Subgroups — #27184540

Order 12928.

1160 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265802	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265775	C₂	1	2	yes	maximal, complemented
3	#20265774	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265773	C₂	1	2	yes	maximal, complemented
5	#20265766	C₂	1	2	yes	maximal, complemented
6	#20265763	C₂	1	2	yes	maximal, complemented
7	#20265760	C₂	1	2	yes	maximal, complemented
8	#20265738	C₂	1	2	yes	maximal, complemented
9	#20265735	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265712	C₂	1	2	yes	maximal, complemented
11	#20265710	C₂	1	2	yes	maximal, complemented
12	#20265704	C₂	1	2	yes	maximal, complemented
13	#20265690	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265690	C₂	1	2	yes	maximal, complemented
15	#20265687	C₂	1	1	yes	maximal, characteristic, complemented
16	#20265685	C₂	1	2	yes	maximal, complemented
17	C₂×#15692217	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₁₀₁	C₂	1	2	yes	maximal, complemented
19	#539×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13108075	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
24	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	#15692250	C₂²	1	2	yes	complemented
28	#15692250	C₂²	1	2	yes	complemented
29	#15692250	C₂²	1	2	yes	complemented
30	#15692249	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	#15692243	C₂²	1	2	yes	complemented
35	#15692241	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	#15692238	C₂²	1	2	yes	complemented
44	#15692238	C₂²	1	2	yes	complemented
45	#15692237	C₂²	1	2	yes	complemented
46	#15692237	C₂²	1	2	yes	complemented
47	#15692235	C₂²	1	2	yes	complemented
48	#15692235	C₂²	1	1	yes	characteristic, complemented
49	#15692234	C₂²	1	1	yes	characteristic, complemented
50	#15692233	C₂²	1	2	yes	complemented
51	#15692233	C₂²	1	2	yes	complemented
52	#15692233	C₂²	1	2	yes	complemented
53	#15692232	C₂²	1	2	yes	complemented
54	#15692231	C₂²	1	1	yes	characteristic, complemented
55	#15692231	C₂²	1	2	yes	complemented
56	#15692230	C₂²	1	2	yes	—
57	#15692230	C₂²	1	2	yes	—
58	#15692230	C₂²	1	1	yes	characteristic, complemented
59	#15692229	C₂²	1	1	yes	characteristic
60	#15692229	C₂²	1	2	yes	complemented
61	#15692228	C₂²	1	2	yes	—
62	#15692228	C₂²	1	2	yes	—
63	#15692228	C₂²	1	2	yes	complemented
64	#15692227	C₂²	1	2	yes	—
65	#15692226	C₂²	1	1	yes	characteristic, complemented
66	#15692225	C₂²	1	2	yes	complemented
67	#15692225	C₂²	1	2	yes	complemented
68	#15692225	C₂²	1	2	yes	complemented
69	#15692225	C₂²	1	2	yes	complemented
70	#15692223	C₂²	1	2	yes	complemented
71	#15692223	C₂²	1	2	yes	complemented
72	#15692220	C₂²	1	2	yes	complemented
73	C₄×D₄₀₄	C₂²	1	2	yes	complemented
74	D₄×Dic₁₀₁	C₂²	1	2	yes	complemented
75	#15692217	C₂²	1	2	yes	complemented
76	#15692217	C₂²	1	2	yes	complemented
77	#15692217	C₂²	1	2	yes	complemented
78	#15692217	C₂²	1	2	yes	complemented
79	#15692217	C₂²	1	2	yes	complemented
80	#15692217	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
83	#15692215	C₂²	1	2	yes	complemented
84	#15692215	C₂²	1	2	yes	complemented
85	#15692215	C₂²	1	2	yes	complemented
86	#15692215	C₂²	1	2	yes	complemented
87	#15692213	C₂²	1	1	yes	characteristic, complemented
88	#15692213	C₂²	1	2	yes	complemented
89	#15692213	C₂²	1	1	yes	characteristic, complemented
90	#15692211	C₂²	1	2	yes	complemented
91	C₄⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
92	C₂×#13108051	C₂²	1	1	yes	characteristic
93	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
94	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
97	C₄²×D₁₀₁	C₂²	1	2	yes	complemented
98	#126×C₁₀₁	C₂²	1	2	yes	complemented
99	#125×C₁₀₁	C₂²	1	2	yes	complemented
100	#123×C₁₀₁	C₂²	1	2	yes	complemented
101	#123×C₁₀₁	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
104	#121×C₁₀₁	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₀₁	C₂³	1	2	yes	—
108	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
109	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
110	#13108075	—	4	2	no	—
111	#13108073	—	4	2	no	—
112	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
113	C₂×Dic₂₀₂	C₂³	1	2	yes	—
114	C₂×D₄₀₄	—	2	4	no	—
115	C₂×D₄₀₄	C₂³	1	2	yes	—
116	C₂×D₄₀₄	C₂³	1	2	yes	—
117	C₂×D₄₀₄	C₂³	1	2	yes	—
118	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
119	C₂×D₄₀₄	C₂³	1	2	yes	—
120	C₂×D₄₀₄	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	D₄×D₁₀₁	—	2	8	no	—
127	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
128	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
129	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₁₀₁	—	4	2	no	—
131	C₂×C₄×D₁₀₁	—	4	4	no	—
132	C₂×C₄×D₁₀₁	—	4	2	no	—
133	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
134	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
136	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
138	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
139	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
141	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
144	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
145	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
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	#13108051	C₂³	1	2	yes	—
160	#13108051	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	C₄×Dic₁₀₁	C₂³	1	2	yes	—
176	C₄×Dic₁₀₁	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	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
182	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
192	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
194	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
200	C₄²×C₁₀₁	C₂³	1	2	yes	—
201	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
202	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
203	C₂²×D₁₀₁	—	2	2	no	—
204	C₂²×D₁₀₁	—	2	4	no	—
205	C₂²×D₁₀₁	—	4	1	no	—
206	C₂²×D₁₀₁	—	4	2	no	—
207	C₂²×D₁₀₁	—	4	1	no	—
208	C₂²×D₁₀₁	—	4	1	no	—
209	C₂²×D₁₀₁	—	4	2	no	—
210	C₂²×D₁₀₁	—	4	1	no	—
211	C₂²×D₁₀₁	#41	1	4	yes	complemented
212	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
213	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
214	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
215	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
216	Q₈×C₁₀₁	—	4	1	no	—
217	D₄×C₁₀₁	—	2	4	no	—
218	D₄×C₁₀₁	—	4	1	no	—
219	C₂×C₄×C₁₀₁	—	2	2	no	—
220	C₂×C₄×C₁₀₁	—	4	1	no	—
221	C₂×C₄×C₁₀₁	—	4	1	no	—
222	C₂×C₄×C₁₀₁	—	4	2	no	—
223	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
224	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
225	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
226	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
227	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
228	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
230	C₂²⋊D₁₀₁	—	2	4	no	—
231	C₂²⋊D₁₀₁	—	2	4	no	—
232	C₂²⋊D₁₀₁	—	4	2	no	—
233	C₂²⋊D₁₀₁	—	4	2	no	—
234	C₂²⋊D₁₀₁	—	4	2	no	—
235	C₂×Dic₁₀₁	—	2	2	no	—
236	C₂×Dic₁₀₁	—	2	4	no	—
237	C₂×Dic₁₀₁	—	4	1	no	—
238	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
239	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
240	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
241	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
243	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
244	D₄₀₄	—	2	4	no	—
245	D₄₀₄	—	2	4	no	—
246	D₄₀₄	—	2	4	no	—
247	D₄₀₄	—	4	2	no	—
248	D₄₀₄	—	4	1	no	—
249	D₄₀₄	—	4	2	no	—
250	C₄×D₁₀₁	—	2	4	no	—
251	C₄×D₁₀₁	—	2	4	no	—
252	C₄×D₁₀₁	—	2	2	no	—
253	C₄×D₁₀₁	—	2	4	no	—
254	C₄×D₁₀₁	—	2	2	no	—
255	C₄×D₁₀₁	—	4	2	no	—
256	C₄×D₁₀₁	—	4	2	no	—
257	C₄×D₁₀₁	—	4	1	no	—
258	C₄×D₁₀₁	—	4	2	no	—
259	C₄×D₁₀₁	—	4	1	no	—
260	C₄×D₁₀₁	—	4	2	no	—
261	Dic₂₀₂	—	4	2	no	—
262	Dic₂₀₂	—	4	1	no	—
263	C₂²×C₁₀₁	—	2	1	no	—
264	C₂²×C₁₀₁	—	2	1	no	—
265	C₂²×C₁₀₁	—	2	2	no	—
266	C₂²×C₁₀₁	—	2	2	no	—
267	C₂²×C₁₀₁	—	2	2	no	—
268	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
269	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
270	C₂×D₁₀₁	—	2	2	no	—
271	C₂×D₁₀₁	—	2	2	no	—
272	C₂×D₁₀₁	—	2	1	no	—
273	C₂×D₁₀₁	—	2	1	no	—
274	C₂×D₁₀₁	—	2	2	no	—
275	C₂×D₁₀₁	—	2	1	no	—
276	C₂×D₁₀₁	—	2	2	no	—
277	C₂×D₁₀₁	—	2	1	no	—
278	C₂×D₁₀₁	—	2	1	no	—
279	C₂×D₁₀₁	—	2	2	no	—
280	C₂×D₁₀₁	—	2	1	no	—
281	C₂×D₁₀₁	—	4	4	no	—
282	C₂×D₁₀₁	—	4	8	no	—
283	C₂×D₁₀₁	—	4	4	no	—
284	C₂×D₁₀₁	C₂×#41	1	4	yes	—
285	C₄×C₁₀₁	—	2	2	no	—
286	C₄×C₁₀₁	—	2	2	no	—
287	C₄×C₁₀₁	—	2	1	no	—
288	C₄×C₁₀₁	—	2	2	no	—
289	C₄×C₁₀₁	—	2	2	no	—
290	C₄×C₁₀₁	—	2	1	no	—
291	C₄×C₁₀₁	—	2	2	no	—
292	Dic₁₀₁	—	2	2	no	—
293	Dic₁₀₁	—	2	2	no	—
294	Dic₁₀₁	—	2	1	no	—
295	Dic₁₀₁	—	2	2	no	—
296	Dic₁₀₁	—	2	2	no	—
297	Dic₁₀₁	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₁₀₁	—	2	2	no	—
299	C₂×C₁₀₁	—	4	2	no	—
300	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
301	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₁₀₁	#585	1	1	yes	characteristic
303	D₁₀₁	—	2	4	no	—
304	D₁₀₁	—	4	1	no	—
305	D₁₀₁	—	4	1	no	—
306	D₁₀₁	—	4	2	no	—
307	#3459	—	101	1	no	maximal, Sylow
308	C₁₀₁	#3459	1	1	yes	characteristic, complemented, Sylow
309	#543	—	101	1	no	—
310	#539	—	101	2	no	—
311	#539	—	101	2	no	—
312	#539	—	101	1	no	—
313	#539	D₁₀₁	1	1	yes	characteristic, complemented
314	#538	—	101	2	no	—
315	#538	—	101	2	no	—
316	#538	—	101	2	no	—
317	#534	—	101	2	no	—
318	#534	—	101	1	no	—
319	#529	—	101	2	no	—
320	#529	—	101	2	no	—
321	#529	—	101	2	no	—
322	#525	—	101	2	no	—
323	#525	—	101	2	no	—
324	#525	—	101	1	no	—
325	#525	—	101	1	no	—
326	C₂×C₄×D₄	—	101	2	no	—
327	C₂×C₄×D₄	—	101	1	no	—
328	C₂×#41	—	101	1	no	—
329	C₂×#41	—	101	1	no	—
330	C₂²×D₄	—	101	2	no	—
331	C₂²×D₄	—	101	1	no	—
332	C₂³×C₄	—	101	1	no	—
333	C₂³×C₄	—	101	1	no	—
334	C₂³×C₄	—	101	2	no	—
335	#126	—	101	2	no	—
336	#126	—	101	2	no	—
337	#126	—	101	2	no	—
338	#126	—	101	2	no	—
339	#126	—	101	2	no	—
340	#126	C₂×D₁₀₁	1	2	yes	complemented
341	#125	—	101	2	no	—
342	#125	—	101	2	no	—
343	#125	C₂×D₁₀₁	1	2	yes	complemented
344	#124	—	101	2	no	—
345	#124	—	101	2	no	—
346	#124	—	101	2	no	—
347	#123	—	101	2	no	—
348	#123	—	101	2	no	—
349	#123	—	101	2	no	—
350	#123	—	101	2	no	—
351	#123	—	101	2	no	—
352	#123	—	101	2	no	—
353	#123	—	101	2	no	—
354	#123	—	101	2	no	—
355	#123	—	101	2	no	—
356	#123	—	101	2	no	—
357	#123	C₂×D₁₀₁	1	2	yes	complemented
358	#123	C₂×D₁₀₁	1	2	yes	complemented
359	C₂²⋊Q₈	—	101	1	no	—
360	C₂²⋊Q₈	—	101	2	no	—
361	C₂²⋊Q₈	—	101	1	no	—
362	C₂²⋊Q₈	—	101	2	no	—
363	C₂²⋊Q₈	—	101	1	no	—
364	C₂²⋊Q₈	—	101	2	no	—
365	C₂²⋊Q₈	—	101	2	no	—
366	C₂²⋊Q₈	—	101	2	no	—
367	C₂²⋊Q₈	—	101	2	no	—
368	C₂²⋊Q₈	C₂×D₁₀₁	1	2	yes	complemented
369	C₂²⋊Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
370	#121	—	101	1	no	—
371	#121	—	101	2	no	—
372	#121	—	101	1	no	—
373	#121	—	101	2	no	—
374	#121	—	101	2	no	—
375	#121	—	101	1	no	—
376	#121	—	101	2	no	—
377	#121	—	101	2	no	—
378	#121	—	101	2	no	—
379	#121	—	101	2	no	—
380	#121	C₂×D₁₀₁	1	1	yes	characteristic
381	#120	—	101	2	no	—
382	#120	—	101	2	no	—
383	#120	—	101	2	no	—
384	#120	—	101	2	no	—
385	#120	—	101	2	no	—
386	#120	—	101	2	no	—
387	C₄×Q₈	—	101	2	no	—
388	C₄×D₄	—	101	2	no	—
389	C₄×D₄	—	101	2	no	—
390	C₄×D₄	—	101	2	no	—
391	C₄×D₄	—	101	2	no	—
392	C₄×D₄	—	101	2	no	—
393	C₄×D₄	—	101	2	no	—
394	C₄×D₄	—	101	2	no	—
395	C₄×D₄	—	101	2	no	—
396	C₄×D₄	—	101	2	no	—
397	C₄×D₄	—	101	2	no	—
398	C₄×D₄	—	101	2	no	—
399	C₄×D₄	—	101	2	no	—
400	C₄×D₄	—	101	2	no	—
401	C₄×D₄	—	101	2	no	—
402	C₄×D₄	C₂×D₁₀₁	1	2	yes	complemented
403	#117	—	101	2	no	—
404	#117	—	101	1	no	—
405	#117	—	101	1	no	—
406	#117	—	101	2	no	—
407	C₂×C₄⋊C₄	—	101	2	no	—
408	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
409	C₂×C₂²⋊C₄	—	101	1	no	—
410	C₂×C₂²⋊C₄	—	101	1	no	—
411	C₂×C₂²⋊C₄	—	101	2	no	—
412	C₂×C₂²⋊C₄	—	101	2	no	—
413	C₂×C₄²	—	101	1	no	—
414	C₂×C₄²	—	101	2	no	—
415	C₂⁴	—	101	1	no	—
416	C₂⁴	—	101	2	no	—
417	C₂⁴	—	101	1	no	—
418	#41	—	404	2	no	—
419	#41	—	404	2	no	—
420	C₂×Q₈	—	101	2	no	—
421	C₂×Q₈	—	101	1	no	—
422	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
423	C₂×D₄	—	101	2	no	—
424	C₂×D₄	—	101	2	no	—
425	C₂×D₄	—	101	2	no	—
426	C₂×D₄	—	101	2	no	—
427	C₂×D₄	—	101	2	no	—
428	C₂×D₄	—	101	2	no	—
429	C₂×D₄	—	101	1	no	—
430	C₂×D₄	—	101	2	no	—
431	C₂×D₄	—	101	2	no	—
432	C₂×D₄	—	101	2	no	—
433	C₂×D₄	—	101	2	no	—
434	C₂×D₄	—	202	4	no	—
435	C₂×D₄	—	202	8	no	—
436	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
437	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
438	C₂²×C₄	—	101	1	no	—
439	C₂²×C₄	—	101	1	no	—
440	C₂²×C₄	—	101	2	no	—
441	C₂²×C₄	—	101	2	no	—
442	C₂²×C₄	—	101	2	no	—
443	C₂²×C₄	—	101	2	no	—
444	C₂²×C₄	—	101	1	no	—
445	C₂²×C₄	—	101	1	no	—
446	C₂²×C₄	—	101	2	no	—
447	C₂²×C₄	—	101	2	no	—
448	C₂²×C₄	—	101	2	no	—
449	C₂²×C₄	—	101	1	no	—
450	C₂²×C₄	—	101	1	no	—
451	C₂²×C₄	—	101	2	no	—
452	C₂²×C₄	—	404	2	no	—
453	C₂²×C₄	—	404	4	no	—
454	C₂²×C₄	—	404	2	no	—
455	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
459	C₄⋊C₄	—	101	2	no	—
460	C₄⋊C₄	—	101	2	no	—
461	C₄⋊C₄	—	101	2	no	—
462	C₄⋊C₄	—	101	2	no	—
463	C₄⋊C₄	—	101	2	no	—
464	C₄⋊C₄	—	101	2	no	—
465	C₄⋊C₄	—	101	2	no	—
466	C₄⋊C₄	—	101	2	no	—
467	C₄⋊C₄	—	101	2	no	—
468	C₄⋊C₄	—	101	1	no	—
469	C₄⋊C₄	—	101	2	no	—
470	C₄⋊C₄	—	101	1	no	—
471	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
472	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
473	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
474	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
476	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
478	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
479	C₂²⋊C₄	—	101	2	no	—
480	C₂²⋊C₄	—	101	2	no	—
481	C₂²⋊C₄	—	101	2	no	—
482	C₂²⋊C₄	—	101	2	no	—
483	C₂²⋊C₄	—	101	2	no	—
484	C₂²⋊C₄	—	101	2	no	—
485	C₂²⋊C₄	—	101	2	no	—
486	C₂²⋊C₄	—	101	2	no	—
487	C₂²⋊C₄	—	101	2	no	—
488	C₂²⋊C₄	—	101	2	no	—
489	C₂²⋊C₄	—	101	2	no	—
490	C₂²⋊C₄	—	101	2	no	—
491	C₂²⋊C₄	—	101	2	no	—
492	C₂²⋊C₄	—	101	2	no	—
493	C₂²⋊C₄	—	101	2	no	—
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	C₂²×D₁₀₁	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
503	C₄²	—	101	2	no	—
504	C₄²	—	101	2	no	—
505	C₄²	—	101	2	no	—
506	C₄²	—	101	2	no	—
507	C₄²	—	101	2	no	—
508	C₄²	C₂²×D₁₀₁	1	2	yes	—
509	C₂³	—	101	4	no	—
510	C₂³	—	101	2	no	—
511	C₂³	—	101	1	no	—
512	C₂³	—	101	2	no	—
513	C₂³	—	101	1	no	—
514	C₂³	—	404	1	no	—
515	C₂³	—	404	1	no	—
516	C₂³	—	404	2	no	—
517	C₂³	—	404	1	no	—
518	C₂³	—	404	1	no	—
519	C₂³	—	404	2	no	—
520	C₂³	—	202	4	no	—
521	C₂³	—	202	2	no	—
522	C₂³	C₂³×D₁₀₁	1	2	yes	—
523	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
524	Q₈	—	4	1	no	—
525	Q₈	—	404	1	no	—
526	Q₈	—	404	2	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	1	no	—
529	D₄	—	404	1	no	—
530	D₄	—	404	2	no	—
531	D₄	—	404	2	no	—
532	D₄	—	404	2	no	—
533	D₄	—	404	2	no	—
534	D₄	—	404	2	no	—
535	D₄	—	202	4	no	—
536	D₄	—	202	4	no	—
537	D₄	—	202	4	no	—
538	D₄	—	202	4	no	—
539	D₄	—	202	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	101	1	no	—
545	C₂×C₄	—	101	2	no	—
546	C₂×C₄	—	101	2	no	—
547	C₂×C₄	—	101	2	no	—
548	C₂×C₄	—	101	1	no	—
549	C₂×C₄	—	101	2	no	—
550	C₂×C₄	—	404	2	no	—
551	C₂×C₄	—	404	2	no	—
552	C₂×C₄	—	404	1	no	—
553	C₂×C₄	—	404	1	no	—
554	C₂×C₄	—	404	2	no	—
555	C₂×C₄	—	404	2	no	—
556	C₂×C₄	—	404	1	no	—
557	C₂×C₄	—	202	4	no	—
558	C₂×C₄	—	202	2	no	—
559	C₂×C₄	—	202	2	no	—
560	C₂×C₄	—	202	4	no	—
561	C₂×C₄	—	202	4	no	—
562	C₂×C₄	—	202	2	no	—
563	C₂×C₄	—	202	4	no	—
564	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
565	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
566	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
567	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
568	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	101	4	no	—
577	C₂²	—	404	4	no	—
578	C₂²	—	404	4	no	—
579	C₂²	—	404	8	no	—
580	C₂²	—	202	1	no	—
581	C₂²	—	202	1	no	—
582	C₂²	—	202	2	no	—
583	C₂²	—	202	1	no	—
584	C₂²	—	202	2	no	—
585	C₂²	—	202	1	no	—
586	C₂²	—	202	1	no	—
587	C₂²	—	202	2	no	—
588	C₂²	—	202	1	no	—
589	C₂²	—	202	2	no	—
590	C₂²	—	202	2	no	—
591	C₂²	#41×D₁₀₁	1	2	yes	—
592	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	2	no	—
600	C₄	—	101	2	no	—
601	C₄	—	202	2	no	—
602	C₄	—	202	1	no	—
603	C₄	—	202	2	no	—
604	C₄	—	202	2	no	—
605	C₄	—	202	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	4	2	no	—
608	C₂	—	404	1	no	—
609	C₂	—	404	1	no	—
610	C₂	—	404	2	no	—
611	C₂	—	202	4	no	—
612	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
613	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
614	C₂	#20266014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#539×C₁₀₁	C₂
hypercenter	#539	D₁₀₁
hypocenter	C₁₀₁	#3459
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #20265802	C₂	semidirect
2. #20265775	C₂	semidirect
3. #20265774	C₂	semidirect
4. #20265773	C₂	semidirect
5. #20265766	C₂	semidirect
6. #20265763	C₂	semidirect
7. #20265760	C₂	semidirect
8. #20265738	C₂	semidirect
9. #20265735	C₂	semidirect
10. #20265712	C₂	semidirect
11. #20265710	C₂	semidirect
12. #20265704	C₂	semidirect
13. #20265690	C₂	semidirect
14. #20265690	C₂	semidirect
15. #20265687	C₂	semidirect
16. #20265685	C₂	semidirect
17. C₂×#15692217	C₂	semidirect
18. C₄×D₄×D₁₀₁	C₂	semidirect
19. #539×C₁₀₁	C₂	semidirect
20. C₂×#13108075	C₂²	semidirect
21. C₂×#13108073	C₂²	semidirect
25. C₂²×C₄×D₁₀₁	C₂²	semidirect
26. C₂²×C₄×D₁₀₁	C₂²	semidirect
27. #15692250	C₂²	semidirect
28. #15692250	C₂²	semidirect
29. #15692250	C₂²	semidirect
30. #15692249	C₂²	semidirect
31. #15692248	C₂²	semidirect
32. #15692245	C₂²	semidirect
33. #15692245	C₂²	semidirect
34. #15692243	C₂²	semidirect
35. #15692241	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. #15692238	C₂²	semidirect
44. #15692238	C₂²	semidirect
45. #15692237	C₂²	semidirect
46. #15692237	C₂²	semidirect
47. #15692235	C₂²	semidirect
48. #15692235	C₂²	semidirect
49. #15692234	C₂²	semidirect
50. #15692233	C₂²	semidirect
51. #15692233	C₂²	semidirect
52. #15692233	C₂²	semidirect
53. #15692232	C₂²	semidirect
54. #15692231	C₂²	semidirect
55. #15692231	C₂²	semidirect
58. #15692230	C₂²	semidirect
60. #15692229	C₂²	semidirect
63. #15692228	C₂²	semidirect
65. #15692226	C₂²	semidirect
66. #15692225	C₂²	semidirect
67. #15692225	C₂²	semidirect
68. #15692225	C₂²	semidirect
69. #15692225	C₂²	semidirect
70. #15692223	C₂²	semidirect
71. #15692223	C₂²	semidirect
72. #15692220	C₂²	semidirect
73. C₄×D₄₀₄	C₂²	semidirect
74. D₄×Dic₁₀₁	C₂²	semidirect
75. #15692217	C₂²	semidirect
76. #15692217	C₂²	semidirect
77. #15692217	C₂²	semidirect
78. #15692217	C₂²	semidirect
79. #15692217	C₂²	semidirect
80. #15692217	C₂²	semidirect
81. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
82. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
83. #15692215	C₂²	semidirect
84. #15692215	C₂²	semidirect
85. #15692215	C₂²	semidirect
86. #15692215	C₂²	semidirect
87. #15692213	C₂²	semidirect
88. #15692213	C₂²	semidirect
89. #15692213	C₂²	semidirect
90. #15692211	C₂²	semidirect
91. C₄⋊C₄×D₁₀₁	C₂²	semidirect
93. C₂×#13108051	C₂²	semidirect
95. C₂²⋊C₄×D₁₀₁	C₂²	semidirect
96. C₂×C₄×Dic₁₀₁	C₂²	semidirect
97. C₄²×D₁₀₁	C₂²	semidirect
98. #126×C₁₀₁	C₂²	semidirect
99. #125×C₁₀₁	C₂²	semidirect
100. #123×C₁₀₁	C₂²	semidirect
101. #123×C₁₀₁	C₂²	semidirect
102. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
103. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
105. C₄×D₄×C₁₀₁	C₂²	semidirect
106. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
211. C₂²×D₁₀₁	#41	semidirect
308. C₁₀₁	#3459	semidirect
313. #539	D₁₀₁	semidirect
340. #126	C₂×D₁₀₁	semidirect
343. #125	C₂×D₁₀₁	semidirect
357. #123	C₂×D₁₀₁	semidirect
358. #123	C₂×D₁₀₁	semidirect
368. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
369. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
402. C₄×D₄	C₂×D₁₀₁	semidirect
408. 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
#20265802	2
#20265775	2
#20265774	2
#20265773	2
#20265766	2
#20265763	2
#20265760	2
#20265738	2
#20265735	2
#20265712	2
#20265710	2
#20265704	2
#20265690	2
#20265687	2
#20265685	2
C₂×#15692217	2
C₄×D₄×D₁₀₁	2
#539×C₁₀₁	2
#3459	101