Subgroups — #27184726

Order 12928.

1112 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265911	C₂	1	2	yes	maximal, complemented
2	#20265910	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265904	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265895	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265894	C₂	1	2	yes	maximal, complemented
6	#20265876	C₂	1	2	yes	maximal, complemented
7	#20265875	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265870	C₂	1	2	yes	maximal, complemented
9	#20265845	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265836	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265833	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265722	C₂	1	1	yes	maximal, characteristic, complemented
13	#20265722	C₂	1	2	yes	maximal, complemented
14	#20265712	C₂	1	1	yes	maximal, characteristic, complemented
15	#20265710	C₂	1	2	yes	maximal, complemented
16	#20265708	C₂	1	1	yes	maximal, characteristic, complemented
17	#20265704	C₂	1	2	yes	maximal, complemented
18	#20265645	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13108073	C₂	1	2	yes	maximal, complemented
22	C₂×#15692220	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13108074	C₂²	1	1	yes	characteristic
25	C₂×#13108073	C₂²	1	1	yes	characteristic
26	C₂×#13108073	C₂²	1	1	yes	characteristic
27	C₂×#13108073	C₂²	1	2	yes	—
28	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic
29	#15692254	C₂²	1	2	yes	—
30	#15692254	C₂²	1	1	yes	characteristic
31	#15692251	C₂²	1	1	yes	characteristic
32	#15692251	C₂²	1	2	yes	—
33	#15692250	C₂²	1	2	yes	—
34	#15692250	C₂²	1	2	yes	—
35	#15692249	C₂²	1	2	yes	—
36	#15692248	C₂²	1	2	yes	—
37	#15692248	C₂²	1	2	yes	—
38	#15692246	C₂²	1	1	yes	characteristic
39	#15692245	C₂²	1	2	yes	—
40	#15692245	C₂²	1	2	yes	—
41	#15692243	C₂²	1	1	yes	characteristic
42	#15692242	C₂²	1	1	yes	characteristic
43	#15692241	C₂²	1	2	yes	—
44	#15692241	C₂²	1	2	yes	—
45	#15692241	C₂²	1	2	yes	—
46	#15692241	C₂²	1	2	yes	—
47	#15692241	C₂²	1	2	yes	—
48	#15692240	C₂²	1	2	yes	—
49	#15692240	C₂²	1	2	yes	—
50	#15692238	C₂²	1	2	yes	—
51	#15692237	C₂²	1	2	yes	—
52	#15692236	C₂²	1	2	yes	—
53	#15692235	C₂²	1	1	yes	characteristic
54	#15692234	C₂²	1	1	yes	characteristic
55	#15692233	C₂²	1	2	yes	—
56	#15692232	C₂²	1	2	yes	—
57	#15692230	C₂²	1	1	yes	characteristic
58	#15692229	C₂²	1	1	yes	characteristic
59	#15692229	C₂²	1	2	yes	—
60	#15692228	C₂²	1	2	yes	—
61	#15692227	C₂²	1	2	yes	—
62	#15692227	C₂²	1	2	yes	—
63	#15692227	C₂²	1	2	yes	—
64	#15692227	C₂²	1	2	yes	—
65	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
66	C₄×Dic₂₀₂	C₂²	1	2	yes	—
67	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic
68	#15692220	C₂²	1	1	yes	characteristic
69	#15692220	C₂²	1	1	yes	characteristic
70	#15692220	C₂²	1	1	yes	characteristic
71	#15692220	C₂²	1	2	yes	—
72	#15692220	C₂²	1	1	yes	characteristic
73	#15692220	C₂²	1	1	yes	characteristic
74	#15692220	C₂²	1	2	yes	—
75	#15692220	C₂²	1	1	yes	characteristic
76	#15692220	C₂²	1	2	yes	—
77	D₄×Dic₁₀₁	C₂²	1	2	yes	—
78	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
79	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
80	D₄×Dic₁₀₁	C₂²	1	2	yes	—
81	#15692217	C₂²	1	1	yes	characteristic
82	#15692217	C₂²	1	1	yes	characteristic
83	#15692217	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
89	#15692215	C₂²	1	2	yes	—
90	#15692215	C₂²	1	2	yes	—
91	#15692215	C₂²	1	2	yes	—
92	#15692215	C₂²	1	1	yes	characteristic
93	#15692215	C₂²	1	1	yes	characteristic
94	#15692215	C₂²	1	2	yes	—
95	#15692215	C₂²	1	2	yes	—
96	#15692215	C₂²	1	2	yes	—
97	#15692213	C₂²	1	1	yes	characteristic
98	#15692213	C₂²	1	2	yes	—
99	#15692213	C₂²	1	1	yes	characteristic
100	#15692212	C₂²	1	2	yes	—
101	#15692211	C₂²	1	2	yes	—
102	#15692211	C₂²	1	1	yes	characteristic
103	#15692211	C₂²	1	1	yes	characteristic
104	#15692211	C₂²	1	2	yes	—
105	C₂×#13108053	C₂²	1	2	yes	—
106	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
107	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
109	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
110	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
111	C₄²×D₁₀₁	C₂²	1	2	yes	—
112	#126×C₁₀₁	C₂²	1	2	yes	—
113	#125×C₁₀₁	C₂²	1	1	yes	characteristic
114	#123×C₁₀₁	C₂²	1	2	yes	—
115	#121×C₁₀₁	C₂²	1	1	yes	characteristic
116	#121×C₁₀₁	C₂²	1	1	yes	characteristic
117	#121×C₁₀₁	C₂²	1	2	yes	—
118	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
120	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
121	#117×C₁₀₁	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
123	#13108074	—	2	4	no	—
124	#13108073	—	2	4	no	—
125	#13108073	—	2	8	no	—
126	#13108073	—	2	4	no	—
127	C₂×Dic₂₀₂	—	2	4	no	—
128	C₂×Dic₂₀₂	C₂³	1	2	yes	—
129	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₀₂	C₂³	1	2	yes	—
132	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
133	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
134	C₂×D₄₀₄	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
142	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
143	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
144	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
146	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₀₁	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	2	yes	—
153	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
155	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
157	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
159	#13108053	C₂³	1	2	yes	—
160	#13108053	C₂³	1	2	yes	—
161	#13108053	C₂³	1	2	yes	—
162	#13108053	C₂³	1	2	yes	—
163	#13108053	C₂³	1	1	yes	characteristic
164	#13108053	C₂³	1	1	yes	characteristic
165	#13108053	C₂³	1	2	yes	—
166	#13108053	C₂³	1	2	yes	—
167	#13108053	C₂³	1	1	yes	characteristic
168	#13108053	C₂³	1	1	yes	characteristic
169	#13108053	C₂³	1	2	yes	—
170	#13108053	C₂³	1	2	yes	—
171	#13108053	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
178	#13108051	C₂³	1	2	yes	—
179	#13108051	C₂³	1	2	yes	—
180	#13108051	C₂³	1	2	yes	—
181	#13108051	C₂³	1	1	yes	characteristic
182	#13108051	C₂³	1	2	yes	—
183	#13108051	C₂³	1	2	yes	—
184	#13108051	C₂³	1	1	yes	characteristic
185	#13108051	C₂³	1	2	yes	—
186	#13108051	C₂³	1	2	yes	—
187	#13108051	C₂³	1	2	yes	—
188	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
189	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
190	C₄×Dic₁₀₁	C₂³	1	2	yes	—
191	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₀₁	C₂³	1	2	yes	—
194	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₀₁	C₂³	1	2	yes	—
196	C₄×Dic₁₀₁	C₂³	1	2	yes	—
197	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₀₁	C₂³	1	2	yes	—
199	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₀₁	C₂³	1	2	yes	—
201	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₀₁	C₂³	1	2	yes	—
203	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
206	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
225	C₄²×C₁₀₁	C₂³	1	2	yes	—
226	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
227	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
228	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
231	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
232	D₄×C₁₀₁	—	2	2	no	—
233	D₄×C₁₀₁	—	2	4	no	—
234	D₄×C₁₀₁	—	2	2	no	—
235	D₄×C₁₀₁	—	4	2	no	—
236	C₂×C₄×C₁₀₁	—	2	2	no	—
237	C₂×C₄×C₁₀₁	—	2	2	no	—
238	C₂×C₄×C₁₀₁	—	4	2	no	—
239	C₂×C₄×C₁₀₁	—	4	2	no	—
240	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₁₀₁	—	2	4	no	—
249	C₂²⋊D₁₀₁	—	2	2	no	—
250	C₂²⋊D₁₀₁	—	2	4	no	—
251	C₂²⋊D₁₀₁	—	2	2	no	—
252	C₂²⋊D₁₀₁	—	2	4	no	—
253	C₂²⋊D₁₀₁	—	2	4	no	—
254	C₂²⋊D₁₀₁	—	4	2	no	—
255	C₂×Dic₁₀₁	—	2	4	no	—
256	C₂×Dic₁₀₁	—	2	4	no	—
257	C₂×Dic₁₀₁	—	2	2	no	—
258	C₂×Dic₁₀₁	—	2	4	no	—
259	C₂×Dic₁₀₁	—	4	1	no	—
260	C₂×Dic₁₀₁	—	4	1	no	—
261	C₂×Dic₁₀₁	#41	1	4	yes	complemented
262	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
266	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
267	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
272	D₄₀₄	—	2	2	no	—
273	D₄₀₄	—	4	2	no	—
274	C₄×D₁₀₁	—	2	2	no	—
275	C₄×D₁₀₁	—	2	2	no	—
276	C₄×D₁₀₁	—	2	4	no	—
277	C₄×D₁₀₁	—	2	4	no	—
278	C₄×D₁₀₁	—	4	2	no	—
279	C₄×D₁₀₁	—	4	1	no	—
280	Dic₂₀₂	—	2	2	no	—
281	Dic₂₀₂	—	2	4	no	—
282	Dic₂₀₂	—	2	2	no	—
283	Dic₂₀₂	—	2	4	no	—
284	Dic₂₀₂	#41	1	4	yes	complemented
285	C₂²×C₁₀₁	—	2	1	no	—
286	C₂²×C₁₀₁	—	2	1	no	—
287	C₂²×C₁₀₁	—	2	2	no	—
288	C₂²×C₁₀₁	—	2	1	no	—
289	C₂²×C₁₀₁	—	2	2	no	—
290	C₂²×C₁₀₁	—	2	1	no	—
291	C₂²×C₁₀₁	—	2	1	no	—
292	C₂²×C₁₀₁	—	2	2	no	—
293	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
294	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
295	C₂×D₁₀₁	—	2	2	no	—
296	C₂×D₁₀₁	—	2	2	no	—
297	C₂×D₁₀₁	—	2	1	no	—
298	C₂×D₁₀₁	—	2	1	no	—
299	C₂×D₁₀₁	—	2	1	no	—
300	C₂×D₁₀₁	—	2	2	no	—
301	C₄×C₁₀₁	—	2	1	no	—
302	C₄×C₁₀₁	—	2	2	no	—
303	C₄×C₁₀₁	—	2	1	no	—
304	C₄×C₁₀₁	—	2	1	no	—
305	C₄×C₁₀₁	—	2	2	no	—
306	C₄×C₁₀₁	—	2	1	no	—
307	C₄×C₁₀₁	—	2	2	no	—
308	C₄×C₁₀₁	C₂×#41	1	2	yes	—
309	Dic₁₀₁	—	2	2	no	—
310	Dic₁₀₁	—	2	2	no	—
311	Dic₁₀₁	—	2	1	no	—
312	Dic₁₀₁	—	2	1	no	—
313	Dic₁₀₁	—	2	1	no	—
314	Dic₁₀₁	—	2	1	no	—
315	Dic₁₀₁	—	2	1	no	—
316	Dic₁₀₁	C₂×#41	1	2	yes	—
317	Dic₁₀₁	C₂×#41	1	4	yes	—
318	Dic₁₀₁	C₂×#41	1	2	yes	—
319	C₂×C₁₀₁	—	2	2	no	—
320	C₂×C₁₀₁	—	4	2	no	—
321	C₂×C₁₀₁	—	4	1	no	—
322	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
323	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₀₁	#585	1	1	yes	characteristic
325	D₁₀₁	—	4	2	no	—
326	D₁₀₁	—	4	1	no	—
327	#3480	—	101	1	no	maximal, Sylow
328	C₁₀₁	#3480	1	1	yes	characteristic, complemented, Sylow
329	#559	—	101	2	no	—
330	#559	—	101	1	no	—
331	#557	—	101	1	no	—
332	#556	—	101	2	no	—
333	#556	—	101	1	no	—
334	#553	—	101	2	no	—
335	#553	—	101	2	no	—
336	#553	—	101	1	no	—
337	#553	D₁₀₁	1	1	yes	characteristic, complemented
338	#550	—	101	1	no	—
339	#548	—	101	1	no	—
340	#548	—	101	1	no	—
341	#532	—	101	1	no	—
342	#532	—	101	2	no	—
343	#529	—	101	2	no	—
344	#529	—	101	1	no	—
345	#529	—	101	2	no	—
346	#529	—	101	1	no	—
347	C₄×#41	—	101	2	no	—
348	C₄×#41	—	101	1	no	—
349	C₄×#41	—	101	1	no	—
350	C₄×#41	—	101	1	no	—
351	C₂×C₄×Q₈	—	101	1	no	—
352	C₂×#41	—	101	2	no	—
353	C₂×#41	—	101	1	no	—
354	C₂×#41	—	101	1	no	—
355	C₂×#41	—	101	1	no	—
356	C₂²×Q₈	—	101	1	no	—
357	C₄⋊Q₈	—	101	2	no	—
358	C₄⋊Q₈	—	101	1	no	—
359	#127	—	101	1	no	—
360	#127	—	101	2	no	—
361	#126	—	101	2	no	—
362	#126	—	101	2	no	—
363	#126	—	101	2	no	—
364	#126	—	101	2	no	—
365	#126	—	101	2	no	—
366	#126	C₂×D₁₀₁	1	2	yes	—
367	#125	—	101	2	no	—
368	#125	—	101	2	no	—
369	#125	—	101	1	no	—
370	#125	C₂×D₁₀₁	1	1	yes	characteristic
371	#124	—	101	1	no	—
372	#124	—	101	2	no	—
373	#124	—	101	2	no	—
374	#124	—	101	2	no	—
375	#124	—	101	2	no	—
376	#124	—	101	2	no	—
377	#124	—	101	1	no	—
378	#123	—	101	2	no	—
379	#123	—	101	2	no	—
380	#123	—	101	2	no	—
381	#123	—	101	2	no	—
382	#123	—	101	2	no	—
383	#123	C₂×D₁₀₁	1	2	yes	—
384	C₂²⋊Q₈	—	101	1	no	—
385	C₂²⋊Q₈	—	101	2	no	—
386	C₂²⋊Q₈	—	101	1	no	—
387	C₂²⋊Q₈	—	101	2	no	—
388	#121	—	101	2	no	—
389	#121	—	101	2	no	—
390	#121	—	101	2	no	—
391	#121	—	101	2	no	—
392	#121	—	101	1	no	—
393	#121	—	101	2	no	—
394	#121	—	101	1	no	—
395	#121	—	101	2	no	—
396	#121	C₂×D₁₀₁	1	1	yes	characteristic
397	#121	C₂×D₁₀₁	1	1	yes	characteristic
398	#121	C₂×D₁₀₁	1	2	yes	—
399	C₄×Q₈	—	101	1	no	—
400	C₄×Q₈	—	101	2	no	—
401	C₄×Q₈	—	101	1	no	—
402	C₄×Q₈	—	101	1	no	—
403	C₄×Q₈	—	101	2	no	—
404	C₄×Q₈	—	101	1	no	—
405	C₄×Q₈	—	101	1	no	—
406	C₄×Q₈	—	101	1	no	—
407	C₄×Q₈	—	101	2	no	—
408	C₄×Q₈	—	101	1	no	—
409	C₄×Q₈	—	101	2	no	—
410	C₄×Q₈	—	101	1	no	—
411	C₄×D₄	—	101	1	no	—
412	C₄×D₄	—	101	2	no	—
413	C₄×D₄	—	101	1	no	—
414	C₄×D₄	—	101	2	no	—
415	C₄×D₄	—	101	1	no	—
416	C₄×D₄	—	101	1	no	—
417	C₄×D₄	—	101	2	no	—
418	C₄×D₄	—	101	2	no	—
419	C₄×D₄	—	101	2	no	—
420	C₄×D₄	—	101	1	no	—
421	C₄×D₄	—	101	1	no	—
422	C₄×D₄	—	101	2	no	—
423	C₄×D₄	—	101	2	no	—
424	C₄×D₄	—	101	2	no	—
425	C₄×D₄	—	101	2	no	—
426	C₄×D₄	—	101	2	no	—
427	C₄×D₄	—	101	1	no	—
428	C₄×D₄	—	101	2	no	—
429	C₄×D₄	—	101	1	no	—
430	C₄×D₄	—	101	2	no	—
431	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic
432	C₄×D₄	C₂×D₁₀₁	1	2	yes	—
433	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic
434	#117	—	101	2	no	—
435	#117	—	101	1	no	—
436	#117	—	101	1	no	—
437	#117	—	101	1	no	—
438	#117	—	101	1	no	—
439	#117	—	101	2	no	—
440	#117	—	101	2	no	—
441	#117	—	101	2	no	—
442	#117	C₂×D₁₀₁	1	1	yes	characteristic
443	C₂×C₄⋊C₄	—	101	2	no	—
444	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
445	C₂×C₄²	—	101	1	no	—
446	C₂×C₄²	—	101	2	no	—
447	C₂×C₄²	—	101	1	no	—
448	C₂×C₄²	—	101	2	no	—
449	C₂×C₄²	—	101	1	no	—
450	C₂×C₄²	—	101	2	no	—
451	#41	—	202	4	no	—
452	#41	—	202	8	no	—
453	#41	—	202	4	no	—
454	#41	—	202	4	no	—
455	C₂×Q₈	—	101	1	no	—
456	C₂×Q₈	—	101	2	no	—
457	C₂×Q₈	—	101	1	no	—
458	C₂×Q₈	—	101	1	no	—
459	C₂×Q₈	—	101	2	no	—
460	C₂×Q₈	—	202	4	no	—
461	C₂×D₄	—	101	2	no	—
462	C₂×D₄	—	101	1	no	—
463	C₂×D₄	—	101	2	no	—
464	C₂×D₄	—	101	2	no	—
465	C₂×D₄	—	101	2	no	—
466	C₂×D₄	—	101	1	no	—
467	C₂×D₄	—	101	2	no	—
468	C₂×D₄	—	101	2	no	—
469	C₂×D₄	—	101	1	no	—
470	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
471	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
472	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
473	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
474	C₂²×C₄	—	101	1	no	—
475	C₂²×C₄	—	101	1	no	—
476	C₂²×C₄	—	101	1	no	—
477	C₂²×C₄	—	101	2	no	—
478	C₂²×C₄	—	101	2	no	—
479	C₂²×C₄	—	101	1	no	—
480	C₂²×C₄	—	101	2	no	—
481	C₂²×C₄	—	101	1	no	—
482	C₂²×C₄	—	101	2	no	—
483	C₂²×C₄	—	101	2	no	—
484	C₂²×C₄	—	101	1	no	—
485	C₂²×C₄	—	101	2	no	—
486	C₂²×C₄	—	101	1	no	—
487	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
490	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
491	C₄⋊C₄	—	101	2	no	—
492	C₄⋊C₄	—	101	2	no	—
493	C₄⋊C₄	—	101	2	no	—
494	C₄⋊C₄	—	101	2	no	—
495	C₄⋊C₄	—	101	1	no	—
496	C₄⋊C₄	—	101	1	no	—
497	C₄⋊C₄	—	101	2	no	—
498	C₄⋊C₄	—	101	2	no	—
499	C₄⋊C₄	—	101	1	no	—
500	C₄⋊C₄	—	101	2	no	—
501	C₄⋊C₄	—	101	2	no	—
502	C₄⋊C₄	—	101	1	no	—
503	C₄⋊C₄	—	101	2	no	—
504	C₄⋊C₄	—	101	1	no	—
505	C₄⋊C₄	—	101	2	no	—
506	C₄⋊C₄	—	101	1	no	—
507	C₄⋊C₄	—	101	2	no	—
508	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
515	C₂²⋊C₄	—	101	1	no	—
516	C₂²⋊C₄	—	101	1	no	—
517	C₂²⋊C₄	—	101	2	no	—
518	C₂²⋊C₄	—	101	2	no	—
519	C₂²⋊C₄	—	101	2	no	—
520	C₂²⋊C₄	—	101	2	no	—
521	C₂²⋊C₄	—	101	2	no	—
522	C₂²⋊C₄	—	101	1	no	—
523	C₂²⋊C₄	—	101	2	no	—
524	C₂²⋊C₄	—	101	2	no	—
525	C₂²⋊C₄	—	101	2	no	—
526	C₂²⋊C₄	—	101	1	no	—
527	C₂²⋊C₄	—	101	2	no	—
528	C₂²⋊C₄	—	101	2	no	—
529	C₂²⋊C₄	—	101	2	no	—
530	C₂²⋊C₄	—	101	2	no	—
531	C₂²⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
537	C₄²	—	101	1	no	—
538	C₄²	—	101	1	no	—
539	C₄²	—	101	2	no	—
540	C₄²	—	101	1	no	—
541	C₄²	—	101	2	no	—
542	C₄²	—	101	1	no	—
543	C₄²	—	101	1	no	—
544	C₄²	—	101	2	no	—
545	C₄²	—	101	1	no	—
546	C₄²	—	101	2	no	—
547	C₄²	—	101	2	no	—
548	C₄²	—	101	1	no	—
549	C₄²	—	101	1	no	—
550	C₄²	—	101	2	no	—
551	C₄²	—	101	2	no	—
552	C₄²	—	101	1	no	—
553	C₄²	C₂²×D₁₀₁	1	2	yes	—
554	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
555	C₂³	—	101	2	no	—
556	C₂³	—	101	1	no	—
557	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
558	C₂³	C₂³×D₁₀₁	1	2	yes	—
559	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
560	Q₈	—	101	4	no	—
561	Q₈	—	202	4	no	—
562	Q₈	—	202	2	no	—
563	Q₈	—	202	4	no	—
564	Q₈	—	202	2	no	—
565	D₄	—	2	4	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	404	2	no	—
570	D₄	—	404	2	no	—
571	D₄	—	202	2	no	—
572	D₄	—	202	4	no	—
573	D₄	—	202	4	no	—
574	D₄	—	202	4	no	—
575	D₄	—	202	2	no	—
576	D₄	—	202	4	no	—
577	D₄	—	202	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	101	4	no	—
583	C₂×C₄	—	101	1	no	—
584	C₂×C₄	—	101	1	no	—
585	C₂×C₄	—	101	2	no	—
586	C₂×C₄	—	101	1	no	—
587	C₂×C₄	—	101	1	no	—
588	C₂×C₄	—	101	1	no	—
589	C₂×C₄	—	101	2	no	—
590	C₂×C₄	—	101	2	no	—
591	C₂×C₄	—	101	1	no	—
592	C₂×C₄	—	101	1	no	—
593	C₂×C₄	—	404	2	no	—
594	C₂×C₄	—	404	1	no	—
595	C₂×C₄	—	404	1	no	—
596	C₂×C₄	—	404	1	no	—
597	C₂×C₄	—	202	4	no	—
598	C₂×C₄	—	202	4	no	—
599	C₂×C₄	—	202	2	no	—
600	C₂×C₄	—	202	4	no	—
601	C₂×C₄	—	202	4	no	—
602	C₂×C₄	—	202	2	no	—
603	C₂×C₄	—	202	4	no	—
604	C₂×C₄	—	202	2	no	—
605	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
607	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
610	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
612	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	202	2	no	—
622	C₂²	—	202	1	no	—
623	C₂²	—	202	2	no	—
624	C₂²	—	202	1	no	—
625	C₂²	—	202	1	no	—
626	C₂²	—	202	2	no	—
627	C₂²	#41×D₁₀₁	1	2	yes	—
628	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	101	2	no	—
637	C₄	—	101	2	no	—
638	C₄	—	101	4	no	—
639	C₄	—	202	1	no	—
640	C₄	—	202	2	no	—
641	C₄	—	202	1	no	—
642	C₄	—	202	2	no	—
643	C₄	—	202	1	no	—
644	C₄	—	202	1	no	—
645	C₄	—	202	1	no	—
646	C₄	#41×D₁₀₁	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	4	2	no	—
650	C₂	—	404	2	no	—
651	C₂	—	404	1	no	—
652	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
653	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
654	C₂	#20266012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#553×C₁₀₁	C₂
hypercenter	#553	D₁₀₁
hypocenter	C₁₀₁	#3480
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #20265911	C₂	semidirect
2. #20265910	C₂	semidirect
3. #20265904	C₂	semidirect
4. #20265895	C₂	semidirect
5. #20265894	C₂	semidirect
6. #20265876	C₂	semidirect
7. #20265875	C₂	semidirect
8. #20265870	C₂	semidirect
9. #20265845	C₂	semidirect
10. #20265836	C₂	semidirect
11. #20265833	C₂	semidirect
12. #20265722	C₂	semidirect
13. #20265722	C₂	semidirect
14. #20265712	C₂	semidirect
15. #20265710	C₂	semidirect
16. #20265708	C₂	semidirect
17. #20265704	C₂	semidirect
18. #20265645	C₂	semidirect
19. C₄×#13108073	C₂	semidirect
20. C₄×#13108073	C₂	semidirect
21. C₄×#13108073	C₂	semidirect
22. C₂×#15692220	C₂	semidirect
23. #553×C₁₀₁	C₂	semidirect
261. C₂×Dic₁₀₁	#41	semidirect
284. Dic₂₀₂	#41	semidirect
328. C₁₀₁	#3480	semidirect
337. #553	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265911	2
#20265910	2
#20265904	2
#20265895	2
#20265894	2
#20265876	2
#20265875	2
#20265870	2
#20265845	2
#20265836	2
#20265833	2
#20265722	2
#20265712	2
#20265710	2
#20265708	2
#20265704	2
#20265645	2
C₄×#13108073	2
C₂×#15692220	2
#553×C₁₀₁	2
#3480	101