Subgroups — C₂₃×#61832 #19209458

Order 5888.

1674 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3507	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3390	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3388	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3377	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3371	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#3232	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3112	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#559	C₂²	1	2	yes	—
17	C₂₃×#557	—	2	2	no	—
18	C₂₃×#557	—	2	2	no	—
19	C₂₃×#557	C₂²	1	4	yes	—
20	C₂₃×#557	C₂²	1	4	yes	—
21	C₂₃×#557	C₂²	1	2	yes	—
22	C₂₃×#556	—	2	2	no	—
23	C₂₃×#556	C₂²	1	2	yes	—
24	C₂₃×#554	C₂²	1	2	yes	—
25	C₂₃×#552	—	2	2	no	—
26	C₂₃×#539	—	2	1	no	—
27	C₂₃×#539	—	2	1	no	—
28	C₂₃×#536	—	2	1	no	—
29	C₂₃×#533	C₂²	1	1	yes	characteristic
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂₃×#529	C₂²	1	2	yes	—
34	C₂₃×#529	C₂²	1	2	yes	—
35	C₂×C₂₃×#125	—	2	1	no	—
36	C₂×C₂₃×#125	—	2	1	no	—
37	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
39	C₂₃×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
41	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#501	C₂²	1	2	yes	—
46	C₂₃×#501	C₂²	1	2	yes	—
47	C₂₃×#501	C₂²	1	4	yes	—
48	C₂₃×#499	C₂²	1	4	yes	—
49	C₂₃×#491	C₂²	1	2	yes	—
50	C₂₃×#490	C₂²	1	2	yes	—
51	C₂₃×#489	C₂²	1	4	yes	—
52	C₂₃×#488	C₂²	1	4	yes	—
53	C₂₃×#484	C₂²	1	2	yes	—
54	C₂₃×#483	C₂²	1	2	yes	—
55	C₂₃×#483	C₂²	1	2	yes	—
56	C₂₃×#481	C₂²	1	2	yes	—
57	C₂₃×#480	C₂²	1	2	yes	—
58	C₂₃×#480	C₂²	1	2	yes	—
59	C₂₃×#479	C₂²	1	4	yes	—
60	C₂₃×#479	C₂²	1	4	yes	—
61	C₂₃×#479	C₂²	1	4	yes	—
62	C₂₃×#479	C₂²	1	4	yes	—
63	C₂₃×#478	C₂²	1	4	yes	—
64	C₂₃×#478	C₂²	1	4	yes	—
65	C₂₃×#477	C₂²	1	4	yes	—
66	C₂₃×#477	C₂²	1	2	yes	—
67	C₂₃×#476	C₂²	1	4	yes	—
68	C₂₃×#475	C₂²	1	2	yes	—
69	C₂₃×#464	C₂²	1	4	yes	—
70	C₂₃×#464	C₂²	1	4	yes	—
71	C₂₃×#462	C₂²	1	2	yes	—
72	C₂₃×#460	C₂²	1	2	yes	—
73	C₂₃×#451	C₂²	1	2	yes	—
74	C₂₃×#448	C₂²	1	2	yes	—
75	C₂₃×#446	C₂²	1	4	yes	—
76	C₂₃×#446	C₂²	1	4	yes	—
77	C₂₃×#441	C₂²	1	4	yes	—
78	C₂₃×#441	C₂²	1	4	yes	—
79	C₂₃×#440	C₂²	1	4	yes	—
80	C₂₃×#440	C₂²	1	4	yes	—
81	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
82	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
83	C₂₃×#432	C₂²	1	1	yes	characteristic
84	C₂₃×#432	C₂²	1	1	yes	characteristic
85	C₂₃×#432	C₂²	1	2	yes	—
86	C₂₃×#431	C₂²	1	2	yes	—
87	C₂×#41×C₂₃	—	2	1	no	—
88	C₂²×Q₈×C₂₃	—	2	1	no	—
89	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
93	C₂₃×C₄⋊Q₈	—	2	2	no	—
94	C₂₃×C₄⋊Q₈	—	2	4	no	—
95	C₂₃×C₄⋊Q₈	—	2	4	no	—
96	C₂₃×C₄⋊Q₈	—	2	2	no	—
97	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₂₃×#127	C₂³	1	1	yes	characteristic
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	4	no	—
109	C₂₃×#125	—	2	4	no	—
110	C₂₃×#125	—	2	4	no	—
111	C₂₃×#125	—	2	4	no	—
112	C₂₃×#125	—	2	1	no	—
113	C₂₃×#125	—	2	2	no	—
114	C₂₃×#125	—	2	1	no	—
115	C₂₃×#125	—	2	1	no	—
116	C₂₃×#125	C₂³	1	2	yes	—
117	C₂₃×#125	C₂³	1	2	yes	—
118	C₂₃×#125	C₂³	1	2	yes	—
119	C₂₃×#125	C₂³	1	4	yes	—
120	C₂₃×#125	C₂³	1	2	yes	—
121	C₂₃×#124	—	2	2	no	—
122	C₂₃×#124	—	2	1	no	—
123	C₂₃×#124	C₂³	1	2	yes	—
124	C₂₃×#124	C₂³	1	2	yes	—
125	C₂₃×#123	—	2	2	no	—
126	C₂₃×#123	—	2	2	no	—
127	C₂₃×#123	—	2	2	no	—
128	C₂₃×#123	—	2	2	no	—
129	C₂₃×C₂²⋊Q₈	—	2	2	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	1	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×#121	—	2	1	no	—
136	C₂₃×#121	C₂³	1	2	yes	—
137	C₄×Q₈×C₂₃	—	2	2	no	—
138	C₄×Q₈×C₂₃	—	2	4	no	—
139	C₄×Q₈×C₂₃	—	2	4	no	—
140	C₄×Q₈×C₂₃	—	2	1	no	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×Q₈×C₂₃	—	2	1	no	—
143	C₄×Q₈×C₂₃	—	2	1	no	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	D₄	1	2	yes	—
146	C₄×Q₈×C₂₃	D₄	1	2	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
151	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
152	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	1	no	—
160	C₄×D₄×C₂₃	C₂³	1	2	yes	—
161	C₄×D₄×C₂₃	C₂³	1	2	yes	—
162	C₄×D₄×C₂₃	C₂³	1	2	yes	—
163	C₂₃×#117	—	2	1	no	—
164	C₂₃×#117	—	2	2	no	—
165	C₂₃×#117	—	2	2	no	—
166	C₂₃×#117	—	2	2	no	—
167	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
172	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
173	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
174	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
175	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
176	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₂₃	—	2	1	no	—
183	C₂×C₄²×C₂₃	—	2	1	no	—
184	C₂×C₄²×C₂₃	—	2	1	no	—
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂₃×#107	C₂³	1	4	yes	—
189	C₂₃×#107	C₂³	1	4	yes	—
190	C₂₃×#107	C₂³	1	4	yes	—
191	C₂₃×#106	C₂³	1	4	yes	—
192	C₂₃×#106	C₂³	1	4	yes	—
193	C₂₃×#106	C₂³	1	4	yes	—
194	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
196	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₂₃×#103	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	4	yes	—
200	C₂₃×#103	C₂³	1	4	yes	—
201	C₂₃×#103	C₂³	1	4	yes	—
202	C₂₃×#103	C₂³	1	4	yes	—
203	C₂₃×#102	C₂³	1	4	yes	—
204	C₂₃×#102	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₂₃×#97	C₂³	1	2	yes	—
209	C₂₃×#97	C₂³	1	4	yes	—
210	C₂₃×#97	C₂³	1	2	yes	—
211	C₄×C₈×C₂₃	C₂³	1	4	yes	—
212	#41×C₂₃	—	4	4	no	—
213	C₂×Q₈×C₂₃	—	2	4	no	—
214	C₂×Q₈×C₂₃	—	2	1	no	—
215	C₂×Q₈×C₂₃	—	2	1	no	—
216	C₂×Q₈×C₂₃	—	2	4	no	—
217	C₂×Q₈×C₂₃	—	2	1	no	—
218	C₂×Q₈×C₂₃	—	4	2	no	—
219	C₂×Q₈×C₂₃	—	4	4	no	—
220	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₂₃	—	2	2	no	—
225	C₂×D₄×C₂₃	—	2	1	no	—
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	2	no	—
233	C₂²×C₄×C₂₃	—	2	2	no	—
234	C₂²×C₄×C₂₃	—	2	2	no	—
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₂₃	—	2	8	no	—
243	SD₁₆×C₂₃	—	2	8	no	—
244	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
245	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	—	2	4	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	—	2	2	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	2	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	—	2	2	no	—
258	C₄⋊C₄×C₂₃	—	2	4	no	—
259	C₄⋊C₄×C₂₃	—	2	2	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₂₃	—	2	2	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	2	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	2	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₄²×C₂₃	—	2	4	no	—
293	C₄²×C₂₃	—	2	2	no	—
294	C₄²×C₂₃	—	2	2	no	—
295	C₄²×C₂₃	—	2	4	no	—
296	C₄²×C₂₃	—	2	2	no	—
297	C₄²×C₂₃	—	2	2	no	—
298	C₄²×C₂₃	—	2	2	no	—
299	C₄²×C₂₃	C₂×D₄	1	2	yes	—
300	C₄²×C₂₃	C₂×D₄	1	2	yes	—
301	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₂₃	C₂⁴	1	2	yes	—
305	C₄²×C₂₃	C₂⁴	1	2	yes	—
306	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
307	#61832	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₂₃	—	2	4	no	—
311	Q₈×C₂₃	—	2	2	no	—
312	Q₈×C₂₃	—	2	4	no	—
313	Q₈×C₂₃	—	4	2	no	—
314	Q₈×C₂₃	—	4	2	no	—
315	Q₈×C₂₃	—	4	8	no	—
316	Q₈×C₂₃	—	4	2	no	—
317	Q₈×C₂₃	—	8	1	no	—
318	Q₈×C₂₃	2₋¹⁺⁴	1	4	yes	—
319	D₄×C₂₃	—	2	4	no	—
320	D₄×C₂₃	—	4	2	no	—
321	D₄×C₂₃	—	4	4	no	—
322	D₄×C₂₃	—	8	1	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	4	no	—
339	C₂×C₄×C₂₃	—	4	2	no	—
340	C₂×C₄×C₂₃	—	4	2	no	—
341	C₂×C₄×C₂₃	—	4	2	no	—
342	C₂×C₄×C₂₃	—	8	2	no	—
343	C₂×C₄×C₂₃	—	8	2	no	—
344	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
354	C₈×C₂₃	—	2	4	no	—
355	C₈×C₂₃	—	2	4	no	—
356	#3507	C₂×C₂₃	1	1	yes	characteristic
357	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#3390	C₂×C₂₃	1	4	yes	complemented
359	#3388	C₂×C₂₃	1	4	yes	complemented
360	#3377	C₂×C₂₃	1	4	yes	complemented
361	#3371	C₂×C₂₃	1	4	yes	complemented
362	#3238	C₂×C₂₃	1	2	yes	complemented
363	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#3234	C₂×C₂₃	1	1	yes	characteristic
365	#3232	C₂×C₂₃	1	2	yes	complemented
366	#3117	C₂×C₂₃	1	2	yes	complemented
367	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#3112	C₂×C₂₃	1	1	yes	characteristic
369	#3108	C₂×C₂₃	1	2	yes	complemented
370	#2983	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂²×C₂₃	—	2	1	no	—
372	C₂²×C₂₃	—	2	1	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	#575	1	2	yes	—
377	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	1	no	—
381	C₄×C₂₃	—	2	1	no	—
382	C₄×C₂₃	—	2	4	no	—
383	C₄×C₂₃	—	2	1	no	—
384	C₄×C₂₃	—	2	1	no	—
385	C₄×C₂₃	—	2	1	no	—
386	C₄×C₂₃	—	2	2	no	—
387	C₄×C₂₃	—	2	2	no	—
388	C₄×C₂₃	—	4	2	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
395	#559	C₂²×C₂₃	1	2	yes	—
396	#557	—	2	2	no	—
397	#557	—	2	2	no	—
398	#557	C₂²×C₂₃	1	4	yes	—
399	#557	C₂²×C₂₃	1	4	yes	—
400	#557	C₂²×C₂₃	1	2	yes	—
401	#556	—	2	2	no	—
402	#556	C₂²×C₂₃	1	2	yes	—
403	#554	C₂²×C₂₃	1	2	yes	—
404	#552	—	2	2	no	—
405	#539	—	2	1	no	—
406	#539	—	2	1	no	—
407	#536	—	2	1	no	—
408	#533	C₂²×C₂₃	1	1	yes	characteristic
409	#532	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×C₄⋊Q₈	—	2	1	no	—
411	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
412	#529	C₂²×C₂₃	1	2	yes	—
413	#529	C₂²×C₂₃	1	2	yes	—
414	C₂×#125	—	2	1	no	—
415	C₂×#125	—	2	1	no	—
416	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
418	#520	—	2	1	no	—
419	C₂×C₄×Q₈	—	2	1	no	—
420	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
424	#501	C₂²×C₂₃	1	2	yes	—
425	#501	C₂²×C₂₃	1	4	yes	—
426	#501	C₂²×C₂₃	1	2	yes	—
427	#499	C₂²×C₂₃	1	4	yes	—
428	#491	C₂²×C₂₃	1	2	yes	—
429	#490	C₂²×C₂₃	1	2	yes	—
430	#489	C₂²×C₂₃	1	4	yes	—
431	#488	C₂²×C₂₃	1	4	yes	—
432	#484	C₂²×C₂₃	1	2	yes	—
433	#483	C₂²×C₂₃	1	2	yes	—
434	#483	C₂²×C₂₃	1	2	yes	—
435	#481	C₂²×C₂₃	1	2	yes	—
436	#480	C₂²×C₂₃	1	2	yes	—
437	#480	C₂²×C₂₃	1	2	yes	—
438	#479	C₂²×C₂₃	1	4	yes	—
439	#479	C₂²×C₂₃	1	4	yes	—
440	#479	C₂²×C₂₃	1	4	yes	—
441	#479	C₂²×C₂₃	1	4	yes	—
442	#478	C₂²×C₂₃	1	4	yes	—
443	#478	C₂²×C₂₃	1	4	yes	—
444	#477	C₂²×C₂₃	1	2	yes	—
445	#477	C₂²×C₂₃	1	4	yes	—
446	#476	C₂²×C₂₃	1	4	yes	—
447	#475	C₂²×C₂₃	1	2	yes	—
448	#464	C₂²×C₂₃	1	4	yes	—
449	#464	C₂²×C₂₃	1	4	yes	—
450	#462	C₂²×C₂₃	1	2	yes	—
451	#460	C₂²×C₂₃	1	2	yes	—
452	#451	C₂²×C₂₃	1	2	yes	—
453	#448	C₂²×C₂₃	1	2	yes	—
454	#446	C₂²×C₂₃	1	4	yes	—
455	#446	C₂²×C₂₃	1	4	yes	—
456	#441	C₂²×C₂₃	1	4	yes	—
457	#441	C₂²×C₂₃	1	4	yes	—
458	#440	C₂²×C₂₃	1	4	yes	—
459	#440	C₂²×C₂₃	1	4	yes	—
460	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
461	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
462	#432	C₂²×C₂₃	1	1	yes	characteristic
463	#432	C₂²×C₂₃	1	1	yes	characteristic
464	#432	C₂²×C₂₃	1	2	yes	—
465	#431	C₂²×C₂₃	1	2	yes	—
466	C₂×C₂₃	—	2	2	no	—
467	C₂×C₂₃	—	8	2	no	—
468	C₂×C₂₃	#3486	1	1	yes	characteristic
469	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
470	C₂×C₂₃	#3586	1	1	yes	characteristic
471	C₂×#41	—	2	1	no	—
472	C₂²×Q₈	—	2	1	no	—
473	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
476	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
477	C₄⋊Q₈	—	2	4	no	—
478	C₄⋊Q₈	—	2	4	no	—
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
483	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
485	#127	C₂³×C₂₃	1	1	yes	characteristic
486	#126	—	2	2	no	—
487	#126	—	2	2	no	—
488	#126	—	2	2	no	—
489	#126	—	2	2	no	—
490	#125	—	2	4	no	—
491	#125	—	2	4	no	—
492	#125	—	2	4	no	—
493	#125	—	2	4	no	—
494	#125	—	2	2	no	—
495	#125	—	2	2	no	—
496	#125	—	2	2	no	—
497	#125	—	2	1	no	—
498	#125	—	2	1	no	—
499	#125	—	2	1	no	—
500	#125	C₂³×C₂₃	1	2	yes	—
501	#125	C₂³×C₂₃	1	4	yes	—
502	#125	C₂³×C₂₃	1	2	yes	—
503	#125	C₂³×C₂₃	1	2	yes	—
504	#125	C₂³×C₂₃	1	2	yes	—
505	#124	—	2	2	no	—
506	#124	—	2	1	no	—
507	#124	C₂³×C₂₃	1	2	yes	—
508	#124	C₂³×C₂₃	1	2	yes	—
509	#123	—	2	2	no	—
510	#123	—	2	2	no	—
511	#123	—	2	2	no	—
512	#123	—	2	2	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	1	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
519	#121	—	2	1	no	—
520	#121	C₂³×C₂₃	1	2	yes	—
521	C₄×Q₈	—	2	4	no	—
522	C₄×Q₈	—	2	4	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	D₄×C₂₃	1	2	yes	—
530	C₄×Q₈	D₄×C₂₃	1	2	yes	—
531	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
532	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
533	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
534	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
535	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
536	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
537	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
538	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
539	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	C₂³×C₂₃	1	2	yes	—
545	C₄×D₄	C₂³×C₂₃	1	2	yes	—
546	C₄×D₄	C₂³×C₂₃	1	2	yes	—
547	#117	—	2	1	no	—
548	#117	—	2	2	no	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
572	#107	C₂³×C₂₃	1	4	yes	—
573	#107	C₂³×C₂₃	1	4	yes	—
574	#107	C₂³×C₂₃	1	4	yes	—
575	#106	C₂³×C₂₃	1	4	yes	—
576	#106	C₂³×C₂₃	1	4	yes	—
577	#106	C₂³×C₂₃	1	4	yes	—
578	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
579	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
580	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
581	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
582	#103	C₂³×C₂₃	1	4	yes	—
583	#103	C₂³×C₂₃	1	4	yes	—
584	#103	C₂³×C₂₃	1	4	yes	—
585	#103	C₂³×C₂₃	1	4	yes	—
586	#103	C₂³×C₂₃	1	4	yes	—
587	#102	C₂³×C₂₃	1	4	yes	—
588	#102	C₂³×C₂₃	1	4	yes	—
589	#102	C₂³×C₂₃	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
591	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
592	#97	C₂³×C₂₃	1	2	yes	—
593	#97	C₂³×C₂₃	1	4	yes	—
594	#97	C₂³×C₂₃	1	2	yes	—
595	C₄×C₈	C₂³×C₂₃	1	4	yes	—
596	C₂₃	#61832	1	1	yes	characteristic, direct product factor, Sylow
597	#41	—	4	4	no	—
598	C₂×Q₈	—	2	4	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	4	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
606	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
627	Q₁₆	—	2	8	no	—
628	SD₁₆	—	2	8	no	—
629	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
630	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
658	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
659	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	C₂×D₄×C₂₃	1	2	yes	—
685	C₄²	C₂×D₄×C₂₃	1	2	yes	—
686	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
687	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
688	C₄²	C₂⁴×C₂₃	1	2	yes	—
689	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₂₃	1	2	yes	—
691	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₂³	—	2	2	no	—
693	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
694	Q₈	—	2	4	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	4	8	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	8	1	no	—
702	Q₈	C₂₃×2₋¹⁺⁴	1	4	yes	—
703	D₄	—	2	4	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	4	no	—
706	D₄	—	8	1	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	—	8	2	no	—
728	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
737	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
738	C₈	—	2	4	no	—
739	C₈	—	2	4	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	C₂₃×#575	1	2	yes	—
746	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
747	C₄	—	2	4	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
764	C₂	—	2	2	no	—
765	C₂	—	8	2	no	—
766	C₂	C₂₃×#3486	1	1	yes	characteristic
767	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
768	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#557	C₂	semidirect
3. C₂₃×#3390	C₂	semidirect
4. C₂₃×#3388	C₂	semidirect
5. C₂₃×#3377	C₂	semidirect
6. C₂₃×#3371	C₂	semidirect
7. C₂₃×#3238	C₂	semidirect
8. C₂₃×#3236	C₂	semidirect
10. C₂₃×#3232	C₂	semidirect
11. C₂₃×#3117	C₂	semidirect
12. C₂₃×#3113	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#2983	C₂	semidirect
307. #61832	C₂₃	direct (N × H)
357. C₂×#557	C₂×C₂₃	semidirect
358. #3390	C₂×C₂₃	semidirect
359. #3388	C₂×C₂₃	semidirect
360. #3377	C₂×C₂₃	semidirect
361. #3371	C₂×C₂₃	semidirect
362. #3238	C₂×C₂₃	semidirect
363. #3236	C₂×C₂₃	semidirect
365. #3232	C₂×C₂₃	semidirect
366. #3117	C₂×C₂₃	semidirect
367. #3113	C₂×C₂₃	semidirect
369. #3108	C₂×C₂₃	semidirect
370. #2983	C₂×C₂₃	semidirect
596. C₂₃	#61832	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×#3507	2
C₂×C₂₃×#557	2
C₂₃×#3390	2
C₂₃×#3388	2
C₂₃×#3377	2
C₂₃×#3371	2
C₂₃×#3238	2
C₂₃×#3236	2
C₂₃×#3234	2
C₂₃×#3232	2
C₂₃×#3117	2
C₂₃×#3113	2
C₂₃×#3112	2
C₂₃×#3108	2
C₂₃×#2983	2
#61832	23

Subgroups — C23×#61832 #19209458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61832 #19209458