Subgroups — #27185169

Order 12928.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265895	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265886	C₂	1	2	yes	maximal, complemented
3	#20265869	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265866	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265858	C₂	1	2	yes	maximal, complemented
6	#20265856	C₂	1	2	yes	maximal, complemented
7	#20265840	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265834	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265833	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265827	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265826	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265814	C₂	1	2	yes	maximal, complemented
13	#20265795	C₂	1	2	yes	maximal, complemented
14	#20265770	C₂	1	2	yes	maximal, complemented
15	#20265769	C₂	1	2	yes	maximal, complemented
16	#20265729	C₂	1	1	yes	maximal, characteristic, complemented
17	#20265708	C₂	1	1	yes	maximal, characteristic, complemented
18	#20265687	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#15692234	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
21	#20265656	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#525×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13108073	C₂²	1	2	yes	—
25	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
30	#15692254	C₂²	1	1	yes	characteristic, complemented
31	#15692254	C₂²	1	2	yes	complemented
32	#15692253	C₂²	1	1	yes	characteristic, complemented
33	#15692250	C₂²	1	2	yes	complemented
34	#15692249	C₂²	1	2	yes	complemented
35	#15692248	C₂²	1	2	yes	complemented
36	#15692248	C₂²	1	2	yes	complemented
37	#15692248	C₂²	1	2	yes	complemented
38	#15692247	C₂²	1	2	yes	complemented
39	#15692246	C₂²	1	2	yes	complemented
40	#15692246	C₂²	1	1	yes	characteristic, complemented
41	#15692245	C₂²	1	2	yes	complemented
42	#15692242	C₂²	1	2	yes	complemented
43	#15692242	C₂²	1	1	yes	characteristic, complemented
44	#15692241	C₂²	1	2	yes	—
45	#15692241	C₂²	1	2	yes	complemented
46	#15692239	C₂²	1	2	yes	—
47	#15692238	C₂²	1	2	yes	complemented
48	#15692237	C₂²	1	2	yes	—
49	#15692237	C₂²	1	2	yes	complemented
50	#15692237	C₂²	1	2	yes	complemented
51	#15692236	C₂²	1	2	yes	—
52	#15692236	C₂²	1	2	yes	complemented
53	#15692236	C₂²	1	2	yes	complemented
54	#15692235	C₂²	1	1	yes	characteristic, complemented
55	#15692235	C₂²	1	1	yes	characteristic, complemented
56	#15692234	C₂²	1	1	yes	characteristic
57	#15692234	C₂²	1	2	yes	—
58	#15692234	C₂²	1	1	yes	characteristic
59	#15692234	C₂²	1	2	yes	complemented
60	#15692234	C₂²	1	2	yes	complemented
61	#15692234	C₂²	1	1	yes	characteristic, complemented
62	#15692234	C₂²	1	1	yes	characteristic, complemented
63	#15692233	C₂²	1	2	yes	complemented
64	#15692233	C₂²	1	2	yes	complemented
65	#15692232	C₂²	1	2	yes	—
66	#15692232	C₂²	1	2	yes	—
67	#15692232	C₂²	1	2	yes	complemented
68	#15692232	C₂²	1	2	yes	complemented
69	#15692232	C₂²	1	2	yes	complemented
70	#15692231	C₂²	1	1	yes	characteristic, complemented
71	#15692227	C₂²	1	2	yes	—
72	#15692227	C₂²	1	2	yes	—
73	#15692226	C₂²	1	2	yes	—
74	#15692226	C₂²	1	1	yes	characteristic, complemented
75	#15692223	C₂²	1	2	yes	—
76	Q₈×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₀₂	C₂²	1	2	yes	complemented
78	#15692220	C₂²	1	2	yes	complemented
79	#15692220	C₂²	1	1	yes	characteristic, complemented
80	#15692220	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₁₀₁	C₂²	1	2	yes	—
82	D₄×Dic₁₀₁	C₂²	1	2	yes	—
83	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
94	#15692215	C₂²	1	2	yes	—
95	#15692215	C₂²	1	2	yes	complemented
96	#15692213	C₂²	1	1	yes	characteristic, complemented
97	#15692212	C₂²	1	2	yes	complemented
98	#15692211	C₂²	1	2	yes	—
99	#15692211	C₂²	1	2	yes	complemented
100	#15692211	C₂²	1	2	yes	complemented
101	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
102	C₂×#13108053	C₂²	1	1	yes	characteristic
103	C₂×#13108053	C₂²	1	2	yes	complemented
104	C₂×#13108053	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	—
108	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
109	C₂×#13108051	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
112	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
113	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
114	#123×C₁₀₁	C₂²	1	2	yes	complemented
115	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₀₁	C₂²	1	1	yes	characteristic
118	#121×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
119	#120×C₁₀₁	C₂²	1	2	yes	—
120	C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
121	C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
122	#117×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
124	#13108073	—	2	8	no	—
125	#13108073	—	4	2	no	—
126	C₂×Dic₂₀₂	—	4	2	no	—
127	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₀₂	C₂³	1	2	yes	—
130	C₂×Dic₂₀₂	C₂³	1	2	yes	—
131	C₂×Dic₂₀₂	C₂³	1	2	yes	—
132	Q₈×D₁₀₁	—	4	2	no	—
133	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
134	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
142	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
143	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
146	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₀₁	—	4	2	no	—
148	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
151	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
154	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
156	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
158	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
159	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
160	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
161	#13108053	C₂³	1	2	yes	—
162	#13108053	C₂³	1	2	yes	—
163	#13108053	C₂³	1	2	yes	—
164	#13108053	C₂³	1	1	yes	characteristic
165	#13108053	C₂³	1	1	yes	characteristic
166	#13108053	C₂³	1	1	yes	characteristic
167	#13108053	C₂³	1	1	yes	characteristic
168	#13108053	C₂³	1	2	yes	—
169	#13108053	C₂³	1	2	yes	—
170	#13108053	C₂³	1	2	yes	—
171	#13108053	C₂³	1	2	yes	—
172	#13108053	C₂³	1	2	yes	—
173	#13108053	C₂³	1	2	yes	—
174	#13108053	C₂³	1	2	yes	—
175	#13108053	C₂³	1	2	yes	—
176	#13108053	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
189	#13108051	C₂³	1	2	yes	—
190	#13108051	C₂³	1	2	yes	—
191	#13108051	C₂³	1	1	yes	characteristic
192	#13108051	C₂³	1	1	yes	characteristic
193	#13108051	C₂³	1	1	yes	characteristic
194	#13108051	C₂³	1	1	yes	characteristic
195	#13108051	C₂³	1	2	yes	—
196	#13108051	C₂³	1	2	yes	—
197	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₀₁	C₂³	1	2	yes	—
202	C₄×Dic₁₀₁	C₂³	1	2	yes	—
203	C₄×Dic₁₀₁	C₂³	1	2	yes	—
204	C₄×Dic₁₀₁	C₂³	1	2	yes	—
205	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
206	#41×C₁₀₁	—	4	2	no	—
207	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
209	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
211	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₀₁	—	4	2	no	—
213	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
218	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
223	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
229	C₄²×C₁₀₁	C₂³	1	2	yes	—
230	C₂³×C₁₀₁	—	2	2	no	—
231	C₂³×C₁₀₁	—	2	2	no	—
232	C₂³×C₁₀₁	—	4	1	no	—
233	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
235	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₀₁	—	2	2	no	—
238	C₂²×D₁₀₁	—	2	2	no	—
239	C₂²×D₁₀₁	—	4	1	no	—
240	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
242	Q₈×C₁₀₁	—	2	2	no	—
243	D₄×C₁₀₁	—	2	4	no	—
244	D₄×C₁₀₁	—	2	4	no	—
245	D₄×C₁₀₁	—	2	2	no	—
246	D₄×C₁₀₁	—	4	2	no	—
247	C₂×C₄×C₁₀₁	—	2	2	no	—
248	C₂×C₄×C₁₀₁	—	2	2	no	—
249	C₂×C₄×C₁₀₁	—	2	2	no	—
250	C₂×C₄×C₁₀₁	—	4	1	no	—
251	C₂×C₄×C₁₀₁	—	4	1	no	—
252	C₂×C₄×C₁₀₁	—	4	1	no	—
253	C₂×C₄×C₁₀₁	—	4	2	no	—
254	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₀₁	—	2	2	no	—
262	C₂²⋊D₁₀₁	—	2	2	no	—
263	C₂²⋊D₁₀₁	—	2	4	no	—
264	C₂²⋊D₁₀₁	—	2	2	no	—
265	C₂²⋊D₁₀₁	—	4	2	no	—
266	C₂²⋊D₁₀₁	#41	1	4	yes	complemented
267	C₂×Dic₁₀₁	—	2	4	no	—
268	C₂×Dic₁₀₁	—	2	2	no	—
269	C₂×Dic₁₀₁	—	2	2	no	—
270	C₂×Dic₁₀₁	—	2	4	no	—
271	C₂×Dic₁₀₁	—	4	1	no	—
272	C₂×Dic₁₀₁	—	4	2	no	—
273	C₂×Dic₁₀₁	—	4	2	no	—
274	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
277	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
280	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
281	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
282	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
284	C₄×D₁₀₁	—	2	4	no	—
285	C₄×D₁₀₁	—	2	2	no	—
286	C₄×D₁₀₁	—	2	2	no	—
287	C₄×D₁₀₁	—	4	1	no	—
288	C₄×D₁₀₁	—	4	1	no	—
289	C₄×D₁₀₁	—	4	2	no	—
290	Dic₂₀₂	—	2	2	no	—
291	Dic₂₀₂	—	2	2	no	—
292	Dic₂₀₂	—	2	4	no	—
293	Dic₂₀₂	—	4	2	no	—
294	Dic₂₀₂	—	4	2	no	—
295	C₂²×C₁₀₁	—	2	1	no	—
296	C₂²×C₁₀₁	—	2	1	no	—
297	C₂²×C₁₀₁	—	2	1	no	—
298	C₂²×C₁₀₁	—	2	1	no	—
299	C₂²×C₁₀₁	—	2	2	no	—
300	C₂²×C₁₀₁	—	2	1	no	—
301	C₂²×C₁₀₁	—	2	2	no	—
302	C₂²×C₁₀₁	—	2	1	no	—
303	C₂²×C₁₀₁	—	2	2	no	—
304	C₂²×C₁₀₁	—	2	1	no	—
305	C₂²×C₁₀₁	—	4	4	no	—
306	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
307	C₂²×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
308	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₀₁	—	2	1	no	—
310	C₂×D₁₀₁	—	2	1	no	—
311	C₂×D₁₀₁	—	2	1	no	—
312	C₂×D₁₀₁	—	2	1	no	—
313	C₂×D₁₀₁	—	2	1	no	—
314	C₂×D₁₀₁	—	4	4	no	—
315	C₂×D₁₀₁	C₂×#41	1	2	yes	—
316	C₄×C₁₀₁	—	2	2	no	—
317	C₄×C₁₀₁	—	2	1	no	—
318	C₄×C₁₀₁	—	2	2	no	—
319	C₄×C₁₀₁	—	2	1	no	—
320	C₄×C₁₀₁	—	2	1	no	—
321	C₄×C₁₀₁	—	2	2	no	—
322	C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
323	Dic₁₀₁	—	2	2	no	—
324	Dic₁₀₁	—	2	2	no	—
325	Dic₁₀₁	—	2	1	no	—
326	Dic₁₀₁	—	2	2	no	—
327	Dic₁₀₁	—	2	2	no	—
328	Dic₁₀₁	—	2	1	no	—
329	Dic₁₀₁	—	2	1	no	—
330	Dic₁₀₁	—	2	1	no	—
331	Dic₁₀₁	—	2	1	no	—
332	Dic₁₀₁	C₂×#41	1	2	yes	—
333	C₂×C₁₀₁	—	2	2	no	—
334	C₂×C₁₀₁	—	2	2	no	—
335	C₂×C₁₀₁	—	4	2	no	—
336	C₂×C₁₀₁	—	4	1	no	—
337	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
338	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	D₁₀₁	—	2	2	no	—
341	D₁₀₁	—	4	1	no	—
342	#3520	—	101	1	no	maximal, Sylow
343	C₁₀₁	#3520	1	1	yes	characteristic, complemented, Sylow
344	#556	—	101	1	no	—
345	#554	—	101	2	no	—
346	#552	—	101	1	no	—
347	#552	—	101	1	no	—
348	#551	—	101	2	no	—
349	#551	—	101	2	no	—
350	D₄×Q₈	—	101	1	no	—
351	#548	—	101	1	no	—
352	#548	—	101	1	no	—
353	#547	—	101	1	no	—
354	#547	—	101	1	no	—
355	#546	—	101	2	no	—
356	#542	—	101	2	no	—
357	#539	—	101	2	no	—
358	#539	—	101	2	no	—
359	#533	—	101	1	no	—
360	#529	—	101	1	no	—
361	#525	—	101	1	no	—
362	#525	D₁₀₁	1	1	yes	characteristic, complemented
363	C₂×C₂²⋊Q₈	—	101	1	no	—
364	C₂×C₂²⋊Q₈	—	101	1	no	—
365	#520	—	101	2	no	—
366	C₂×C₄×D₄	—	101	1	no	—
367	C₂×#41	—	101	1	no	—
368	C₂×#41	—	101	2	no	—
369	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic, complemented
370	C₂²×Q₈	—	101	1	no	—
371	C₂²×Q₈	—	101	1	no	—
372	C₂²×D₄	—	101	1	no	—
373	C₂³×C₄	—	101	1	no	—
374	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
375	C₄⋊Q₈	—	101	1	no	—
376	C₄⋊Q₈	—	101	1	no	—
377	C₄⋊Q₈	—	101	2	no	—
378	#126	—	101	2	no	—
379	#126	—	101	2	no	—
380	#126	—	101	2	no	—
381	#126	—	101	2	no	—
382	#126	—	101	2	no	—
383	#125	—	101	1	no	—
384	#125	—	101	2	no	—
385	#125	—	101	2	no	—
386	#125	—	101	2	no	—
387	#124	—	101	1	no	—
388	#124	—	101	2	no	—
389	#124	—	101	2	no	—
390	#124	—	101	2	no	—
391	#123	—	101	2	no	—
392	#123	—	101	2	no	—
393	#123	—	101	2	no	—
394	#123	—	101	2	no	—
395	#123	—	101	2	no	—
396	#123	—	101	2	no	—
397	#123	—	101	2	no	—
398	#123	—	101	2	no	—
399	#123	C₂×D₁₀₁	1	2	yes	complemented
400	C₂²⋊Q₈	—	101	1	no	—
401	C₂²⋊Q₈	—	101	1	no	—
402	C₂²⋊Q₈	—	101	1	no	—
403	C₂²⋊Q₈	—	101	2	no	—
404	C₂²⋊Q₈	—	101	1	no	—
405	C₂²⋊Q₈	—	101	1	no	—
406	C₂²⋊Q₈	—	101	2	no	—
407	C₂²⋊Q₈	—	101	2	no	—
408	C₂²⋊Q₈	—	101	2	no	—
409	C₂²⋊Q₈	—	101	1	no	—
410	C₂²⋊Q₈	—	101	1	no	—
411	C₂²⋊Q₈	—	101	2	no	—
412	C₂²⋊Q₈	—	101	2	no	—
413	C₂²⋊Q₈	—	101	2	no	—
414	C₂²⋊Q₈	—	101	2	no	—
415	C₂²⋊Q₈	—	101	2	no	—
416	C₂²⋊Q₈	—	101	2	no	—
417	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
419	#121	—	101	1	no	—
420	#121	—	101	2	no	—
421	#121	—	101	2	no	—
422	#121	—	101	2	no	—
423	#121	C₂×D₁₀₁	1	1	yes	characteristic
424	#121	C₂×D₁₀₁	1	1	yes	characteristic, complemented
425	#120	—	101	2	no	—
426	#120	C₂×D₁₀₁	1	2	yes	—
427	C₄×Q₈	—	101	1	no	—
428	C₄×Q₈	—	101	2	no	—
429	C₄×Q₈	—	101	1	no	—
430	C₄×Q₈	—	101	1	no	—
431	C₄×Q₈	—	101	2	no	—
432	C₄×D₄	—	101	2	no	—
433	C₄×D₄	—	101	2	no	—
434	C₄×D₄	—	101	2	no	—
435	C₄×D₄	—	101	1	no	—
436	C₄×D₄	—	101	1	no	—
437	C₄×D₄	—	101	1	no	—
438	C₄×D₄	—	101	1	no	—
439	C₄×D₄	—	101	1	no	—
440	C₄×D₄	—	101	1	no	—
441	C₄×D₄	—	101	1	no	—
442	C₄×D₄	—	101	1	no	—
443	C₄×D₄	—	101	1	no	—
444	C₄×D₄	—	101	2	no	—
445	C₄×D₄	—	101	2	no	—
446	C₄×D₄	—	101	2	no	—
447	C₄×D₄	C₂×D₁₀₁	1	2	yes	—
448	C₄×D₄	C₂×D₁₀₁	1	2	yes	complemented
449	#117	—	101	1	no	—
450	#117	—	101	2	no	—
451	#117	—	101	2	no	—
452	#117	—	101	2	no	—
453	#117	—	101	2	no	—
454	#117	C₂×D₁₀₁	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	101	1	no	—
456	C₂×C₄⋊C₄	—	101	2	no	—
457	C₂×C₄⋊C₄	—	101	2	no	—
458	C₂×C₄⋊C₄	—	101	1	no	—
459	C₂×C₄⋊C₄	—	101	2	no	—
460	C₂×C₄⋊C₄	—	101	1	no	—
461	C₂×C₂²⋊C₄	—	101	1	no	—
462	C₂×C₂²⋊C₄	—	101	2	no	—
463	C₂×C₂²⋊C₄	—	101	1	no	—
464	C₂×C₂²⋊C₄	—	101	2	no	—
465	C₂×C₄²	—	101	1	no	—
466	C₂⁴	—	101	1	no	—
467	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
468	#41	—	4	2	no	—
469	#41	—	404	2	no	—
470	#41	—	202	8	no	—
471	C₂×Q₈	—	101	2	no	—
472	C₂×Q₈	—	101	2	no	—
473	C₂×Q₈	—	101	2	no	—
474	C₂×Q₈	—	101	1	no	—
475	C₂×Q₈	—	101	1	no	—
476	C₂×Q₈	—	404	2	no	—
477	C₂×Q₈	—	404	2	no	—
478	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
479	C₂×D₄	—	101	1	no	—
480	C₂×D₄	—	101	2	no	—
481	C₂×D₄	—	101	2	no	—
482	C₂×D₄	—	101	1	no	—
483	C₂×D₄	—	101	1	no	—
484	C₂×D₄	—	101	1	no	—
485	C₂×D₄	—	202	4	no	—
486	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
487	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
488	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	101	2	no	—
492	C₂²×C₄	—	101	1	no	—
493	C₂²×C₄	—	101	2	no	—
494	C₂²×C₄	—	101	1	no	—
495	C₂²×C₄	—	101	1	no	—
496	C₂²×C₄	—	101	2	no	—
497	C₂²×C₄	—	101	2	no	—
498	C₂²×C₄	—	101	2	no	—
499	C₂²×C₄	—	101	1	no	—
500	C₂²×C₄	—	101	1	no	—
501	C₂²×C₄	—	101	2	no	—
502	C₂²×C₄	—	101	1	no	—
503	C₂²×C₄	—	101	1	no	—
504	C₂²×C₄	—	404	2	no	—
505	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
511	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
512	C₄⋊C₄	—	101	1	no	—
513	C₄⋊C₄	—	101	2	no	—
514	C₄⋊C₄	—	101	2	no	—
515	C₄⋊C₄	—	101	2	no	—
516	C₄⋊C₄	—	101	1	no	—
517	C₄⋊C₄	—	101	1	no	—
518	C₄⋊C₄	—	101	1	no	—
519	C₄⋊C₄	—	101	2	no	—
520	C₄⋊C₄	—	101	2	no	—
521	C₄⋊C₄	—	101	2	no	—
522	C₄⋊C₄	—	101	2	no	—
523	C₄⋊C₄	—	101	2	no	—
524	C₄⋊C₄	—	101	2	no	—
525	C₄⋊C₄	—	101	2	no	—
526	C₄⋊C₄	—	101	2	no	—
527	C₄⋊C₄	—	101	2	no	—
528	C₄⋊C₄	—	101	1	no	—
529	C₄⋊C₄	—	101	1	no	—
530	C₄⋊C₄	—	101	2	no	—
531	C₄⋊C₄	—	101	2	no	—
532	C₄⋊C₄	—	101	2	no	—
533	C₄⋊C₄	—	101	2	no	—
534	C₄⋊C₄	—	101	2	no	—
535	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
537	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
539	C₂²⋊C₄	—	101	2	no	—
540	C₂²⋊C₄	—	101	1	no	—
541	C₂²⋊C₄	—	101	2	no	—
542	C₂²⋊C₄	—	101	1	no	—
543	C₂²⋊C₄	—	101	1	no	—
544	C₂²⋊C₄	—	101	1	no	—
545	C₂²⋊C₄	—	101	2	no	—
546	C₂²⋊C₄	—	101	2	no	—
547	C₂²⋊C₄	—	101	2	no	—
548	C₂²⋊C₄	—	101	2	no	—
549	C₂²⋊C₄	—	101	2	no	—
550	C₂²⋊C₄	—	101	2	no	—
551	C₂²⋊C₄	—	101	1	no	—
552	C₂²⋊C₄	—	101	1	no	—
553	C₂²⋊C₄	—	101	1	no	—
554	C₂²⋊C₄	—	101	1	no	—
555	C₂²⋊C₄	—	101	2	no	—
556	C₂²⋊C₄	—	101	2	no	—
557	C₂²⋊C₄	—	101	2	no	—
558	C₂²⋊C₄	—	101	2	no	—
559	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
564	C₄²	—	101	1	no	—
565	C₄²	—	101	1	no	—
566	C₄²	—	101	1	no	—
567	C₄²	—	101	1	no	—
568	C₄²	—	101	2	no	—
569	C₄²	—	101	2	no	—
570	C₄²	—	101	2	no	—
571	C₄²	—	101	2	no	—
572	C₄²	C₂²×D₁₀₁	1	2	yes	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	101	1	no	—
577	C₂³	—	101	1	no	—
578	C₂³	—	404	1	no	—
579	C₂³	—	202	2	no	—
580	C₂³	—	202	2	no	—
581	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
582	C₂³	C₂³×D₁₀₁	1	2	yes	—
583	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
584	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	404	2	no	—
587	Q₈	—	404	2	no	—
588	Q₈	—	202	4	no	—
589	Q₈	—	202	2	no	—
590	Q₈	—	202	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	101	4	no	—
596	D₄	—	404	2	no	—
597	D₄	—	202	2	no	—
598	D₄	—	202	2	no	—
599	D₄	—	202	4	no	—
600	D₄	—	202	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	101	1	no	—
609	C₂×C₄	—	101	1	no	—
610	C₂×C₄	—	101	1	no	—
611	C₂×C₄	—	101	2	no	—
612	C₂×C₄	—	101	1	no	—
613	C₂×C₄	—	101	1	no	—
614	C₂×C₄	—	101	2	no	—
615	C₂×C₄	—	101	2	no	—
616	C₂×C₄	—	101	2	no	—
617	C₂×C₄	—	101	1	no	—
618	C₂×C₄	—	404	1	no	—
619	C₂×C₄	—	404	1	no	—
620	C₂×C₄	—	404	2	no	—
621	C₂×C₄	—	404	1	no	—
622	C₂×C₄	—	404	2	no	—
623	C₂×C₄	—	404	2	no	—
624	C₂×C₄	—	202	4	no	—
625	C₂×C₄	—	202	2	no	—
626	C₂×C₄	—	202	4	no	—
627	C₂×C₄	—	202	4	no	—
628	C₂×C₄	—	202	2	no	—
629	C₂×C₄	—	202	2	no	—
630	C₂×C₄	—	202	2	no	—
631	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
632	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
634	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
635	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	101	2	no	—
650	C₂²	—	404	4	no	—
651	C₂²	—	202	1	no	—
652	C₂²	—	202	1	no	—
653	C₂²	—	202	1	no	—
654	C₂²	—	202	1	no	—
655	C₂²	—	202	1	no	—
656	C₂²	#41×D₁₀₁	1	2	yes	—
657	C₂²	#15692302	1	2	yes	—
658	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	101	2	no	—
666	C₄	—	202	2	no	—
667	C₄	—	202	1	no	—
668	C₄	—	202	2	no	—
669	C₄	—	202	1	no	—
670	C₄	—	202	1	no	—
671	C₄	—	202	2	no	—
672	C₄	—	202	2	no	—
673	C₄	—	202	1	no	—
674	C₄	—	202	1	no	—
675	C₄	#15692300	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	2	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	2	no	—
680	C₂	—	404	1	no	—
681	C₂	—	202	2	no	—
682	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
683	C₂	C₂×#15692300	1	1	yes	characteristic
684	C₂	C₂×#15692302	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#525×C₁₀₁	C₂
hypercenter	#525	D₁₀₁
hypocenter	C₁₀₁	#3520
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #20265895	C₂	semidirect
2. #20265886	C₂	semidirect
3. #20265869	C₂	semidirect
4. #20265866	C₂	semidirect
5. #20265858	C₂	semidirect
6. #20265856	C₂	semidirect
7. #20265840	C₂	semidirect
8. #20265834	C₂	semidirect
9. #20265833	C₂	semidirect
10. #20265827	C₂	semidirect
11. #20265826	C₂	semidirect
12. #20265814	C₂	semidirect
13. #20265795	C₂	semidirect
14. #20265770	C₂	semidirect
15. #20265769	C₂	semidirect
16. #20265729	C₂	semidirect
17. #20265708	C₂	semidirect
18. #20265687	C₂	semidirect
19. C₂×#15692234	C₂	semidirect
20. C₂²⋊Q₈×D₁₀₁	C₂	semidirect
21. #20265656	C₂	semidirect
22. C₂×C₄×C₂²⋊D₁₀₁	C₂	semidirect
23. #525×C₁₀₁	C₂	semidirect
25. C₂×#13108073	C₂²	semidirect
26. C₂²×Dic₂₀₂	C₂²	semidirect
27. C₂×Q₈×D₁₀₁	C₂²	semidirect
30. #15692254	C₂²	semidirect
31. #15692254	C₂²	semidirect
32. #15692253	C₂²	semidirect
33. #15692250	C₂²	semidirect
34. #15692249	C₂²	semidirect
35. #15692248	C₂²	semidirect
36. #15692248	C₂²	semidirect
37. #15692248	C₂²	semidirect
38. #15692247	C₂²	semidirect
39. #15692246	C₂²	semidirect
40. #15692246	C₂²	semidirect
41. #15692245	C₂²	semidirect
42. #15692242	C₂²	semidirect
43. #15692242	C₂²	semidirect
45. #15692241	C₂²	semidirect
47. #15692238	C₂²	semidirect
49. #15692237	C₂²	semidirect
50. #15692237	C₂²	semidirect
52. #15692236	C₂²	semidirect
53. #15692236	C₂²	semidirect
54. #15692235	C₂²	semidirect
55. #15692235	C₂²	semidirect
59. #15692234	C₂²	semidirect
60. #15692234	C₂²	semidirect
61. #15692234	C₂²	semidirect
62. #15692234	C₂²	semidirect
63. #15692233	C₂²	semidirect
64. #15692233	C₂²	semidirect
67. #15692232	C₂²	semidirect
68. #15692232	C₂²	semidirect
69. #15692232	C₂²	semidirect
70. #15692231	C₂²	semidirect
74. #15692226	C₂²	semidirect
76. Q₈×Dic₁₀₁	C₂²	semidirect
77. C₄×Dic₂₀₂	C₂²	semidirect
78. #15692220	C₂²	semidirect
79. #15692220	C₂²	semidirect
80. #15692220	C₂²	semidirect
83. D₄×Dic₁₀₁	C₂²	semidirect
84. D₄×Dic₁₀₁	C₂²	semidirect
93. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
95. #15692215	C₂²	semidirect
96. #15692213	C₂²	semidirect
97. #15692212	C₂²	semidirect
99. #15692211	C₂²	semidirect
100. #15692211	C₂²	semidirect
101. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
103. C₂×#13108053	C₂²	semidirect
104. C₂×#13108053	C₂²	semidirect
105. C₄⋊C₄×D₁₀₁	C₂²	semidirect
106. C₄⋊C₄×D₁₀₁	C₂²	semidirect
112. C₂×#41×C₁₀₁	C₂²	semidirect
114. #123×C₁₀₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
118. #121×C₁₀₁	C₂²	semidirect
121. C₄×D₄×C₁₀₁	C₂²	semidirect
122. #117×C₁₀₁	C₂²	semidirect
266. C₂²⋊D₁₀₁	#41	semidirect
343. C₁₀₁	#3520	semidirect
362. #525	D₁₀₁	semidirect
369. C₂×#41	C₂×D₁₀₁	semidirect
399. #123	C₂×D₁₀₁	semidirect
418. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
424. #121	C₂×D₁₀₁	semidirect
448. C₄×D₄	C₂×D₁₀₁	semidirect
454. #117	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265895	2
#20265886	2
#20265869	2
#20265866	2
#20265858	2
#20265856	2
#20265840	2
#20265834	2
#20265833	2
#20265827	2
#20265826	2
#20265814	2
#20265795	2
#20265770	2
#20265769	2
#20265729	2
#20265708	2
#20265687	2
C₂×#15692234	2
C₂²⋊Q₈×D₁₀₁	2
#20265656	2
C₂×C₄×C₂²⋊D₁₀₁	2
#525×C₁₀₁	2
#3520	101