²⋊C₄	C₂⁴×C₂₃	1	3	yes	—
569	C₂²⋊C₄	C₂⁴×C₂₃	1	3	yes	—
570	C₄²	C₂⁴×C₂₃	1	2	yes	—
571	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
572	C₄²	C₂⁴×C₂₃	1	3	yes	—
573	C₄²	C₂⁴×C₂₃	1	3	yes	—
574	C₄²	C₂⁴×C₂₃	1	6	yes	—
575	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
576	C₄²	C₂⁴×C₂₃	1	24	yes	—
577	C₄²	C₂⁴×C₂₃	1	3	yes	—
578	C₄²	C₂⁴×C₂₃	1	6	yes	—
579	C₄²	C₂⁴×C₂₃	1	3	yes	—
580	C₄²	C₂⁴×C₂₃	1	12	yes	—
581	C₄²	C₂⁴×C₂₃	1	12	yes	—
582	C₂³	—	4	3	no	—
583	C₂³	—	4	12	no	—
584	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
585	C₂³	C₂⁵×C₂₃	1	3	yes	—
586	C₂³	C₂⁵×C₂₃	1	8	yes	—
587	C₂³	C₂⁵×C₂₃	1	3	yes	—
588	Q₈	—	2	24	no	—
589	Q₈	—	4	12	no	—
590	Q₈	—	4	3	no	—
591	Q₈	—	4	3	no	—
592	D₄	—	2	24	no	—
593	D₄	—	4	12	no	—
594	D₄	—	4	6	no	—
595	D₄	—	4	3	no	—
596	D₄	—	4	3	no	—
597	D₄	—	4	3	no	—
598	D₄	—	4	3	no	—
599	D₄	—	4	24	no	—
600	D₄	—	4	24	no	—
601	C₂×C₄	—	2	12	no	—
602	C₂×C₄	—	2	6	no	—
603	C₂×C₄	—	2	6	no	—
604	C₂×C₄	—	2	6	no	—
605	C₂×C₄	—	2	12	no	—
606	C₂×C₄	—	4	3	no	—
607	C₂×C₄	—	4	6	no	—
608	C₂×C₄	—	4	12	no	—
609	C₂×C₄	—	4	24	no	—
610	C₂×C₄	—	4	24	no	—
611	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
612	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
613	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
614	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
615	C₂×C₄	C₂⁵×C₂₃	1	24	yes	—
616	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
617	C₂×C₄	C₂⁵×C₂₃	1	3	yes	—
618	C₂²	—	2	3	no	—
619	C₂²	—	2	6	no	—
620	C₂²	—	2	3	no	—
621	C₂²	—	2	6	no	—
622	C₂²	—	2	3	no	—
623	C₂²	—	2	24	no	—
624	C₂²	—	4	4	no	—
625	C₂²	—	16	4	no	—
626	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
627	C₄	—	2	6	no	—
628	C₄	—	2	6	no	—
629	C₄	—	2	3	no	—
630	C₄	—	2	3	no	—
631	C₄	—	2	3	no	—
632	C₄	—	2	24	no	—
633	C₄	C₂₃×#585	1	6	yes	—
634	C₂	—	4	3	no	—
635	C₂	—	4	1	no	—
636	C₂	—	4	8	no	—
637	C₂	—	4	3	no	—
638	C₂	C₂×C₂₃×#585	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3557	C₂	semidirect
2. C₂₃×#3551	C₂	semidirect
3. C₂₃×#3540	C₂	semidirect
4. C₂₃×#3539	C₂	semidirect
5. C₂₃×#3524	C₂	semidirect
6. C₂₃×#3521	C₂	semidirect
7. C₂₃×#3511	C₂	semidirect
8. C₂₃×#3509	C₂	semidirect
9. C₂₃×#3508	C₂	semidirect
10. C₂₃×#3444	C₂	semidirect
11. C₂₃×#3444	C₂	semidirect
12. C₂₃×#563	C₂²	semidirect
14. C₂₃×#560	C₂²	semidirect
15. C₂₃×#560	C₂²	semidirect
16. C₂₃×#559	C₂²	semidirect
17. C₂₃×#559	C₂²	semidirect
18. C₂₃×#557	C₂²	semidirect
20. C₂₃×#556	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#555	C₂²	semidirect
23. C₂₃×#554	C₂²	semidirect
24. C₂₃×#553	C₂²	semidirect
25. C₂₃×#553	C₂²	semidirect
26. C₂₃×#553	C₂²	semidirect
27. C₂₃×#552	C₂²	semidirect
28. C₂₃×#552	C₂²	semidirect
29. C₂₃×#552	C₂²	semidirect
31. C₂₃×#551	C₂²	semidirect
33. C₂₃×#548	C₂²	semidirect
34. C₂₃×#548	C₂²	semidirect
35. C₂₃×#547	C₂²	semidirect
37. C₂₃×#546	C₂²	semidirect
38. C₂₃×#542	C₂²	semidirect
39. C₂₃×#542	C₂²	semidirect
40. C₂₃×#542	C₂²	semidirect
41. C₂₃×#541	C₂²	semidirect
42. C₂₃×#541	C₂²	semidirect
44. C₂₃×#540	C₂²	semidirect
45. C₂₃×#540	C₂²	semidirect
46. C₂₃×#539	C₂²	semidirect
48. C₂₃×#537	C₂²	semidirect
51. C₂₃×#533	C₂²	semidirect
52. C₂₃×#533	C₂²	semidirect
53. C₂₃×#533	C₂²	semidirect
54. C₂₃×#533	C₂²	semidirect
57. C₂₃×#532	C₂²	semidirect
58. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
59. C₂×C₂₃×#127	C₂²	semidirect
61. C₂₃×#529	C₂²	semidirect
62. C₂₃×#529	C₂²	semidirect
63. C₂₃×#529	C₂²	semidirect
64. C₂₃×#529	C₂²	semidirect
65. C₂×C₂₃×#126	C₂²	semidirect
67. C₂₃×#525	C₂²	semidirect
68. C₂₃×#525	C₂²	semidirect
69. C₂₃×#520	C₂²	semidirect
70. C₂₃×#519	C₂²	semidirect
71. C₂₃×#518	C₂²	semidirect
73. C₄×#41×C₂₃	C₂²	semidirect
74. C₄×#41×C₂₃	C₂²	semidirect
75. C₂²×C₄²×C₂₃	C₂²	semidirect
262. #62839	C₂₃	direct (N × H)
299. #3557	C₂×C₂₃	semidirect
300. #3551	C₂×C₂₃	semidirect
301. #3540	C₂×C₂₃	semidirect
302. #3539	C₂×C₂₃	semidirect
303. #3524	C₂×C₂₃	semidirect
304. #3521	C₂×C₂₃	semidirect
305. #3511	C₂×C₂₃	semidirect
306. #3509	C₂×C₂₃	semidirect
307. #3508	C₂×C₂₃	semidirect
308. #3444	C₂×C₂₃	semidirect
309. #3444	C₂×C₂₃	semidirect
326. #563	C₂²×C₂₃	semidirect
328. #560	C₂²×C₂₃	semidirect
329. #560	C₂²×C₂₃	semidirect
330. #559	C₂²×C₂₃	semidirect
331. #559	C₂²×C₂₃	semidirect
332. #557	C₂²×C₂₃	semidirect
334. #556	C₂²×C₂₃	semidirect
335. #555	C₂²×C₂₃	semidirect
336. #555	C₂²×C₂₃	semidirect
337. #554	C₂²×C₂₃	semidirect
338. #553	C₂²×C₂₃	semidirect
339. #553	C₂²×C₂₃	semidirect
340. #553	C₂²×C₂₃	semidirect
341. #552	C₂²×C₂₃	semidirect
342. #552	C₂²×C₂₃	semidirect
343. #552	C₂²×C₂₃	semidirect
345. #551	C₂²×C₂₃	semidirect
347. #548	C₂²×C₂₃	semidirect
348. #548	C₂²×C₂₃	semidirect
349. #547	C₂²×C₂₃	semidirect
351. #546	C₂²×C₂₃	semidirect
352. #542	C₂²×C₂₃	semidirect
353. #542	C₂²×C₂₃	semidirect
354. #542	C₂²×C₂₃	semidirect
355. #541	C₂²×C₂₃	semidirect
356. #541	C₂²×C₂₃	semidirect
358. #540	C₂²×C₂₃	semidirect
359. #540	C₂²×C₂₃	semidirect
360. #539	C₂²×C₂₃	semidirect
362. #537	C₂²×C₂₃	semidirect
365. #533	C₂²×C₂₃	semidirect
366. #533	C₂²×C₂₃	semidirect
367. #533	C₂²×C₂₃	semidirect
368. #533	C₂²×C₂₃	semidirect
371. #532	C₂²×C₂₃	semidirect
372. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
373. C₂×#127	C₂²×C₂₃	semidirect
375. #529	C₂²×C₂₃	semidirect
376. #529	C₂²×C₂₃	semidirect
377. #529	C₂²×C₂₃	semidirect
378. #529	C₂²×C₂₃	semidirect
379. C₂×#126	C₂²×C₂₃	semidirect
381. #525	C₂²×C₂₃	semidirect
382. #525	C₂²×C₂₃	semidirect
383. #520	C₂²×C₂₃	semidirect
384. #519	C₂²×C₂₃	semidirect
385. #518	C₂²×C₂₃	semidirect
387. C₄×#41	C₂²×C₂₃	semidirect
388. C₄×#41	C₂²×C₂₃	semidirect
389. C₂²×C₄²	C₂²×C₂₃	semidirect
510. C₂₃	#62839	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×#3557	2
C₂₃×#3551	2
C₂₃×#3540	2
C₂₃×#3539	2
C₂₃×#3524	2
C₂₃×#3521	2
C₂₃×#3511	2
C₂₃×#3509	2
C₂₃×#3508	2
C₂₃×#3444	2
#62839	23

Subgroups — C23×#62839 #19210465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62839 #19210465