Subgroups — #15687536

Order 2944.

1058 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093171	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093169	C₂	1	2	yes	maximal, complemented
3	#13093165	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093164	C₂	1	2	yes	maximal, complemented
5	#13093163	C₂	1	2	yes	maximal, complemented
6	#13093161	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093159	C₂	1	1	yes	maximal, characteristic, complemented
8	#13093158	C₂	1	2	yes	maximal, complemented
9	#13093157	C₂	1	2	yes	maximal, complemented
10	#13093155	C₂	1	2	yes	maximal, complemented
11	#13092967	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092964	C₂	1	2	yes	maximal, complemented
13	#13092954	C₂	1	2	yes	maximal, complemented
14	#13092951	C₂	1	1	yes	maximal, characteristic, complemented
15	#13092945	C₂	1	2	yes	maximal, complemented
16	#13092929	C₂	1	2	yes	maximal, complemented
17	#13092926	C₂	1	2	yes	maximal, complemented
18	#13092926	C₂	1	2	yes	maximal, complemented
19	C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#67288	C₂²	1	1	yes	characteristic
21	C₂×#67288	C₂²	1	2	yes	—
22	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#126	C₂²	1	2	yes	complemented
25	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#124	C₂²	1	1	yes	characteristic
27	C₂₃×#123	C₂²	1	2	yes	complemented
28	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
33	C₂₃×#117	C₂²	1	2	yes	complemented
34	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	#10625118	C₂²	1	2	yes	—
36	#10625117	C₂²	1	2	yes	complemented
37	#10625111	C₂²	1	2	yes	—
38	#10625110	C₂²	1	2	yes	—
39	#10625110	C₂²	1	2	yes	—
40	#10625109	C₂²	1	2	yes	complemented
41	#10625108	C₂²	1	2	yes	—
42	#10625108	C₂²	1	2	yes	complemented
43	#10625101	C₂²	1	1	yes	characteristic
44	#10625101	C₂²	1	2	yes	complemented
45	#10625101	C₂²	1	2	yes	complemented
46	#10625100	C₂²	1	2	yes	complemented
47	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
50	#10625095	C₂²	1	1	yes	characteristic, complemented
51	#10625069	C₂²	1	2	yes	complemented
52	#10625069	C₂²	1	2	yes	complemented
53	#10625069	C₂²	1	2	yes	complemented
54	#10625068	C₂²	1	2	yes	complemented
55	#10625068	C₂²	1	2	yes	complemented
56	#10625067	C₂²	1	2	yes	complemented
57	#10625067	C₂²	1	2	yes	complemented
58	#10625067	C₂²	1	2	yes	complemented
59	#10625066	C₂²	1	2	yes	—
60	#10625066	C₂²	1	2	yes	—
61	#10625066	C₂²	1	2	yes	—
62	#10625066	C₂²	1	2	yes	complemented
63	#10625065	C₂²	1	2	yes	—
64	#10625065	C₂²	1	2	yes	complemented
65	#10625065	C₂²	1	2	yes	complemented
66	#10625065	C₂²	1	2	yes	complemented
67	#10625065	C₂²	1	2	yes	complemented
68	#10625061	C₂²	1	2	yes	complemented
69	#10625060	C₂²	1	2	yes	complemented
70	#10625059	C₂²	1	2	yes	complemented
71	#10625057	C₂²	1	2	yes	—
72	#10625057	C₂²	1	2	yes	complemented
73	#10625056	C₂²	1	2	yes	—
74	#10625056	C₂²	1	2	yes	—
75	#10625056	C₂²	1	2	yes	complemented
76	#10625055	C₂²	1	2	yes	—
77	#10625055	C₂²	1	2	yes	—
78	#10625055	C₂²	1	2	yes	—
79	#10625055	C₂²	1	2	yes	complemented
80	#10625055	C₂²	1	2	yes	complemented
81	#10625054	C₂²	1	2	yes	—
82	#10625054	C₂²	1	2	yes	complemented
83	#10625054	C₂²	1	2	yes	complemented
84	#10625053	C₂²	1	2	yes	—
85	#10625053	C₂²	1	2	yes	—
86	#10625053	C₂²	1	2	yes	complemented
87	#10625053	C₂²	1	2	yes	complemented
88	#10625050	C₂²	1	2	yes	complemented
89	#10625049	C₂²	1	2	yes	complemented
90	#10625049	C₂²	1	2	yes	complemented
91	#10625047	C₂²	1	2	yes	complemented
92	#10625046	C₂²	1	1	yes	characteristic
93	#10625046	C₂²	1	1	yes	characteristic
94	#10625046	C₂²	1	1	yes	characteristic, complemented
95	#10625045	C₂²	1	1	yes	characteristic
96	C₄×D₉₂	C₂²	1	2	yes	—
97	C₄×D₉₂	C₂²	1	1	yes	characteristic
98	C₄×D₉₂	C₂²	1	2	yes	complemented
99	C₄×D₉₂	C₂²	1	2	yes	complemented
100	C₄×D₉₂	C₂²	1	2	yes	complemented
101	#10625043	C₂²	1	2	yes	complemented
102	#10625043	C₂²	1	2	yes	complemented
103	C₄²×D₂₃	C₂²	1	2	yes	complemented
104	#10625041	C₂²	1	1	yes	characteristic, complemented
105	#10625040	C₂²	1	1	yes	characteristic, complemented
106	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₃	C₂³	1	2	yes	—
108	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
122	C₂²×Dic₂₃	C₂³	1	2	yes	—
123	#67288	—	4	2	no	—
124	#67288	—	4	4	no	—
125	#67288	—	4	2	no	—
126	C₂×D₉₂	C₂³	1	1	yes	characteristic
127	C₂×D₉₂	C₂³	1	2	yes	—
128	C₂×D₉₂	C₂³	1	2	yes	—
129	C₂×D₉₂	C₂³	1	2	yes	—
130	C₂×D₉₂	C₂³	1	2	yes	—
131	C₂×D₉₂	C₂³	1	1	yes	characteristic
132	C₂×D₉₂	C₂³	1	1	yes	characteristic
133	C₂×D₉₂	C₂³	1	2	yes	—
134	C₂×C₄×D₂₃	—	4	4	no	—
135	C₂×C₄×D₂₃	C₂³	1	2	yes	—
136	C₂×C₄×D₂₃	C₂³	1	2	yes	—
137	C₂×C₄×D₂₃	C₂³	1	2	yes	—
138	C₂×C₄×D₂₃	C₂³	1	2	yes	—
139	C₂×C₄×D₂₃	C₂³	1	2	yes	—
140	C₂×C₄×D₂₃	C₂³	1	2	yes	—
141	C₂×C₄×D₂₃	C₂³	1	2	yes	—
142	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
143	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₄₆	C₂³	1	2	yes	—
146	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₄²×C₂₃	C₂³	1	1	yes	characteristic
158	C₄²×C₂₃	C₂³	1	1	yes	characteristic
159	C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₄²×C₂₃	C₂³	1	2	yes	—
161	C₄²×C₂₃	C₂³	1	1	yes	characteristic
162	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
165	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₂₃	C₂³	1	2	yes	—
183	C₄⋊Dic₂₃	C₂³	1	2	yes	—
184	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₂₃	C₂³	1	2	yes	—
186	C₄⋊Dic₂₃	C₂³	1	2	yes	—
187	Dic₂₃⋊C₄	C₂³	1	2	yes	—
188	Dic₂₃⋊C₄	C₂³	1	2	yes	—
189	Dic₂₃⋊C₄	C₂³	1	2	yes	—
190	Dic₂₃⋊C₄	C₂³	1	2	yes	—
191	Dic₂₃⋊C₄	C₂³	1	2	yes	—
192	Dic₂₃⋊C₄	C₂³	1	2	yes	—
193	Dic₂₃⋊C₄	C₂³	1	2	yes	—
194	Dic₂₃⋊C₄	C₂³	1	2	yes	—
195	C₄×Dic₂₃	C₂³	1	2	yes	—
196	C₄×Dic₂₃	C₂³	1	2	yes	—
197	C₄×Dic₂₃	C₂³	1	2	yes	—
198	C₂³×C₂₃	C₂⁴	1	2	yes	—
199	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
200	C₂²×D₂₃	—	4	2	no	—
201	C₂²×D₂₃	—	4	2	no	—
202	C₂²×D₂₃	—	4	2	no	—
203	C₂²×D₂₃	C₂⁴	1	2	yes	—
204	C₂²×D₂₃	C₂⁴	1	2	yes	—
205	C₂²×D₂₃	C₂⁴	1	2	yes	—
206	Q₈×C₂₃	—	4	1	no	—
207	D₄×C₂₃	—	4	2	no	—
208	D₄×C₂₃	—	4	1	no	—
209	C₂×C₄×C₂₃	—	2	4	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	4	1	no	—
212	C₂×C₄×C₂₃	—	4	1	no	—
213	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
221	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²⋊D₂₃	—	4	2	no	—
223	C₂²⋊D₂₃	—	4	2	no	—
224	C₂²⋊D₂₃	—	4	2	no	—
225	C₂²⋊D₂₃	—	4	2	no	—
226	C₂²⋊D₂₃	—	4	2	no	—
227	C₂²⋊D₂₃	—	4	2	no	—
228	C₂²⋊D₂₃	—	4	2	no	—
229	C₂×Dic₂₃	—	4	2	no	—
230	C₂×Dic₂₃	C₂⁴	1	2	yes	—
231	C₂×Dic₂₃	C₂⁴	1	2	yes	—
232	C₂×Dic₂₃	C₂⁴	1	2	yes	—
233	C₂×Dic₂₃	C₂⁴	1	2	yes	—
234	C₂×Dic₂₃	C₂⁴	1	2	yes	—
235	D₉₂	—	4	1	no	—
236	D₉₂	—	4	2	no	—
237	D₉₂	—	4	2	no	—
238	D₉₂	—	4	2	no	—
239	D₉₂	—	4	2	no	—
240	D₉₂	—	4	1	no	—
241	D₉₂	—	4	1	no	—
242	D₉₂	—	4	2	no	—
243	C₄×D₂₃	—	2	4	no	—
244	C₄×D₂₃	—	2	4	no	—
245	C₄×D₂₃	—	2	4	no	—
246	C₄×D₂₃	—	4	2	no	—
247	C₄×D₂₃	—	4	2	no	—
248	C₄×D₂₃	—	4	2	no	—
249	C₄×D₂₃	—	4	2	no	—
250	Dic₄₆	—	4	1	no	—
251	Dic₄₆	—	4	1	no	—
252	Dic₄₆	—	4	2	no	—
253	Dic₄₆	—	4	1	no	—
254	#3529	—	23	1	no	maximal, Sylow
255	C₂²×C₂₃	—	2	2	no	—
256	C₂²×C₂₃	—	2	1	no	—
257	C₂²×C₂₃	—	2	1	no	—
258	C₂²×C₂₃	—	2	2	no	—
259	C₂²×C₂₃	—	2	2	no	—
260	C₂²×C₂₃	—	2	1	no	—
261	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
262	C₂×D₂₃	—	2	2	no	—
263	C₂×D₂₃	—	2	2	no	—
264	C₂×D₂₃	—	2	2	no	—
265	C₂×D₂₃	—	2	2	no	—
266	C₂×D₂₃	—	2	2	no	—
267	C₂×D₂₃	—	2	2	no	—
268	C₂×D₂₃	—	2	2	no	—
269	C₂×D₂₃	—	2	2	no	—
270	C₂×D₂₃	—	2	2	no	—
271	C₂×D₂₃	—	4	8	no	—
272	C₄×C₂₃	—	2	1	no	—
273	C₄×C₂₃	—	2	2	no	—
274	C₄×C₂₃	—	2	1	no	—
275	C₄×C₂₃	—	2	2	no	—
276	C₄×C₂₃	—	2	2	no	—
277	C₄×C₂₃	—	2	1	no	—
278	C₄×C₂₃	—	2	1	no	—
279	C₄×C₂₃	—	2	1	no	—
280	C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
281	Dic₂₃	—	2	2	no	—
282	Dic₂₃	—	2	2	no	—
283	Dic₂₃	—	2	2	no	—
284	Dic₂₃	—	2	2	no	—
285	Dic₂₃	—	2	2	no	—
286	#563	—	23	2	no	—
287	#563	—	23	1	no	—
288	#562	—	23	1	no	—
289	#562	—	23	1	no	—
290	#562	—	23	2	no	—
291	#562	—	23	2	no	—
292	H(3,𝔽₄)	—	23	1	no	—
293	#560	—	23	2	no	—
294	#560	—	23	2	no	—
295	#560	—	23	2	no	—
296	#532	—	23	2	no	—
297	#532	—	23	1	no	—
298	#529	—	23	2	no	—
299	#529	—	23	2	no	—
300	#529	—	23	1	no	—
301	#529	D₂₃	1	1	yes	characteristic, complemented
302	#525	—	23	2	no	—
303	#525	—	23	2	no	—
304	#525	—	23	2	no	—
305	C₂×C₂₃	—	4	2	no	—
306	C₂×C₂₃	—	4	1	no	—
307	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₂₃	#585	1	1	yes	characteristic
309	C₂×C₂₃	#585	1	1	yes	characteristic
310	D₂₃	—	4	2	no	—
311	D₂₃	—	4	2	no	—
312	D₂₃	—	4	2	no	—
313	C₂×#41	—	23	2	no	—
314	C₂×#41	—	23	1	no	—
315	C₂×#41	—	23	1	no	—
316	C₂³×C₄	—	23	2	no	—
317	C₄⋊Q₈	—	23	2	no	—
318	C₄⋊Q₈	—	23	1	no	—
319	#127	—	23	2	no	—
320	#127	—	23	1	no	—
321	#126	—	23	2	no	—
322	#126	—	23	2	no	—
323	#126	—	23	2	no	—
324	#126	—	23	2	no	—
325	#126	—	23	2	no	—
326	#126	C₂×D₂₃	1	2	yes	complemented
327	#125	—	23	2	no	—
328	#125	—	23	2	no	—
329	#125	—	23	1	no	—
330	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
331	#124	—	23	2	no	—
332	#124	—	23	2	no	—
333	#124	—	23	2	no	—
334	#124	—	23	2	no	—
335	#124	—	23	1	no	—
336	#124	—	23	1	no	—
337	#124	—	23	1	no	—
338	#124	C₂×D₂₃	1	1	yes	characteristic
339	#123	—	23	2	no	—
340	#123	—	23	2	no	—
341	#123	—	23	2	no	—
342	#123	—	23	2	no	—
343	#123	—	23	2	no	—
344	#123	—	23	2	no	—
345	#123	—	23	2	no	—
346	#123	—	23	2	no	—
347	#123	—	23	2	no	—
348	#123	—	23	2	no	—
349	#123	—	23	2	no	—
350	#123	C₂×D₂₃	1	2	yes	complemented
351	C₂²⋊Q₈	—	23	2	no	—
352	C₂²⋊Q₈	—	23	1	no	—
353	C₂²⋊Q₈	—	23	2	no	—
354	C₂²⋊Q₈	—	23	2	no	—
355	C₂²⋊Q₈	—	23	2	no	—
356	C₂²⋊Q₈	—	23	2	no	—
357	C₂²⋊Q₈	—	23	2	no	—
358	C₂²⋊Q₈	—	23	2	no	—
359	C₂²⋊Q₈	—	23	2	no	—
360	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
361	#121	—	23	2	no	—
362	#121	—	23	2	no	—
363	#121	—	23	2	no	—
364	#121	—	23	1	no	—
365	#121	—	23	2	no	—
366	#121	—	23	2	no	—
367	#121	—	23	2	no	—
368	#121	—	23	2	no	—
369	#121	—	23	2	no	—
370	#121	—	23	2	no	—
371	#121	—	23	2	no	—
372	#121	—	23	2	no	—
373	#121	—	23	2	no	—
374	#121	—	23	2	no	—
375	#121	—	23	2	no	—
376	#121	C₂×D₂₃	1	1	yes	characteristic
377	#120	—	23	2	no	—
378	#120	—	23	2	no	—
379	#120	—	23	2	no	—
380	#120	—	23	2	no	—
381	#120	—	23	2	no	—
382	#120	—	23	2	no	—
383	C₄×Q₈	—	23	1	no	—
384	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
385	C₄×D₄	—	23	2	no	—
386	C₄×D₄	—	23	2	no	—
387	C₄×D₄	—	23	2	no	—
388	C₄×D₄	—	23	2	no	—
389	C₄×D₄	—	23	1	no	—
390	C₄×D₄	—	23	2	no	—
391	C₄×D₄	—	23	2	no	—
392	C₄×D₄	—	23	2	no	—
393	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
394	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
395	#117	—	23	2	no	—
396	#117	—	23	2	no	—
397	#117	C₂×D₂₃	1	2	yes	complemented
398	C₂×C₄²	—	23	2	no	—
399	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic, complemented
400	C₂₃	#3529	1	1	yes	characteristic, complemented, Sylow
401	C₂⁴	—	23	2	no	—
402	#41	—	92	4	no	—
403	#41	—	92	2	no	—
404	#41	—	92	2	no	—
405	C₂×Q₈	—	23	1	no	—
406	C₂×Q₈	—	23	2	no	—
407	C₂×Q₈	—	23	1	no	—
408	C₂×Q₈	—	23	1	no	—
409	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
410	C₂×D₄	—	23	2	no	—
411	C₂×D₄	—	23	2	no	—
412	C₂×D₄	—	23	2	no	—
413	C₂×D₄	—	23	2	no	—
414	C₂×D₄	—	23	2	no	—
415	C₂×D₄	—	23	2	no	—
416	C₂×D₄	—	23	2	no	—
417	C₂×D₄	—	23	2	no	—
418	C₂×D₄	—	23	1	no	—
419	C₂×D₄	—	23	2	no	—
420	C₂×D₄	—	23	2	no	—
421	C₂×D₄	—	23	2	no	—
422	C₂×D₄	—	23	1	no	—
423	C₂×D₄	—	23	2	no	—
424	C₂×D₄	—	23	1	no	—
425	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
426	C₂×D₄	C₂²×D₂₃	1	2	yes	—
427	C₂²×C₄	—	23	2	no	—
428	C₂²×C₄	—	23	2	no	—
429	C₂²×C₄	—	23	2	no	—
430	C₂²×C₄	—	23	2	no	—
431	C₂²×C₄	—	23	2	no	—
432	C₂²×C₄	—	23	2	no	—
433	C₂²×C₄	—	23	2	no	—
434	C₂²×C₄	—	23	2	no	—
435	C₂²×C₄	—	92	4	no	—
436	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
438	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
440	C₄⋊C₄	—	23	2	no	—
441	C₄⋊C₄	—	23	2	no	—
442	C₄⋊C₄	—	23	2	no	—
443	C₄⋊C₄	—	23	2	no	—
444	C₄⋊C₄	—	23	2	no	—
445	C₄⋊C₄	—	23	2	no	—
446	C₄⋊C₄	—	23	2	no	—
447	C₄⋊C₄	—	23	2	no	—
448	C₄⋊C₄	—	23	2	no	—
449	C₄⋊C₄	—	23	2	no	—
450	C₄⋊C₄	—	23	2	no	—
451	C₄⋊C₄	—	23	1	no	—
452	C₄⋊C₄	—	23	2	no	—
453	C₄⋊C₄	—	23	1	no	—
454	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
455	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
458	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
459	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
460	C₂²⋊C₄	—	23	2	no	—
461	C₂²⋊C₄	—	23	2	no	—
462	C₂²⋊C₄	—	23	2	no	—
463	C₂²⋊C₄	—	23	2	no	—
464	C₂²⋊C₄	—	23	2	no	—
465	C₂²⋊C₄	—	23	2	no	—
466	C₂²⋊C₄	—	23	2	no	—
467	C₂²⋊C₄	—	23	2	no	—
468	C₂²⋊C₄	—	23	2	no	—
469	C₂²⋊C₄	—	23	2	no	—
470	C₂²⋊C₄	—	23	2	no	—
471	C₂²⋊C₄	—	23	2	no	—
472	C₂²⋊C₄	—	23	2	no	—
473	C₂²⋊C₄	—	23	2	no	—
474	C₂²⋊C₄	—	23	2	no	—
475	C₂²⋊C₄	—	23	2	no	—
476	C₂²⋊C₄	—	23	2	no	—
477	C₂²⋊C₄	—	23	2	no	—
478	C₂²⋊C₄	—	23	2	no	—
479	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
484	C₄²	—	23	2	no	—
485	C₄²	—	23	2	no	—
486	C₄²	—	23	2	no	—
487	C₄²	C₂²×D₂₃	1	1	yes	characteristic
488	C₄²	C₂²×D₂₃	1	1	yes	characteristic
489	C₄²	C₂²×D₂₃	1	2	yes	—
490	C₄²	C₂²×D₂₃	1	1	yes	characteristic
491	C₄²	C₂²×D₂₃	1	1	yes	characteristic
492	C₂³	—	23	2	no	—
493	C₂³	—	23	2	no	—
494	C₂³	—	23	2	no	—
495	C₂³	—	92	2	no	—
496	C₂³	—	92	2	no	—
497	C₂³	—	92	2	no	—
498	C₂³	C₂³×D₂₃	1	2	yes	—
499	C₂³	C₂³×D₂₃	1	1	yes	characteristic
500	Q₈	—	4	1	no	—
501	Q₈	—	92	2	no	—
502	Q₈	—	92	1	no	—
503	Q₈	—	92	1	no	—
504	Q₈	—	92	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	2	no	—
507	D₄	—	92	2	no	—
508	D₄	—	92	1	no	—
509	D₄	—	92	1	no	—
510	D₄	—	92	2	no	—
511	D₄	—	92	2	no	—
512	D₄	—	92	1	no	—
513	D₄	—	92	2	no	—
514	D₄	—	92	2	no	—
515	D₄	—	92	2	no	—
516	D₄	—	92	2	no	—
517	D₄	—	92	2	no	—
518	D₄	—	92	2	no	—
519	D₄	—	92	2	no	—
520	D₄	—	92	2	no	—
521	D₄	—	92	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	23	2	no	—
527	C₂×C₄	—	23	2	no	—
528	C₂×C₄	—	23	2	no	—
529	C₂×C₄	—	23	2	no	—
530	C₂×C₄	—	23	2	no	—
531	C₂×C₄	—	46	4	no	—
532	C₂×C₄	—	46	4	no	—
533	C₂×C₄	—	46	4	no	—
534	C₂×C₄	—	92	2	no	—
535	C₂×C₄	—	92	2	no	—
536	C₂×C₄	—	92	2	no	—
537	C₂×C₄	—	92	2	no	—
538	C₂×C₄	—	92	2	no	—
539	C₂×C₄	C₂³×D₂₃	1	2	yes	—
540	C₂×C₄	C₂³×D₂₃	1	2	yes	—
541	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
542	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₂₃	1	2	yes	—
547	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
548	C₂²	—	2	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	46	2	no	—
555	C₂²	—	46	2	no	—
556	C₂²	—	46	2	no	—
557	C₂²	—	46	2	no	—
558	C₂²	—	46	2	no	—
559	C₂²	—	46	2	no	—
560	C₂²	—	46	2	no	—
561	C₂²	—	46	2	no	—
562	C₂²	—	46	2	no	—
563	C₂²	—	92	8	no	—
564	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	46	2	no	—
574	C₄	—	46	2	no	—
575	C₄	—	46	2	no	—
576	C₄	—	46	2	no	—
577	C₄	—	46	2	no	—
578	C₄	#10625160	1	2	yes	—
579	C₂	—	4	2	no	—
580	C₂	—	4	1	no	—
581	C₂	—	92	2	no	—
582	C₂	—	92	2	no	—
583	C₂	—	92	2	no	—
584	C₂	C₂×#10625160	1	1	yes	characteristic
585	C₂	#13093253	1	1	yes	characteristic
586	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×#529	C₂
hypercenter	#529	D₂₃
hypocenter	C₂₃	#3529
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #13093171	C₂	semidirect
2. #13093169	C₂	semidirect
3. #13093165	C₂	semidirect
4. #13093164	C₂	semidirect
5. #13093163	C₂	semidirect
6. #13093161	C₂	semidirect
7. #13093159	C₂	semidirect
8. #13093158	C₂	semidirect
9. #13093157	C₂	semidirect
10. #13093155	C₂	semidirect
11. #13092967	C₂	semidirect
12. #13092964	C₂	semidirect
13. #13092954	C₂	semidirect
14. #13092951	C₂	semidirect
15. #13092945	C₂	semidirect
16. #13092929	C₂	semidirect
17. #13092926	C₂	semidirect
18. #13092926	C₂	semidirect
19. C₂₃×#529	C₂	semidirect
22. C₂×#67288	C₂²	semidirect
23. C₂²×C₄×D₂₃	C₂²	semidirect
24. C₂₃×#126	C₂²	semidirect
25. C₂₃×#125	C₂²	semidirect
27. C₂₃×#123	C₂²	semidirect
28. C₂₃×C₂²⋊Q₈	C₂²	semidirect
30. C₄×Q₈×C₂₃	C₂²	semidirect
32. C₄×D₄×C₂₃	C₂²	semidirect
33. C₂₃×#117	C₂²	semidirect
34. C₂×C₄²×C₂₃	C₂²	semidirect
36. #10625117	C₂²	semidirect
40. #10625109	C₂²	semidirect
42. #10625108	C₂²	semidirect
44. #10625101	C₂²	semidirect
45. #10625101	C₂²	semidirect
46. #10625100	C₂²	semidirect
48. C₄×C₂²⋊D₂₃	C₂²	semidirect
49. C₄×C₂²⋊D₂₃	C₂²	semidirect
50. #10625095	C₂²	semidirect
51. #10625069	C₂²	semidirect
52. #10625069	C₂²	semidirect
53. #10625069	C₂²	semidirect
54. #10625068	C₂²	semidirect
55. #10625068	C₂²	semidirect
56. #10625067	C₂²	semidirect
57. #10625067	C₂²	semidirect
58. #10625067	C₂²	semidirect
62. #10625066	C₂²	semidirect
64. #10625065	C₂²	semidirect
65. #10625065	C₂²	semidirect
66. #10625065	C₂²	semidirect
67. #10625065	C₂²	semidirect
68. #10625061	C₂²	semidirect
69. #10625060	C₂²	semidirect
70. #10625059	C₂²	semidirect
72. #10625057	C₂²	semidirect
75. #10625056	C₂²	semidirect
79. #10625055	C₂²	semidirect
80. #10625055	C₂²	semidirect
82. #10625054	C₂²	semidirect
83. #10625054	C₂²	semidirect
86. #10625053	C₂²	semidirect
87. #10625053	C₂²	semidirect
88. #10625050	C₂²	semidirect
89. #10625049	C₂²	semidirect
90. #10625049	C₂²	semidirect
91. #10625047	C₂²	semidirect
94. #10625046	C₂²	semidirect
98. C₄×D₉₂	C₂²	semidirect
99. C₄×D₉₂	C₂²	semidirect
100. C₄×D₉₂	C₂²	semidirect
101. #10625043	C₂²	semidirect
102. #10625043	C₂²	semidirect
103. C₄²×D₂₃	C₂²	semidirect
104. #10625041	C₂²	semidirect
105. #10625040	C₂²	semidirect
106. C₄×Dic₄₆	C₂²	semidirect
301. #529	D₂₃	semidirect
326. #126	C₂×D₂₃	semidirect
330. #125	C₂×D₂₃	semidirect
350. #123	C₂×D₂₃	semidirect
360. C₂²⋊Q₈	C₂×D₂₃	semidirect
384. C₄×Q₈	C₂×D₂₃	semidirect
394. C₄×D₄	C₂×D₂₃	semidirect
397. #117	C₂×D₂₃	semidirect
399. C₂×C₄²	C₂×D₂₃	semidirect
400. C₂₃	#3529	semidirect

Maximal subgroups

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

subgroup	index
#13093171	2
#13093169	2
#13093165	2
#13093164	2
#13093163	2
#13093161	2
#13093159	2
#13093158	2
#13093157	2
#13093155	2
#13092967	2
#13092964	2
#13092954	2
#13092951	2
#13092945	2
#13092929	2
#13092926	2
C₂₃×#529	2
#3529	23