Subgroups — #27185311

Order 12928.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265923	C₂	1	2	yes	maximal, complemented
2	#20265915	C₂	1	2	yes	maximal, complemented
3	#20265870	C₂	1	2	yes	maximal, complemented
4	#20265854	C₂	1	2	yes	maximal, complemented
5	#20265816	C₂	1	2	yes	maximal, complemented
6	#20265815	C₂	1	2	yes	maximal, complemented
7	#20265815	C₂	1	2	yes	maximal, complemented
8	#20265811	C₂	1	2	yes	maximal, complemented
9	#20265777	C₂	1	2	yes	maximal, complemented
10	#20265774	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265773	C₂	1	2	yes	maximal, complemented
12	#20265767	C₂	1	2	yes	maximal, complemented
13	#20265764	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265735	C₂	1	2	yes	maximal, complemented
15	#20265735	C₂	1	1	yes	maximal, characteristic, complemented
16	#20265687	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#15692240	C₂	1	1	yes	maximal, characteristic, complemented
18	#121×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#537×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₁₀₁	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₀₁	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₀₁	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	#15692251	C₂²	1	2	yes	complemented
28	#15692250	C₂²	1	2	yes	complemented
29	#15692250	C₂²	1	2	yes	complemented
30	#15692250	C₂²	1	2	yes	complemented
31	#15692248	C₂²	1	2	yes	complemented
32	#15692245	C₂²	1	2	yes	complemented
33	#15692245	C₂²	1	2	yes	complemented
34	#15692244	C₂²	1	2	yes	complemented
35	#15692244	C₂²	1	2	yes	complemented
36	#15692241	C₂²	1	2	yes	complemented
37	#15692240	C₂²	1	2	yes	complemented
38	#15692240	C₂²	1	2	yes	complemented
39	#15692240	C₂²	1	2	yes	complemented
40	#15692240	C₂²	1	2	yes	complemented
41	#15692240	C₂²	1	2	yes	complemented
42	#15692240	C₂²	1	2	yes	complemented
43	#15692239	C₂²	1	2	yes	complemented
44	#15692238	C₂²	1	2	yes	complemented
45	#15692238	C₂²	1	2	yes	complemented
46	#15692238	C₂²	1	2	yes	complemented
47	#15692237	C₂²	1	2	yes	complemented
48	#15692237	C₂²	1	2	yes	complemented
49	#15692237	C₂²	1	2	yes	complemented
50	#15692236	C₂²	1	2	yes	complemented
51	#15692235	C₂²	1	1	yes	characteristic, complemented
52	#15692234	C₂²	1	1	yes	characteristic, complemented
53	#15692233	C₂²	1	2	yes	complemented
54	#15692231	C₂²	1	2	yes	complemented
55	#15692231	C₂²	1	2	yes	complemented
56	#15692230	C₂²	1	1	yes	characteristic, complemented
57	#15692230	C₂²	1	2	yes	complemented
58	#15692229	C₂²	1	1	yes	characteristic
59	#15692229	C₂²	1	2	yes	complemented
60	#15692229	C₂²	1	2	yes	complemented
61	#15692228	C₂²	1	2	yes	—
62	#15692228	C₂²	1	2	yes	complemented
63	#15692228	C₂²	1	2	yes	complemented
64	#15692227	C₂²	1	2	yes	complemented
65	#15692227	C₂²	1	2	yes	complemented
66	#15692227	C₂²	1	2	yes	complemented
67	#15692227	C₂²	1	2	yes	complemented
68	#15692227	C₂²	1	2	yes	complemented
69	#15692227	C₂²	1	2	yes	complemented
70	#15692226	C₂²	1	1	yes	characteristic, complemented
71	#15692226	C₂²	1	1	yes	characteristic, complemented
72	#15692225	C₂²	1	2	yes	—
73	#15692225	C₂²	1	2	yes	complemented
74	#15692225	C₂²	1	2	yes	complemented
75	#15692223	C₂²	1	2	yes	complemented
76	#15692223	C₂²	1	2	yes	complemented
77	#15692223	C₂²	1	2	yes	complemented
78	#15692223	C₂²	1	2	yes	complemented
79	#15692223	C₂²	1	2	yes	complemented
80	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
81	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
82	#15692217	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
86	#15692215	C₂²	1	2	yes	complemented
87	#15692215	C₂²	1	2	yes	complemented
88	#15692213	C₂²	1	1	yes	characteristic, complemented
89	#15692211	C₂²	1	2	yes	complemented
90	C₂×#13108053	C₂²	1	1	yes	characteristic, complemented
91	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
92	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
93	C₂×#13108051	C₂²	1	2	yes	complemented
94	C₂×#13108051	C₂²	1	2	yes	complemented
95	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
96	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
98	C₂×#41×C₁₀₁	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
101	#121×C₁₀₁	C₂²	1	2	yes	complemented
102	#121×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
103	#121×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
104	#121×C₁₀₁	C₂²	1	2	yes	complemented
105	#121×C₁₀₁	C₂²	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
108	C₂³×D₁₀₁	C₂³	1	2	yes	—
109	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
110	C₂³×D₁₀₁	C₂³	1	2	yes	—
111	#13108073	—	4	2	no	—
112	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
113	C₂×D₄₀₄	—	4	2	no	—
114	C₂×D₄₀₄	C₂³	1	2	yes	—
115	C₂×D₄₀₄	C₂³	1	2	yes	—
116	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
117	C₂×D₄₀₄	C₂³	1	2	yes	—
118	C₂×D₄₀₄	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
128	D₄×D₁₀₁	—	4	2	no	—
129	D₄×D₁₀₁	—	4	4	no	—
130	D₄×D₁₀₁	—	4	4	no	—
131	D₄×D₁₀₁	—	4	4	no	—
132	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
134	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
136	C₂×C₄×D₁₀₁	—	4	2	no	—
137	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
142	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
144	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
147	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
148	#13108053	C₂³	1	2	yes	—
149	#13108053	C₂³	1	2	yes	—
150	#13108053	C₂³	1	2	yes	—
151	#13108053	C₂³	1	2	yes	—
152	#13108053	C₂³	1	2	yes	—
153	#13108053	C₂³	1	2	yes	—
154	#13108053	C₂³	1	2	yes	—
155	#13108053	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
161	#13108051	C₂³	1	2	yes	—
162	#13108051	C₂³	1	2	yes	—
163	#13108051	C₂³	1	2	yes	—
164	#13108051	C₂³	1	2	yes	—
165	#13108051	C₂³	1	2	yes	—
166	#13108051	C₂³	1	2	yes	—
167	#13108051	C₂³	1	2	yes	—
168	#13108051	C₂³	1	2	yes	—
169	#13108051	C₂³	1	2	yes	—
170	#13108051	C₂³	1	2	yes	—
171	#13108051	C₂³	1	2	yes	—
172	#13108051	C₂³	1	2	yes	—
173	#13108051	C₂³	1	2	yes	—
174	#13108051	C₂³	1	2	yes	—
175	#13108051	C₂³	1	2	yes	—
176	#13108051	C₂³	1	2	yes	—
177	C₄×Dic₁₀₁	C₂³	1	2	yes	—
178	C₄×Dic₁₀₁	C₂³	1	2	yes	—
179	C₄×Dic₁₀₁	C₂³	1	2	yes	—
180	#41×C₁₀₁	—	4	4	no	—
181	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
182	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
183	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
184	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
185	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
186	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
187	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
188	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
192	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
194	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
195	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
196	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
197	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
202	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
203	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
204	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
205	C₂²×D₁₀₁	—	2	2	no	—
206	C₂²×D₁₀₁	—	2	2	no	—
207	C₂²×D₁₀₁	—	2	2	no	—
208	C₂²×D₁₀₁	—	2	4	no	—
209	C₂²×D₁₀₁	—	4	1	no	—
210	C₂²×D₁₀₁	—	4	2	no	—
211	C₂²×D₁₀₁	—	4	2	no	—
212	C₂²×D₁₀₁	—	4	2	no	—
213	C₂²×D₁₀₁	—	4	1	no	—
214	C₂²×D₁₀₁	—	4	2	no	—
215	C₂²×D₁₀₁	—	4	1	no	—
216	C₂²×D₁₀₁	—	4	2	no	—
217	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
218	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
219	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
220	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
221	Q₈×C₁₀₁	—	4	2	no	—
222	D₄×C₁₀₁	—	2	4	no	—
223	D₄×C₁₀₁	—	2	4	no	—
224	D₄×C₁₀₁	—	4	2	no	—
225	D₄×C₁₀₁	—	4	1	no	—
226	D₄×C₁₀₁	—	4	2	no	—
227	D₄×C₁₀₁	—	4	1	no	—
228	C₂×C₄×C₁₀₁	—	2	2	no	—
229	C₂×C₄×C₁₀₁	—	4	2	no	—
230	C₂×C₄×C₁₀₁	—	4	2	no	—
231	C₂×C₄×C₁₀₁	—	4	1	no	—
232	C₂×C₄×C₁₀₁	—	4	1	no	—
233	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
234	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
237	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
239	C₂²⋊D₁₀₁	—	2	4	no	—
240	C₂²⋊D₁₀₁	—	2	4	no	—
241	C₂²⋊D₁₀₁	—	4	2	no	—
242	C₂²⋊D₁₀₁	—	4	2	no	—
243	C₂²⋊D₁₀₁	—	4	2	no	—
244	C₂²⋊D₁₀₁	—	4	2	no	—
245	C₂²⋊D₁₀₁	—	4	2	no	—
246	C₂²⋊D₁₀₁	—	4	2	no	—
247	C₂²⋊D₁₀₁	—	4	2	no	—
248	C₂×Dic₁₀₁	—	4	1	no	—
249	C₂×Dic₁₀₁	—	4	1	no	—
250	C₂×Dic₁₀₁	—	4	2	no	—
251	C₂×Dic₁₀₁	—	4	2	no	—
252	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
253	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
255	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
256	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
257	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
258	D₄₀₄	—	2	4	no	—
259	D₄₀₄	—	4	1	no	—
260	D₄₀₄	—	4	2	no	—
261	D₄₀₄	—	4	2	no	—
262	D₄₀₄	—	4	2	no	—
263	C₄×D₁₀₁	—	2	2	no	—
264	C₄×D₁₀₁	—	2	2	no	—
265	C₄×D₁₀₁	—	4	1	no	—
266	C₄×D₁₀₁	—	4	1	no	—
267	C₄×D₁₀₁	—	4	2	no	—
268	C₄×D₁₀₁	—	4	2	no	—
269	C₄×D₁₀₁	—	4	2	no	—
270	Dic₂₀₂	—	4	1	no	—
271	C₂²×C₁₀₁	—	2	1	no	—
272	C₂²×C₁₀₁	—	2	1	no	—
273	C₂²×C₁₀₁	—	2	2	no	—
274	C₂²×C₁₀₁	—	2	2	no	—
275	C₂²×C₁₀₁	—	2	2	no	—
276	C₂²×C₁₀₁	—	2	2	no	—
277	C₂²×C₁₀₁	—	2	2	no	—
278	C₂²×C₁₀₁	—	2	2	no	—
279	C₂²×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
280	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
281	C₂×D₁₀₁	—	2	1	no	—
282	C₂×D₁₀₁	—	2	1	no	—
283	C₂×D₁₀₁	—	2	1	no	—
284	C₂×D₁₀₁	—	2	2	no	—
285	C₂×D₁₀₁	—	2	2	no	—
286	C₂×D₁₀₁	—	2	2	no	—
287	C₂×D₁₀₁	—	2	2	no	—
288	C₂×D₁₀₁	—	2	1	no	—
289	C₂×D₁₀₁	—	2	1	no	—
290	C₂×D₁₀₁	—	2	2	no	—
291	C₂×D₁₀₁	—	2	2	no	—
292	C₂×D₁₀₁	—	4	4	no	—
293	C₂×D₁₀₁	—	8	4	no	—
294	C₂×D₁₀₁	—	8	2	no	—
295	C₂×D₁₀₁	—	8	4	no	—
296	C₂×D₁₀₁	H(5,𝔽₂)	1	2	yes	—
297	C₄×C₁₀₁	—	2	1	no	—
298	C₄×C₁₀₁	—	2	1	no	—
299	C₄×C₁₀₁	—	2	2	no	—
300	C₄×C₁₀₁	—	2	2	no	—
301	C₄×C₁₀₁	—	2	2	no	—
302	C₄×C₁₀₁	—	2	2	no	—
303	Dic₁₀₁	—	2	2	no	—
304	Dic₁₀₁	—	2	1	no	—
305	Dic₁₀₁	—	2	1	no	—
306	Dic₁₀₁	—	2	2	no	—
307	Dic₁₀₁	—	2	2	no	—
308	Dic₁₀₁	—	2	2	no	—
309	C₂×C₁₀₁	—	2	2	no	—
310	C₂×C₁₀₁	—	4	2	no	—
311	C₂×C₁₀₁	—	4	2	no	—
312	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₁₀₁	#585	1	1	yes	characteristic
315	D₁₀₁	—	2	2	no	—
316	D₁₀₁	—	4	1	no	—
317	D₁₀₁	—	4	2	no	—
318	D₁₀₁	—	4	2	no	—
319	#3534	—	101	1	no	maximal, Sylow
320	C₁₀₁	#3534	1	1	yes	characteristic, complemented, Sylow
321	#562	—	101	2	no	—
322	#560	—	101	2	no	—
323	#553	—	101	2	no	—
324	#551	—	101	2	no	—
325	#546	—	101	2	no	—
326	#546	—	101	2	no	—
327	#546	—	101	2	no	—
328	D₄²	—	101	2	no	—
329	#540	—	101	2	no	—
330	#539	—	101	2	no	—
331	#539	—	101	1	no	—
332	#538	—	101	2	no	—
333	#538	—	101	1	no	—
334	#537	D₁₀₁	1	1	yes	characteristic, complemented
335	#534	—	101	1	no	—
336	#534	—	101	2	no	—
337	#525	—	101	1	no	—
338	C₂×#123	—	101	1	no	—
339	C₂×#121	—	101	1	no	—
340	C₂×#41	—	101	1	no	—
341	C₂×#41	C₂×D₁₀₁	1	2	yes	complemented
342	C₂²×D₄	—	101	1	no	—
343	C₂²×D₄	—	101	2	no	—
344	C₂²×D₄	—	101	2	no	—
345	C₂²×D₄	—	101	2	no	—
346	C₂²×D₄	—	101	1	no	—
347	C₂³×C₄	—	101	1	no	—
348	#127	—	101	2	no	—
349	#126	—	101	2	no	—
350	#126	—	101	2	no	—
351	#126	—	101	2	no	—
352	#126	—	101	2	no	—
353	#125	—	101	2	no	—
354	#125	—	101	2	no	—
355	#124	—	101	2	no	—
356	#124	—	101	2	no	—
357	#124	—	101	2	no	—
358	#123	—	101	2	no	—
359	#123	—	101	2	no	—
360	#123	—	101	2	no	—
361	#123	—	101	2	no	—
362	#123	—	101	2	no	—
363	#123	—	101	2	no	—
364	#123	—	101	2	no	—
365	#123	—	101	2	no	—
366	#123	—	101	2	no	—
367	#123	—	101	2	no	—
368	#123	—	101	2	no	—
369	#123	—	101	2	no	—
370	#123	—	101	2	no	—
371	#123	—	101	2	no	—
372	C₂²⋊Q₈	—	101	2	no	—
373	C₂²⋊Q₈	—	101	2	no	—
374	C₂²⋊Q₈	—	101	1	no	—
375	C₂²⋊Q₈	—	101	1	no	—
376	C₂²⋊Q₈	—	101	2	no	—
377	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
378	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
379	#121	—	101	1	no	—
380	#121	—	101	2	no	—
381	#121	—	101	1	no	—
382	#121	—	101	2	no	—
383	#121	—	101	2	no	—
384	#121	—	101	2	no	—
385	#121	—	101	2	no	—
386	#121	—	101	2	no	—
387	#121	—	101	1	no	—
388	#121	—	101	2	no	—
389	#121	—	101	2	no	—
390	#121	—	101	1	no	—
391	#121	—	101	2	no	—
392	#121	—	101	2	no	—
393	#121	—	101	2	no	—
394	#121	—	101	2	no	—
395	#121	C₂×D₁₀₁	1	1	yes	characteristic, complemented
396	#121	C₂×D₁₀₁	1	1	yes	characteristic, complemented
397	#121	C₂×D₁₀₁	1	2	yes	complemented
398	#121	C₂×D₁₀₁	1	2	yes	complemented
399	#121	C₂×D₁₀₁	1	2	yes	complemented
400	#120	—	101	2	no	—
401	#120	—	101	2	no	—
402	#120	—	101	2	no	—
403	#120	—	101	2	no	—
404	#120	—	101	2	no	—
405	#120	—	101	2	no	—
406	#120	—	101	2	no	—
407	#120	—	101	2	no	—
408	C₄×D₄	—	101	2	no	—
409	C₄×D₄	—	101	2	no	—
410	C₄×D₄	—	101	2	no	—
411	C₄×D₄	—	101	2	no	—
412	C₄×D₄	—	101	2	no	—
413	C₄×D₄	—	101	2	no	—
414	C₄×D₄	—	101	2	no	—
415	C₄×D₄	—	101	2	no	—
416	#117	—	101	1	no	—
417	#117	—	101	2	no	—
418	C₂×C₄⋊C₄	—	101	1	no	—
419	C₂×C₄⋊C₄	—	101	1	no	—
420	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	101	1	no	—
422	C₂×C₂²⋊C₄	—	101	1	no	—
423	C₂×C₂²⋊C₄	—	101	1	no	—
424	C₂×C₂²⋊C₄	—	101	2	no	—
425	C₂×C₂²⋊C₄	—	101	2	no	—
426	C₂×C₂²⋊C₄	—	101	2	no	—
427	C₂⁴	—	101	2	no	—
428	C₂⁴	—	101	2	no	—
429	C₂⁴	—	101	1	no	—
430	C₂⁴	—	101	1	no	—
431	#41	—	4	4	no	—
432	#41	—	404	2	no	—
433	C₂×Q₈	—	101	1	no	—
434	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
435	C₂×D₄	—	101	2	no	—
436	C₂×D₄	—	101	2	no	—
437	C₂×D₄	—	101	2	no	—
438	C₂×D₄	—	101	2	no	—
439	C₂×D₄	—	101	2	no	—
440	C₂×D₄	—	101	2	no	—
441	C₂×D₄	—	101	2	no	—
442	C₂×D₄	—	101	2	no	—
443	C₂×D₄	—	101	2	no	—
444	C₂×D₄	—	101	1	no	—
445	C₂×D₄	—	101	2	no	—
446	C₂×D₄	—	101	2	no	—
447	C₂×D₄	—	101	2	no	—
448	C₂×D₄	—	101	2	no	—
449	C₂×D₄	—	404	2	no	—
450	C₂×D₄	—	404	4	no	—
451	C₂×D₄	—	404	4	no	—
452	C₂×D₄	—	404	4	no	—
453	C₂×D₄	—	404	2	no	—
454	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
455	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
456	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
457	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
458	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
459	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
460	C₂²×C₄	—	101	1	no	—
461	C₂²×C₄	—	101	1	no	—
462	C₂²×C₄	—	101	2	no	—
463	C₂²×C₄	—	101	2	no	—
464	C₂²×C₄	—	101	2	no	—
465	C₂²×C₄	—	101	1	no	—
466	C₂²×C₄	—	101	2	no	—
467	C₂²×C₄	—	101	2	no	—
468	C₂²×C₄	—	101	1	no	—
469	C₂²×C₄	—	101	1	no	—
470	C₂²×C₄	—	101	1	no	—
471	C₂²×C₄	—	404	2	no	—
472	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
477	C₄⋊C₄	—	101	2	no	—
478	C₄⋊C₄	—	101	2	no	—
479	C₄⋊C₄	—	101	2	no	—
480	C₄⋊C₄	—	101	2	no	—
481	C₄⋊C₄	—	101	2	no	—
482	C₄⋊C₄	—	101	2	no	—
483	C₄⋊C₄	—	101	2	no	—
484	C₄⋊C₄	—	101	2	no	—
485	C₄⋊C₄	—	101	1	no	—
486	C₄⋊C₄	—	101	1	no	—
487	C₄⋊C₄	—	101	2	no	—
488	C₄⋊C₄	—	101	2	no	—
489	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
494	C₂²⋊C₄	—	101	2	no	—
495	C₂²⋊C₄	—	101	2	no	—
496	C₂²⋊C₄	—	101	2	no	—
497	C₂²⋊C₄	—	101	2	no	—
498	C₂²⋊C₄	—	101	2	no	—
499	C₂²⋊C₄	—	101	2	no	—
500	C₂²⋊C₄	—	101	2	no	—
501	C₂²⋊C₄	—	101	2	no	—
502	C₂²⋊C₄	—	101	2	no	—
503	C₂²⋊C₄	—	101	2	no	—
504	C₂²⋊C₄	—	101	2	no	—
505	C₂²⋊C₄	—	101	2	no	—
506	C₂²⋊C₄	—	101	2	no	—
507	C₂²⋊C₄	—	101	2	no	—
508	C₂²⋊C₄	—	101	2	no	—
509	C₂²⋊C₄	—	101	2	no	—
510	C₂²⋊C₄	—	101	2	no	—
511	C₂²⋊C₄	—	101	2	no	—
512	C₂²⋊C₄	—	101	2	no	—
513	C₂²⋊C₄	—	101	2	no	—
514	C₂²⋊C₄	—	101	2	no	—
515	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
519	C₄²	—	101	2	no	—
520	C₄²	—	101	2	no	—
521	C₄²	—	101	2	no	—
522	C₂³	—	101	1	no	—
523	C₂³	—	101	2	no	—
524	C₂³	—	101	2	no	—
525	C₂³	—	101	1	no	—
526	C₂³	—	404	1	no	—
527	C₂³	—	404	2	no	—
528	C₂³	—	404	2	no	—
529	C₂³	—	404	2	no	—
530	C₂³	—	404	1	no	—
531	C₂³	—	404	2	no	—
532	C₂³	—	404	2	no	—
533	C₂³	—	404	1	no	—
534	C₂³	—	202	4	no	—
535	C₂³	—	202	2	no	—
536	C₂³	—	202	2	no	—
537	C₂³	—	202	2	no	—
538	C₂³	C₂³×D₁₀₁	1	2	yes	—
539	C₂³	C₂³×D₁₀₁	1	2	yes	—
540	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
541	Q₈	—	4	2	no	—
542	Q₈	—	404	1	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	4	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	404	1	no	—
550	D₄	—	404	2	no	—
551	D₄	—	404	2	no	—
552	D₄	—	404	2	no	—
553	D₄	—	404	2	no	—
554	D₄	—	404	2	no	—
555	D₄	—	404	2	no	—
556	D₄	—	404	2	no	—
557	D₄	—	404	2	no	—
558	D₄	—	404	2	no	—
559	D₄	—	404	2	no	—
560	D₄	—	202	4	no	—
561	D₄	—	202	4	no	—
562	D₄	—	202	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	101	2	no	—
569	C₂×C₄	—	101	1	no	—
570	C₂×C₄	—	101	2	no	—
571	C₂×C₄	—	101	2	no	—
572	C₂×C₄	—	101	2	no	—
573	C₂×C₄	—	101	1	no	—
574	C₂×C₄	—	404	1	no	—
575	C₂×C₄	—	404	1	no	—
576	C₂×C₄	—	404	2	no	—
577	C₂×C₄	—	404	2	no	—
578	C₂×C₄	—	404	2	no	—
579	C₂×C₄	—	404	1	no	—
580	C₂×C₄	—	404	2	no	—
581	C₂×C₄	—	404	1	no	—
582	C₂×C₄	—	404	2	no	—
583	C₂×C₄	—	202	2	no	—
584	C₂×C₄	—	202	2	no	—
585	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
586	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
587	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
588	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
589	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	808	2	no	—
600	C₂²	—	808	4	no	—
601	C₂²	—	808	4	no	—
602	C₂²	—	101	2	no	—
603	C₂²	—	404	4	no	—
604	C₂²	—	202	1	no	—
605	C₂²	—	202	2	no	—
606	C₂²	—	202	2	no	—
607	C₂²	—	202	2	no	—
608	C₂²	—	202	1	no	—
609	C₂²	—	202	2	no	—
610	C₂²	—	202	1	no	—
611	C₂²	—	202	2	no	—
612	C₂²	—	202	2	no	—
613	C₂²	—	202	1	no	—
614	C₂²	—	202	1	no	—
615	C₂²	#15692300	1	2	yes	—
616	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	202	1	no	—
624	C₄	—	202	1	no	—
625	C₄	—	202	2	no	—
626	C₄	—	202	2	no	—
627	C₄	—	202	2	no	—
628	C₄	—	202	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	4	2	no	—
631	C₂	—	4	2	no	—
632	C₂	—	404	2	no	—
633	C₂	—	404	2	no	—
634	C₂	—	404	1	no	—
635	C₂	—	202	2	no	—
636	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
637	C₂	C₂×#15692300	1	1	yes	characteristic
638	C₂	#20266014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#537×C₁₀₁	C₂
hypercenter	#537	D₁₀₁
hypocenter	C₁₀₁	#3534
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #20265923	C₂	semidirect
2. #20265915	C₂	semidirect
3. #20265870	C₂	semidirect
4. #20265854	C₂	semidirect
5. #20265816	C₂	semidirect
6. #20265815	C₂	semidirect
7. #20265815	C₂	semidirect
8. #20265811	C₂	semidirect
9. #20265777	C₂	semidirect
10. #20265774	C₂	semidirect
11. #20265773	C₂	semidirect
12. #20265767	C₂	semidirect
13. #20265764	C₂	semidirect
14. #20265735	C₂	semidirect
15. #20265735	C₂	semidirect
16. #20265687	C₂	semidirect
17. C₂×#15692240	C₂	semidirect
18. #121×D₁₀₁	C₂	semidirect
19. #537×C₁₀₁	C₂	semidirect
20. C₂×#13108073	C₂²	semidirect
22. C₂×D₄×D₁₀₁	C₂²	semidirect
23. C₂×D₄×D₁₀₁	C₂²	semidirect
24. C₂×D₄×D₁₀₁	C₂²	semidirect
25. C₂×D₄×D₁₀₁	C₂²	semidirect
26. C₂²×C₄×D₁₀₁	C₂²	semidirect
27. #15692251	C₂²	semidirect
28. #15692250	C₂²	semidirect
29. #15692250	C₂²	semidirect
30. #15692250	C₂²	semidirect
31. #15692248	C₂²	semidirect
32. #15692245	C₂²	semidirect
33. #15692245	C₂²	semidirect
34. #15692244	C₂²	semidirect
35. #15692244	C₂²	semidirect
36. #15692241	C₂²	semidirect
37. #15692240	C₂²	semidirect
38. #15692240	C₂²	semidirect
39. #15692240	C₂²	semidirect
40. #15692240	C₂²	semidirect
41. #15692240	C₂²	semidirect
42. #15692240	C₂²	semidirect
43. #15692239	C₂²	semidirect
44. #15692238	C₂²	semidirect
45. #15692238	C₂²	semidirect
46. #15692238	C₂²	semidirect
47. #15692237	C₂²	semidirect
48. #15692237	C₂²	semidirect
49. #15692237	C₂²	semidirect
50. #15692236	C₂²	semidirect
51. #15692235	C₂²	semidirect
52. #15692234	C₂²	semidirect
53. #15692233	C₂²	semidirect
54. #15692231	C₂²	semidirect
55. #15692231	C₂²	semidirect
56. #15692230	C₂²	semidirect
57. #15692230	C₂²	semidirect
59. #15692229	C₂²	semidirect
60. #15692229	C₂²	semidirect
62. #15692228	C₂²	semidirect
63. #15692228	C₂²	semidirect
64. #15692227	C₂²	semidirect
65. #15692227	C₂²	semidirect
66. #15692227	C₂²	semidirect
67. #15692227	C₂²	semidirect
68. #15692227	C₂²	semidirect
69. #15692227	C₂²	semidirect
70. #15692226	C₂²	semidirect
71. #15692226	C₂²	semidirect
73. #15692225	C₂²	semidirect
74. #15692225	C₂²	semidirect
75. #15692223	C₂²	semidirect
76. #15692223	C₂²	semidirect
77. #15692223	C₂²	semidirect
78. #15692223	C₂²	semidirect
79. #15692223	C₂²	semidirect
80. D₄×Dic₁₀₁	C₂²	semidirect
81. D₄×Dic₁₀₁	C₂²	semidirect
82. #15692217	C₂²	semidirect
83. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
84. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
85. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
86. #15692215	C₂²	semidirect
87. #15692215	C₂²	semidirect
88. #15692213	C₂²	semidirect
89. #15692211	C₂²	semidirect
90. C₂×#13108053	C₂²	semidirect
91. C₄⋊C₄×D₁₀₁	C₂²	semidirect
92. C₂×#13108051	C₂²	semidirect
93. C₂×#13108051	C₂²	semidirect
94. C₂×#13108051	C₂²	semidirect
95. C₂×#13108051	C₂²	semidirect
96. C₂×#13108051	C₂²	semidirect
97. C₂²⋊C₄×D₁₀₁	C₂²	semidirect
98. C₂×#41×C₁₀₁	C₂²	semidirect
99. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
100. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
101. #121×C₁₀₁	C₂²	semidirect
102. #121×C₁₀₁	C₂²	semidirect
103. #121×C₁₀₁	C₂²	semidirect
104. #121×C₁₀₁	C₂²	semidirect
105. #121×C₁₀₁	C₂²	semidirect
106. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
320. C₁₀₁	#3534	semidirect
334. #537	D₁₀₁	semidirect
341. C₂×#41	C₂×D₁₀₁	semidirect
377. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
378. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
395. #121	C₂×D₁₀₁	semidirect
396. #121	C₂×D₁₀₁	semidirect
397. #121	C₂×D₁₀₁	semidirect
398. #121	C₂×D₁₀₁	semidirect
399. #121	C₂×D₁₀₁	semidirect
420. C₂×C₄⋊C₄	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265923	2
#20265915	2
#20265870	2
#20265854	2
#20265816	2
#20265815	2
#20265811	2
#20265777	2
#20265774	2
#20265773	2
#20265767	2
#20265764	2
#20265735	2
#20265687	2
C₂×#15692240	2
#121×D₁₀₁	2
#537×C₁₀₁	2
#3534	101