Subgroups — C₂₃×#61427 #19209053

Order 5888.

1890 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3360	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3303	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3296	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3280	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3102	C₂	1	4	yes	maximal, complemented
14	C₂₃×#3101	C₂	1	2	yes	maximal, complemented
15	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×#135	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#135	C₂²	1	2	yes	—
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#556	C₂²	1	2	yes	complemented
21	C₂₃×#555	C₂²	1	2	yes	complemented
22	C₂₃×#554	C₂²	1	2	yes	complemented
23	C₂₃×#553	—	2	2	no	—
24	C₂₃×#552	—	2	2	no	—
25	C₂₃×#552	C₂²	1	4	yes	—
26	C₂₃×#551	—	2	4	no	—
27	C₂₃×#547	C₂²	1	2	yes	complemented
28	C₂₃×#546	C₂²	1	4	yes	—
29	C₂₃×#533	C₂²	1	2	yes	—
30	C₂₃×#529	—	2	4	no	—
31	C₂₃×#529	C₂²	1	4	yes	complemented
32	C₂₃×#525	—	2	2	no	—
33	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
34	C₄×#41×C₂₃	C₂²	1	4	yes	complemented
35	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
36	C₂×C₂₃×#117	—	2	2	no	—
37	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#499	C₂²	1	2	yes	complemented
39	C₂₃×#495	C₂²	1	2	yes	—
40	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#488	C₂²	1	4	yes	complemented
42	C₂₃×#487	C₂²	1	2	yes	complemented
43	C₂₃×#485	C₂²	1	4	yes	complemented
44	C₂₃×#483	C₂²	1	4	yes	—
45	C₂₃×#482	C₂²	1	4	yes	complemented
46	C₂₃×#479	C₂²	1	4	yes	complemented
47	C₂₃×#478	C₂²	1	4	yes	complemented
48	C₂₃×#476	C₂²	1	2	yes	complemented
49	C₂₃×#476	C₂²	1	2	yes	complemented
50	C₂₃×#467	C₂²	1	2	yes	—
51	C₂₃×#467	C₂²	1	2	yes	—
52	C₂₃×#467	C₂²	1	2	yes	complemented
53	C₂₃×#466	C₂²	1	2	yes	—
54	C₂₃×#465	C₂²	1	4	yes	complemented
55	C₂₃×#464	C₂²	1	4	yes	complemented
56	C₂₃×#463	C₂²	1	4	yes	—
57	C₂₃×#461	C₂²	1	2	yes	complemented
58	C₂₃×#461	C₂²	1	2	yes	complemented
59	C₂₃×#452	C₂²	1	4	yes	complemented
60	C₂₃×#450	C₂²	1	4	yes	—
61	C₂₃×#449	C₂²	1	4	yes	—
62	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
65	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
66	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
67	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
68	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
69	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
70	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
71	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
72	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
73	C₄×D₈×C₂₃	C₂²	1	2	yes	—
74	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
75	C₄×D₈×C₂₃	C₂²	1	2	yes	—
76	C₄×D₈×C₂₃	C₂²	1	2	yes	—
77	C₈×D₄×C₂₃	C₂²	1	2	yes	—
78	C₈×D₄×C₂₃	C₂²	1	2	yes	—
79	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#431	C₂²	1	1	yes	characteristic
82	C₂₃×#431	C₂²	1	2	yes	complemented
83	C₂₃×#427	C₂²	1	2	yes	complemented
84	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
85	C₂₃×#416	C₂²	1	4	yes	complemented
86	C₂×C₂₃×#102	C₂²	1	2	yes	—
87	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
89	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
90	C₂×#41×C₂₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₂₃	—	2	2	no	—
93	C₂₃×#135	—	2	8	no	—
94	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
95	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
96	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂×D₈×C₂₃	—	2	4	no	—
99	C₂×D₈×C₂₃	C₂³	1	2	yes	—
100	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
106	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₂₃×#126	—	2	4	no	—
109	C₂₃×#126	—	2	4	no	—
110	C₂₃×#126	—	2	4	no	—
111	C₂₃×#125	—	2	4	no	—
112	C₂₃×#125	—	2	2	no	—
113	C₂₃×#125	C₂³	1	4	yes	—
114	C₂₃×#124	—	2	4	no	—
115	C₂₃×#124	C₂³	1	4	yes	—
116	C₂₃×#123	—	2	4	no	—
117	C₂₃×#123	—	2	4	no	—
118	C₂₃×#123	—	2	4	no	—
119	C₂₃×#123	—	2	4	no	—
120	C₂₃×C₂²⋊Q₈	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	4	no	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₂₃×#121	—	2	2	no	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	4	no	—
129	C₂₃×#121	C₂³	1	4	yes	—
130	C₂₃×#120	—	2	4	no	—
131	C₄×Q₈×C₂₃	—	2	2	no	—
132	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
133	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
134	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
135	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₂₃	—	2	4	no	—
137	C₄×D₄×C₂₃	—	2	4	no	—
138	C₄×D₄×C₂₃	—	2	4	no	—
139	C₄×D₄×C₂₃	—	2	2	no	—
140	C₄×D₄×C₂₃	—	2	2	no	—
141	C₄×D₄×C₂₃	D₄	1	2	yes	—
142	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
143	C₄×D₄×C₂₃	C₂³	1	2	yes	—
144	C₄×D₄×C₂₃	C₂³	1	4	yes	—
145	C₄×D₄×C₂₃	C₂³	1	2	yes	—
146	C₄×D₄×C₂₃	C₂³	1	2	yes	—
147	C₄×D₄×C₂₃	C₂³	1	2	yes	—
148	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₄×D₄×C₂₃	C₂³	1	2	yes	—
150	C₂₃×#117	—	2	2	no	—
151	C₂₃×#117	—	2	2	no	—
152	C₂₃×#117	—	2	2	no	—
153	C₂₃×#117	—	2	4	no	—
154	C₂₃×#117	—	2	4	no	—
155	C₂₃×#117	—	2	4	no	—
156	C₂₃×#117	D₄	1	1	yes	characteristic
157	C₂₃×#117	D₄	1	2	yes	—
158	C₂₃×#117	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
160	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
163	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
164	C₂×C₄²×C₂₃	—	2	4	no	—
165	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
167	C₂₃×#107	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	1	yes	characteristic
169	C₂₃×#107	C₂³	1	2	yes	—
170	C₂₃×#107	C₂³	1	2	yes	—
171	C₂₃×#107	C₂³	1	2	yes	—
172	C₂₃×#106	C₂³	1	4	yes	—
173	C₂₃×#106	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×#103	C₂³	1	4	yes	—
179	C₂₃×#103	C₂³	1	4	yes	—
180	C₂₃×#103	C₂³	1	4	yes	—
181	C₂₃×#103	C₂³	1	4	yes	—
182	C₂₃×#102	C₂³	1	2	yes	—
183	C₂₃×#102	C₂³	1	2	yes	—
184	C₂₃×#102	C₂³	1	2	yes	—
185	C₂₃×#102	C₂³	1	2	yes	—
186	C₂₃×#102	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₂₃	C₂³	1	2	yes	—
196	C₄×C₈×C₂₃	C₂³	1	2	yes	—
197	C₄×C₈×C₂₃	C₂³	1	2	yes	—
198	C₂⁴×C₂₃	—	2	2	no	—
199	#41×C₂₃	—	2	4	no	—
200	#41×C₂₃	—	2	8	no	—
201	#41×C₂₃	—	4	4	no	—
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	4	no	—
208	C₂×D₄×C₂₃	—	2	2	no	—
209	C₂×D₄×C₂₃	—	4	2	no	—
210	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	4	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	2	yes	—
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	Q₁₆×C₂₃	—	2	4	no	—
229	Q₁₆×C₂₃	—	4	2	no	—
230	SD₁₆×C₂₃	—	2	8	no	—
231	SD₁₆×C₂₃	—	4	4	no	—
232	D₈×C₂₃	—	2	4	no	—
233	D₈×C₂₃	—	2	2	no	—
234	D₈×C₂₃	#41	1	4	yes	complemented
235	C₂×C₈×C₂₃	—	2	2	no	—
236	C₂×C₈×C₂₃	—	2	4	no	—
237	C₂×C₈×C₂₃	—	4	2	no	—
238	C₂×C₈×C₂₃	—	4	1	no	—
239	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₂₃	—	2	2	no	—
246	C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	—	2	2	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	2	no	—
255	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	4	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	2	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	2	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₄²×C₂₃	—	2	4	no	—
277	C₄²×C₂₃	—	2	4	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	C₂×D₄	1	2	yes	—
280	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₂₃	C₂×D₄	1	2	yes	—
282	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₄²×C₂₃	C₂⁴	1	2	yes	—
285	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
286	#61427	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₂₃	—	2	2	no	—
288	C₂³×C₂₃	—	2	2	no	—
289	C₂³×C₂₃	—	4	4	no	—
290	C₂³×C₂₃	—	4	4	no	—
291	C₂³×C₂₃	—	8	2	no	—
292	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
293	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₂₃	—	2	2	no	—
295	Q₈×C₂₃	—	2	4	no	—
296	Q₈×C₂₃	—	2	4	no	—
297	Q₈×C₂₃	—	8	2	no	—
298	D₄×C₂₃	—	2	4	no	—
299	D₄×C₂₃	—	2	2	no	—
300	D₄×C₂₃	—	2	2	no	—
301	D₄×C₂₃	—	2	2	no	—
302	D₄×C₂₃	—	2	2	no	—
303	D₄×C₂₃	—	4	4	no	—
304	D₄×C₂₃	—	4	8	no	—
305	D₄×C₂₃	—	8	4	no	—
306	D₄×C₂₃	C₂×#41	1	4	yes	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	4	no	—
314	C₂×C₄×C₂₃	—	2	4	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	8	no	—
319	C₂×C₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	4	4	no	—
321	C₂×C₄×C₂₃	—	4	4	no	—
322	C₂×C₄×C₂₃	—	4	4	no	—
323	C₂×C₄×C₂₃	—	4	4	no	—
324	C₂×C₄×C₂₃	—	8	4	no	—
325	C₂×C₄×C₂₃	#135	1	4	yes	complemented
326	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
335	C₈×C₂₃	—	2	1	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	2	1	no	—
338	C₈×C₂₃	—	2	2	no	—
339	C₈×C₂₃	—	2	1	no	—
340	C₈×C₂₃	C₂×#41	1	2	yes	—
341	#3475	C₂×C₂₃	1	2	yes	complemented
342	#3393	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#3380	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#3360	C₂×C₂₃	1	2	yes	complemented
345	#3341	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#3336	C₂×C₂₃	1	2	yes	complemented
347	#3303	C₂×C₂₃	1	2	yes	complemented
348	#3296	C₂×C₂₃	1	4	yes	complemented
349	#3283	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#3280	C₂×C₂₃	1	2	yes	complemented
351	#3170	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#3168	C₂×C₂₃	1	2	yes	complemented
353	#3102	C₂×C₂₃	1	4	yes	complemented
354	#3101	C₂×C₂₃	1	2	yes	complemented
355	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₄×#135	C₂×C₂₃	1	2	yes	complemented
357	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
358	C₂²×C₂₃	—	2	1	no	—
359	C₂²×C₂₃	—	2	1	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	2	2	no	—
362	C₂²×C₂₃	—	2	4	no	—
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	8	8	no	—
370	C₂²×C₂₃	C₂×#135	1	2	yes	—
371	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
372	C₄×C₂₃	—	2	1	no	—
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	2	1	no	—
375	C₄×C₂₃	—	2	2	no	—
376	C₄×C₂₃	—	2	1	no	—
377	C₄×C₂₃	—	2	2	no	—
378	C₄×C₂₃	—	4	4	no	—
379	C₄×C₂₃	—	4	4	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	2	no	—
382	C₄×C₂₃	C₂×#135	1	2	yes	—
383	C₄×C₂₃	C₂×#135	1	2	yes	—
384	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
385	C₄×C₂₃	#585	1	1	yes	characteristic
386	C₂×#135	C₂²×C₂₃	1	2	yes	—
387	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
388	#556	C₂²×C₂₃	1	2	yes	complemented
389	#555	C₂²×C₂₃	1	2	yes	complemented
390	#554	C₂²×C₂₃	1	2	yes	complemented
391	#553	—	2	2	no	—
392	#552	—	2	2	no	—
393	#552	C₂²×C₂₃	1	4	yes	—
394	#551	—	2	4	no	—
395	#547	C₂²×C₂₃	1	2	yes	complemented
396	#546	C₂²×C₂₃	1	4	yes	—
397	#533	C₂²×C₂₃	1	2	yes	—
398	#529	—	2	4	no	—
399	#529	C₂²×C₂₃	1	4	yes	complemented
400	#525	—	2	2	no	—
401	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
402	C₄×#41	C₂²×C₂₃	1	4	yes	complemented
403	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
404	C₂×#117	—	2	2	no	—
405	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
406	#499	C₂²×C₂₃	1	2	yes	complemented
407	#495	C₂²×C₂₃	1	2	yes	—
408	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
409	#488	C₂²×C₂₃	1	4	yes	complemented
410	#487	C₂²×C₂₃	1	2	yes	complemented
411	#485	C₂²×C₂₃	1	4	yes	complemented
412	#483	C₂²×C₂₃	1	4	yes	—
413	#482	C₂²×C₂₃	1	4	yes	complemented
414	#479	C₂²×C₂₃	1	4	yes	complemented
415	#478	C₂²×C₂₃	1	4	yes	complemented
416	#476	C₂²×C₂₃	1	2	yes	complemented
417	#476	C₂²×C₂₃	1	2	yes	complemented
418	#467	C₂²×C₂₃	1	2	yes	—
419	#467	C₂²×C₂₃	1	2	yes	—
420	#467	C₂²×C₂₃	1	2	yes	complemented
421	#466	C₂²×C₂₃	1	2	yes	—
422	#465	C₂²×C₂₃	1	4	yes	complemented
423	#464	C₂²×C₂₃	1	4	yes	complemented
424	#463	C₂²×C₂₃	1	4	yes	—
425	#461	C₂²×C₂₃	1	2	yes	complemented
426	#461	C₂²×C₂₃	1	2	yes	complemented
427	#452	C₂²×C₂₃	1	4	yes	complemented
428	#450	C₂²×C₂₃	1	4	yes	—
429	#449	C₂²×C₂₃	1	4	yes	—
430	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
433	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
434	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
435	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
436	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
437	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
438	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₄×D₈	C₂²×C₂₃	1	2	yes	—
440	C₄×D₈	C₂²×C₂₃	1	2	yes	—
441	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₄×D₈	C₂²×C₂₃	1	2	yes	—
443	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₈×D₄	C₂²×C₂₃	1	2	yes	—
446	C₈×D₄	C₂²×C₂₃	1	2	yes	—
447	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#431	C₂²×C₂₃	1	1	yes	characteristic
450	#431	C₂²×C₂₃	1	2	yes	complemented
451	#427	C₂²×C₂₃	1	2	yes	complemented
452	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
453	#416	C₂²×C₂₃	1	4	yes	complemented
454	C₂×#102	C₂²×C₂₃	1	2	yes	—
455	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
457	C₂×C₂₃	—	2	2	no	—
458	C₂×C₂₃	—	4	2	no	—
459	C₂×C₂₃	—	4	4	no	—
460	C₂×C₂₃	—	8	2	no	—
461	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
462	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
463	C₂×C₂₃	#3584	1	1	yes	characteristic
464	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
465	C₂×#41	C₂³×C₂₃	1	4	yes	—
466	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
467	C₂³×C₄	—	2	2	no	—
468	#135	—	2	8	no	—
469	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
470	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
471	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
472	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
473	C₂×D₈	—	2	4	no	—
474	C₂×D₈	C₂³×C₂₃	1	2	yes	—
475	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
479	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
481	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
482	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
483	#126	—	2	4	no	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#125	—	2	4	no	—
487	#125	—	2	2	no	—
488	#125	C₂³×C₂₃	1	4	yes	—
489	#124	—	2	4	no	—
490	#124	C₂³×C₂₃	1	4	yes	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	4	no	—
504	#121	C₂³×C₂₃	1	4	yes	—
505	#120	—	2	4	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
508	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
509	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
510	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	D₄×C₂₃	1	2	yes	—
517	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
518	C₄×D₄	C₂³×C₂₃	1	2	yes	—
519	C₄×D₄	C₂³×C₂₃	1	2	yes	—
520	C₄×D₄	C₂³×C₂₃	1	2	yes	—
521	C₄×D₄	C₂³×C₂₃	1	2	yes	—
522	C₄×D₄	C₂³×C₂₃	1	4	yes	—
523	C₄×D₄	C₂³×C₂₃	1	2	yes	—
524	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
525	#117	—	2	2	no	—
526	#117	—	2	2	no	—
527	#117	—	2	2	no	—
528	#117	—	2	4	no	—
529	#117	—	2	4	no	—
530	#117	—	2	4	no	—
531	#117	D₄×C₂₃	1	1	yes	characteristic
532	#117	D₄×C₂₃	1	2	yes	—
533	#117	C₂³×C₂₃	1	4	yes	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
537	C₂×C₂²⋊C₄	—	2	2	no	—
538	C₂×C₂²⋊C₄	—	2	4	no	—
539	C₂×C₄²	—	2	4	no	—
540	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
542	#107	C₂³×C₂₃	1	1	yes	characteristic
543	#107	C₂³×C₂₃	1	1	yes	characteristic
544	#107	C₂³×C₂₃	1	2	yes	—
545	#107	C₂³×C₂₃	1	2	yes	—
546	#107	C₂³×C₂₃	1	2	yes	—
547	#106	C₂³×C₂₃	1	4	yes	—
548	#106	C₂³×C₂₃	1	4	yes	—
549	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
550	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
552	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
553	#103	C₂³×C₂₃	1	4	yes	—
554	#103	C₂³×C₂₃	1	4	yes	—
555	#103	C₂³×C₂₃	1	4	yes	—
556	#103	C₂³×C₂₃	1	4	yes	—
557	#102	C₂³×C₂₃	1	2	yes	—
558	#102	C₂³×C₂₃	1	2	yes	—
559	#102	C₂³×C₂₃	1	2	yes	—
560	#102	C₂³×C₂₃	1	2	yes	—
561	#102	C₂³×C₂₃	1	4	yes	—
562	#102	C₂³×C₂₃	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
564	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
566	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
567	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
568	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₂₃	1	2	yes	—
571	C₄×C₈	C₂³×C₂₃	1	2	yes	—
572	C₄×C₈	C₂³×C₂₃	1	2	yes	—
573	C₂₃	#61427	1	1	yes	characteristic, direct product factor, Sylow
574	C₂⁴	—	2	2	no	—
575	#41	—	2	4	no	—
576	#41	—	2	8	no	—
577	#41	—	4	4	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
580	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
587	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
588	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
589	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	4	8	no	—
598	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	Q₁₆	—	2	4	no	—
605	Q₁₆	—	4	2	no	—
606	SD₁₆	—	2	8	no	—
607	SD₁₆	—	4	4	no	—
608	D₈	—	2	4	no	—
609	D₈	—	2	2	no	—
610	D₈	#41×C₂₃	1	4	yes	complemented
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	4	no	—
613	C₂×C₈	—	4	2	no	—
614	C₂×C₈	—	4	1	no	—
615	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
619	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
650	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
651	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	C₂×D₄×C₂₃	1	2	yes	—
656	C₄²	C₂×D₄×C₂₃	1	2	yes	—
657	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
660	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
661	C₄²	C₂⁴×C₂₃	1	2	yes	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	4	4	no	—
666	C₂³	—	8	2	no	—
667	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	2	4	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	8	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	4	no	—
679	D₄	—	4	8	no	—
680	D₄	—	8	4	no	—
681	D₄	C₂×#41×C₂₃	1	4	yes	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	C₂₃×#135	1	4	yes	complemented
701	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
709	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
710	C₈	—	2	1	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	C₂×#41×C₂₃	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	8	no	—
728	C₂²	C₂×C₂₃×#135	1	2	yes	—
729	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	1	no	—
736	C₄	—	4	4	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	4	no	—
740	C₄	C₂×C₂₃×#135	1	2	yes	—
741	C₄	C₂×C₂₃×#135	1	2	yes	—
742	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
743	C₄	C₂₃×#585	1	1	yes	characteristic
744	C₂	—	2	2	no	—
745	C₂	—	4	2	no	—
746	C₂	—	4	4	no	—
747	C₂	—	8	2	no	—
748	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
749	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
750	C₂	C₂₃×#3584	1	1	yes	characteristic

	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3475	C₂	semidirect
2. C₂₃×#3393	C₂	semidirect
3. C₂₃×#3380	C₂	semidirect
4. C₂₃×#3360	C₂	semidirect
5. C₂₃×#3341	C₂	semidirect
6. C₂₃×#3336	C₂	semidirect
7. C₂₃×#3303	C₂	semidirect
8. C₂₃×#3296	C₂	semidirect
9. C₂₃×#3283	C₂	semidirect
10. C₂₃×#3280	C₂	semidirect
11. C₂₃×#3170	C₂	semidirect
12. C₂₃×#3168	C₂	semidirect
13. C₂₃×#3102	C₂	semidirect
14. C₂₃×#3101	C₂	semidirect
15. C₈×#41×C₂₃	C₂	semidirect
16. C₄×C₂₃×#135	C₂	semidirect
17. C₂×C₄×D₈×C₂₃	C₂	semidirect
20. C₂₃×#556	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#554	C₂²	semidirect
27. C₂₃×#547	C₂²	semidirect
31. C₂₃×#529	C₂²	semidirect
34. C₄×#41×C₂₃	C₂²	semidirect
37. C₂₃×#500	C₂²	semidirect
38. C₂₃×#499	C₂²	semidirect
40. C₂₃×#494	C₂²	semidirect
41. C₂₃×#488	C₂²	semidirect
42. C₂₃×#487	C₂²	semidirect
43. C₂₃×#485	C₂²	semidirect
45. C₂₃×#482	C₂²	semidirect
46. C₂₃×#479	C₂²	semidirect
47. C₂₃×#478	C₂²	semidirect
48. C₂₃×#476	C₂²	semidirect
49. C₂₃×#476	C₂²	semidirect
52. C₂₃×#467	C₂²	semidirect
54. C₂₃×#465	C₂²	semidirect
55. C₂₃×#464	C₂²	semidirect
57. C₂₃×#461	C₂²	semidirect
58. C₂₃×#461	C₂²	semidirect
59. C₂₃×#452	C₂²	semidirect
62. C₈×Q₈×C₂₃	C₂²	semidirect
63. C₈×Q₈×C₂₃	C₂²	semidirect
64. C₄×Q₁₆×C₂₃	C₂²	semidirect
65. C₄×Q₁₆×C₂₃	C₂²	semidirect
66. C₄×Q₁₆×C₂₃	C₂²	semidirect
67. C₄×SD₁₆×C₂₃	C₂²	semidirect
68. C₄×SD₁₆×C₂₃	C₂²	semidirect
69. C₄×SD₁₆×C₂₃	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₈×D₄×C₂₃	C₂²	semidirect
82. C₂₃×#431	C₂²	semidirect
83. C₂₃×#427	C₂²	semidirect
85. C₂₃×#416	C₂²	semidirect
88. C₂×C₄×C₈×C₂₃	C₂²	semidirect
234. D₈×C₂₃	#41	semidirect
286. #61427	C₂₃	direct (N × H)
325. C₂×C₄×C₂₃	#135	semidirect
341. #3475	C₂×C₂₃	semidirect
342. #3393	C₂×C₂₃	semidirect
343. #3380	C₂×C₂₃	semidirect
344. #3360	C₂×C₂₃	semidirect
345. #3341	C₂×C₂₃	semidirect
346. #3336	C₂×C₂₃	semidirect
347. #3303	C₂×C₂₃	semidirect
348. #3296	C₂×C₂₃	semidirect
349. #3283	C₂×C₂₃	semidirect
350. #3280	C₂×C₂₃	semidirect
351. #3170	C₂×C₂₃	semidirect
352. #3168	C₂×C₂₃	semidirect
353. #3102	C₂×C₂₃	semidirect
354. #3101	C₂×C₂₃	semidirect
355. C₈×#41	C₂×C₂₃	semidirect
356. C₄×#135	C₂×C₂₃	semidirect
357. C₂×C₄×D₈	C₂×C₂₃	semidirect
388. #556	C₂²×C₂₃	semidirect
389. #555	C₂²×C₂₃	semidirect
390. #554	C₂²×C₂₃	semidirect
395. #547	C₂²×C₂₃	semidirect
399. #529	C₂²×C₂₃	semidirect
402. C₄×#41	C₂²×C₂₃	semidirect
405. #500	C₂²×C₂₃	semidirect
406. #499	C₂²×C₂₃	semidirect
408. #494	C₂²×C₂₃	semidirect
409. #488	C₂²×C₂₃	semidirect
410. #487	C₂²×C₂₃	semidirect
411. #485	C₂²×C₂₃	semidirect
413. #482	C₂²×C₂₃	semidirect
414. #479	C₂²×C₂₃	semidirect
415. #478	C₂²×C₂₃	semidirect
416. #476	C₂²×C₂₃	semidirect
417. #476	C₂²×C₂₃	semidirect
420. #467	C₂²×C₂₃	semidirect
422. #465	C₂²×C₂₃	semidirect
423. #464	C₂²×C₂₃	semidirect
425. #461	C₂²×C₂₃	semidirect
426. #461	C₂²×C₂₃	semidirect
427. #452	C₂²×C₂₃	semidirect
430. C₈×Q₈	C₂²×C₂₃	semidirect
431. C₈×Q₈	C₂²×C₂₃	semidirect
432. C₄×Q₁₆	C₂²×C₂₃	semidirect
433. C₄×Q₁₆	C₂²×C₂₃	semidirect
434. C₄×Q₁₆	C₂²×C₂₃	semidirect
435. C₄×SD₁₆	C₂²×C₂₃	semidirect
436. C₄×SD₁₆	C₂²×C₂₃	semidirect
437. C₄×SD₁₆	C₂²×C₂₃	semidirect
447. C₈×D₄	C₂²×C₂₃	semidirect
448. C₈×D₄	C₂²×C₂₃	semidirect
450. #431	C₂²×C₂₃	semidirect
451. #427	C₂²×C₂₃	semidirect
453. #416	C₂²×C₂₃	semidirect
456. C₂×C₄×C₈	C₂²×C₂₃	semidirect
573. C₂₃	#61427	direct (N × H)
610. D₈	#41×C₂₃	semidirect
700. C₂×C₄	C₂₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3475	2
C₂₃×#3393	2
C₂₃×#3380	2
C₂₃×#3360	2
C₂₃×#3341	2
C₂₃×#3336	2
C₂₃×#3303	2
C₂₃×#3296	2
C₂₃×#3283	2
C₂₃×#3280	2
C₂₃×#3170	2
C₂₃×#3168	2
C₂₃×#3102	2
C₂₃×#3101	2
C₈×#41×C₂₃	2
C₄×C₂₃×#135	2
C₂×C₄×D₈×C₂₃	2
#61427	23

Subgroups — C23×#61427 #19209053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61427 #19209053