Subgroups — #15686999

Order 2944.

1242 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093151	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093121	C₂	1	2	yes	maximal, complemented
3	#13093112	C₂	1	2	yes	maximal, complemented
4	#13093110	C₂	1	2	yes	maximal, complemented
5	#13093098	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093095	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093094	C₂	1	2	yes	maximal, complemented
8	#13093056	C₂	1	2	yes	maximal, complemented
9	#13093054	C₂	1	2	yes	maximal, complemented
10	#13093049	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092963	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092947	C₂	1	2	yes	maximal, complemented
13	#13092945	C₂	1	2	yes	maximal, complemented
14	#13092926	C₂	1	2	yes	maximal, complemented
15	#13092924	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#67290	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₂₃	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
19	C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	—
23	C₂×#67290	C₂²	1	2	yes	—
24	C₂×D₄×D₂₃	C₂²	1	2	yes	—
25	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
28	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
31	C₂₃×#121	C₂²	1	2	yes	complemented
32	C₂₃×#120	C₂²	1	1	yes	characteristic
33	C₂₃×#120	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
35	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
36	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
38	#10625118	C₂²	1	1	yes	characteristic, complemented
39	#10625117	C₂²	1	2	yes	complemented
40	#10625115	C₂²	1	1	yes	characteristic, complemented
41	#10625111	C₂²	1	1	yes	characteristic
42	#10625110	C₂²	1	2	yes	—
43	#10625110	C₂²	1	2	yes	complemented
44	#10625110	C₂²	1	2	yes	complemented
45	#10625110	C₂²	1	2	yes	complemented
46	#10625109	C₂²	1	2	yes	complemented
47	#10625108	C₂²	1	1	yes	characteristic
48	#10625108	C₂²	1	1	yes	characteristic, complemented
49	#10625108	C₂²	1	2	yes	complemented
50	#10625107	C₂²	1	1	yes	characteristic, complemented
51	#10625106	C₂²	1	1	yes	characteristic, complemented
52	#10625106	C₂²	1	1	yes	characteristic, complemented
53	#10625106	C₂²	1	2	yes	complemented
54	D₄×Dic₂₃	C₂²	1	2	yes	complemented
55	D₄×Dic₂₃	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
66	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
67	#10625097	C₂²	1	1	yes	characteristic, complemented
68	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
70	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
71	#10625069	C₂²	1	2	yes	complemented
72	#10625069	C₂²	1	2	yes	complemented
73	#10625067	C₂²	1	2	yes	complemented
74	#10625067	C₂²	1	2	yes	complemented
75	#10625065	C₂²	1	2	yes	complemented
76	#10625065	C₂²	1	2	yes	complemented
77	#10625064	C₂²	1	2	yes	complemented
78	#10625063	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
80	#10625060	C₂²	1	2	yes	complemented
81	#10625060	C₂²	1	2	yes	complemented
82	#10625058	C₂²	1	2	yes	complemented
83	#10625057	C₂²	1	2	yes	complemented
84	#10625056	C₂²	1	2	yes	complemented
85	#10625056	C₂²	1	2	yes	complemented
86	#10625055	C₂²	1	2	yes	—
87	#10625055	C₂²	1	2	yes	complemented
88	#10625054	C₂²	1	2	yes	complemented
89	#10625054	C₂²	1	2	yes	complemented
90	#10625053	C₂²	1	2	yes	—
91	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
93	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
94	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
97	#10625050	C₂²	1	2	yes	complemented
98	#10625050	C₂²	1	2	yes	complemented
99	#10625049	C₂²	1	2	yes	complemented
100	#10625049	C₂²	1	2	yes	complemented
101	#10625048	C₂²	1	2	yes	complemented
102	#10625048	C₂²	1	2	yes	complemented
103	C₄×D₉₂	C₂²	1	2	yes	complemented
104	#10625043	C₂²	1	2	yes	complemented
105	C₄²×D₂₃	C₂²	1	2	yes	complemented
106	C₄×Dic₄₆	C₂²	1	2	yes	complemented
107	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×D₂₃	C₂³	1	1	yes	characteristic
109	C₂³×D₂₃	C₂³	1	2	yes	—
110	#41×C₂₃	—	4	2	no	—
111	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂×D₄×C₂₃	C₂³	1	2	yes	—
114	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₂₃	—	4	2	no	—
118	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
123	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₂₃	—	2	8	no	—
125	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
132	C₂²×Dic₂₃	C₂³	1	2	yes	—
133	C₂²×Dic₂₃	C₂³	1	2	yes	—
134	C₂²×Dic₂₃	C₂³	1	2	yes	—
135	C₂²×Dic₂₃	C₂³	1	2	yes	—
136	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
137	#67290	—	2	8	no	—
138	D₄×D₂₃	—	2	8	no	—
139	#67288	—	4	2	no	—
140	C₂×D₉₂	C₂³	1	2	yes	—
141	C₂×D₉₂	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₂₃	—	4	2	no	—
143	C₂×C₄×D₂₃	—	4	4	no	—
144	C₂×C₄×D₂₃	C₂³	1	2	yes	—
145	C₂×C₄×D₂₃	C₂³	1	2	yes	—
146	C₂×C₄×D₂₃	C₂³	1	2	yes	—
147	C₂×C₄×D₂₃	C₂³	1	2	yes	—
148	C₂×C₄×D₂₃	C₂³	1	2	yes	—
149	C₂×C₄×D₂₃	C₂³	1	2	yes	—
150	C₂×C₄×D₂₃	C₂³	1	2	yes	—
151	C₂×Dic₄₆	C₂³	1	2	yes	—
152	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
167	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₄⋊Dic₂₃	C₂³	1	2	yes	—
183	C₄⋊Dic₂₃	C₂³	1	2	yes	—
184	Dic₂₃⋊C₄	C₂³	1	2	yes	—
185	Dic₂₃⋊C₄	C₂³	1	2	yes	—
186	Dic₂₃⋊C₄	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	C₄×Dic₂₃	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	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₃	C₂³	1	2	yes	—
200	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₃	C₂³	1	2	yes	—
202	C₂³×C₂₃	—	2	4	no	—
203	C₂³×C₂₃	—	4	1	no	—
204	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₂₃	C₂⁴	1	2	yes	—
208	C₂²×D₂₃	—	2	4	no	—
209	C₂²×D₂₃	—	2	4	no	—
210	C₂²×D₂₃	—	2	4	no	—
211	C₂²×D₂₃	—	4	1	no	—
212	C₂²×D₂₃	—	4	2	no	—
213	C₂²×D₂₃	C₂⁴	1	2	yes	—
214	C₂²×D₂₃	C₂⁴	1	2	yes	—
215	Q₈×C₂₃	—	4	1	no	—
216	D₄×C₂₃	—	2	4	no	—
217	D₄×C₂₃	—	2	4	no	—
218	D₄×C₂₃	—	4	1	no	—
219	D₄×C₂₃	—	4	1	no	—
220	D₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	2	4	no	—
222	C₂×C₄×C₂₃	—	2	2	no	—
223	C₂×C₄×C₂₃	—	2	2	no	—
224	C₂×C₄×C₂₃	—	2	2	no	—
225	C₂×C₄×C₂₃	—	4	1	no	—
226	C₂×C₄×C₂₃	—	4	2	no	—
227	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₂²⋊D₂₃	—	2	4	no	—
235	C₂²⋊D₂₃	—	2	4	no	—
236	C₂²⋊D₂₃	—	2	4	no	—
237	C₂²⋊D₂₃	—	2	4	no	—
238	C₂²⋊D₂₃	—	2	4	no	—
239	C₂²⋊D₂₃	—	4	2	no	—
240	C₂²⋊D₂₃	#41	1	8	yes	complemented
241	C₂×Dic₂₃	—	2	4	no	—
242	C₂×Dic₂₃	—	2	4	no	—
243	C₂×Dic₂₃	—	2	4	no	—
244	C₂×Dic₂₃	—	4	2	no	—
245	C₂×Dic₂₃	—	4	1	no	—
246	C₂×Dic₂₃	C₂⁴	1	2	yes	—
247	C₂×Dic₂₃	C₂⁴	1	2	yes	—
248	C₂×Dic₂₃	C₂⁴	1	2	yes	—
249	C₂×Dic₂₃	C₂⁴	1	2	yes	—
250	C₂×Dic₂₃	C₂⁴	1	2	yes	—
251	C₂×Dic₂₃	C₂⁴	1	2	yes	—
252	D₉₂	—	2	4	no	—
253	D₉₂	—	4	1	no	—
254	C₄×D₂₃	—	2	4	no	—
255	C₄×D₂₃	—	2	4	no	—
256	C₄×D₂₃	—	2	4	no	—
257	C₄×D₂₃	—	2	4	no	—
258	C₄×D₂₃	—	4	2	no	—
259	C₄×D₂₃	—	4	2	no	—
260	C₄×D₂₃	—	4	2	no	—
261	Dic₄₆	—	2	4	no	—
262	Dic₄₆	—	4	1	no	—
263	#3481	—	23	1	no	maximal, Sylow
264	C₂²×C₂₃	—	2	2	no	—
265	C₂²×C₂₃	—	2	2	no	—
266	C₂²×C₂₃	—	2	2	no	—
267	C₂²×C₂₃	—	2	2	no	—
268	C₂²×C₂₃	—	2	2	no	—
269	C₂²×C₂₃	—	2	1	no	—
270	C₂²×C₂₃	—	2	1	no	—
271	C₂²×C₂₃	—	2	1	no	—
272	C₂²×C₂₃	—	4	4	no	—
273	C₂²×C₂₃	C₂×#41	1	4	yes	—
274	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
275	C₂×D₂₃	—	2	2	no	—
276	C₂×D₂₃	—	2	2	no	—
277	C₂×D₂₃	—	2	2	no	—
278	C₂×D₂₃	—	2	2	no	—
279	C₂×D₂₃	—	2	2	no	—
280	C₂×D₂₃	—	4	4	no	—
281	C₂×D₂₃	—	4	8	no	—
282	C₂×D₂₃	C₂×#41	1	4	yes	—
283	C₄×C₂₃	—	2	2	no	—
284	C₄×C₂₃	—	2	2	no	—
285	C₄×C₂₃	—	2	1	no	—
286	C₄×C₂₃	—	2	2	no	—
287	C₄×C₂₃	—	2	1	no	—
288	C₄×C₂₃	—	2	1	no	—
289	C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
290	Dic₂₃	—	2	2	no	—
291	Dic₂₃	—	2	2	no	—
292	Dic₂₃	—	2	2	no	—
293	Dic₂₃	—	2	2	no	—
294	Dic₂₃	—	2	2	no	—
295	Dic₂₃	C₂×#41	1	4	yes	—
296	#559	—	23	1	no	—
297	#554	—	23	2	no	—
298	#553	—	23	2	no	—
299	#553	—	23	2	no	—
300	#551	—	23	1	no	—
301	#551	—	23	2	no	—
302	#551	—	23	1	no	—
303	#546	—	23	2	no	—
304	#546	—	23	2	no	—
305	D₄²	—	23	1	no	—
306	#532	—	23	1	no	—
307	#529	—	23	2	no	—
308	#529	—	23	2	no	—
309	#525	—	23	1	no	—
310	#525	—	23	2	no	—
311	#525	D₂₃	1	1	yes	characteristic, complemented
312	C₄×#41	—	23	2	no	—
313	C₂×C₄×D₄	—	23	2	no	—
314	C₂×C₄×D₄	—	23	2	no	—
315	C₂×C₂₃	—	2	4	no	—
316	C₂×C₂₃	—	4	1	no	—
317	C₂×C₂₃	—	4	1	no	—
318	C₂×C₂₃	—	4	1	no	—
319	C₂×C₂₃	C₂²×#41	1	2	yes	—
320	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
321	D₂₃	—	2	4	no	—
322	D₂₃	—	4	2	no	—
323	C₂×#41	—	23	2	no	—
324	C₂×#41	—	23	1	no	—
325	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
326	C₂²×D₄	—	23	2	no	—
327	C₂²×D₄	—	23	2	no	—
328	C₂³×C₄	—	23	2	no	—
329	C₂³×C₄	—	23	1	no	—
330	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
331	C₄⋊Q₈	—	23	1	no	—
332	#127	—	23	1	no	—
333	#126	—	23	2	no	—
334	#126	—	23	2	no	—
335	#126	—	23	2	no	—
336	#126	—	23	2	no	—
337	#125	—	23	2	no	—
338	#125	—	23	2	no	—
339	#124	—	23	1	no	—
340	#124	—	23	1	no	—
341	#124	—	23	2	no	—
342	#124	—	23	2	no	—
343	#123	—	23	1	no	—
344	#123	—	23	1	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	—	23	2	no	—
351	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
352	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
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	C₂×D₂₃	1	2	yes	complemented
359	#121	—	23	2	no	—
360	#121	—	23	2	no	—
361	#121	—	23	2	no	—
362	#121	—	23	2	no	—
363	#121	—	23	2	no	—
364	#121	—	23	2	no	—
365	#121	—	23	2	no	—
366	#121	C₂×D₂₃	1	2	yes	complemented
367	#120	—	23	1	no	—
368	#120	—	23	2	no	—
369	#120	—	23	1	no	—
370	#120	—	23	2	no	—
371	#120	C₂×D₂₃	1	1	yes	characteristic
372	#120	C₂×D₂₃	1	1	yes	characteristic, complemented
373	C₄×Q₈	—	23	2	no	—
374	C₄×Q₈	—	23	2	no	—
375	C₄×D₄	—	23	2	no	—
376	C₄×D₄	—	23	2	no	—
377	C₄×D₄	—	23	2	no	—
378	C₄×D₄	—	23	2	no	—
379	C₄×D₄	—	23	2	no	—
380	C₄×D₄	—	23	2	no	—
381	C₄×D₄	—	23	2	no	—
382	C₄×D₄	—	23	2	no	—
383	C₄×D₄	—	23	2	no	—
384	C₄×D₄	—	23	2	no	—
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	2	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	2	yes	complemented
394	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
395	#117	—	23	1	no	—
396	#117	—	23	2	no	—
397	#117	—	23	2	no	—
398	#117	—	23	2	no	—
399	#117	—	23	2	no	—
400	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
401	C₂×C₄⋊C₄	—	23	2	no	—
402	C₂×C₄⋊C₄	—	23	2	no	—
403	C₂×C₂²⋊C₄	—	23	2	no	—
404	C₂×C₂²⋊C₄	—	23	2	no	—
405	C₂×C₂²⋊C₄	—	23	2	no	—
406	C₂×C₂²⋊C₄	—	23	2	no	—
407	C₂×C₄²	—	23	2	no	—
408	C₂×C₄²	—	23	1	no	—
409	C₂×C₄²	—	23	2	no	—
410	C₂₃	#3481	1	1	yes	characteristic, complemented, Sylow
411	C₂⁴	—	23	1	no	—
412	C₂⁴	—	23	2	no	—
413	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
414	#41	—	4	2	no	—
415	#41	—	46	8	no	—
416	#41	—	92	2	no	—
417	C₂×Q₈	—	23	2	no	—
418	C₂×Q₈	—	23	1	no	—
419	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
420	C₂×D₄	—	23	2	no	—
421	C₂×D₄	—	23	2	no	—
422	C₂×D₄	—	23	2	no	—
423	C₂×D₄	—	23	2	no	—
424	C₂×D₄	—	23	2	no	—
425	C₂×D₄	—	23	2	no	—
426	C₂×D₄	—	23	2	no	—
427	C₂×D₄	—	23	2	no	—
428	C₂×D₄	—	23	1	no	—
429	C₂×D₄	—	46	8	no	—
430	C₂×D₄	—	46	8	no	—
431	C₂×D₄	C₂²×D₂₃	1	2	yes	—
432	C₂×D₄	C₂²×D₂₃	1	2	yes	—
433	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	23	2	no	—
438	C₂²×C₄	—	23	2	no	—
439	C₂²×C₄	—	23	2	no	—
440	C₂²×C₄	—	23	2	no	—
441	C₂²×C₄	—	23	1	no	—
442	C₂²×C₄	—	23	2	no	—
443	C₂²×C₄	—	23	2	no	—
444	C₂²×C₄	—	23	2	no	—
445	C₂²×C₄	—	23	2	no	—
446	C₂²×C₄	—	23	2	no	—
447	C₂²×C₄	—	23	2	no	—
448	C₂²×C₄	—	23	2	no	—
449	C₂²×C₄	—	92	4	no	—
450	C₂²×C₄	—	92	2	no	—
451	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
452	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
457	C₄⋊C₄	—	23	2	no	—
458	C₄⋊C₄	—	23	2	no	—
459	C₄⋊C₄	—	23	2	no	—
460	C₄⋊C₄	—	23	2	no	—
461	C₄⋊C₄	—	23	2	no	—
462	C₄⋊C₄	—	23	2	no	—
463	C₄⋊C₄	—	23	2	no	—
464	C₄⋊C₄	—	23	2	no	—
465	C₄⋊C₄	—	23	2	no	—
466	C₄⋊C₄	—	23	2	no	—
467	C₄⋊C₄	—	23	2	no	—
468	C₄⋊C₄	—	23	2	no	—
469	C₄⋊C₄	—	23	2	no	—
470	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
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	—	23	1	no	—
480	C₂²⋊C₄	—	23	1	no	—
481	C₂²⋊C₄	—	23	2	no	—
482	C₂²⋊C₄	—	23	2	no	—
483	C₂²⋊C₄	—	23	2	no	—
484	C₂²⋊C₄	—	23	2	no	—
485	C₂²⋊C₄	—	23	2	no	—
486	C₂²⋊C₄	—	23	2	no	—
487	C₂²⋊C₄	—	23	2	no	—
488	C₂²⋊C₄	—	23	2	no	—
489	C₂²⋊C₄	—	23	2	no	—
490	C₂²⋊C₄	—	23	2	no	—
491	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
496	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
497	C₄²	—	23	1	no	—
498	C₄²	—	23	2	no	—
499	C₄²	—	23	2	no	—
500	C₄²	—	23	2	no	—
501	C₄²	—	23	2	no	—
502	C₄²	—	23	1	no	—
503	C₄²	—	23	2	no	—
504	C₄²	—	23	2	no	—
505	C₄²	C₂²×D₂₃	1	2	yes	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	23	2	no	—
509	C₂³	—	23	2	no	—
510	C₂³	—	46	4	no	—
511	C₂³	—	46	4	no	—
512	C₂³	—	46	4	no	—
513	C₂³	—	92	2	no	—
514	C₂³	—	92	1	no	—
515	C₂³	C₂³×D₂₃	1	1	yes	characteristic
516	C₂³	C₂³×D₂₃	1	1	yes	characteristic
517	C₂³	C₂³×D₂₃	1	1	yes	characteristic
518	C₂³	C₂³×D₂₃	1	2	yes	—
519	Q₈	—	4	1	no	—
520	Q₈	—	46	4	no	—
521	Q₈	—	92	1	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	23	8	no	—
528	D₄	—	46	4	no	—
529	D₄	—	46	4	no	—
530	D₄	—	46	4	no	—
531	D₄	—	46	4	no	—
532	D₄	—	46	4	no	—
533	D₄	—	46	4	no	—
534	D₄	—	92	1	no	—
535	D₄	—	92	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	23	2	no	—
543	C₂×C₄	—	23	2	no	—
544	C₂×C₄	—	23	2	no	—
545	C₂×C₄	—	23	2	no	—
546	C₂×C₄	—	23	2	no	—
547	C₂×C₄	—	23	2	no	—
548	C₂×C₄	—	46	4	no	—
549	C₂×C₄	—	46	4	no	—
550	C₂×C₄	—	46	4	no	—
551	C₂×C₄	—	46	4	no	—
552	C₂×C₄	—	46	4	no	—
553	C₂×C₄	—	46	4	no	—
554	C₂×C₄	—	46	4	no	—
555	C₂×C₄	—	92	2	no	—
556	C₂×C₄	—	92	2	no	—
557	C₂×C₄	—	92	2	no	—
558	C₂×C₄	—	92	1	no	—
559	C₂×C₄	—	92	2	no	—
560	C₂×C₄	C₂³×D₂₃	1	2	yes	—
561	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₂₃	1	2	yes	—
563	C₂×C₄	C₂³×D₂₃	1	2	yes	—
564	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	23	4	no	—
577	C₂²	—	46	2	no	—
578	C₂²	—	46	2	no	—
579	C₂²	—	46	2	no	—
580	C₂²	—	46	2	no	—
581	C₂²	—	46	2	no	—
582	C₂²	—	92	8	no	—
583	C₂²	—	92	4	no	—
584	C₂²	#41×D₂₃	1	4	yes	—
585	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	23	4	no	—
593	C₄	—	46	2	no	—
594	C₄	—	46	2	no	—
595	C₄	—	46	2	no	—
596	C₄	—	46	2	no	—
597	C₄	—	46	2	no	—
598	C₄	#10625155	1	2	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	46	4	no	—
604	C₂	—	92	2	no	—
605	C₂	C₂×#41×D₂₃	1	2	yes	—
606	C₂	C₂×#10625155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#525	C₂
hypercenter	#525	D₂₃
hypocenter	C₂₃	#3481
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #13093151	C₂	semidirect
2. #13093121	C₂	semidirect
3. #13093112	C₂	semidirect
4. #13093110	C₂	semidirect
5. #13093098	C₂	semidirect
6. #13093095	C₂	semidirect
7. #13093094	C₂	semidirect
8. #13093056	C₂	semidirect
9. #13093054	C₂	semidirect
10. #13093049	C₂	semidirect
11. #13092963	C₂	semidirect
12. #13092947	C₂	semidirect
13. #13092945	C₂	semidirect
14. #13092926	C₂	semidirect
15. #13092924	C₂	semidirect
16. C₄×#67290	C₂	semidirect
17. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
18. C₄×D₄×D₂₃	C₂	semidirect
19. C₂₃×#525	C₂	semidirect
20. C₂×#41×C₂₃	C₂²	semidirect
21. C₂³×C₄×C₂₃	C₂²	semidirect
25. C₂×#67288	C₂²	semidirect
26. C₂²×C₄×D₂₃	C₂²	semidirect
27. C₂²×C₄×D₂₃	C₂²	semidirect
28. C₂₃×#123	C₂²	semidirect
29. C₂₃×#123	C₂²	semidirect
30. C₂₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂₃×#121	C₂²	semidirect
33. C₂₃×#120	C₂²	semidirect
34. C₄×D₄×C₂₃	C₂²	semidirect
35. C₄×D₄×C₂₃	C₂²	semidirect
36. C₂₃×#117	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
38. #10625118	C₂²	semidirect
39. #10625117	C₂²	semidirect
40. #10625115	C₂²	semidirect
43. #10625110	C₂²	semidirect
44. #10625110	C₂²	semidirect
45. #10625110	C₂²	semidirect
46. #10625109	C₂²	semidirect
48. #10625108	C₂²	semidirect
49. #10625108	C₂²	semidirect
50. #10625107	C₂²	semidirect
51. #10625106	C₂²	semidirect
52. #10625106	C₂²	semidirect
53. #10625106	C₂²	semidirect
54. D₄×Dic₂₃	C₂²	semidirect
55. D₄×Dic₂₃	C₂²	semidirect
58. C₄×C₂²⋊D₂₃	C₂²	semidirect
59. C₄×C₂²⋊D₂₃	C₂²	semidirect
60. C₄×C₂²⋊D₂₃	C₂²	semidirect
61. C₄×C₂²⋊D₂₃	C₂²	semidirect
62. C₄×C₂²⋊D₂₃	C₂²	semidirect
63. C₄×C₂²⋊D₂₃	C₂²	semidirect
64. C₄×C₂²⋊D₂₃	C₂²	semidirect
65. C₄×C₂²⋊D₂₃	C₂²	semidirect
66. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
67. #10625097	C₂²	semidirect
68. C₂×Dic₂₃⋊C₄	C₂²	semidirect
69. C₂×C₄×Dic₂₃	C₂²	semidirect
70. C₂×C₄×Dic₂₃	C₂²	semidirect
71. #10625069	C₂²	semidirect
72. #10625069	C₂²	semidirect
73. #10625067	C₂²	semidirect
74. #10625067	C₂²	semidirect
75. #10625065	C₂²	semidirect
76. #10625065	C₂²	semidirect
77. #10625064	C₂²	semidirect
78. #10625063	C₂²	semidirect
79. C₄⋊C₄×D₂₃	C₂²	semidirect
80. #10625060	C₂²	semidirect
81. #10625060	C₂²	semidirect
82. #10625058	C₂²	semidirect
83. #10625057	C₂²	semidirect
84. #10625056	C₂²	semidirect
85. #10625056	C₂²	semidirect
87. #10625055	C₂²	semidirect
88. #10625054	C₂²	semidirect
89. #10625054	C₂²	semidirect
93. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
94. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
95. C₂²⋊C₄×D₂₃	C₂²	semidirect
96. C₂²⋊C₄×D₂₃	C₂²	semidirect
97. #10625050	C₂²	semidirect
98. #10625050	C₂²	semidirect
99. #10625049	C₂²	semidirect
100. #10625049	C₂²	semidirect
101. #10625048	C₂²	semidirect
102. #10625048	C₂²	semidirect
103. C₄×D₉₂	C₂²	semidirect
104. #10625043	C₂²	semidirect
105. C₄²×D₂₃	C₂²	semidirect
106. C₄×Dic₄₆	C₂²	semidirect
240. C₂²⋊D₂₃	#41	semidirect
311. #525	D₂₃	semidirect
325. C₂×#41	C₂×D₂₃	semidirect
330. C₂³×C₄	C₂×D₂₃	semidirect
351. #123	C₂×D₂₃	semidirect
352. #123	C₂×D₂₃	semidirect
358. C₂²⋊Q₈	C₂×D₂₃	semidirect
366. #121	C₂×D₂₃	semidirect
372. #120	C₂×D₂₃	semidirect
393. C₄×D₄	C₂×D₂₃	semidirect
394. C₄×D₄	C₂×D₂₃	semidirect
400. #117	C₂×D₂₃	semidirect
410. C₂₃	#3481	semidirect

Maximal subgroups

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

subgroup	index
#13093151	2
#13093121	2
#13093112	2
#13093110	2
#13093098	2
#13093095	2
#13093094	2
#13093056	2
#13093054	2
#13093049	2
#13092963	2
#13092947	2
#13092945	2
#13092926	2
#13092924	2
C₄×#67290	2
C₂×C₄×C₂²⋊D₂₃	2
C₄×D₄×D₂₃	2
C₂₃×#525	2
#3481	23