Subgroups — #27174114

Order 12928.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692225	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15692215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13108051	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265079	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265069	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265068	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265056	C₂	1	1	yes	maximal, characteristic, complemented
10	#20265055	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265055	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265052	C₂	1	1	yes	maximal, characteristic, complemented
13	#20265051	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13108051	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
18	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
20	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
24	#15692225	C₄	1	8	yes	complemented
25	C₄×D₄₀₄	—	2	4	no	—
26	#15692215	—	2	4	no	—
27	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13108053	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
31	C₂×#13108051	—	2	4	no	—
32	C₂×#13108051	C₂²	1	1	yes	characteristic
33	C₂×#13108051	C₂²	1	1	yes	characteristic
34	C₂×#13108051	C₂²	1	1	yes	characteristic
35	C₂×#13108051	C₂²	1	1	yes	characteristic
36	C₂×#13108051	C₂²	1	1	yes	characteristic
37	C₂×#13108051	C₂²	1	1	yes	characteristic
38	C₂×#13108051	C₂²	1	1	yes	characteristic
39	C₂×#13108051	C₂²	1	1	yes	characteristic
40	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊C₄×D₁₀₁	—	2	4	no	—
44	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
45	#15692162	C₂²	1	1	yes	characteristic, complemented
46	#15692162	C₂²	1	1	yes	characteristic, complemented
47	#15692162	C₂²	1	1	yes	characteristic, complemented
48	#15692162	C₂²	1	1	yes	characteristic, complemented
49	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
52	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
54	#95×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
55	#95×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
56	C₂³×D₁₀₁	—	2	2	no	—
57	C₂³×D₁₀₁	—	2	2	no	—
58	C₂³×D₁₀₁	—	2	2	no	—
59	C₂³×D₁₀₁	—	2	2	no	—
60	C₂³×D₁₀₁	—	4	1	no	—
61	C₂³×D₁₀₁	—	4	1	no	—
62	C₂³×D₁₀₁	C₂×C₄	1	4	yes	complemented
63	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
64	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
65	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
66	C₂×D₄₀₄	—	2	2	no	—
67	C₂×D₄₀₄	—	2	2	no	—
68	C₂×D₄₀₄	—	4	1	no	—
69	C₂×D₄₀₄	—	4	1	no	—
70	C₂×D₄₀₄	C₂×C₄	1	4	yes	complemented
71	C₂×D₄₀₄	C₂×C₄	1	4	yes	complemented
72	C₂×C₂²⋊D₁₀₁	—	2	2	no	—
73	C₂×C₂²⋊D₁₀₁	—	2	2	no	—
74	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	4	yes	complemented
75	C₂²×Dic₁₀₁	—	2	2	no	—
76	C₂²×Dic₁₀₁	—	2	2	no	—
77	C₂²×Dic₁₀₁	—	4	1	no	—
78	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₁₀₁	—	2	2	no	—
84	C₂×C₄×D₁₀₁	—	2	2	no	—
85	C₂×C₄×D₁₀₁	—	2	2	no	—
86	C₂×C₄×D₁₀₁	—	2	2	no	—
87	C₂×C₄×D₁₀₁	—	2	2	no	—
88	C₂×C₄×D₁₀₁	—	2	2	no	—
89	C₂×C₄×D₁₀₁	—	4	1	no	—
90	C₂×C₄×D₁₀₁	—	4	1	no	—
91	C₂×C₄×D₁₀₁	—	4	1	no	—
92	C₄⋊Dic₁₀₁	—	2	2	no	—
93	C₄⋊Dic₁₀₁	—	4	1	no	—
94	#13108053	—	2	2	no	—
95	C₂²⋊Dic₁₀₁	—	2	2	no	—
96	#13108051	—	2	2	no	—
97	#13108051	—	2	2	no	—
98	#13108051	—	2	2	no	—
99	#13108051	—	2	2	no	—
100	#13108051	—	2	2	no	—
101	#13108051	—	2	2	no	—
102	#13108051	—	2	2	no	—
103	#13108051	—	4	1	no	—
104	#13108051	C₂×C₄	1	4	yes	complemented
105	#13108051	C₂×C₄	1	4	yes	complemented
106	#13108051	D₄	1	4	yes	complemented
107	C₄×Dic₁₀₁	—	2	2	no	—
108	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	4	1	no	—
112	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	complemented
119	C₂²⋊C₄×C₁₀₁	D₄	1	4	yes	complemented
120	C₄²×C₁₀₁	—	2	2	no	—
121	C₄²×C₁₀₁	—	4	1	no	—
122	C₂³×C₁₀₁	—	2	1	no	—
123	C₂³×C₁₀₁	—	2	1	no	—
124	C₂³×C₁₀₁	—	2	1	no	—
125	C₂³×C₁₀₁	—	2	1	no	—
126	C₂³×C₁₀₁	C₂²×C₄	1	2	yes	—
127	C₂³×C₁₀₁	C₂×D₄	1	2	yes	—
128	C₂³×C₁₀₁	#41	1	2	yes	—
129	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
130	C₂²×D₁₀₁	—	2	1	no	—
131	C₂²×D₁₀₁	—	2	1	no	—
132	C₂²×D₁₀₁	—	2	1	no	—
133	C₂²×D₁₀₁	—	2	1	no	—
134	C₂²×D₁₀₁	—	2	8	no	—
135	C₂²×D₁₀₁	—	2	1	no	—
136	C₂²×D₁₀₁	—	2	1	no	—
137	C₂²×D₁₀₁	—	2	1	no	—
138	C₂²×D₁₀₁	—	2	1	no	—
139	C₂²×D₁₀₁	—	2	1	no	—
140	C₂²×D₁₀₁	—	2	1	no	—
141	C₂²×D₁₀₁	—	2	1	no	—
142	C₂²×D₁₀₁	—	2	1	no	—
143	C₂²×D₁₀₁	—	2	1	no	—
144	C₂²×D₁₀₁	—	2	1	no	—
145	C₂²×D₁₀₁	—	2	1	no	—
146	C₂²×D₁₀₁	—	2	1	no	—
147	C₂²×D₁₀₁	—	2	8	no	—
148	C₂²×D₁₀₁	—	4	4	no	—
149	C₂²×D₁₀₁	—	4	4	no	—
150	C₂²×D₁₀₁	—	4	4	no	—
151	C₂²×D₁₀₁	—	4	4	no	—
152	C₂²×D₁₀₁	—	4	4	no	—
153	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
154	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
155	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
156	C₂²×D₁₀₁	C₂×D₄	1	2	yes	—
157	C₂²×D₁₀₁	#41	1	2	yes	—
158	C₂×C₄×C₁₀₁	—	2	1	no	—
159	C₂×C₄×C₁₀₁	—	2	1	no	—
160	C₂×C₄×C₁₀₁	—	2	1	no	—
161	C₂×C₄×C₁₀₁	—	2	1	no	—
162	C₂×C₄×C₁₀₁	—	2	1	no	—
163	C₂×C₄×C₁₀₁	—	2	1	no	—
164	C₂×C₄×C₁₀₁	—	2	1	no	—
165	C₂×C₄×C₁₀₁	—	2	1	no	—
166	C₂×C₄×C₁₀₁	—	2	1	no	—
167	C₂×C₄×C₁₀₁	—	2	1	no	—
168	C₂×C₄×C₁₀₁	—	2	1	no	—
169	C₂×C₄×C₁₀₁	—	2	1	no	—
170	C₂×C₄×C₁₀₁	—	2	1	no	—
171	C₂×C₄×C₁₀₁	—	4	4	no	—
172	C₂×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
173	C₂×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
174	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
175	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
176	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
177	C₂²⋊D₁₀₁	—	2	8	no	—
178	C₂×Dic₁₀₁	—	2	1	no	—
179	C₂×Dic₁₀₁	—	2	1	no	—
180	C₂×Dic₁₀₁	—	2	1	no	—
181	C₂×Dic₁₀₁	—	2	1	no	—
182	C₂×Dic₁₀₁	—	2	1	no	—
183	C₂×Dic₁₀₁	—	2	1	no	—
184	C₂×Dic₁₀₁	—	2	1	no	—
185	C₂×Dic₁₀₁	—	2	1	no	—
186	C₂×Dic₁₀₁	—	2	1	no	—
187	C₂×Dic₁₀₁	—	2	1	no	—
188	C₂×Dic₁₀₁	—	2	1	no	—
189	C₂×Dic₁₀₁	—	2	1	no	—
190	C₂×Dic₁₀₁	—	2	1	no	—
191	C₂×Dic₁₀₁	—	4	4	no	—
192	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	—
193	C₂×Dic₁₀₁	C₂×D₄	1	2	yes	—
194	D₄₀₄	—	2	8	no	—
195	D₄₀₄	—	4	4	no	—
196	C₄×D₁₀₁	—	4	4	no	—
197	C₄×D₁₀₁	—	4	4	no	—
198	C₄×D₁₀₁	—	4	4	no	—
199	C₂²×C₁₀₁	—	2	2	no	—
200	C₂²×C₁₀₁	—	2	2	no	—
201	C₂²×C₁₀₁	—	2	2	no	—
202	C₂²×C₁₀₁	—	2	2	no	—
203	C₂²×C₁₀₁	—	2	2	no	—
204	C₂²×C₁₀₁	—	2	2	no	—
205	C₂²×C₁₀₁	C₄×D₄	1	4	yes	complemented
206	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
207	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
208	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
209	C₂²×C₁₀₁	C₂×#41	1	1	yes	characteristic
210	C₂²×C₁₀₁	C₂×#41	1	1	yes	characteristic
211	C₂²×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×D₁₀₁	—	2	2	no	—
214	C₂×D₁₀₁	—	2	2	no	—
215	C₂×D₁₀₁	—	2	2	no	—
216	C₂×D₁₀₁	—	2	2	no	—
217	C₂×D₁₀₁	—	2	2	no	—
218	C₂×D₁₀₁	—	2	2	no	—
219	C₂×D₁₀₁	—	2	2	no	—
220	C₂×D₁₀₁	—	2	2	no	—
221	C₂×D₁₀₁	—	2	2	no	—
222	C₂×D₁₀₁	—	2	2	no	—
223	C₂×D₁₀₁	—	2	2	no	—
224	C₂×D₁₀₁	—	2	2	no	—
225	C₂×D₁₀₁	—	4	16	no	—
226	C₂×D₁₀₁	—	4	1	no	—
227	C₂×D₁₀₁	—	4	1	no	—
228	C₂×D₁₀₁	—	4	1	no	—
229	C₂×D₁₀₁	—	4	1	no	—
230	C₂×D₁₀₁	—	4	1	no	—
231	C₂×D₁₀₁	—	4	1	no	—
232	C₂×D₁₀₁	—	4	1	no	—
233	C₂×D₁₀₁	—	4	1	no	—
234	C₂×D₁₀₁	C₄×D₄	1	4	yes	complemented
235	C₄×C₁₀₁	—	2	2	no	—
236	C₄×C₁₀₁	—	2	2	no	—
237	C₄×C₁₀₁	—	2	2	no	—
238	C₄×C₁₀₁	—	2	2	no	—
239	C₄×C₁₀₁	—	2	2	no	—
240	C₄×C₁₀₁	—	4	1	no	—
241	Dic₁₀₁	—	2	2	no	—
242	Dic₁₀₁	—	2	2	no	—
243	Dic₁₀₁	—	4	1	no	—
244	Dic₁₀₁	—	4	1	no	—
245	Dic₁₀₁	—	4	1	no	—
246	C₂×C₁₀₁	—	2	4	no	—
247	C₂×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
248	C₂×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂×C₁₀₁	#518	1	1	yes	characteristic
250	C₂×C₁₀₁	D₄²	1	1	yes	characteristic
251	C₂×C₁₀₁	#546	1	1	yes	characteristic
252	C₂×C₁₀₁	#546	1	1	yes	characteristic
253	C₂×C₁₀₁	#551	1	1	yes	characteristic
254	D₁₀₁	—	2	4	no	—
255	D₁₀₁	—	4	2	no	—
256	D₁₀₁	—	4	2	no	—
257	#2358	—	101	1	no	maximal, Sylow
258	C₁₀₁	#2358	1	1	yes	characteristic, complemented, Sylow
259	C₂×#120	—	101	1	no	—
260	C₂×C₄×D₄	—	101	1	no	—
261	C₂×C₄×D₄	—	101	1	no	—
262	C₂²×C₂²⋊C₄	—	101	1	no	—
263	C₂²×C₂²⋊C₄	—	101	1	no	—
264	#390	—	101	1	no	—
265	#388	—	101	1	no	—
266	#388	—	101	1	no	—
267	#386	—	101	1	no	—
268	#386	—	101	1	no	—
269	#386	—	101	1	no	—
270	#385	—	101	1	no	—
271	#385	—	101	1	no	—
272	C₄×C₂²⋊C₄	—	101	1	no	—
273	C₄×C₂²⋊C₄	D₁₀₁	1	1	yes	characteristic, complemented
274	C₂⁵	—	101	1	no	—
275	C₂²×D₄	—	101	1	no	—
276	C₂²×D₄	—	101	1	no	—
277	C₂²×D₄	—	101	1	no	—
278	C₂³×C₄	—	101	1	no	—
279	C₂³×C₄	—	101	1	no	—
280	C₂³×C₄	—	101	1	no	—
281	C₂³×C₄	—	101	1	no	—
282	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
283	#120	—	101	8	no	—
284	C₄×D₄	—	202	4	no	—
285	C₄×D₄	—	202	4	no	—
286	C₂×C₄⋊C₄	—	101	1	no	—
287	C₂×C₄⋊C₄	—	101	1	no	—
288	C₂×C₄⋊C₄	—	101	1	no	—
289	C₂×C₂²⋊C₄	—	101	1	no	—
290	C₂×C₂²⋊C₄	—	101	1	no	—
291	C₂×C₂²⋊C₄	—	101	1	no	—
292	C₂×C₂²⋊C₄	—	101	1	no	—
293	C₂×C₂²⋊C₄	—	101	1	no	—
294	C₂×C₂²⋊C₄	—	101	1	no	—
295	C₂×C₂²⋊C₄	—	101	1	no	—
296	C₂×C₂²⋊C₄	—	101	1	no	—
297	C₂×C₂²⋊C₄	—	101	1	no	—
298	C₂×C₂²⋊C₄	—	101	1	no	—
299	C₂×C₂²⋊C₄	—	101	1	no	—
300	C₂×C₂²⋊C₄	—	101	1	no	—
301	C₂×C₂²⋊C₄	—	202	4	no	—
302	C₂×C₂²⋊C₄	—	202	4	no	—
303	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
305	C₂×C₄²	—	101	1	no	—
306	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic, complemented
307	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic, complemented
308	#95	—	101	1	no	—
309	#95	—	101	1	no	—
310	#95	—	101	1	no	—
311	#95	—	101	1	no	—
312	#95	C₂×D₁₀₁	1	1	yes	characteristic, complemented
313	#95	C₂×D₁₀₁	1	1	yes	characteristic, complemented
314	C₂⁴	—	101	1	no	—
315	C₂⁴	—	101	4	no	—
316	C₂⁴	—	101	1	no	—
317	C₂⁴	—	101	1	no	—
318	C₂⁴	—	404	1	no	—
319	C₂⁴	—	404	1	no	—
320	C₂⁴	—	202	2	no	—
321	C₂⁴	—	202	2	no	—
322	C₂⁴	—	202	2	no	—
323	C₂⁴	—	202	2	no	—
324	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
325	C₂×D₄	—	101	4	no	—
326	C₂×D₄	—	101	4	no	—
327	C₂×D₄	—	101	4	no	—
328	C₂×D₄	—	404	1	no	—
329	C₂×D₄	—	404	1	no	—
330	C₂×D₄	—	202	2	no	—
331	C₂×D₄	—	202	2	no	—
332	C₂×D₄	—	202	2	no	—
333	C₂×D₄	—	202	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	101	1	no	—
338	C₂²×C₄	—	101	1	no	—
339	C₂²×C₄	—	101	1	no	—
340	C₂²×C₄	—	101	1	no	—
341	C₂²×C₄	—	101	1	no	—
342	C₂²×C₄	—	404	1	no	—
343	C₂²×C₄	—	404	1	no	—
344	C₂²×C₄	—	404	1	no	—
345	C₂²×C₄	—	404	1	no	—
346	C₂²×C₄	—	202	2	no	—
347	C₂²×C₄	—	202	2	no	—
348	C₂²×C₄	—	202	2	no	—
349	C₂²×C₄	—	202	2	no	—
350	C₂²×C₄	—	202	2	no	—
351	C₂²×C₄	—	202	2	no	—
352	C₂²×C₄	—	202	2	no	—
353	C₂²×C₄	—	202	2	no	—
354	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
356	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
357	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
359	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
360	C₄⋊C₄	—	404	1	no	—
361	C₄⋊C₄	—	202	2	no	—
362	C₄⋊C₄	—	202	2	no	—
363	C₂²⋊C₄	—	101	4	no	—
364	C₂²⋊C₄	—	101	4	no	—
365	C₂²⋊C₄	—	101	4	no	—
366	C₂²⋊C₄	—	404	1	no	—
367	C₂²⋊C₄	—	202	2	no	—
368	C₂²⋊C₄	—	202	2	no	—
369	C₂²⋊C₄	—	202	2	no	—
370	C₂²⋊C₄	—	202	2	no	—
371	C₂²⋊C₄	—	202	2	no	—
372	C₂²⋊C₄	—	202	2	no	—
373	C₂²⋊C₄	—	202	2	no	—
374	C₂²⋊C₄	—	202	2	no	—
375	C₂²⋊C₄	C₄×D₁₀₁	1	4	yes	complemented
376	C₂²⋊C₄	D₄₀₄	1	4	yes	complemented
377	C₄²	—	2	2	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	202	2	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	101	2	no	—
385	C₂³	—	101	2	no	—
386	C₂³	—	101	2	no	—
387	C₂³	—	101	2	no	—
388	C₂³	—	101	2	no	—
389	C₂³	—	404	4	no	—
390	C₂³	—	404	4	no	—
391	C₂³	—	404	4	no	—
392	C₂³	—	404	4	no	—
393	C₂³	—	404	4	no	—
394	C₂³	—	202	8	no	—
395	C₂³	—	202	1	no	—
396	C₂³	—	202	1	no	—
397	C₂³	—	202	1	no	—
398	C₂³	—	202	1	no	—
399	C₂³	—	202	1	no	—
400	C₂³	—	202	1	no	—
401	C₂³	—	202	1	no	—
402	C₂³	—	202	1	no	—
403	C₂³	—	202	1	no	—
404	C₂³	—	202	1	no	—
405	C₂³	—	202	1	no	—
406	C₂³	—	202	1	no	—
407	C₂³	—	202	8	no	—
408	C₂³	—	202	1	no	—
409	C₂³	—	202	1	no	—
410	C₂³	—	202	1	no	—
411	C₂³	—	202	1	no	—
412	C₂³	C₂×C₄×D₁₀₁	1	2	yes	—
413	C₂³	C₂×D₄₀₄	1	2	yes	—
414	C₂³	#13108074	1	2	yes	—
415	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
416	D₄	—	404	4	no	—
417	D₄	—	202	8	no	—
418	D₄	—	202	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	101	2	no	—
434	C₂×C₄	—	101	2	no	—
435	C₂×C₄	—	404	4	no	—
436	C₂×C₄	—	404	4	no	—
437	C₂×C₄	—	404	4	no	—
438	C₂×C₄	—	404	4	no	—
439	C₂×C₄	—	202	1	no	—
440	C₂×C₄	—	202	1	no	—
441	C₂×C₄	—	202	1	no	—
442	C₂×C₄	—	202	1	no	—
443	C₂×C₄	—	202	1	no	—
444	C₂×C₄	—	202	1	no	—
445	C₂×C₄	—	202	1	no	—
446	C₂×C₄	—	202	1	no	—
447	C₂×C₄	—	202	1	no	—
448	C₂×C₄	—	202	1	no	—
449	C₂×C₄	—	202	1	no	—
450	C₂×C₄	—	202	1	no	—
451	C₂×C₄	—	202	1	no	—
452	C₂×C₄	C₂×C₄×D₁₀₁	1	2	yes	—
453	C₂×C₄	C₂×C₄×D₁₀₁	1	2	yes	—
454	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
455	C₂×C₄	C₂×D₄₀₄	1	2	yes	—
456	C₂×C₄	C₂×D₄₀₄	1	2	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	101	4	no	—
464	C₂²	—	404	16	no	—
465	C₂²	—	404	1	no	—
466	C₂²	—	404	1	no	—
467	C₂²	—	404	1	no	—
468	C₂²	—	404	1	no	—
469	C₂²	—	404	1	no	—
470	C₂²	—	404	1	no	—
471	C₂²	—	404	1	no	—
472	C₂²	—	404	1	no	—
473	C₂²	—	202	2	no	—
474	C₂²	—	202	2	no	—
475	C₂²	—	202	2	no	—
476	C₂²	—	202	2	no	—
477	C₂²	—	202	2	no	—
478	C₂²	—	202	2	no	—
479	C₂²	—	202	2	no	—
480	C₂²	—	202	2	no	—
481	C₂²	—	202	2	no	—
482	C₂²	—	202	2	no	—
483	C₂²	—	202	2	no	—
484	C₂²	—	202	2	no	—
485	C₂²	C₄×D₄₀₄	1	4	yes	complemented
486	C₂²	C₂²×C₄×D₁₀₁	1	1	yes	characteristic
487	C₂²	C₂×D₄×D₁₀₁	1	1	yes	characteristic
488	C₂²	C₂²×D₄₀₄	1	1	yes	characteristic
489	C₂²	#41×D₁₀₁	1	1	yes	characteristic
490	C₂²	C₂×#13108074	1	1	yes	characteristic
491	C₂²	#15692300	1	1	yes	characteristic
492	C₂²	#15692301	1	1	yes	characteristic
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	404	1	no	—
500	C₄	—	404	1	no	—
501	C₄	—	404	1	no	—
502	C₄	—	202	2	no	—
503	C₄	—	202	2	no	—
504	C₂	—	2	4	no	—
505	C₂	—	404	2	no	—
506	C₂	—	404	2	no	—
507	C₂	—	202	4	no	—
508	C₂	C₄×D₄×D₁₀₁	1	1	yes	characteristic
509	C₂	C₂×C₄×D₄₀₄	1	1	yes	characteristic
510	C₂	#20265649	1	1	yes	characteristic
511	C₂	D₄×D₄₀₄	1	1	yes	characteristic
512	C₂	#20265817	1	1	yes	characteristic
513	C₂	#20265822	1	1	yes	characteristic
514	C₂	#20265851	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₀₁
commutator	C₂²×C₁₀₁	C₂³×C₄
Fitting	C₄×C₂²⋊C₄×C₁₀₁	C₂
socle, cosocle	C₂³×C₁₀₁	C₂⁴
prime radical	C₂×#15692225	C₂
hypercenter	C₄×C₂²⋊C₄	D₁₀₁
hypocenter	C₁₀₁	#2358
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄₀₄	C₂	semidirect
3. C₂×#15692215	C₂	semidirect
4. C₂²×#13108051	C₂	semidirect
5. C₂×C₂²⋊C₄×D₁₀₁	C₂	semidirect
6. #20265079	C₂	semidirect
7. #20265069	C₂	semidirect
8. #20265068	C₂	semidirect
9. #20265056	C₂	semidirect
10. #20265055	C₂	semidirect
11. #20265055	C₂	semidirect
12. #20265052	C₂	semidirect
13. #20265051	C₂	semidirect
14. C₄×#13108051	C₂	semidirect
15. C₄×C₂²⋊C₄×C₁₀₁	C₂	semidirect
23. C₂²×C₄×D₁₀₁	C₂²	semidirect
24. #15692225	C₄	semidirect
27. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
28. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
29. C₂×#13108053	C₂²	semidirect
40. C₂×#13108051	C₂²	semidirect
41. C₂×#13108051	C₂²	semidirect
42. C₂×#13108051	C₂²	semidirect
44. C₂×C₄×Dic₁₀₁	C₂²	semidirect
45. #15692162	C₂²	semidirect
46. #15692162	C₂²	semidirect
47. #15692162	C₂²	semidirect
48. #15692162	C₂²	semidirect
52. C₂×C₄²×C₁₀₁	C₂²	semidirect
53. C₂×C₄²×C₁₀₁	C₂²	semidirect
54. #95×C₁₀₁	C₂²	semidirect
55. #95×C₁₀₁	C₂²	semidirect
62. C₂³×D₁₀₁	C₂×C₄	semidirect
70. C₂×D₄₀₄	C₂×C₄	semidirect
71. C₂×D₄₀₄	C₂×C₄	semidirect
74. C₂×C₂²⋊D₁₀₁	C₂×C₄	semidirect
104. #13108051	C₂×C₄	semidirect
105. #13108051	C₂×C₄	semidirect
106. #13108051	D₄	semidirect
118. C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
119. C₂²⋊C₄×C₁₀₁	D₄	semidirect
205. C₂²×C₁₀₁	C₄×D₄	semidirect
234. C₂×D₁₀₁	C₄×D₄	semidirect
258. C₁₀₁	#2358	semidirect
273. C₄×C₂²⋊C₄	D₁₀₁	semidirect
306. C₂×C₄²	C₂×D₁₀₁	semidirect
307. C₂×C₄²	C₂×D₁₀₁	semidirect
312. #95	C₂×D₁₀₁	semidirect
313. #95	C₂×D₁₀₁	semidirect
375. C₂²⋊C₄	C₄×D₁₀₁	semidirect
376. C₂²⋊C₄	D₄₀₄	semidirect
485. C₂²	C₄×D₄₀₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15692225	2
C₂×C₄×D₄₀₄	2
C₂×#15692215	2
C₂²×#13108051	2
C₂×C₂²⋊C₄×D₁₀₁	2
#20265079	2
#20265069	2
#20265068	2
#20265056	2
#20265055	2
#20265052	2
#20265051	2
C₄×#13108051	2
C₄×C₂²⋊C₄×C₁₀₁	2
#2358	101