Subgroups — C₄×#400×C₁₀₁ #38796015

Order 25856.

1398 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#400×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1445	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1443	C₂	1	2	yes	maximal
6	C₁₀₁×#1442	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1442	C₂	1	2	yes	maximal
8	C₁₀₁×#1441	C₂	1	1	yes	maximal, characteristic
9	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
10	C₄×#95×C₁₀₁	C₂	1	2	yes	maximal
11	C₄×#95×C₁₀₁	C₂	1	2	yes	maximal
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
21	#400×C₁₀₁	C₄	1	8	yes	direct product factor
22	C₄×C₄⋊C₄×C₁₀₁	—	2	4	no	—
23	C₄×C₄⋊C₄×C₁₀₁	—	2	4	no	—
24	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
34	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
35	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
36	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₁₀₁	—	2	2	no	—
61	C₂×C₄²×C₁₀₁	—	2	2	no	—
62	C₂×C₄²×C₁₀₁	—	2	4	no	—
63	C₂×C₄²×C₁₀₁	—	2	2	no	—
64	C₂×C₄²×C₁₀₁	—	2	4	no	—
65	C₂×C₄²×C₁₀₁	—	2	4	no	—
66	C₂×C₄²×C₁₀₁	—	2	4	no	—
67	C₂×C₄²×C₁₀₁	—	2	4	no	—
68	C₂×C₄²×C₁₀₁	—	2	4	no	—
69	C₂×C₄²×C₁₀₁	—	2	4	no	—
70	C₂×C₄²×C₁₀₁	—	2	4	no	—
71	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
72	C₂×C₄²×C₁₀₁	Q₈	1	4	yes	—
73	#95×C₁₀₁	—	2	2	no	—
74	#95×C₁₀₁	—	2	2	no	—
75	#95×C₁₀₁	—	2	4	no	—
76	#95×C₁₀₁	—	2	4	no	—
77	#95×C₁₀₁	—	2	4	no	—
78	#95×C₁₀₁	—	2	4	no	—
79	#95×C₁₀₁	—	2	4	no	—
80	#95×C₁₀₁	—	2	4	no	—
81	#95×C₁₀₁	—	2	4	no	—
82	#95×C₁₀₁	—	2	2	no	—
83	#95×C₁₀₁	—	2	4	no	—
84	#95×C₁₀₁	C₂×C₄	1	4	yes	—
85	#95×C₁₀₁	C₂×C₄	1	8	yes	—
86	#95×C₁₀₁	C₂×C₄	1	8	yes	—
87	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₁	—	2	1	no	—
89	C₂²×C₄×C₁₀₁	—	2	1	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	1	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	1	no	—
94	C₂²×C₄×C₁₀₁	—	2	1	no	—
95	C₂²×C₄×C₁₀₁	—	2	1	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	2	no	—
113	C₂²×C₄×C₁₀₁	—	2	2	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	2	1	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	—	2	1	no	—
129	C₂²×C₄×C₁₀₁	—	2	2	no	—
130	C₂²×C₄×C₁₀₁	—	2	1	no	—
131	C₂²×C₄×C₁₀₁	—	2	1	no	—
132	C₂²×C₄×C₁₀₁	—	2	1	no	—
133	C₂²×C₄×C₁₀₁	—	2	2	no	—
134	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
146	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
147	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
148	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
149	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
150	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
151	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
152	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
153	C₄⋊C₄×C₁₀₁	—	2	8	no	—
154	C₄⋊C₄×C₁₀₁	—	2	8	no	—
155	C₄⋊C₄×C₁₀₁	—	2	8	no	—
156	C₄⋊C₄×C₁₀₁	—	2	8	no	—
157	C₄²×C₁₀₁	—	2	8	no	—
158	C₄²×C₁₀₁	—	2	8	no	—
159	C₄²×C₁₀₁	—	4	4	no	—
160	C₄²×C₁₀₁	—	4	8	no	—
161	C₄²×C₁₀₁	—	4	8	no	—
162	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
163	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
164	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
165	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
166	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
167	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
168	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
169	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
170	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
171	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
172	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
173	C₂×C₄×C₁₀₁	—	2	2	no	—
174	C₂×C₄×C₁₀₁	—	2	4	no	—
175	C₂×C₄×C₁₀₁	—	2	2	no	—
176	C₂×C₄×C₁₀₁	—	2	2	no	—
177	C₂×C₄×C₁₀₁	—	2	2	no	—
178	C₂×C₄×C₁₀₁	—	2	2	no	—
179	C₂×C₄×C₁₀₁	—	2	2	no	—
180	C₂×C₄×C₁₀₁	—	2	4	no	—
181	C₂×C₄×C₁₀₁	—	2	2	no	—
182	C₂×C₄×C₁₀₁	—	2	2	no	—
183	C₂×C₄×C₁₀₁	—	2	2	no	—
184	C₂×C₄×C₁₀₁	—	2	4	no	—
185	C₂×C₄×C₁₀₁	—	2	4	no	—
186	C₂×C₄×C₁₀₁	—	2	4	no	—
187	C₂×C₄×C₁₀₁	—	2	4	no	—
188	C₂×C₄×C₁₀₁	—	2	4	no	—
189	C₂×C₄×C₁₀₁	—	2	4	no	—
190	C₂×C₄×C₁₀₁	—	2	4	no	—
191	C₂×C₄×C₁₀₁	—	2	2	no	—
192	C₂×C₄×C₁₀₁	—	2	2	no	—
193	C₂×C₄×C₁₀₁	—	2	2	no	—
194	C₂×C₄×C₁₀₁	—	2	2	no	—
195	C₂×C₄×C₁₀₁	—	2	4	no	—
196	C₂×C₄×C₁₀₁	—	2	4	no	—
197	C₂×C₄×C₁₀₁	—	2	4	no	—
198	C₂×C₄×C₁₀₁	—	2	4	no	—
199	C₂×C₄×C₁₀₁	—	2	4	no	—
200	C₂×C₄×C₁₀₁	—	2	4	no	—
201	C₂×C₄×C₁₀₁	—	2	4	no	—
202	C₂×C₄×C₁₀₁	—	2	2	no	—
203	C₂×C₄×C₁₀₁	—	2	4	no	—
204	C₂×C₄×C₁₀₁	—	4	1	no	—
205	C₂×C₄×C₁₀₁	—	4	1	no	—
206	C₂×C₄×C₁₀₁	—	4	1	no	—
207	C₂×C₄×C₁₀₁	—	4	2	no	—
208	C₂×C₄×C₁₀₁	—	4	1	no	—
209	C₂×C₄×C₁₀₁	—	4	2	no	—
210	C₂×C₄×C₁₀₁	—	4	2	no	—
211	C₂×C₄×C₁₀₁	—	4	2	no	—
212	C₂×C₄×C₁₀₁	—	4	2	no	—
213	C₂×C₄×C₁₀₁	—	4	2	no	—
214	C₂×C₄×C₁₀₁	—	4	2	no	—
215	C₂×C₄×C₁₀₁	—	4	2	no	—
216	C₂×C₄×C₁₀₁	—	4	2	no	—
217	C₂×C₄×C₁₀₁	—	4	2	no	—
218	C₂×C₄×C₁₀₁	—	4	2	no	—
219	C₂×C₄×C₁₀₁	—	4	2	no	—
220	C₂×C₄×C₁₀₁	—	4	2	no	—
221	C₂×C₄×C₁₀₁	—	4	2	no	—
222	C₂×C₄×C₁₀₁	—	4	2	no	—
223	C₂×C₄×C₁₀₁	—	4	2	no	—
224	C₂×C₄×C₁₀₁	—	4	2	no	—
225	C₂×C₄×C₁₀₁	—	4	2	no	—
226	C₂×C₄×C₁₀₁	—	4	2	no	—
227	C₂×C₄×C₁₀₁	—	4	2	no	—
228	C₂×C₄×C₁₀₁	—	4	1	no	—
229	C₂×C₄×C₁₀₁	—	4	1	no	—
230	C₂×C₄×C₁₀₁	—	4	2	no	—
231	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
232	C₂×C₄×C₁₀₁	C₄×Q₈	1	4	yes	—
233	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
234	C₂×C₄×C₁₀₁	#123	1	4	yes	—
235	C₂×C₄×C₁₀₁	#124	1	4	yes	—
236	C₂×C₄×C₁₀₁	#125	1	8	yes	—
237	C₂×C₄×C₁₀₁	#126	1	8	yes	—
238	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂²×C₁₀₁	C₂×C₄×Q₈	1	1	yes	characteristic
240	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
241	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
242	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
243	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
244	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
245	C₂²×C₁₀₁	#525	1	1	yes	characteristic
246	C₂²×C₁₀₁	#525	1	1	yes	characteristic
247	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
248	C₂²×C₁₀₁	C₂×#125	1	2	yes	—
249	C₂²×C₁₀₁	C₂×#126	1	2	yes	—
250	C₂²×C₁₀₁	#529	1	2	yes	—
251	C₂²×C₁₀₁	#529	1	2	yes	—
252	C₂²×C₁₀₁	#529	1	2	yes	—
253	C₂²×C₁₀₁	#529	1	2	yes	—
254	C₂²×C₁₀₁	#529	1	2	yes	—
255	C₂²×C₁₀₁	#529	1	1	yes	characteristic
256	C₂²×C₁₀₁	#529	1	2	yes	—
257	C₂²×C₁₀₁	#529	1	2	yes	—
258	C₂²×C₁₀₁	#532	1	1	yes	characteristic
259	C₂²×C₁₀₁	#533	1	2	yes	—
260	C₂²×C₁₀₁	#533	1	1	yes	characteristic
261	C₄×C₁₀₁	—	2	4	no	—
262	C₄×C₁₀₁	—	2	4	no	—
263	C₄×C₁₀₁	—	4	4	no	—
264	C₄×C₁₀₁	—	4	2	no	—
265	C₄×C₁₀₁	—	4	2	no	—
266	C₄×C₁₀₁	—	4	2	no	—
267	C₄×C₁₀₁	—	4	4	no	—
268	C₄×C₁₀₁	—	4	4	no	—
269	C₄×C₁₀₁	—	4	2	no	—
270	C₄×C₁₀₁	—	4	4	no	—
271	C₄×C₁₀₁	#400	1	8	yes	direct product factor
272	C₄×#400	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂×C₁₀₁	C₄×#123	1	1	yes	characteristic
274	C₂×C₁₀₁	C₄×C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₁₀₁	C₄×#124	1	1	yes	characteristic
276	C₂×C₁₀₁	C₄×#126	1	2	yes	—
277	C₂×C₁₀₁	C₄×#125	1	2	yes	—
278	C₂×C₁₀₁	C₂×#400	1	1	yes	characteristic
279	C₂×C₁₀₁	#2395	1	1	yes	characteristic
280	C₂×C₁₀₁	#2396	1	1	yes	characteristic
281	C₂×C₁₀₁	#2398	1	1	yes	characteristic
282	C₂×C₁₀₁	#2401	1	2	yes	—
283	C₂×C₁₀₁	#2402	1	2	yes	—
284	C₂×#400	C₂×C₁₀₁	1	1	yes	characteristic
285	C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
286	C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
287	#1445	C₂×C₁₀₁	1	1	yes	characteristic
288	#1443	C₂×C₁₀₁	1	2	yes	—
289	#1442	C₂×C₁₀₁	1	1	yes	characteristic
290	#1442	C₂×C₁₀₁	1	2	yes	—
291	#1441	C₂×C₁₀₁	1	1	yes	characteristic
292	C₄×#95	C₂×C₁₀₁	1	2	yes	—
293	C₄×#95	C₂×C₁₀₁	1	2	yes	—
294	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic
295	C₁₀₁	C₄×#400	1	1	yes	characteristic, direct product factor, Sylow
296	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
300	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
301	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
303	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
304	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
305	#400	C₄×C₁₀₁	1	8	yes	direct product factor
306	C₄×C₄⋊C₄	—	2	4	no	—
307	C₄×C₄⋊C₄	—	2	4	no	—
308	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
309	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
310	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
311	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
312	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
313	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
314	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
315	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
316	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
317	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
318	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
319	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
320	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
321	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
328	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
343	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	4	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	4	no	—
349	C₂×C₄²	—	2	4	no	—
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	—	2	4	no	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	—	2	4	no	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
356	C₂×C₄²	Q₈×C₁₀₁	1	4	yes	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	#95	—	2	4	no	—
360	#95	—	2	4	no	—
361	#95	—	2	4	no	—
362	#95	—	2	4	no	—
363	#95	—	2	4	no	—
364	#95	—	2	4	no	—
365	#95	—	2	4	no	—
366	#95	—	2	2	no	—
367	#95	—	2	4	no	—
368	#95	C₂×C₄×C₁₀₁	1	4	yes	—
369	#95	C₂×C₄×C₁₀₁	1	8	yes	—
370	#95	C₂×C₄×C₁₀₁	1	8	yes	—
371	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
419	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
420	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
421	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
422	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
426	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
427	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
428	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
429	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
430	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
431	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
432	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
433	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
434	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
435	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
436	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	2	8	no	—
443	C₄²	—	4	4	no	—
444	C₄²	—	4	8	no	—
445	C₄²	—	4	8	no	—
446	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
447	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
448	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
449	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
450	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
451	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
452	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
453	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
454	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
455	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
456	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
516	C₂×C₄	C₄×Q₈×C₁₀₁	1	4	yes	—
517	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
518	C₂×C₄	#123×C₁₀₁	1	4	yes	—
519	C₂×C₄	#124×C₁₀₁	1	4	yes	—
520	C₂×C₄	#125×C₁₀₁	1	8	yes	—
521	C₂×C₄	#126×C₁₀₁	1	8	yes	—
522	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
523	C₂²	C₂×C₄×Q₈×C₁₀₁	1	1	yes	characteristic
524	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
525	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
526	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
527	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
528	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
529	C₂²	#525×C₁₀₁	1	1	yes	characteristic
530	C₂²	#525×C₁₀₁	1	1	yes	characteristic
531	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
532	C₂²	C₂×#125×C₁₀₁	1	2	yes	—
533	C₂²	C₂×#126×C₁₀₁	1	2	yes	—
534	C₂²	#529×C₁₀₁	1	2	yes	—
535	C₂²	#529×C₁₀₁	1	2	yes	—
536	C₂²	#529×C₁₀₁	1	2	yes	—
537	C₂²	#529×C₁₀₁	1	2	yes	—
538	C₂²	#529×C₁₀₁	1	2	yes	—
539	C₂²	#529×C₁₀₁	1	1	yes	characteristic
540	C₂²	#529×C₁₀₁	1	2	yes	—
541	C₂²	#529×C₁₀₁	1	2	yes	—
542	C₂²	#532×C₁₀₁	1	1	yes	characteristic
543	C₂²	#533×C₁₀₁	1	2	yes	—
544	C₂²	#533×C₁₀₁	1	1	yes	characteristic
545	C₄	—	2	4	no	—
546	C₄	—	2	4	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₄	#400×C₁₀₁	1	8	yes	direct product factor
556	C₂	C₄×#123×C₁₀₁	1	1	yes	characteristic
557	C₂	C₄×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
558	C₂	C₄×#124×C₁₀₁	1	1	yes	characteristic
559	C₂	C₄×#126×C₁₀₁	1	2	yes	—
560	C₂	C₄×#125×C₁₀₁	1	2	yes	—
561	C₂	C₂×#400×C₁₀₁	1	1	yes	characteristic
562	C₂	C₁₀₁×#2395	1	1	yes	characteristic
563	C₂	C₁₀₁×#2396	1	1	yes	characteristic
564	C₂	C₁₀₁×#2398	1	1	yes	characteristic
565	C₂	C₁₀₁×#2401	1	2	yes	—
566	C₂	C₁₀₁×#2402	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₀₁	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
21. #400×C₁₀₁	C₄	direct (N × H)
271. C₄×C₁₀₁	#400	direct (N × H)
272. C₄×#400	C₁₀₁	direct (N × H)
295. C₁₀₁	C₄×#400	direct (N × H)
305. #400	C₄×C₁₀₁	direct (N × H)
555. C₄	#400×C₁₀₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#400×C₁₀₁	2
C₂×C₄×C₄⋊C₄×C₁₀₁	2
C₁₀₁×#1445	2
C₁₀₁×#1443	2
C₁₀₁×#1442	2
C₁₀₁×#1441	2
C₄×#95×C₁₀₁	2
C₄×#400	101

Subgroups — C4×#400×C101 #38796015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#400×C₁₀₁ #38796015