Subgroups — #15687559

Order 2944.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093168	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093164	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093155	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093149	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093114	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093110	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093105	C₂	1	1	yes	maximal, characteristic, complemented
8	#13093101	C₂	1	1	yes	maximal, characteristic, complemented
9	#13093094	C₂	1	1	yes	maximal, characteristic, complemented
10	#13093090	C₂	1	1	yes	maximal, characteristic, complemented
11	#13093090	C₂	1	1	yes	maximal, characteristic, complemented
12	#13093069	C₂	1	1	yes	maximal, characteristic, complemented
13	#13093065	C₂	1	1	yes	maximal, characteristic, complemented
14	#13093060	C₂	1	1	yes	maximal, characteristic, complemented
15	#13093056	C₂	1	1	yes	maximal, characteristic, complemented
16	#13093040	C₂	1	1	yes	maximal, characteristic, complemented
17	#13093031	C₂	1	1	yes	maximal, characteristic, complemented
18	#13093020	C₂	1	1	yes	maximal, characteristic, complemented
19	#13093019	C₂	1	1	yes	maximal, characteristic, complemented
20	#13093016	C₂	1	1	yes	maximal, characteristic, complemented
21	#13093015	C₂	1	1	yes	maximal, characteristic, complemented
22	#13093007	C₂	1	1	yes	maximal, characteristic, complemented
23	#13093003	C₂	1	1	yes	maximal, characteristic, complemented
24	#13093003	C₂	1	1	yes	maximal, characteristic, complemented
25	#13093001	C₂	1	1	yes	maximal, characteristic, complemented
26	#13092983	C₂	1	1	yes	maximal, characteristic, complemented
27	#13092975	C₂	1	1	yes	maximal, characteristic, complemented
28	#13092930	C₂	1	1	yes	maximal, characteristic, complemented
29	#13092927	C₂	1	1	yes	maximal, characteristic, complemented
30	#123×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#67292	C₂²	1	1	yes	characteristic
33	C₂×#67290	C₂²	1	1	yes	characteristic
34	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
36	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#121	C₂²	1	1	yes	characteristic
50	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
53	#10625118	C₂²	1	1	yes	characteristic, complemented
54	#10625118	C₂²	1	1	yes	characteristic, complemented
55	#10625117	C₂²	1	1	yes	characteristic, complemented
56	#10625117	C₂²	1	1	yes	characteristic, complemented
57	#10625117	C₂²	1	1	yes	characteristic, complemented
58	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
59	#10625115	C₂²	1	1	yes	characteristic, complemented
60	#10625111	C₂²	1	1	yes	characteristic
61	#10625111	C₂²	1	1	yes	characteristic, complemented
62	#10625110	C₂²	1	1	yes	characteristic
63	#10625110	C₂²	1	1	yes	characteristic
64	#10625110	C₂²	1	1	yes	characteristic, complemented
65	#10625110	C₂²	1	1	yes	characteristic, complemented
66	#10625110	C₂²	1	1	yes	characteristic, complemented
67	#10625109	C₂²	1	1	yes	characteristic, complemented
68	#10625109	C₂²	1	1	yes	characteristic, complemented
69	#10625109	C₂²	1	1	yes	characteristic, complemented
70	#10625109	C₂²	1	1	yes	characteristic, complemented
71	#10625108	C₂²	1	1	yes	characteristic
72	#10625108	C₂²	1	1	yes	characteristic
73	#10625108	C₂²	1	1	yes	characteristic
74	#10625108	C₂²	1	1	yes	characteristic, complemented
75	#10625108	C₂²	1	1	yes	characteristic, complemented
76	#10625106	C₂²	1	1	yes	characteristic, complemented
77	#10625106	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
81	#10625101	C₂²	1	1	yes	characteristic
82	#10625101	C₂²	1	1	yes	characteristic
83	#10625101	C₂²	1	1	yes	characteristic, complemented
84	#10625101	C₂²	1	1	yes	characteristic, complemented
85	#10625100	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
90	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	#10625097	C₂²	1	1	yes	characteristic, complemented
92	#10625097	C₂²	1	1	yes	characteristic, complemented
93	#10625095	C₂²	1	1	yes	characteristic, complemented
94	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	#10625069	C₂²	1	1	yes	characteristic, complemented
96	#10625069	C₂²	1	1	yes	characteristic, complemented
97	#10625069	C₂²	1	1	yes	characteristic, complemented
98	#10625069	C₂²	1	1	yes	characteristic, complemented
99	#10625069	C₂²	1	1	yes	characteristic, complemented
100	#10625069	C₂²	1	1	yes	characteristic, complemented
101	#10625069	C₂²	1	1	yes	characteristic, complemented
102	#10625068	C₂²	1	1	yes	characteristic, complemented
103	#10625068	C₂²	1	1	yes	characteristic, complemented
104	#10625068	C₂²	1	1	yes	characteristic, complemented
105	#10625068	C₂²	1	1	yes	characteristic, complemented
106	#10625067	C₂²	1	1	yes	characteristic, complemented
107	#10625067	C₂²	1	1	yes	characteristic, complemented
108	#10625066	C₂²	1	1	yes	characteristic
109	#10625066	C₂²	1	1	yes	characteristic, complemented
110	#10625065	C₂²	1	1	yes	characteristic
111	#10625065	C₂²	1	1	yes	characteristic
112	#10625065	C₂²	1	1	yes	characteristic
113	#10625065	C₂²	1	1	yes	characteristic
114	#10625065	C₂²	1	1	yes	characteristic
115	#10625065	C₂²	1	1	yes	characteristic, complemented
116	#10625065	C₂²	1	1	yes	characteristic, complemented
117	#10625065	C₂²	1	1	yes	characteristic, complemented
118	#10625065	C₂²	1	1	yes	characteristic, complemented
119	#10625064	C₂²	1	1	yes	characteristic, complemented
120	#10625064	C₂²	1	1	yes	characteristic, complemented
121	#10625064	C₂²	1	1	yes	characteristic, complemented
122	#10625063	C₂²	1	1	yes	characteristic, complemented
123	#10625063	C₂²	1	1	yes	characteristic, complemented
124	#10625063	C₂²	1	1	yes	characteristic, complemented
125	#10625063	C₂²	1	1	yes	characteristic, complemented
126	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
128	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
129	#10625061	C₂²	1	1	yes	characteristic, complemented
130	#10625061	C₂²	1	1	yes	characteristic, complemented
131	#10625061	C₂²	1	1	yes	characteristic, complemented
132	#10625060	C₂²	1	1	yes	characteristic, complemented
133	#10625060	C₂²	1	1	yes	characteristic, complemented
134	#10625059	C₂²	1	1	yes	characteristic, complemented
135	#10625057	C₂²	1	1	yes	characteristic
136	#10625057	C₂²	1	1	yes	characteristic, complemented
137	#10625057	C₂²	1	1	yes	characteristic, complemented
138	#10625057	C₂²	1	1	yes	characteristic, complemented
139	#10625057	C₂²	1	1	yes	characteristic, complemented
140	#10625056	C₂²	1	1	yes	characteristic
141	#10625056	C₂²	1	1	yes	characteristic, complemented
142	#10625056	C₂²	1	1	yes	characteristic, complemented
143	#10625056	C₂²	1	1	yes	characteristic, complemented
144	#10625056	C₂²	1	1	yes	characteristic, complemented
145	#10625056	C₂²	1	1	yes	characteristic, complemented
146	#10625055	C₂²	1	1	yes	characteristic
147	#10625055	C₂²	1	1	yes	characteristic
148	#10625055	C₂²	1	1	yes	characteristic, complemented
149	#10625055	C₂²	1	1	yes	characteristic, complemented
150	#10625055	C₂²	1	1	yes	characteristic, complemented
151	#10625054	C₂²	1	1	yes	characteristic
152	#10625054	C₂²	1	1	yes	characteristic
153	#10625054	C₂²	1	1	yes	characteristic
154	#10625054	C₂²	1	1	yes	characteristic, complemented
155	#10625054	C₂²	1	1	yes	characteristic, complemented
156	#10625054	C₂²	1	1	yes	characteristic, complemented
157	#10625054	C₂²	1	1	yes	characteristic, complemented
158	#10625054	C₂²	1	1	yes	characteristic, complemented
159	#10625054	C₂²	1	1	yes	characteristic, complemented
160	#10625053	C₂²	1	1	yes	characteristic
161	#10625053	C₂²	1	1	yes	characteristic
162	#10625053	C₂²	1	1	yes	characteristic
163	#10625053	C₂²	1	1	yes	characteristic, complemented
164	#10625053	C₂²	1	1	yes	characteristic, complemented
165	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
171	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
173	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
174	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
175	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
176	#10625050	C₂²	1	1	yes	characteristic, complemented
177	#10625050	C₂²	1	1	yes	characteristic, complemented
178	#10625050	C₂²	1	1	yes	characteristic, complemented
179	#10625050	C₂²	1	1	yes	characteristic, complemented
180	#10625049	C₂²	1	1	yes	characteristic, complemented
181	#10625049	C₂²	1	1	yes	characteristic, complemented
182	#10625048	C₂²	1	1	yes	characteristic, complemented
183	#10625047	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₉₂	C₂²	1	1	yes	characteristic
185	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₃	C₂³	1	1	yes	characteristic
188	C₂³×D₂₃	C₂³	1	1	yes	characteristic
189	C₂³×D₂₃	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
216	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
217	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
218	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
219	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
221	#67292	—	4	2	no	—
222	#67290	—	4	2	no	—
223	D₄×D₂₃	—	4	2	no	—
224	D₄×D₂₃	—	4	2	no	—
225	#67288	—	4	2	no	—
226	C₂×D₉₂	C₂³	1	1	yes	characteristic
227	C₂×D₉₂	C₂³	1	1	yes	characteristic
228	C₂×D₉₂	C₂³	1	1	yes	characteristic
229	C₂×D₉₂	C₂³	1	1	yes	characteristic
230	C₂×D₉₂	C₂³	1	1	yes	characteristic
231	C₂×D₉₂	C₂³	1	1	yes	characteristic
232	C₂×D₉₂	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₂₃	—	4	2	no	—
234	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
247	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
248	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
249	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
252	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
254	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
270	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₄²×C₂₃	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
283	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
323	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
339	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
342	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
345	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
346	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
347	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
348	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₂₃	—	2	2	no	—
353	C₂²×D₂₃	—	2	2	no	—
354	C₂²×D₂₃	—	4	1	no	—
355	C₂²×D₂₃	—	4	1	no	—
356	C₂²×D₂₃	—	4	1	no	—
357	C₂²×D₂₃	—	4	1	no	—
358	C₂²×D₂₃	—	4	1	no	—
359	C₂²×D₂₃	—	4	1	no	—
360	C₂²×D₂₃	—	4	1	no	—
361	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
364	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
365	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
366	Q₈×C₂₃	—	4	1	no	—
367	Q₈×C₂₃	—	4	1	no	—
368	D₄×C₂₃	—	4	1	no	—
369	D₄×C₂₃	—	4	1	no	—
370	D₄×C₂₃	—	4	1	no	—
371	D₄×C₂₃	—	4	1	no	—
372	D₄×C₂₃	—	4	1	no	—
373	D₄×C₂₃	—	4	1	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	1	no	—
376	C₂×C₄×C₂₃	—	4	1	no	—
377	C₂×C₄×C₂₃	—	4	1	no	—
378	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂²⋊D₂₃	—	2	2	no	—
390	C₂²⋊D₂₃	—	2	2	no	—
391	C₂²⋊D₂₃	—	4	1	no	—
392	C₂²⋊D₂₃	—	4	1	no	—
393	C₂²⋊D₂₃	—	4	1	no	—
394	C₂²⋊D₂₃	—	4	1	no	—
395	C₂²⋊D₂₃	—	4	1	no	—
396	C₂²⋊D₂₃	—	4	1	no	—
397	C₂²⋊D₂₃	—	4	1	no	—
398	C₂²⋊D₂₃	—	4	1	no	—
399	C₂²⋊D₂₃	—	4	1	no	—
400	C₂²⋊D₂₃	—	4	1	no	—
401	C₂²⋊D₂₃	—	4	1	no	—
402	C₂²⋊D₂₃	—	4	1	no	—
403	C₂×Dic₂₃	—	4	1	no	—
404	C₂×Dic₂₃	—	4	1	no	—
405	C₂×Dic₂₃	—	4	1	no	—
406	C₂×Dic₂₃	—	4	1	no	—
407	C₂×Dic₂₃	—	4	1	no	—
408	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
419	D₉₂	—	2	2	no	—
420	D₉₂	—	2	2	no	—
421	D₉₂	—	4	1	no	—
422	D₉₂	—	4	1	no	—
423	D₉₂	—	4	1	no	—
424	D₉₂	—	4	1	no	—
425	D₉₂	—	4	1	no	—
426	C₄×D₂₃	—	2	2	no	—
427	C₄×D₂₃	—	2	2	no	—
428	C₄×D₂₃	—	2	2	no	—
429	C₄×D₂₃	—	4	1	no	—
430	C₄×D₂₃	—	4	1	no	—
431	C₄×D₂₃	—	4	1	no	—
432	C₄×D₂₃	—	4	1	no	—
433	C₄×D₂₃	—	4	1	no	—
434	C₄×D₂₃	—	4	1	no	—
435	C₄×D₂₃	—	4	1	no	—
436	C₄×D₂₃	—	4	1	no	—
437	C₄×D₂₃	—	4	1	no	—
438	C₄×D₂₃	—	4	1	no	—
439	Dic₄₆	—	4	1	no	—
440	Dic₄₆	—	4	1	no	—
441	Dic₄₆	—	4	1	no	—
442	#3533	—	23	1	no	maximal, Sylow
443	C₂²×C₂₃	—	2	1	no	—
444	C₂²×C₂₃	—	2	1	no	—
445	C₂²×C₂₃	—	2	1	no	—
446	C₂²×C₂₃	—	2	1	no	—
447	C₂²×C₂₃	—	2	1	no	—
448	C₂²×C₂₃	—	2	1	no	—
449	C₂²×C₂₃	—	2	1	no	—
450	C₂²×C₂₃	—	2	1	no	—
451	C₂²×C₂₃	—	2	1	no	—
452	C₂²×C₂₃	—	2	1	no	—
453	C₂²×C₂₃	—	2	1	no	—
454	C₂²×C₂₃	—	2	1	no	—
455	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
456	C₂×D₂₃	—	2	1	no	—
457	C₂×D₂₃	—	2	1	no	—
458	C₂×D₂₃	—	2	1	no	—
459	C₂×D₂₃	—	2	1	no	—
460	C₂×D₂₃	—	2	1	no	—
461	C₂×D₂₃	—	2	1	no	—
462	C₂×D₂₃	—	2	1	no	—
463	C₂×D₂₃	—	2	1	no	—
464	C₂×D₂₃	—	2	1	no	—
465	C₂×D₂₃	—	2	1	no	—
466	C₂×D₂₃	—	2	1	no	—
467	C₂×D₂₃	—	2	1	no	—
468	C₂×D₂₃	—	2	1	no	—
469	C₂×D₂₃	—	2	1	no	—
470	C₂×D₂₃	—	4	4	no	—
471	C₂×D₂₃	—	8	2	no	—
472	C₂×D₂₃	—	8	2	no	—
473	C₂×D₂₃	H(5,𝔽₂)	1	2	yes	—
474	C₄×C₂₃	—	2	1	no	—
475	C₄×C₂₃	—	2	1	no	—
476	C₄×C₂₃	—	2	1	no	—
477	C₄×C₂₃	—	2	1	no	—
478	C₄×C₂₃	—	2	1	no	—
479	C₄×C₂₃	—	2	1	no	—
480	C₄×C₂₃	—	2	1	no	—
481	C₄×C₂₃	—	2	1	no	—
482	C₄×C₂₃	—	2	1	no	—
483	C₄×C₂₃	—	2	1	no	—
484	C₄×C₂₃	—	2	1	no	—
485	Dic₂₃	—	2	1	no	—
486	Dic₂₃	—	2	1	no	—
487	Dic₂₃	—	2	1	no	—
488	Dic₂₃	—	2	1	no	—
489	Dic₂₃	—	2	1	no	—
490	Dic₂₃	—	2	1	no	—
491	Dic₂₃	—	2	1	no	—
492	Dic₂₃	—	2	1	no	—
493	Dic₂₃	—	2	1	no	—
494	Dic₂₃	—	2	1	no	—
495	Dic₂₃	—	2	1	no	—
496	#563	—	23	1	no	—
497	#562	—	23	1	no	—
498	#562	D₂₃	1	1	yes	characteristic, complemented
499	#560	—	23	1	no	—
500	#559	—	23	1	no	—
501	#553	—	23	1	no	—
502	#553	—	23	1	no	—
503	#552	—	23	1	no	—
504	#552	—	23	1	no	—
505	#551	—	23	1	no	—
506	#551	—	23	1	no	—
507	#551	—	23	1	no	—
508	#547	—	23	1	no	—
509	#547	—	23	1	no	—
510	#546	—	23	1	no	—
511	#546	—	23	1	no	—
512	#542	—	23	1	no	—
513	#542	—	23	1	no	—
514	#540	—	23	1	no	—
515	#540	—	23	1	no	—
516	#539	—	23	1	no	—
517	#539	—	23	1	no	—
518	#538	—	23	1	no	—
519	#538	—	23	1	no	—
520	#538	—	23	1	no	—
521	#538	—	23	1	no	—
522	#535	—	23	1	no	—
523	#534	—	23	1	no	—
524	#525	—	23	1	no	—
525	#525	—	23	1	no	—
526	C₂×#123	—	23	1	no	—
527	C₂×C₂₃	—	4	1	no	—
528	C₂×C₂₃	—	4	1	no	—
529	C₂×C₂₃	—	4	1	no	—
530	C₂×C₂₃	—	4	1	no	—
531	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₂₃	#585	1	1	yes	characteristic
533	C₂×C₂₃	#585	1	1	yes	characteristic
534	D₂₃	—	2	2	no	—
535	D₂₃	—	4	1	no	—
536	D₂₃	—	4	1	no	—
537	D₂₃	—	4	1	no	—
538	D₂₃	—	4	1	no	—
539	C₂×#41	—	23	1	no	—
540	C₂×#41	—	23	1	no	—
541	C₂×#41	—	23	1	no	—
542	C₂²×D₄	—	23	1	no	—
543	C₂²×D₄	—	23	1	no	—
544	C₂³×C₄	—	23	1	no	—
545	C₄⋊Q₈	—	23	1	no	—
546	C₄⋊Q₈	—	23	1	no	—
547	#127	—	23	1	no	—
548	#127	—	23	1	no	—
549	#126	—	23	1	no	—
550	#126	—	23	1	no	—
551	#126	—	23	1	no	—
552	#126	—	23	1	no	—
553	#126	—	23	1	no	—
554	#126	—	23	1	no	—
555	#126	—	23	1	no	—
556	#126	—	23	1	no	—
557	#126	—	23	1	no	—
558	#126	—	23	1	no	—
559	#126	—	23	1	no	—
560	#126	—	23	1	no	—
561	#125	—	23	1	no	—
562	#125	—	23	1	no	—
563	#125	—	23	1	no	—
564	#125	—	23	1	no	—
565	#125	—	23	1	no	—
566	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
567	#124	—	23	1	no	—
568	#124	—	23	1	no	—
569	#124	—	23	1	no	—
570	#124	—	23	1	no	—
571	#124	—	23	1	no	—
572	#124	—	23	1	no	—
573	#124	—	23	1	no	—
574	#124	—	23	1	no	—
575	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
576	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
577	#123	—	23	1	no	—
578	#123	—	23	1	no	—
579	#123	—	23	1	no	—
580	#123	—	23	1	no	—
581	#123	—	23	1	no	—
582	#123	—	23	1	no	—
583	#123	—	23	1	no	—
584	#123	—	23	1	no	—
585	#123	—	23	1	no	—
586	#123	—	23	1	no	—
587	#123	—	23	1	no	—
588	#123	—	23	1	no	—
589	#123	—	23	1	no	—
590	#123	—	23	1	no	—
591	#123	—	23	1	no	—
592	#123	—	23	1	no	—
593	#123	—	23	1	no	—
594	#123	—	23	1	no	—
595	#123	—	23	1	no	—
596	#123	—	23	1	no	—
597	#123	—	23	1	no	—
598	#123	—	23	1	no	—
599	#123	—	23	1	no	—
600	#123	—	23	1	no	—
601	#123	—	23	1	no	—
602	#123	—	23	1	no	—
603	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
604	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
605	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
606	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
607	C₂²⋊Q₈	—	23	1	no	—
608	C₂²⋊Q₈	—	23	1	no	—
609	C₂²⋊Q₈	—	23	1	no	—
610	C₂²⋊Q₈	—	23	1	no	—
611	C₂²⋊Q₈	—	23	1	no	—
612	C₂²⋊Q₈	—	23	1	no	—
613	C₂²⋊Q₈	—	23	1	no	—
614	C₂²⋊Q₈	—	23	1	no	—
615	C₂²⋊Q₈	—	23	1	no	—
616	C₂²⋊Q₈	—	23	1	no	—
617	C₂²⋊Q₈	—	23	1	no	—
618	C₂²⋊Q₈	—	23	1	no	—
619	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
620	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
621	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
622	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
623	#121	—	23	1	no	—
624	#121	—	23	1	no	—
625	#121	—	23	1	no	—
626	#121	—	23	1	no	—
627	#121	—	23	1	no	—
628	#121	—	23	1	no	—
629	#121	—	23	1	no	—
630	#121	—	23	1	no	—
631	#121	—	23	1	no	—
632	#121	—	23	1	no	—
633	#121	—	23	1	no	—
634	#121	—	23	1	no	—
635	#121	—	23	1	no	—
636	#121	—	23	1	no	—
637	#121	—	23	1	no	—
638	#121	—	23	1	no	—
639	#121	—	23	1	no	—
640	#121	—	23	1	no	—
641	#121	—	23	1	no	—
642	#121	—	23	1	no	—
643	#121	C₂×D₂₃	1	1	yes	characteristic
644	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
645	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
646	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
647	#120	—	23	1	no	—
648	#120	—	23	1	no	—
649	#120	—	23	1	no	—
650	#120	—	23	1	no	—
651	#120	—	23	1	no	—
652	#120	—	23	1	no	—
653	#120	—	23	1	no	—
654	#120	—	23	1	no	—
655	#120	—	23	1	no	—
656	#120	—	23	1	no	—
657	C₄×Q₈	—	23	1	no	—
658	C₄×Q₈	—	23	1	no	—
659	C₄×D₄	—	23	1	no	—
660	C₄×D₄	—	23	1	no	—
661	C₄×D₄	—	23	1	no	—
662	C₄×D₄	—	23	1	no	—
663	C₄×D₄	—	23	1	no	—
664	C₄×D₄	—	23	1	no	—
665	C₄×D₄	—	23	1	no	—
666	C₄×D₄	—	23	1	no	—
667	C₄×D₄	—	23	1	no	—
668	C₄×D₄	—	23	1	no	—
669	C₄×D₄	—	23	1	no	—
670	C₄×D₄	—	23	1	no	—
671	C₄×D₄	—	23	1	no	—
672	C₄×D₄	—	23	1	no	—
673	C₄×D₄	—	23	1	no	—
674	C₄×D₄	—	23	1	no	—
675	C₄×D₄	—	23	1	no	—
676	C₄×D₄	—	23	1	no	—
677	#117	—	23	1	no	—
678	#117	—	23	1	no	—
679	#117	—	23	1	no	—
680	#117	—	23	1	no	—
681	#117	—	23	1	no	—
682	#117	—	23	1	no	—
683	#117	—	23	1	no	—
684	C₂×C₄⋊C₄	—	23	1	no	—
685	C₂×C₄⋊C₄	—	23	1	no	—
686	C₂×C₄⋊C₄	—	23	1	no	—
687	C₂×C₄⋊C₄	—	23	1	no	—
688	C₂×C₂²⋊C₄	—	23	1	no	—
689	C₂×C₂²⋊C₄	—	23	1	no	—
690	C₂×C₂²⋊C₄	—	23	1	no	—
691	C₂×C₂²⋊C₄	—	23	1	no	—
692	C₂×C₂²⋊C₄	—	23	1	no	—
693	C₂×C₂²⋊C₄	—	23	1	no	—
694	C₂₃	#3533	1	1	yes	characteristic, complemented, Sylow
695	C₂⁴	—	23	1	no	—
696	C₂⁴	—	23	1	no	—
697	C₂⁴	—	23	1	no	—
698	#41	—	92	2	no	—
699	#41	—	92	2	no	—
700	#41	—	92	2	no	—
701	C₂×Q₈	—	23	1	no	—
702	C₂×Q₈	—	23	1	no	—
703	C₂×Q₈	—	23	1	no	—
704	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
705	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
706	C₂×D₄	—	23	1	no	—
707	C₂×D₄	—	23	1	no	—
708	C₂×D₄	—	23	1	no	—
709	C₂×D₄	—	23	1	no	—
710	C₂×D₄	—	23	1	no	—
711	C₂×D₄	—	23	1	no	—
712	C₂×D₄	—	23	1	no	—
713	C₂×D₄	—	23	1	no	—
714	C₂×D₄	—	23	1	no	—
715	C₂×D₄	—	23	1	no	—
716	C₂×D₄	—	23	1	no	—
717	C₂×D₄	—	23	1	no	—
718	C₂×D₄	—	23	1	no	—
719	C₂×D₄	—	23	1	no	—
720	C₂×D₄	—	23	1	no	—
721	C₂×D₄	—	23	1	no	—
722	C₂×D₄	—	23	1	no	—
723	C₂×D₄	—	23	1	no	—
724	C₂×D₄	—	23	1	no	—
725	C₂×D₄	—	23	1	no	—
726	C₂×D₄	—	23	1	no	—
727	C₂×D₄	—	92	2	no	—
728	C₂×D₄	—	92	2	no	—
729	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
730	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
731	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
735	C₂²×C₄	—	23	1	no	—
736	C₂²×C₄	—	23	1	no	—
737	C₂²×C₄	—	23	1	no	—
738	C₂²×C₄	—	23	1	no	—
739	C₂²×C₄	—	23	1	no	—
740	C₂²×C₄	—	23	1	no	—
741	C₂²×C₄	—	23	1	no	—
742	C₂²×C₄	—	23	1	no	—
743	C₂²×C₄	—	23	1	no	—
744	C₂²×C₄	—	23	1	no	—
745	C₂²×C₄	—	23	1	no	—
746	C₂²×C₄	—	23	1	no	—
747	C₂²×C₄	—	23	1	no	—
748	C₂²×C₄	—	23	1	no	—
749	C₂²×C₄	—	23	1	no	—
750	C₂²×C₄	—	23	1	no	—
751	C₂²×C₄	—	23	1	no	—
752	C₂²×C₄	—	23	1	no	—
753	C₂²×C₄	—	92	2	no	—
754	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
758	C₄⋊C₄	—	23	1	no	—
759	C₄⋊C₄	—	23	1	no	—
760	C₄⋊C₄	—	23	1	no	—
761	C₄⋊C₄	—	23	1	no	—
762	C₄⋊C₄	—	23	1	no	—
763	C₄⋊C₄	—	23	1	no	—
764	C₄⋊C₄	—	23	1	no	—
765	C₄⋊C₄	—	23	1	no	—
766	C₄⋊C₄	—	23	1	no	—
767	C₄⋊C₄	—	23	1	no	—
768	C₄⋊C₄	—	23	1	no	—
769	C₄⋊C₄	—	23	1	no	—
770	C₄⋊C₄	—	23	1	no	—
771	C₄⋊C₄	—	23	1	no	—
772	C₄⋊C₄	—	23	1	no	—
773	C₄⋊C₄	—	23	1	no	—
774	C₄⋊C₄	—	23	1	no	—
775	C₄⋊C₄	—	23	1	no	—
776	C₄⋊C₄	—	23	1	no	—
777	C₄⋊C₄	—	23	1	no	—
778	C₄⋊C₄	—	23	1	no	—
779	C₄⋊C₄	—	23	1	no	—
780	C₄⋊C₄	—	23	1	no	—
781	C₄⋊C₄	—	23	1	no	—
782	C₄⋊C₄	—	23	1	no	—
783	C₄⋊C₄	—	23	1	no	—
784	C₄⋊C₄	—	23	1	no	—
785	C₄⋊C₄	—	23	1	no	—
786	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
796	C₂²⋊C₄	—	23	1	no	—
797	C₂²⋊C₄	—	23	1	no	—
798	C₂²⋊C₄	—	23	1	no	—
799	C₂²⋊C₄	—	23	1	no	—
800	C₂²⋊C₄	—	23	1	no	—
801	C₂²⋊C₄	—	23	1	no	—
802	C₂²⋊C₄	—	23	1	no	—
803	C₂²⋊C₄	—	23	1	no	—
804	C₂²⋊C₄	—	23	1	no	—
805	C₂²⋊C₄	—	23	1	no	—
806	C₂²⋊C₄	—	23	1	no	—
807	C₂²⋊C₄	—	23	1	no	—
808	C₂²⋊C₄	—	23	1	no	—
809	C₂²⋊C₄	—	23	1	no	—
810	C₂²⋊C₄	—	23	1	no	—
811	C₂²⋊C₄	—	23	1	no	—
812	C₂²⋊C₄	—	23	1	no	—
813	C₂²⋊C₄	—	23	1	no	—
814	C₂²⋊C₄	—	23	1	no	—
815	C₂²⋊C₄	—	23	1	no	—
816	C₂²⋊C₄	—	23	1	no	—
817	C₂²⋊C₄	—	23	1	no	—
818	C₂²⋊C₄	—	23	1	no	—
819	C₂²⋊C₄	—	23	1	no	—
820	C₂²⋊C₄	—	23	1	no	—
821	C₂²⋊C₄	—	23	1	no	—
822	C₂²⋊C₄	—	23	1	no	—
823	C₂²⋊C₄	—	23	1	no	—
824	C₂²⋊C₄	—	23	1	no	—
825	C₂²⋊C₄	—	23	1	no	—
826	C₂²⋊C₄	—	23	1	no	—
827	C₂²⋊C₄	—	23	1	no	—
828	C₂²⋊C₄	—	23	1	no	—
829	C₂²⋊C₄	—	23	1	no	—
830	C₂²⋊C₄	—	23	1	no	—
831	C₂²⋊C₄	—	23	1	no	—
832	C₂²⋊C₄	—	23	1	no	—
833	C₂²⋊C₄	—	23	1	no	—
834	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
846	C₄²	—	23	1	no	—
847	C₄²	—	23	1	no	—
848	C₄²	—	23	1	no	—
849	C₄²	—	23	1	no	—
850	C₄²	—	23	1	no	—
851	C₄²	—	23	1	no	—
852	C₄²	—	23	1	no	—
853	C₄²	—	23	1	no	—
854	C₄²	—	23	1	no	—
855	C₄²	C₂²×D₂₃	1	1	yes	characteristic
856	C₂³	—	23	1	no	—
857	C₂³	—	23	1	no	—
858	C₂³	—	23	1	no	—
859	C₂³	—	23	1	no	—
860	C₂³	—	23	1	no	—
861	C₂³	—	46	2	no	—
862	C₂³	—	46	2	no	—
863	C₂³	—	92	1	no	—
864	C₂³	—	92	1	no	—
865	C₂³	—	92	1	no	—
866	C₂³	—	92	1	no	—
867	C₂³	—	92	1	no	—
868	C₂³	—	92	1	no	—
869	C₂³	—	92	1	no	—
870	C₂³	C₂³×D₂₃	1	1	yes	characteristic
871	C₂³	C₂³×D₂₃	1	1	yes	characteristic
872	C₂³	C₂³×D₂₃	1	1	yes	characteristic
873	C₂³	C₂³×D₂₃	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	4	1	no	—
876	Q₈	—	92	1	no	—
877	Q₈	—	92	1	no	—
878	Q₈	—	92	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	1	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	46	2	no	—
886	D₄	—	46	2	no	—
887	D₄	—	46	2	no	—
888	D₄	—	46	2	no	—
889	D₄	—	92	1	no	—
890	D₄	—	92	1	no	—
891	D₄	—	92	1	no	—
892	D₄	—	92	1	no	—
893	D₄	—	92	1	no	—
894	D₄	—	92	1	no	—
895	D₄	—	92	1	no	—
896	D₄	—	92	1	no	—
897	D₄	—	92	1	no	—
898	D₄	—	92	1	no	—
899	D₄	—	92	1	no	—
900	D₄	—	92	1	no	—
901	D₄	—	92	1	no	—
902	D₄	—	92	1	no	—
903	D₄	—	92	1	no	—
904	D₄	—	92	1	no	—
905	D₄	—	92	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	23	1	no	—
911	C₂×C₄	—	23	1	no	—
912	C₂×C₄	—	23	1	no	—
913	C₂×C₄	—	23	1	no	—
914	C₂×C₄	—	23	1	no	—
915	C₂×C₄	—	23	1	no	—
916	C₂×C₄	—	23	1	no	—
917	C₂×C₄	—	23	1	no	—
918	C₂×C₄	—	23	1	no	—
919	C₂×C₄	—	23	1	no	—
920	C₂×C₄	—	23	1	no	—
921	C₂×C₄	—	46	2	no	—
922	C₂×C₄	—	46	2	no	—
923	C₂×C₄	—	46	2	no	—
924	C₂×C₄	—	92	1	no	—
925	C₂×C₄	—	92	1	no	—
926	C₂×C₄	—	92	1	no	—
927	C₂×C₄	—	92	1	no	—
928	C₂×C₄	—	92	1	no	—
929	C₂×C₄	—	92	1	no	—
930	C₂×C₄	—	92	1	no	—
931	C₂×C₄	—	92	1	no	—
932	C₂×C₄	—	92	1	no	—
933	C₂×C₄	—	92	1	no	—
934	C₂×C₄	—	92	1	no	—
935	C₂×C₄	—	92	1	no	—
936	C₂×C₄	—	92	1	no	—
937	C₂×C₄	—	92	1	no	—
938	C₂×C₄	—	92	1	no	—
939	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	23	2	no	—
963	C₂²	—	46	1	no	—
964	C₂²	—	46	1	no	—
965	C₂²	—	46	1	no	—
966	C₂²	—	46	1	no	—
967	C₂²	—	46	1	no	—
968	C₂²	—	46	1	no	—
969	C₂²	—	46	1	no	—
970	C₂²	—	46	1	no	—
971	C₂²	—	46	1	no	—
972	C₂²	—	46	1	no	—
973	C₂²	—	46	1	no	—
974	C₂²	—	46	1	no	—
975	C₂²	—	46	1	no	—
976	C₂²	—	46	1	no	—
977	C₂²	—	92	4	no	—
978	C₂²	—	184	2	no	—
979	C₂²	—	184	2	no	—
980	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	46	1	no	—
993	C₄	—	46	1	no	—
994	C₄	—	46	1	no	—
995	C₄	—	46	1	no	—
996	C₄	—	46	1	no	—
997	C₄	—	46	1	no	—
998	C₄	—	46	1	no	—
999	C₄	—	46	1	no	—
1000	C₄	—	46	1	no	—
1001	C₄	—	46	1	no	—
1002	C₄	—	46	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	46	2	no	—
1008	C₂	—	92	1	no	—
1009	C₂	—	92	1	no	—
1010	C₂	—	92	1	no	—
1011	C₂	—	92	1	no	—
1012	C₂	H(5,𝔽₂)×D₂₃	1	1	yes	characteristic
1013	C₂	#13093252	1	1	yes	characteristic
1014	C₂	#13093254	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#562	C₂
hypercenter	#562	D₂₃
hypocenter	C₂₃	#3533
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #13093168	C₂	semidirect
2. #13093164	C₂	semidirect
3. #13093155	C₂	semidirect
4. #13093149	C₂	semidirect
5. #13093114	C₂	semidirect
6. #13093110	C₂	semidirect
7. #13093105	C₂	semidirect
8. #13093101	C₂	semidirect
9. #13093094	C₂	semidirect
10. #13093090	C₂	semidirect
11. #13093090	C₂	semidirect
12. #13093069	C₂	semidirect
13. #13093065	C₂	semidirect
14. #13093060	C₂	semidirect
15. #13093056	C₂	semidirect
16. #13093040	C₂	semidirect
17. #13093031	C₂	semidirect
18. #13093020	C₂	semidirect
19. #13093019	C₂	semidirect
20. #13093016	C₂	semidirect
21. #13093015	C₂	semidirect
22. #13093007	C₂	semidirect
23. #13093003	C₂	semidirect
24. #13093003	C₂	semidirect
25. #13093001	C₂	semidirect
26. #13092983	C₂	semidirect
27. #13092975	C₂	semidirect
28. #13092930	C₂	semidirect
29. #13092927	C₂	semidirect
30. #123×D₂₃	C₂	semidirect
31. C₂₃×#562	C₂	semidirect
36. C₂×#67288	C₂²	semidirect
37. C₂²×C₄×D₂₃	C₂²	semidirect
38. C₂₃×#125	C₂²	semidirect
39. C₂₃×#124	C₂²	semidirect
40. C₂₃×#124	C₂²	semidirect
41. C₂₃×#123	C₂²	semidirect
42. C₂₃×#123	C₂²	semidirect
43. C₂₃×#123	C₂²	semidirect
44. C₂₃×#123	C₂²	semidirect
45. C₂₃×C₂²⋊Q₈	C₂²	semidirect
46. C₂₃×C₂²⋊Q₈	C₂²	semidirect
47. C₂₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂₃×C₂²⋊Q₈	C₂²	semidirect
50. C₂₃×#121	C₂²	semidirect
51. C₂₃×#121	C₂²	semidirect
52. C₂₃×#121	C₂²	semidirect
53. #10625118	C₂²	semidirect
54. #10625118	C₂²	semidirect
55. #10625117	C₂²	semidirect
56. #10625117	C₂²	semidirect
57. #10625117	C₂²	semidirect
58. Q₈×Dic₂₃	C₂²	semidirect
59. #10625115	C₂²	semidirect
61. #10625111	C₂²	semidirect
64. #10625110	C₂²	semidirect
65. #10625110	C₂²	semidirect
66. #10625110	C₂²	semidirect
67. #10625109	C₂²	semidirect
68. #10625109	C₂²	semidirect
69. #10625109	C₂²	semidirect
70. #10625109	C₂²	semidirect
74. #10625108	C₂²	semidirect
75. #10625108	C₂²	semidirect
76. #10625106	C₂²	semidirect
77. #10625106	C₂²	semidirect
78. D₄×Dic₂₃	C₂²	semidirect
79. D₄×Dic₂₃	C₂²	semidirect
80. D₄×Dic₂₃	C₂²	semidirect
83. #10625101	C₂²	semidirect
84. #10625101	C₂²	semidirect
87. C₄×C₂²⋊D₂₃	C₂²	semidirect
88. C₄×C₂²⋊D₂₃	C₂²	semidirect
90. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
91. #10625097	C₂²	semidirect
92. #10625097	C₂²	semidirect
93. #10625095	C₂²	semidirect
94. C₂×Dic₂₃⋊C₄	C₂²	semidirect
95. #10625069	C₂²	semidirect
96. #10625069	C₂²	semidirect
97. #10625069	C₂²	semidirect
98. #10625069	C₂²	semidirect
99. #10625069	C₂²	semidirect
100. #10625069	C₂²	semidirect
101. #10625069	C₂²	semidirect
102. #10625068	C₂²	semidirect
103. #10625068	C₂²	semidirect
104. #10625068	C₂²	semidirect
105. #10625068	C₂²	semidirect
106. #10625067	C₂²	semidirect
107. #10625067	C₂²	semidirect
109. #10625066	C₂²	semidirect
115. #10625065	C₂²	semidirect
116. #10625065	C₂²	semidirect
117. #10625065	C₂²	semidirect
118. #10625065	C₂²	semidirect
119. #10625064	C₂²	semidirect
120. #10625064	C₂²	semidirect
121. #10625064	C₂²	semidirect
122. #10625063	C₂²	semidirect
123. #10625063	C₂²	semidirect
124. #10625063	C₂²	semidirect
125. #10625063	C₂²	semidirect
126. C₄⋊C₄×D₂₃	C₂²	semidirect
127. C₄⋊C₄×D₂₃	C₂²	semidirect
128. C₄⋊C₄×D₂₃	C₂²	semidirect
129. #10625061	C₂²	semidirect
130. #10625061	C₂²	semidirect
131. #10625061	C₂²	semidirect
132. #10625060	C₂²	semidirect
133. #10625060	C₂²	semidirect
134. #10625059	C₂²	semidirect
136. #10625057	C₂²	semidirect
137. #10625057	C₂²	semidirect
138. #10625057	C₂²	semidirect
139. #10625057	C₂²	semidirect
141. #10625056	C₂²	semidirect
142. #10625056	C₂²	semidirect
143. #10625056	C₂²	semidirect
144. #10625056	C₂²	semidirect
145. #10625056	C₂²	semidirect
148. #10625055	C₂²	semidirect
149. #10625055	C₂²	semidirect
150. #10625055	C₂²	semidirect
154. #10625054	C₂²	semidirect
155. #10625054	C₂²	semidirect
156. #10625054	C₂²	semidirect
157. #10625054	C₂²	semidirect
158. #10625054	C₂²	semidirect
159. #10625054	C₂²	semidirect
163. #10625053	C₂²	semidirect
164. #10625053	C₂²	semidirect
165. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
166. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
167. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
168. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
169. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
170. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
171. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
174. C₂²⋊C₄×D₂₃	C₂²	semidirect
175. C₂²⋊C₄×D₂₃	C₂²	semidirect
176. #10625050	C₂²	semidirect
177. #10625050	C₂²	semidirect
178. #10625050	C₂²	semidirect
179. #10625050	C₂²	semidirect
180. #10625049	C₂²	semidirect
181. #10625049	C₂²	semidirect
182. #10625048	C₂²	semidirect
183. #10625047	C₂²	semidirect
185. C₄×D₉₂	C₂²	semidirect
186. C₄×Dic₄₆	C₂²	semidirect
498. #562	D₂₃	semidirect
566. #125	C₂×D₂₃	semidirect
575. #124	C₂×D₂₃	semidirect
576. #124	C₂×D₂₃	semidirect
603. #123	C₂×D₂₃	semidirect
604. #123	C₂×D₂₃	semidirect
605. #123	C₂×D₂₃	semidirect
606. #123	C₂×D₂₃	semidirect
619. C₂²⋊Q₈	C₂×D₂₃	semidirect
620. C₂²⋊Q₈	C₂×D₂₃	semidirect
621. C₂²⋊Q₈	C₂×D₂₃	semidirect
622. C₂²⋊Q₈	C₂×D₂₃	semidirect
644. #121	C₂×D₂₃	semidirect
645. #121	C₂×D₂₃	semidirect
646. #121	C₂×D₂₃	semidirect
694. C₂₃	#3533	semidirect

Maximal subgroups

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

subgroup	index
#13093168	2
#13093164	2
#13093155	2
#13093149	2
#13093114	2
#13093110	2
#13093105	2
#13093101	2
#13093094	2
#13093090	2
#13093069	2
#13093065	2
#13093060	2
#13093056	2
#13093040	2
#13093031	2
#13093020	2
#13093019	2
#13093016	2
#13093015	2
#13093007	2
#13093003	2
#13093001	2
#13092983	2
#13092975	2
#13092930	2
#13092927	2
#123×D₂₃	2
C₂₃×#562	2
#3533	23