Subgroups — #15686828

Order 2944.

1012 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093044	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093041	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093040	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093037	C₂	1	2	yes	maximal, complemented
5	#13093028	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093027	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093026	C₂	1	2	yes	maximal, complemented
8	#13093015	C₂	1	2	yes	maximal, complemented
9	#13093013	C₂	1	2	yes	maximal, complemented
10	#13092997	C₂	1	1	yes	maximal, characteristic
11	#13092992	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092990	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092971	C₂	1	2	yes	maximal, complemented
14	#13092971	C₂	1	1	yes	maximal, characteristic, complemented
15	#13092954	C₂	1	2	yes	maximal, complemented
16	#13092954	C₂	1	1	yes	maximal, characteristic, complemented
17	#13092951	C₂	1	1	yes	maximal, characteristic, complemented
18	#13092945	C₂	1	2	yes	maximal, complemented
19	#13092945	C₂	1	2	yes	maximal, complemented
20	C₄×#67292	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#67288	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#67292	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
26	C₂×#67288	C₂²	1	1	yes	characteristic
27	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂₃×#125	C₂²	1	2	yes	—
30	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
36	C₂₃×#117	C₂²	1	2	yes	—
37	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
38	#10625118	C₂²	1	1	yes	characteristic
39	#10625118	C₂²	1	2	yes	—
40	#10625117	C₂²	1	1	yes	characteristic
41	#10625117	C₂²	1	2	yes	—
42	#10625117	C₂²	1	1	yes	characteristic
43	#10625117	C₂²	1	2	yes	—
44	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic
45	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic
46	#10625115	C₂²	1	1	yes	characteristic
47	#10625115	C₂²	1	2	yes	—
48	#10625101	C₂²	1	1	yes	characteristic
49	#10625100	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
55	#10625097	C₂²	1	1	yes	characteristic
56	#10625095	C₂²	1	1	yes	characteristic
57	#10625069	C₂²	1	2	yes	—
58	#10625069	C₂²	1	2	yes	—
59	#10625069	C₂²	1	2	yes	—
60	#10625069	C₂²	1	2	yes	—
61	#10625069	C₂²	1	2	yes	—
62	#10625068	C₂²	1	1	yes	characteristic
63	#10625068	C₂²	1	2	yes	—
64	#10625067	C₂²	1	2	yes	—
65	#10625067	C₂²	1	2	yes	—
66	#10625067	C₂²	1	2	yes	—
67	#10625067	C₂²	1	2	yes	—
68	#10625067	C₂²	1	2	yes	—
69	#10625066	C₂²	1	2	yes	—
70	#10625066	C₂²	1	1	yes	characteristic
71	#10625065	C₂²	1	2	yes	—
72	#10625065	C₂²	1	2	yes	—
73	#10625065	C₂²	1	2	yes	—
74	#10625065	C₂²	1	2	yes	—
75	#10625065	C₂²	1	2	yes	—
76	#10625064	C₂²	1	2	yes	—
77	#10625064	C₂²	1	1	yes	characteristic
78	#10625063	C₂²	1	1	yes	characteristic
79	#10625063	C₂²	1	2	yes	—
80	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
82	#10625061	C₂²	1	2	yes	—
83	#10625061	C₂²	1	1	yes	characteristic
84	#10625060	C₂²	1	2	yes	—
85	#10625060	C₂²	1	2	yes	—
86	#10625060	C₂²	1	2	yes	—
87	#10625060	C₂²	1	2	yes	—
88	#10625060	C₂²	1	2	yes	—
89	#10625059	C₂²	1	2	yes	—
90	#10625059	C₂²	1	1	yes	characteristic
91	#10625058	C₂²	1	2	yes	—
92	#10625058	C₂²	1	1	yes	characteristic
93	#10625056	C₂²	1	2	yes	—
94	#10625056	C₂²	1	2	yes	—
95	#10625055	C₂²	1	2	yes	—
96	#10625055	C₂²	1	2	yes	—
97	#10625054	C₂²	1	2	yes	—
98	#10625054	C₂²	1	2	yes	—
99	#10625050	C₂²	1	2	yes	—
100	#10625050	C₂²	1	2	yes	—
101	#10625047	C₂²	1	2	yes	—
102	#10625046	C₂²	1	1	yes	characteristic
103	C₄×D₉₂	C₂²	1	1	yes	characteristic
104	C₄×D₉₂	C₂²	1	1	yes	characteristic
105	C₄×D₉₂	C₂²	1	2	yes	—
106	C₄×D₉₂	C₂²	1	1	yes	characteristic
107	C₄×D₉₂	C₂²	1	2	yes	—
108	#10625043	C₂²	1	1	yes	characteristic
109	#10625043	C₂²	1	1	yes	characteristic
110	#10625043	C₂²	1	2	yes	—
111	#10625043	C₂²	1	2	yes	—
112	#10625043	C₂²	1	2	yes	—
113	C₄²×D₂₃	C₂²	1	1	yes	characteristic
114	C₄²×D₂₃	C₂²	1	2	yes	—
115	C₄²×D₂₃	C₂²	1	1	yes	characteristic
116	C₄²×D₂₃	C₂²	1	2	yes	—
117	#10625041	C₂²	1	1	yes	characteristic
118	C₄×Dic₄₆	C₂²	1	2	yes	—
119	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
120	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
121	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₄₆	C₂²	1	2	yes	—
123	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
126	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
132	#67292	—	2	4	no	—
133	Q₈×D₂₃	—	2	4	no	—
134	#67288	—	2	4	no	—
135	C₂×D₉₂	C₂³	1	1	yes	characteristic
136	C₂×D₉₂	C₂³	1	1	yes	characteristic
137	C₂×D₉₂	C₂³	1	2	yes	—
138	C₂×D₉₂	C₂³	1	2	yes	—
139	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₂₃	C₂³	1	2	yes	—
142	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₂₃	C₂³	1	2	yes	—
144	C₂×C₄×D₂₃	C₂³	1	2	yes	—
145	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₂₃	C₂³	1	2	yes	—
148	C₂×C₄×D₂₃	C₂³	1	2	yes	—
149	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
150	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
152	C₂×Dic₄₆	C₂³	1	2	yes	—
153	C₂×Dic₄₆	C₂³	1	2	yes	—
154	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₄²×C₂₃	C₂³	1	2	yes	—
167	C₄²×C₂₃	C₂³	1	2	yes	—
168	C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₄²×C₂₃	C₂³	1	1	yes	characteristic
170	C₄²×C₂₃	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
174	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
175	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
176	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
190	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₂₃	C₂³	1	2	yes	—
194	C₄⋊Dic₂₃	C₂³	1	2	yes	—
195	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₂₃	C₂³	1	2	yes	—
197	C₄⋊Dic₂₃	C₂³	1	2	yes	—
198	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₂₃⋊C₄	C₂³	1	2	yes	—
203	Dic₂₃⋊C₄	C₂³	1	2	yes	—
204	Dic₂₃⋊C₄	C₂³	1	2	yes	—
205	Dic₂₃⋊C₄	C₂³	1	2	yes	—
206	Dic₂₃⋊C₄	C₂³	1	2	yes	—
207	Dic₂₃⋊C₄	C₂³	1	2	yes	—
208	Dic₂₃⋊C₄	C₂³	1	2	yes	—
209	Dic₂₃⋊C₄	C₂³	1	2	yes	—
210	Dic₂₃⋊C₄	C₂³	1	2	yes	—
211	Dic₂₃⋊C₄	C₂³	1	2	yes	—
212	Dic₂₃⋊C₄	C₂³	1	2	yes	—
213	Dic₂₃⋊C₄	C₂³	1	2	yes	—
214	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₂₃	C₂³	1	2	yes	—
216	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₂₃	C₂³	1	2	yes	—
222	C₄×Dic₂₃	C₂³	1	2	yes	—
223	C₄×Dic₂₃	C₂³	1	2	yes	—
224	C₄×Dic₂₃	C₂³	1	2	yes	—
225	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₂₃	C₂⁴	1	2	yes	—
227	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
229	Q₈×C₂₃	—	2	2	no	—
230	Q₈×C₂₃	—	2	2	no	—
231	Q₈×C₂₃	—	4	2	no	—
232	C₂×C₄×C₂₃	—	2	2	no	—
233	C₂×C₄×C₂₃	—	2	2	no	—
234	C₂×C₄×C₂₃	—	4	1	no	—
235	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₂₃	—	2	2	no	—
246	C₂²⋊D₂₃	—	2	2	no	—
247	C₂²⋊D₂₃	—	4	2	no	—
248	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₂₃	C₂⁴	1	2	yes	—
252	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₂₃	C₂⁴	1	2	yes	—
254	C₂×Dic₂₃	C₂⁴	1	2	yes	—
255	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
257	D₉₂	—	2	2	no	—
258	D₉₂	—	2	4	no	—
259	D₉₂	—	2	2	no	—
260	D₉₂	—	4	2	no	—
261	C₄×D₂₃	—	2	4	no	—
262	C₄×D₂₃	—	2	2	no	—
263	C₄×D₂₃	—	2	2	no	—
264	C₄×D₂₃	—	2	2	no	—
265	C₄×D₂₃	—	2	4	no	—
266	C₄×D₂₃	—	2	4	no	—
267	C₄×D₂₃	—	4	1	no	—
268	C₄×D₂₃	—	4	2	no	—
269	C₄×D₂₃	—	4	2	no	—
270	C₄×D₂₃	—	4	1	no	—
271	C₄×D₂₃	#41	1	4	yes	—
272	Dic₄₆	—	2	2	no	—
273	Dic₄₆	—	2	2	no	—
274	Dic₄₆	—	2	4	no	—
275	Dic₄₆	—	4	2	no	—
276	#3461	—	23	1	no	maximal, Sylow
277	C₂²×C₂₃	—	2	1	no	—
278	C₂²×C₂₃	—	2	1	no	—
279	C₂²×C₂₃	—	2	1	no	—
280	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
281	C₂×D₂₃	—	2	1	no	—
282	C₂×D₂₃	—	2	1	no	—
283	C₂×D₂₃	—	2	2	no	—
284	C₂×D₂₃	—	2	1	no	—
285	C₂×D₂₃	—	2	2	no	—
286	C₂×D₂₃	—	2	1	no	—
287	C₂×D₂₃	—	2	1	no	—
288	C₂×D₂₃	—	2	2	no	—
289	C₂×D₂₃	C₂×#41	1	2	yes	—
290	C₄×C₂₃	—	2	2	no	—
291	C₄×C₂₃	—	2	1	no	—
292	C₄×C₂₃	—	2	2	no	—
293	C₄×C₂₃	—	2	1	no	—
294	C₄×C₂₃	—	2	2	no	—
295	C₄×C₂₃	—	2	1	no	—
296	C₄×C₂₃	—	2	2	no	—
297	C₄×C₂₃	—	2	1	no	—
298	C₄×C₂₃	C₂×#41	1	2	yes	—
299	C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
300	Dic₂₃	—	2	2	no	—
301	Dic₂₃	—	2	1	no	—
302	Dic₂₃	—	2	1	no	—
303	Dic₂₃	—	2	1	no	—
304	Dic₂₃	—	2	2	no	—
305	Dic₂₃	—	2	1	no	—
306	Dic₂₃	—	2	2	no	—
307	Dic₂₃	—	2	1	no	—
308	Dic₂₃	C₂×#41	1	2	yes	—
309	#544	—	23	1	no	—
310	#542	—	23	1	no	—
311	#542	—	23	2	no	—
312	#542	—	23	1	no	—
313	#541	—	23	1	no	—
314	#541	—	23	2	no	—
315	#541	—	23	1	no	—
316	#539	—	23	2	no	—
317	#539	—	23	2	no	—
318	#537	—	23	1	no	—
319	#536	—	23	1	no	—
320	#536	—	23	1	no	—
321	#533	—	23	2	no	—
322	#533	—	23	1	no	—
323	#533	D₂₃	1	1	yes	characteristic, complemented
324	#529	—	23	2	no	—
325	#529	—	23	1	no	—
326	#529	—	23	2	no	—
327	#529	—	23	2	no	—
328	#529	—	23	1	no	—
329	C₄×#41	—	23	1	no	—
330	C₄×#41	—	23	1	no	—
331	C₂×C₄×Q₈	—	23	1	no	—
332	C₂×C₂₃	—	4	1	no	—
333	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
334	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×C₂₃	#585	1	1	yes	characteristic
336	D₂₃	—	2	2	no	—
337	D₂₃	—	4	2	no	—
338	D₂₃	—	4	1	no	—
339	C₂×#41	—	23	1	no	—
340	C₂×#41	—	23	1	no	—
341	C₂²×Q₈	—	23	1	no	—
342	C₄⋊Q₈	—	23	1	no	—
343	C₄⋊Q₈	—	23	2	no	—
344	C₄⋊Q₈	—	23	2	no	—
345	C₄⋊Q₈	—	23	1	no	—
346	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
347	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
348	#126	—	23	2	no	—
349	#126	—	23	2	no	—
350	#126	—	23	2	no	—
351	#126	—	23	2	no	—
352	#126	—	23	2	no	—
353	#126	—	23	2	no	—
354	#126	—	23	2	no	—
355	#126	—	23	2	no	—
356	#125	—	23	2	no	—
357	#125	—	23	2	no	—
358	#125	—	23	2	no	—
359	#125	—	23	1	no	—
360	#125	—	23	2	no	—
361	#125	—	23	2	no	—
362	#125	—	23	2	no	—
363	#125	—	23	1	no	—
364	#125	C₂×D₂₃	1	2	yes	—
365	#124	—	23	1	no	—
366	#124	—	23	2	no	—
367	#124	—	23	2	no	—
368	#124	—	23	2	no	—
369	#124	—	23	1	no	—
370	#123	—	23	2	no	—
371	#123	—	23	2	no	—
372	#123	—	23	2	no	—
373	#123	—	23	2	no	—
374	#123	—	23	2	no	—
375	#123	—	23	2	no	—
376	#123	—	23	2	no	—
377	#123	—	23	2	no	—
378	C₂²⋊Q₈	—	23	1	no	—
379	C₂²⋊Q₈	—	23	2	no	—
380	C₂²⋊Q₈	—	23	1	no	—
381	C₂²⋊Q₈	—	23	2	no	—
382	C₂²⋊Q₈	—	23	1	no	—
383	C₂²⋊Q₈	—	23	2	no	—
384	C₂²⋊Q₈	—	23	2	no	—
385	C₂²⋊Q₈	—	23	2	no	—
386	C₂²⋊Q₈	—	23	1	no	—
387	C₂²⋊Q₈	—	23	2	no	—
388	C₂²⋊Q₈	—	23	2	no	—
389	C₂²⋊Q₈	—	23	2	no	—
390	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	—
393	#121	—	23	1	no	—
394	#121	—	23	2	no	—
395	#121	—	23	1	no	—
396	#121	—	23	2	no	—
397	#121	—	23	2	no	—
398	C₄×Q₈	—	23	1	no	—
399	C₄×Q₈	—	23	1	no	—
400	C₄×Q₈	—	23	2	no	—
401	C₄×Q₈	—	23	1	no	—
402	C₄×Q₈	—	23	2	no	—
403	C₄×Q₈	—	23	1	no	—
404	C₄×Q₈	—	23	1	no	—
405	C₄×Q₈	—	23	1	no	—
406	C₄×Q₈	—	23	2	no	—
407	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic
408	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic
409	C₄×Q₈	C₂×D₂₃	1	2	yes	—
410	C₄×D₄	—	23	1	no	—
411	C₄×D₄	—	23	1	no	—
412	C₄×D₄	—	23	1	no	—
413	C₄×D₄	—	23	1	no	—
414	C₄×D₄	—	23	2	no	—
415	C₄×D₄	—	23	2	no	—
416	C₄×D₄	—	23	1	no	—
417	C₄×D₄	—	23	1	no	—
418	C₄×D₄	—	23	2	no	—
419	C₄×D₄	—	23	1	no	—
420	C₄×D₄	—	23	1	no	—
421	C₄×D₄	—	23	2	no	—
422	#117	—	23	1	no	—
423	#117	—	23	1	no	—
424	#117	—	23	2	no	—
425	#117	—	23	1	no	—
426	#117	—	23	1	no	—
427	#117	—	23	2	no	—
428	#117	—	23	2	no	—
429	#117	—	23	2	no	—
430	#117	C₂×D₂₃	1	2	yes	—
431	C₂×C₄⋊C₄	—	23	1	no	—
432	C₂×C₄⋊C₄	—	23	2	no	—
433	C₂×C₄²	—	23	1	no	—
434	C₂×C₄²	—	23	2	no	—
435	C₂×C₄²	—	23	2	no	—
436	C₂×C₄²	—	23	1	no	—
437	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
438	C₂₃	#3461	1	1	yes	characteristic, complemented, Sylow
439	#41	—	46	4	no	—
440	#41	—	46	4	no	—
441	C₂×Q₈	—	23	2	no	—
442	C₂×Q₈	—	23	1	no	—
443	C₂×Q₈	—	23	1	no	—
444	C₂×Q₈	—	23	2	no	—
445	C₂×Q₈	—	46	4	no	—
446	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
449	C₂×D₄	—	23	1	no	—
450	C₂×D₄	—	23	1	no	—
451	C₂×D₄	—	23	2	no	—
452	C₂×D₄	—	23	2	no	—
453	C₂×D₄	—	23	1	no	—
454	C₂×D₄	—	23	1	no	—
455	C₂×D₄	—	23	2	no	—
456	C₂²×C₄	—	23	1	no	—
457	C₂²×C₄	—	23	2	no	—
458	C₂²×C₄	—	23	2	no	—
459	C₂²×C₄	—	23	1	no	—
460	C₂²×C₄	—	23	1	no	—
461	C₂²×C₄	—	23	1	no	—
462	C₂²×C₄	—	23	2	no	—
463	C₂²×C₄	—	23	1	no	—
464	C₂²×C₄	—	23	2	no	—
465	C₂²×C₄	—	23	2	no	—
466	C₂²×C₄	—	23	1	no	—
467	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
470	C₄⋊C₄	—	23	2	no	—
471	C₄⋊C₄	—	23	1	no	—
472	C₄⋊C₄	—	23	2	no	—
473	C₄⋊C₄	—	23	2	no	—
474	C₄⋊C₄	—	23	2	no	—
475	C₄⋊C₄	—	23	1	no	—
476	C₄⋊C₄	—	23	1	no	—
477	C₄⋊C₄	—	23	1	no	—
478	C₄⋊C₄	—	23	1	no	—
479	C₄⋊C₄	—	23	1	no	—
480	C₄⋊C₄	—	23	1	no	—
481	C₄⋊C₄	—	23	2	no	—
482	C₄⋊C₄	—	23	1	no	—
483	C₄⋊C₄	—	23	2	no	—
484	C₄⋊C₄	—	23	2	no	—
485	C₄⋊C₄	—	23	2	no	—
486	C₄⋊C₄	—	23	2	no	—
487	C₄⋊C₄	—	23	2	no	—
488	C₄⋊C₄	—	23	2	no	—
489	C₄⋊C₄	—	23	2	no	—
490	C₄⋊C₄	—	23	2	no	—
491	C₄⋊C₄	—	23	2	no	—
492	C₄⋊C₄	—	23	2	no	—
493	C₄⋊C₄	—	23	2	no	—
494	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
496	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
497	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
503	C₂²⋊C₄	—	23	1	no	—
504	C₂²⋊C₄	—	23	1	no	—
505	C₂²⋊C₄	—	23	2	no	—
506	C₂²⋊C₄	—	23	2	no	—
507	C₂²⋊C₄	—	23	1	no	—
508	C₂²⋊C₄	—	23	1	no	—
509	C₂²⋊C₄	—	23	1	no	—
510	C₂²⋊C₄	—	23	2	no	—
511	C₂²⋊C₄	—	23	2	no	—
512	C₂²⋊C₄	—	23	1	no	—
513	C₂²⋊C₄	—	23	2	no	—
514	C₂²⋊C₄	—	23	2	no	—
515	C₂²⋊C₄	—	23	2	no	—
516	C₂²⋊C₄	—	23	2	no	—
517	C₂²⋊C₄	—	23	2	no	—
518	C₂²⋊C₄	—	23	2	no	—
519	C₂²⋊C₄	—	23	2	no	—
520	C₂²⋊C₄	—	23	2	no	—
521	C₂²⋊C₄	—	23	2	no	—
522	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
524	C₄²	—	23	1	no	—
525	C₄²	—	23	1	no	—
526	C₄²	—	23	2	no	—
527	C₄²	—	23	1	no	—
528	C₄²	—	23	2	no	—
529	C₄²	—	23	1	no	—
530	C₄²	—	23	2	no	—
531	C₄²	—	23	2	no	—
532	C₄²	—	23	1	no	—
533	C₄²	—	23	2	no	—
534	C₄²	—	23	1	no	—
535	C₄²	C₂²×D₂₃	1	1	yes	characteristic
536	C₄²	C₂²×D₂₃	1	1	yes	characteristic
537	C₄²	C₂²×D₂₃	1	1	yes	characteristic
538	C₄²	C₂²×D₂₃	1	2	yes	—
539	C₄²	C₂²×D₂₃	1	2	yes	—
540	C₄²	C₂²×D₂₃	1	1	yes	characteristic
541	C₂³	—	23	1	no	—
542	C₂³	—	23	1	no	—
543	C₂³	—	23	2	no	—
544	C₂³	C₂³×D₂₃	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	46	4	no	—
549	Q₈	—	46	2	no	—
550	Q₈	—	46	2	no	—
551	Q₈	—	92	2	no	—
552	D₄	—	46	2	no	—
553	D₄	—	46	4	no	—
554	D₄	—	46	2	no	—
555	D₄	—	46	2	no	—
556	D₄	—	46	2	no	—
557	D₄	—	92	2	no	—
558	D₄	—	92	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	23	1	no	—
563	C₂×C₄	—	23	4	no	—
564	C₂×C₄	—	23	1	no	—
565	C₂×C₄	—	23	1	no	—
566	C₂×C₄	—	23	1	no	—
567	C₂×C₄	—	23	2	no	—
568	C₂×C₄	—	23	2	no	—
569	C₂×C₄	—	23	1	no	—
570	C₂×C₄	—	23	1	no	—
571	C₂×C₄	—	23	2	no	—
572	C₂×C₄	—	46	4	no	—
573	C₂×C₄	—	46	4	no	—
574	C₂×C₄	—	46	2	no	—
575	C₂×C₄	—	46	2	no	—
576	C₂×C₄	—	46	4	no	—
577	C₂×C₄	—	46	2	no	—
578	C₂×C₄	—	92	1	no	—
579	C₂×C₄	—	92	1	no	—
580	C₂×C₄	—	92	2	no	—
581	C₂×C₄	—	92	2	no	—
582	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₂₃	1	2	yes	—
584	C₂×C₄	C₂³×D₂₃	1	2	yes	—
585	C₂×C₄	C₂³×D₂₃	1	2	yes	—
586	C₂×C₄	C₂³×D₂₃	1	2	yes	—
587	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	23	2	no	—
596	C₂²	—	46	1	no	—
597	C₂²	—	46	1	no	—
598	C₂²	—	46	2	no	—
599	C₂²	—	46	1	no	—
600	C₂²	—	46	1	no	—
601	C₂²	—	46	2	no	—
602	C₂²	—	46	1	no	—
603	C₂²	—	46	2	no	—
604	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	23	2	no	—
614	C₄	—	46	1	no	—
615	C₄	—	46	2	no	—
616	C₄	—	46	1	no	—
617	C₄	—	46	1	no	—
618	C₄	—	46	2	no	—
619	C₄	—	46	1	no	—
620	C₄	—	46	2	no	—
621	C₄	—	46	1	no	—
622	C₄	#10625158	1	2	yes	—
623	C₄	#41×D₂₃	1	2	yes	—
624	C₂	—	4	1	no	—
625	C₂	—	46	2	no	—
626	C₂	—	92	2	no	—
627	C₂	—	92	1	no	—
628	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
629	C₂	C₂×#10625158	1	1	yes	characteristic
630	C₂	#13093253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#533	C₂
prime radical	#13092997	C₂
hypercenter	#533	D₂₃
hypocenter	C₂₃	#3461
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #13093044	C₂	semidirect
2. #13093041	C₂	semidirect
3. #13093040	C₂	semidirect
4. #13093037	C₂	semidirect
5. #13093028	C₂	semidirect
6. #13093027	C₂	semidirect
7. #13093026	C₂	semidirect
8. #13093015	C₂	semidirect
9. #13093013	C₂	semidirect
11. #13092992	C₂	semidirect
12. #13092990	C₂	semidirect
13. #13092971	C₂	semidirect
14. #13092971	C₂	semidirect
15. #13092954	C₂	semidirect
16. #13092954	C₂	semidirect
17. #13092951	C₂	semidirect
18. #13092945	C₂	semidirect
19. #13092945	C₂	semidirect
20. C₄×#67292	C₂	semidirect
21. C₄×#67288	C₂	semidirect
22. C₄×Q₈×D₂₃	C₂	semidirect
23. C₂₃×#533	C₂	semidirect
323. #533	D₂₃	semidirect
438. C₂₃	#3461	semidirect

Maximal subgroups

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

subgroup	index
#13093044	2
#13093041	2
#13093040	2
#13093037	2
#13093028	2
#13093027	2
#13093026	2
#13093015	2
#13093013	2
#13092997	2
#13092992	2
#13092990	2
#13092971	2
#13092954	2
#13092951	2
#13092945	2
C₄×#67292	2
C₄×#67288	2
C₄×Q₈×D₂₃	2
C₂₃×#533	2
#3461	23