Subgroups — C₂×C₁₀₁×#2021 #38805592

Order 25856.

3986 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂²×#99×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#379×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2021	C₂	1	8	yes	maximal, direct product factor
6	C₂×#342×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₀₁	—	2	2	no	—
9	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
10	#534×C₁₀₁	—	2	4	no	—
11	#534×C₁₀₁	—	2	2	no	—
12	#534×C₁₀₁	C₂²	1	4	yes	complemented
13	C₂×#123×C₁₀₁	—	2	2	no	—
14	C₂×#121×C₁₀₁	—	2	2	no	—
15	C₂×#120×C₁₀₁	—	2	8	no	—
16	C₂×#120×C₁₀₁	—	2	2	no	—
17	C₂×#120×C₁₀₁	—	2	4	no	—
18	C₂×#120×C₁₀₁	—	2	8	no	—
19	C₂×#120×C₁₀₁	C₂²	1	8	yes	complemented
20	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
21	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
22	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#99×C₁₀₁	—	2	8	no	—
26	C₂×#99×C₁₀₁	C₂²	1	8	yes	complemented
27	#379×C₁₀₁	—	2	2	no	—
28	#379×C₁₀₁	C₂²	1	4	yes	complemented
29	#342×C₁₀₁	C₂²	1	4	yes	complemented
30	C₂⁵×C₁₀₁	—	2	1	no	—
31	C₂⁵×C₁₀₁	—	2	2	no	—
32	C₂⁵×C₁₀₁	—	2	4	no	—
33	C₂⁵×C₁₀₁	—	2	2	no	—
34	C₂⁵×C₁₀₁	—	2	1	no	—
35	C₂⁵×C₁₀₁	—	2	2	no	—
36	C₂⁵×C₁₀₁	—	4	8	no	—
37	C₂⁵×C₁₀₁	D₄	1	4	yes	complemented
38	C₂⁵×C₁₀₁	D₄	1	2	yes	complemented
39	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
40	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₀₁	—	2	16	no	—
42	C₂²×D₄×C₁₀₁	—	2	4	no	—
43	C₂²×D₄×C₁₀₁	—	2	4	no	—
44	C₂²×D₄×C₁₀₁	—	2	4	no	—
45	C₂²×D₄×C₁₀₁	—	2	2	no	—
46	C₂²×D₄×C₁₀₁	—	2	2	no	—
47	C₂²×D₄×C₁₀₁	—	2	2	no	—
48	C₂²×D₄×C₁₀₁	—	2	2	no	—
49	C₂²×D₄×C₁₀₁	—	2	8	no	—
50	C₂²×D₄×C₁₀₁	—	2	4	no	—
51	C₂²×D₄×C₁₀₁	—	2	2	no	—
52	C₂²×D₄×C₁₀₁	—	4	16	no	—
53	C₂²×D₄×C₁₀₁	D₄	1	4	yes	complemented
54	C₂²×D₄×C₁₀₁	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₀₁	—	2	2	no	—
56	C₂³×C₄×C₁₀₁	—	2	1	no	—
57	C₂³×C₄×C₁₀₁	D₄	1	2	yes	complemented
58	C₂³×C₄×C₁₀₁	D₄	1	2	yes	complemented
59	#123×C₁₀₁	—	2	8	no	—
60	#123×C₁₀₁	—	2	8	no	—
61	#121×C₁₀₁	—	2	8	no	—
62	#121×C₁₀₁	—	2	8	no	—
63	#120×C₁₀₁	—	2	32	no	—
64	#120×C₁₀₁	—	2	8	no	—
65	#120×C₁₀₁	—	2	16	no	—
66	#120×C₁₀₁	—	2	8	no	—
67	#120×C₁₀₁	—	2	16	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	—	4	8	no	—
80	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	complemented
81	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	complemented
82	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
85	#99×C₁₀₁	—	2	16	no	—
86	C₂⁴×C₁₀₁	—	2	8	no	—
87	C₂⁴×C₁₀₁	—	2	16	no	—
88	C₂⁴×C₁₀₁	—	2	8	no	—
89	C₂⁴×C₁₀₁	—	2	4	no	—
90	C₂⁴×C₁₀₁	—	2	2	no	—
91	C₂⁴×C₁₀₁	—	2	4	no	—
92	C₂⁴×C₁₀₁	—	2	8	no	—
93	C₂⁴×C₁₀₁	—	2	4	no	—
94	C₂⁴×C₁₀₁	—	2	2	no	—
95	C₂⁴×C₁₀₁	—	2	4	no	—
96	C₂⁴×C₁₀₁	—	2	4	no	—
97	C₂⁴×C₁₀₁	—	2	2	no	—
98	C₂⁴×C₁₀₁	—	2	2	no	—
99	C₂⁴×C₁₀₁	—	2	4	no	—
100	C₂⁴×C₁₀₁	—	4	16	no	—
101	C₂⁴×C₁₀₁	—	4	8	no	—
102	C₂⁴×C₁₀₁	—	4	4	no	—
103	C₂⁴×C₁₀₁	—	4	4	no	—
104	C₂⁴×C₁₀₁	—	4	8	no	—
105	C₂⁴×C₁₀₁	—	4	8	no	—
106	C₂⁴×C₁₀₁	—	4	16	no	—
107	C₂⁴×C₁₀₁	—	4	32	no	—
108	C₂⁴×C₁₀₁	—	4	16	no	—
109	C₂⁴×C₁₀₁	—	4	8	no	—
110	C₂⁴×C₁₀₁	—	4	2	no	—
111	C₂⁴×C₁₀₁	—	4	1	no	—
112	C₂⁴×C₁₀₁	—	4	1	no	—
113	C₂⁴×C₁₀₁	—	4	4	no	—
114	C₂⁴×C₁₀₁	—	4	4	no	—
115	C₂⁴×C₁₀₁	—	4	2	no	—
116	C₂⁴×C₁₀₁	—	4	2	no	—
117	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
118	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
120	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
121	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	complemented
124	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	complemented
125	C₂⁴×C₁₀₁	#41	1	2	yes	—
126	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
127	C₂×D₄×C₁₀₁	—	2	32	no	—
128	C₂×D₄×C₁₀₁	—	2	8	no	—
129	C₂×D₄×C₁₀₁	—	2	4	no	—
130	C₂×D₄×C₁₀₁	—	2	4	no	—
131	C₂×D₄×C₁₀₁	—	2	8	no	—
132	C₂×D₄×C₁₀₁	—	2	4	no	—
133	C₂×D₄×C₁₀₁	—	2	4	no	—
134	C₂×D₄×C₁₀₁	—	2	4	no	—
135	C₂×D₄×C₁₀₁	—	2	4	no	—
136	C₂×D₄×C₁₀₁	—	2	4	no	—
137	C₂×D₄×C₁₀₁	—	2	4	no	—
138	C₂×D₄×C₁₀₁	—	2	8	no	—
139	C₂×D₄×C₁₀₁	—	4	32	no	—
140	C₂×D₄×C₁₀₁	—	4	64	no	—
141	C₂×D₄×C₁₀₁	—	4	4	no	—
142	C₂×D₄×C₁₀₁	—	4	4	no	—
143	C₂×D₄×C₁₀₁	—	4	4	no	—
144	C₂×D₄×C₁₀₁	—	4	4	no	—
145	C₂×D₄×C₁₀₁	—	4	4	no	—
146	C₂×D₄×C₁₀₁	—	4	4	no	—
147	C₂×D₄×C₁₀₁	—	4	4	no	—
148	C₂×D₄×C₁₀₁	—	4	4	no	—
149	C₂×D₄×C₁₀₁	—	8	4	no	—
150	C₂²×C₄×C₁₀₁	—	2	4	no	—
151	C₂²×C₄×C₁₀₁	—	2	8	no	—
152	C₂²×C₄×C₁₀₁	—	2	2	no	—
153	C₂²×C₄×C₁₀₁	—	2	2	no	—
154	C₂²×C₄×C₁₀₁	—	2	2	no	—
155	C₂²×C₄×C₁₀₁	—	2	4	no	—
156	C₂²×C₄×C₁₀₁	—	2	4	no	—
157	C₂²×C₄×C₁₀₁	—	2	2	no	—
158	C₂²×C₄×C₁₀₁	—	2	2	no	—
159	C₂²×C₄×C₁₀₁	—	4	8	no	—
160	C₂²×C₄×C₁₀₁	—	4	4	no	—
161	C₂²×C₄×C₁₀₁	—	4	4	no	—
162	C₂²×C₄×C₁₀₁	—	4	2	no	—
163	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	complemented
164	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	complemented
165	C₄⋊C₄×C₁₀₁	—	2	8	no	—
166	C₂²⋊C₄×C₁₀₁	—	2	32	no	—
167	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
168	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
169	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
170	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
171	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
172	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
173	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
174	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
175	C₂²⋊C₄×C₁₀₁	C₂×D₄	1	8	yes	complemented
176	C₂³×C₁₀₁	—	2	4	no	—
177	C₂³×C₁₀₁	—	2	8	no	—
178	C₂³×C₁₀₁	—	2	8	no	—
179	C₂³×C₁₀₁	—	2	16	no	—
180	C₂³×C₁₀₁	—	2	32	no	—
181	C₂³×C₁₀₁	—	2	16	no	—
182	C₂³×C₁₀₁	—	2	8	no	—
183	C₂³×C₁₀₁	—	2	4	no	—
184	C₂³×C₁₀₁	—	2	4	no	—
185	C₂³×C₁₀₁	—	2	4	no	—
186	C₂³×C₁₀₁	—	2	4	no	—
187	C₂³×C₁₀₁	—	4	2	no	—
188	C₂³×C₁₀₁	—	4	4	no	—
189	C₂³×C₁₀₁	—	4	4	no	—
190	C₂³×C₁₀₁	—	4	8	no	—
191	C₂³×C₁₀₁	—	4	8	no	—
192	C₂³×C₁₀₁	—	4	4	no	—
193	C₂³×C₁₀₁	—	4	2	no	—
194	C₂³×C₁₀₁	—	4	4	no	—
195	C₂³×C₁₀₁	—	4	8	no	—
196	C₂³×C₁₀₁	—	4	8	no	—
197	C₂³×C₁₀₁	—	4	16	no	—
198	C₂³×C₁₀₁	—	4	16	no	—
199	C₂³×C₁₀₁	—	4	16	no	—
200	C₂³×C₁₀₁	—	4	8	no	—
201	C₂³×C₁₀₁	—	4	32	no	—
202	C₂³×C₁₀₁	—	4	32	no	—
203	C₂³×C₁₀₁	—	4	16	no	—
204	C₂³×C₁₀₁	—	4	16	no	—
205	C₂³×C₁₀₁	—	4	8	no	—
206	C₂³×C₁₀₁	—	4	8	no	—
207	C₂³×C₁₀₁	—	4	16	no	—
208	C₂³×C₁₀₁	—	4	32	no	—
209	C₂³×C₁₀₁	—	4	16	no	—
210	C₂³×C₁₀₁	—	4	2	no	—
211	C₂³×C₁₀₁	—	4	4	no	—
212	C₂³×C₁₀₁	—	4	2	no	—
213	C₂³×C₁₀₁	—	4	8	no	—
214	C₂³×C₁₀₁	—	4	4	no	—
215	C₂³×C₁₀₁	—	4	4	no	—
216	C₂³×C₁₀₁	—	4	8	no	—
217	C₂³×C₁₀₁	—	4	4	no	—
218	C₂³×C₁₀₁	—	4	4	no	—
219	C₂³×C₁₀₁	—	4	8	no	—
220	C₂³×C₁₀₁	—	8	4	no	—
221	C₂³×C₁₀₁	—	8	8	no	—
222	C₂³×C₁₀₁	#120	1	2	yes	—
223	C₂³×C₁₀₁	#120	1	4	yes	—
224	C₂³×C₁₀₁	#120	1	1	yes	characteristic
225	C₂³×C₁₀₁	#120	1	4	yes	—
226	C₂³×C₁₀₁	#120	1	1	yes	characteristic
227	C₂³×C₁₀₁	#121	1	4	yes	—
228	C₂³×C₁₀₁	#121	1	2	yes	—
229	C₂³×C₁₀₁	#121	1	4	yes	—
230	C₂³×C₁₀₁	#121	1	2	yes	—
231	C₂³×C₁₀₁	#127	1	2	yes	—
232	C₂³×C₁₀₁	#127	1	2	yes	—
233	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
234	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
235	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
236	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
237	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
238	D₄×C₁₀₁	—	4	64	no	—
239	D₄×C₁₀₁	—	4	4	no	—
240	D₄×C₁₀₁	—	4	4	no	—
241	D₄×C₁₀₁	—	4	4	no	—
242	D₄×C₁₀₁	—	4	4	no	—
243	D₄×C₁₀₁	—	4	8	no	—
244	D₄×C₁₀₁	—	4	8	no	—
245	D₄×C₁₀₁	—	8	8	no	—
246	C₂×C₄×C₁₀₁	—	2	4	no	—
247	C₂×C₄×C₁₀₁	—	2	4	no	—
248	C₂×C₄×C₁₀₁	—	2	8	no	—
249	C₂×C₄×C₁₀₁	—	2	4	no	—
250	C₂×C₄×C₁₀₁	—	2	4	no	—
251	C₂×C₄×C₁₀₁	—	4	8	no	—
252	C₂×C₄×C₁₀₁	—	4	16	no	—
253	C₂×C₄×C₁₀₁	—	4	4	no	—
254	C₂×C₄×C₁₀₁	—	4	4	no	—
255	C₂×C₄×C₁₀₁	—	4	4	no	—
256	C₂×C₄×C₁₀₁	—	4	4	no	—
257	C₂×C₄×C₁₀₁	—	4	4	no	—
258	C₂×C₄×C₁₀₁	—	4	2	no	—
259	C₂×C₄×C₁₀₁	—	8	2	no	—
260	C₂×C₄×C₁₀₁	—	8	4	no	—
261	C₂²×C₁₀₁	—	2	2	no	—
262	C₂²×C₁₀₁	—	2	4	no	—
263	C₂²×C₁₀₁	—	2	2	no	—
264	C₂²×C₁₀₁	—	2	4	no	—
265	C₂²×C₁₀₁	—	2	8	no	—
266	C₂²×C₁₀₁	—	2	4	no	—
267	C₂²×C₁₀₁	—	2	4	no	—
268	C₂²×C₁₀₁	—	2	8	no	—
269	C₂²×C₁₀₁	—	2	16	no	—
270	C₂²×C₁₀₁	—	2	8	no	—
271	C₂²×C₁₀₁	—	4	4	no	—
272	C₂²×C₁₀₁	—	4	2	no	—
273	C₂²×C₁₀₁	—	4	4	no	—
274	C₂²×C₁₀₁	—	4	2	no	—
275	C₂²×C₁₀₁	—	4	1	no	—
276	C₂²×C₁₀₁	—	4	2	no	—
277	C₂²×C₁₀₁	—	4	1	no	—
278	C₂²×C₁₀₁	—	4	8	no	—
279	C₂²×C₁₀₁	—	4	8	no	—
280	C₂²×C₁₀₁	—	4	4	no	—
281	C₂²×C₁₀₁	—	4	16	no	—
282	C₂²×C₁₀₁	—	4	32	no	—
283	C₂²×C₁₀₁	—	4	16	no	—
284	C₂²×C₁₀₁	—	4	8	no	—
285	C₂²×C₁₀₁	—	4	4	no	—
286	C₂²×C₁₀₁	—	4	8	no	—
287	C₂²×C₁₀₁	—	4	16	no	—
288	C₂²×C₁₀₁	—	4	4	no	—
289	C₂²×C₁₀₁	—	4	8	no	—
290	C₂²×C₁₀₁	—	8	4	no	—
291	C₂²×C₁₀₁	—	8	8	no	—
292	C₂²×C₁₀₁	—	8	8	no	—
293	C₂²×C₁₀₁	#392	1	4	yes	—
294	C₂²×C₁₀₁	#392	1	2	yes	—
295	C₂²×C₁₀₁	#392	1	2	yes	—
296	C₂²×C₁₀₁	B(4,𝔽₂)	1	4	yes	—
297	C₂²×C₁₀₁	C₂×#120	1	2	yes	—
298	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
299	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
300	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
301	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
302	C₄×C₁₀₁	—	4	8	no	—
303	C₄×C₁₀₁	—	4	4	no	—
304	C₄×C₁₀₁	—	4	4	no	—
305	C₄×C₁₀₁	—	8	2	no	—
306	C₂×#2021	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂×C₁₀₁	—	2	2	no	—
308	C₂×C₁₀₁	—	2	1	no	—
309	C₂×C₁₀₁	—	2	1	no	—
310	C₂×C₁₀₁	—	2	2	no	—
311	C₂×C₁₀₁	—	2	4	no	—
312	C₂×C₁₀₁	—	2	2	no	—
313	C₂×C₁₀₁	—	4	8	no	—
314	C₂×C₁₀₁	—	8	4	no	—
315	C₂×C₁₀₁	#2021	1	4	yes	direct product factor
316	C₂×C₁₀₁	C₂×#392	1	1	yes	characteristic
317	C₂×C₁₀₁	C₂×B(4,𝔽₂)	1	2	yes	—
318	C₂×#534	C₂×C₁₀₁	1	1	yes	characteristic, complemented
319	C₂²×#120	C₂×C₁₀₁	1	2	yes	complemented
320	C₂²×#99	C₂×C₁₀₁	1	2	yes	complemented
321	C₂×#379	C₂×C₁₀₁	1	1	yes	characteristic, complemented
322	#2021	C₂×C₁₀₁	1	8	yes	direct product factor
323	C₂×#342	C₂×C₁₀₁	1	1	yes	characteristic, complemented
324	C₁₀₁	C₂×#2021	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁶	C₂²×C₁₀₁	1	1	yes	characteristic
326	C₂³×D₄	—	2	2	no	—
327	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
328	#534	—	2	4	no	—
329	#534	—	2	2	no	—
330	#534	C₂²×C₁₀₁	1	4	yes	complemented
331	C₂×#123	—	2	2	no	—
332	C₂×#121	—	2	2	no	—
333	C₂×#120	—	2	8	no	—
334	C₂×#120	—	2	2	no	—
335	C₂×#120	—	2	4	no	—
336	C₂×#120	—	2	8	no	—
337	C₂×#120	C₂²×C₁₀₁	1	8	yes	complemented
338	C₂²×C₂²⋊C₄	—	2	2	no	—
339	C₂²×C₂²⋊C₄	—	2	2	no	—
340	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
343	C₂×#99	—	2	8	no	—
344	C₂×#99	C₂²×C₁₀₁	1	8	yes	complemented
345	#379	—	2	2	no	—
346	#379	C₂²×C₁₀₁	1	4	yes	complemented
347	#342	C₂²×C₁₀₁	1	4	yes	complemented
348	C₂⁵	—	2	1	no	—
349	C₂⁵	—	2	2	no	—
350	C₂⁵	—	2	4	no	—
351	C₂⁵	—	2	2	no	—
352	C₂⁵	—	2	1	no	—
353	C₂⁵	—	2	2	no	—
354	C₂⁵	—	4	8	no	—
355	C₂⁵	D₄×C₁₀₁	1	4	yes	complemented
356	C₂⁵	D₄×C₁₀₁	1	2	yes	complemented
357	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
358	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
359	C₂²×D₄	—	2	16	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	4	no	—
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	4	no	—
367	C₂²×D₄	—	2	8	no	—
368	C₂²×D₄	—	2	4	no	—
369	C₂²×D₄	—	2	2	no	—
370	C₂²×D₄	—	4	16	no	—
371	C₂²×D₄	D₄×C₁₀₁	1	4	yes	complemented
372	C₂²×D₄	C₂³×C₁₀₁	1	4	yes	—
373	C₂³×C₄	—	2	2	no	—
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	D₄×C₁₀₁	1	2	yes	complemented
376	C₂³×C₄	D₄×C₁₀₁	1	2	yes	complemented
377	#123	—	2	8	no	—
378	#123	—	2	8	no	—
379	#121	—	2	8	no	—
380	#121	—	2	8	no	—
381	#120	—	2	32	no	—
382	#120	—	2	8	no	—
383	#120	—	2	16	no	—
384	#120	—	2	8	no	—
385	#120	—	2	16	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	16	no	—
388	C₂×C₂²⋊C₄	—	2	4	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	4	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	8	no	—
394	C₂×C₂²⋊C₄	—	2	4	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	8	no	—
397	C₂×C₂²⋊C₄	—	4	8	no	—
398	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	complemented
399	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	complemented
400	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
403	#99	—	2	16	no	—
404	C₂⁴	—	2	8	no	—
405	C₂⁴	—	2	16	no	—
406	C₂⁴	—	2	8	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	8	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	4	8	no	—
421	C₂⁴	—	4	4	no	—
422	C₂⁴	—	4	8	no	—
423	C₂⁴	—	4	8	no	—
424	C₂⁴	—	4	16	no	—
425	C₂⁴	—	4	32	no	—
426	C₂⁴	—	4	16	no	—
427	C₂⁴	—	4	8	no	—
428	C₂⁴	—	4	2	no	—
429	C₂⁴	—	4	1	no	—
430	C₂⁴	—	4	1	no	—
431	C₂⁴	—	4	4	no	—
432	C₂⁴	—	4	4	no	—
433	C₂⁴	—	4	2	no	—
434	C₂⁴	—	4	2	no	—
435	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
436	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
437	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
438	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
439	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
440	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
441	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	complemented
442	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	complemented
443	C₂⁴	#41×C₁₀₁	1	2	yes	—
444	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
445	C₂×D₄	—	2	32	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	4	32	no	—
458	C₂×D₄	—	4	64	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	4	4	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	8	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	8	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	complemented
482	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	complemented
483	C₄⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	32	no	—
485	C₂²⋊C₄	—	2	16	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	4	16	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	C₂×D₄×C₁₀₁	1	8	yes	complemented
494	C₂³	—	2	4	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	16	no	—
498	C₂³	—	2	32	no	—
499	C₂³	—	2	16	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	4	no	—
507	C₂³	—	4	4	no	—
508	C₂³	—	4	8	no	—
509	C₂³	—	4	8	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	8	no	—
515	C₂³	—	4	16	no	—
516	C₂³	—	4	16	no	—
517	C₂³	—	4	16	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	32	no	—
520	C₂³	—	4	32	no	—
521	C₂³	—	4	16	no	—
522	C₂³	—	4	16	no	—
523	C₂³	—	4	8	no	—
524	C₂³	—	4	8	no	—
525	C₂³	—	4	16	no	—
526	C₂³	—	4	32	no	—
527	C₂³	—	4	16	no	—
528	C₂³	—	4	8	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	8	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	8	4	no	—
539	C₂³	—	8	8	no	—
540	C₂³	#120×C₁₀₁	1	2	yes	—
541	C₂³	#120×C₁₀₁	1	4	yes	—
542	C₂³	#120×C₁₀₁	1	1	yes	characteristic
543	C₂³	#120×C₁₀₁	1	4	yes	—
544	C₂³	#120×C₁₀₁	1	1	yes	characteristic
545	C₂³	#121×C₁₀₁	1	4	yes	—
546	C₂³	#121×C₁₀₁	1	2	yes	—
547	C₂³	#121×C₁₀₁	1	4	yes	—
548	C₂³	#121×C₁₀₁	1	2	yes	—
549	C₂³	#127×C₁₀₁	1	2	yes	—
550	C₂³	#127×C₁₀₁	1	2	yes	—
551	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
552	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
553	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
554	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
555	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
556	D₄	—	4	64	no	—
557	D₄	—	4	4	no	—
558	D₄	—	4	4	no	—
559	D₄	—	4	4	no	—
560	D₄	—	4	4	no	—
561	D₄	—	4	8	no	—
562	D₄	—	4	8	no	—
563	D₄	—	8	8	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	4	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	16	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	8	no	—
597	C₂²	—	4	8	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	16	no	—
600	C₂²	—	4	32	no	—
601	C₂²	—	4	16	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	8	no	—
604	C₂²	—	4	16	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	4	8	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	8	4	no	—
609	C₂²	—	8	8	no	—
610	C₂²	—	8	8	no	—
611	C₂²	#392×C₁₀₁	1	4	yes	—
612	C₂²	#392×C₁₀₁	1	2	yes	—
613	C₂²	#392×C₁₀₁	1	2	yes	—
614	C₂²	B(4,𝔽₂)×C₁₀₁	1	4	yes	—
615	C₂²	C₂×#120×C₁₀₁	1	2	yes	—
616	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
617	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
618	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
619	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
620	C₄	—	4	8	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	4	no	—
623	C₄	—	8	2	no	—
624	C₂	—	2	2	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	2	2	no	—
628	C₂	—	2	4	no	—
629	C₂	—	2	2	no	—
630	C₂	—	4	8	no	—
631	C₂	—	8	4	no	—
632	C₂	C₁₀₁×#2021	1	4	yes	direct product factor
633	C₂	C₂×#392×C₁₀₁	1	1	yes	characteristic
634	C₂	C₂×B(4,𝔽₂)×C₁₀₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂⁵×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#534×C₁₀₁	C₂	semidirect
2. C₂²×#120×C₁₀₁	C₂	semidirect
3. C₂²×#99×C₁₀₁	C₂	semidirect
4. C₂×#379×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2021	C₂	direct (N × H)
6. C₂×#342×C₁₀₁	C₂	semidirect
12. #534×C₁₀₁	C₂²	semidirect
19. C₂×#120×C₁₀₁	C₂²	semidirect
26. C₂×#99×C₁₀₁	C₂²	semidirect
28. #379×C₁₀₁	C₂²	semidirect
29. #342×C₁₀₁	C₂²	semidirect
37. C₂⁵×C₁₀₁	D₄	semidirect
38. C₂⁵×C₁₀₁	D₄	semidirect
53. C₂²×D₄×C₁₀₁	D₄	semidirect
57. C₂³×C₄×C₁₀₁	D₄	semidirect
58. C₂³×C₄×C₁₀₁	D₄	semidirect
80. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
81. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
123. C₂⁴×C₁₀₁	C₂×D₄	semidirect
124. C₂⁴×C₁₀₁	C₂×D₄	semidirect
163. C₂²×C₄×C₁₀₁	C₂×D₄	semidirect
164. C₂²×C₄×C₁₀₁	C₂×D₄	semidirect
175. C₂²⋊C₄×C₁₀₁	C₂×D₄	semidirect
306. C₂×#2021	C₁₀₁	direct (N × H)
315. C₂×C₁₀₁	#2021	direct (N × H)
318. C₂×#534	C₂×C₁₀₁	semidirect
319. C₂²×#120	C₂×C₁₀₁	semidirect
320. C₂²×#99	C₂×C₁₀₁	semidirect
321. C₂×#379	C₂×C₁₀₁	semidirect
322. #2021	C₂×C₁₀₁	direct (N × H)
323. C₂×#342	C₂×C₁₀₁	semidirect
324. C₁₀₁	C₂×#2021	direct (N × H)
330. #534	C₂²×C₁₀₁	semidirect
337. C₂×#120	C₂²×C₁₀₁	semidirect
344. C₂×#99	C₂²×C₁₀₁	semidirect
346. #379	C₂²×C₁₀₁	semidirect
347. #342	C₂²×C₁₀₁	semidirect
355. C₂⁵	D₄×C₁₀₁	semidirect
356. C₂⁵	D₄×C₁₀₁	semidirect
371. C₂²×D₄	D₄×C₁₀₁	semidirect
375. C₂³×C₄	D₄×C₁₀₁	semidirect
376. C₂³×C₄	D₄×C₁₀₁	semidirect
398. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
399. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
441. C₂⁴	C₂×D₄×C₁₀₁	semidirect
442. C₂⁴	C₂×D₄×C₁₀₁	semidirect
481. C₂²×C₄	C₂×D₄×C₁₀₁	semidirect
482. C₂²×C₄	C₂×D₄×C₁₀₁	semidirect
493. C₂²⋊C₄	C₂×D₄×C₁₀₁	semidirect
632. C₂	C₁₀₁×#2021	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×#534×C₁₀₁	2
C₂²×#120×C₁₀₁	2
C₂²×#99×C₁₀₁	2
C₂×#379×C₁₀₁	2
C₁₀₁×#2021	2
C₂×#342×C₁₀₁	2
C₂×#2021	101

Subgroups — C2×C101×#2021 #38805592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#2021 #38805592