Subgroups — C₁₀₁×#14358 #38796509

Order 25856.

3538 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#390×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#388×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#379×C₁₀₁	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1439	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1438	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1437	C₂	1	2	yes	maximal, complemented
10	C₂⁶×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#120×C₁₀₁	—	2	8	no	—
14	C₂×#120×C₁₀₁	C₄	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
16	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	complemented
28	#390×C₁₀₁	—	2	8	no	—
29	#388×C₁₀₁	—	2	8	no	—
30	#379×C₁₀₁	—	2	8	no	—
31	C₂×#95×C₁₀₁	C₂²	1	2	yes	complemented
32	C₂×#95×C₁₀₁	C₂²	1	2	yes	complemented
33	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×#95×C₁₀₁	C₂²	1	2	yes	complemented
35	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
36	C₂⁵×C₁₀₁	—	2	4	no	—
37	C₂⁵×C₁₀₁	—	2	4	no	—
38	C₂⁵×C₁₀₁	—	2	4	no	—
39	C₂⁵×C₁₀₁	—	4	2	no	—
40	C₂⁵×C₁₀₁	—	4	2	no	—
41	C₂⁵×C₁₀₁	—	4	1	no	—
42	C₂⁵×C₁₀₁	—	4	1	no	—
43	C₂⁵×C₁₀₁	—	4	2	no	—
44	C₂⁵×C₁₀₁	C₂×C₄	1	4	yes	—
45	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₀₁	—	2	4	no	—
49	C₂²×D₄×C₁₀₁	—	2	4	no	—
50	C₂²×D₄×C₁₀₁	—	2	4	no	—
51	C₂²×D₄×C₁₀₁	—	2	4	no	—
52	C₂²×D₄×C₁₀₁	—	2	4	no	—
53	C₂²×D₄×C₁₀₁	—	4	2	no	—
54	C₂²×D₄×C₁₀₁	—	4	2	no	—
55	C₂²×D₄×C₁₀₁	—	4	2	no	—
56	C₂²×D₄×C₁₀₁	—	4	1	no	—
57	C₂²×D₄×C₁₀₁	—	4	1	no	—
58	C₂²×D₄×C₁₀₁	C₂×C₄	1	8	yes	—
59	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
60	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
66	#120×C₁₀₁	—	2	32	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
69	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
85	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
86	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
87	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
88	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
89	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
90	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
91	C₂×C₂²⋊C₄×C₁₀₁	—	4	1	no	—
92	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
93	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	—	4	1	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
97	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	—
99	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	complemented
100	C₂×C₄²×C₁₀₁	—	2	4	no	—
101	C₂×C₄²×C₁₀₁	—	2	4	no	—
102	C₂×C₄²×C₁₀₁	—	4	2	no	—
103	#95×C₁₀₁	—	2	4	no	—
104	#95×C₁₀₁	—	2	4	no	—
105	#95×C₁₀₁	—	4	1	no	—
106	#95×C₁₀₁	—	4	2	no	—
107	#95×C₁₀₁	—	4	1	no	—
108	C₂⁴×C₁₀₁	—	2	2	no	—
109	C₂⁴×C₁₀₁	—	2	2	no	—
110	C₂⁴×C₁₀₁	—	2	2	no	—
111	C₂⁴×C₁₀₁	—	2	2	no	—
112	C₂⁴×C₁₀₁	—	2	2	no	—
113	C₂⁴×C₁₀₁	—	2	2	no	—
114	C₂⁴×C₁₀₁	—	2	2	no	—
115	C₂⁴×C₁₀₁	—	2	2	no	—
116	C₂⁴×C₁₀₁	—	2	2	no	—
117	C₂⁴×C₁₀₁	—	2	2	no	—
118	C₂⁴×C₁₀₁	—	2	2	no	—
119	C₂⁴×C₁₀₁	—	2	2	no	—
120	C₂⁴×C₁₀₁	—	2	2	no	—
121	C₂⁴×C₁₀₁	—	2	2	no	—
122	C₂⁴×C₁₀₁	—	2	2	no	—
123	C₂⁴×C₁₀₁	—	2	1	no	—
124	C₂⁴×C₁₀₁	—	2	1	no	—
125	C₂⁴×C₁₀₁	—	2	2	no	—
126	C₂⁴×C₁₀₁	—	2	2	no	—
127	C₂⁴×C₁₀₁	—	2	8	no	—
128	C₂⁴×C₁₀₁	—	2	16	no	—
129	C₂⁴×C₁₀₁	—	2	2	no	—
130	C₂⁴×C₁₀₁	—	2	2	no	—
131	C₂⁴×C₁₀₁	—	2	2	no	—
132	C₂⁴×C₁₀₁	—	2	2	no	—
133	C₂⁴×C₁₀₁	—	2	2	no	—
134	C₂⁴×C₁₀₁	—	2	1	no	—
135	C₂⁴×C₁₀₁	—	2	1	no	—
136	C₂⁴×C₁₀₁	—	2	2	no	—
137	C₂⁴×C₁₀₁	—	4	4	no	—
138	C₂⁴×C₁₀₁	—	4	8	no	—
139	C₂⁴×C₁₀₁	—	4	4	no	—
140	C₂⁴×C₁₀₁	—	4	4	no	—
141	C₂⁴×C₁₀₁	—	4	8	no	—
142	C₂⁴×C₁₀₁	—	4	8	no	—
143	C₂⁴×C₁₀₁	—	4	8	no	—
144	C₂⁴×C₁₀₁	—	4	8	no	—
145	C₂⁴×C₁₀₁	—	4	8	no	—
146	C₂⁴×C₁₀₁	—	4	4	no	—
147	C₂⁴×C₁₀₁	—	4	8	no	—
148	C₂⁴×C₁₀₁	—	4	8	no	—
149	C₂⁴×C₁₀₁	—	4	8	no	—
150	C₂⁴×C₁₀₁	—	4	8	no	—
151	C₂⁴×C₁₀₁	—	4	8	no	—
152	C₂⁴×C₁₀₁	—	4	8	no	—
153	C₂⁴×C₁₀₁	—	4	8	no	—
154	C₂⁴×C₁₀₁	—	4	4	no	—
155	C₂⁴×C₁₀₁	—	4	4	no	—
156	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
157	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
158	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
159	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
160	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
161	C₂⁴×C₁₀₁	#41	1	4	yes	—
162	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
163	C₂×D₄×C₁₀₁	—	2	8	no	—
164	C₂×D₄×C₁₀₁	—	2	16	no	—
165	C₂×D₄×C₁₀₁	—	2	16	no	—
166	C₂×D₄×C₁₀₁	—	4	8	no	—
167	C₂×D₄×C₁₀₁	—	4	4	no	—
168	C₂×D₄×C₁₀₁	—	4	4	no	—
169	C₂×D₄×C₁₀₁	—	4	8	no	—
170	C₂×D₄×C₁₀₁	—	4	8	no	—
171	C₂×D₄×C₁₀₁	—	4	8	no	—
172	C₂×D₄×C₁₀₁	—	4	8	no	—
173	C₂×D₄×C₁₀₁	—	4	8	no	—
174	C₂×D₄×C₁₀₁	—	4	8	no	—
175	C₂²×C₄×C₁₀₁	—	2	2	no	—
176	C₂²×C₄×C₁₀₁	—	2	2	no	—
177	C₂²×C₄×C₁₀₁	—	2	2	no	—
178	C₂²×C₄×C₁₀₁	—	2	2	no	—
179	C₂²×C₄×C₁₀₁	—	2	2	no	—
180	C₂²×C₄×C₁₀₁	—	2	2	no	—
181	C₂²×C₄×C₁₀₁	—	2	2	no	—
182	C₂²×C₄×C₁₀₁	—	2	2	no	—
183	C₂²×C₄×C₁₀₁	—	2	2	no	—
184	C₂²×C₄×C₁₀₁	—	2	2	no	—
185	C₂²×C₄×C₁₀₁	—	2	2	no	—
186	C₂²×C₄×C₁₀₁	—	2	2	no	—
187	C₂²×C₄×C₁₀₁	—	2	1	no	—
188	C₂²×C₄×C₁₀₁	—	2	1	no	—
189	C₂²×C₄×C₁₀₁	—	2	2	no	—
190	C₂²×C₄×C₁₀₁	—	2	2	no	—
191	C₂²×C₄×C₁₀₁	—	2	2	no	—
192	C₂²×C₄×C₁₀₁	—	2	2	no	—
193	C₂²×C₄×C₁₀₁	—	2	2	no	—
194	C₂²×C₄×C₁₀₁	—	2	2	no	—
195	C₂²×C₄×C₁₀₁	—	2	2	no	—
196	C₂²×C₄×C₁₀₁	—	2	2	no	—
197	C₂²×C₄×C₁₀₁	—	2	2	no	—
198	C₂²×C₄×C₁₀₁	—	2	2	no	—
199	C₂²×C₄×C₁₀₁	—	2	2	no	—
200	C₂²×C₄×C₁₀₁	—	2	2	no	—
201	C₂²×C₄×C₁₀₁	—	2	2	no	—
202	C₂²×C₄×C₁₀₁	—	2	2	no	—
203	C₂²×C₄×C₁₀₁	—	2	2	no	—
204	C₂²×C₄×C₁₀₁	—	2	2	no	—
205	C₂²×C₄×C₁₀₁	—	2	2	no	—
206	C₂²×C₄×C₁₀₁	—	2	2	no	—
207	C₂²×C₄×C₁₀₁	—	2	2	no	—
208	C₂²×C₄×C₁₀₁	—	2	2	no	—
209	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
210	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
211	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
215	C₄⋊C₄×C₁₀₁	—	4	8	no	—
216	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
217	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
218	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
219	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
220	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
221	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
222	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
223	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
224	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
225	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
226	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
227	C₄²×C₁₀₁	—	4	8	no	—
228	C₂³×C₁₀₁	—	2	4	no	—
229	C₂³×C₁₀₁	—	2	4	no	—
230	C₂³×C₁₀₁	—	2	4	no	—
231	C₂³×C₁₀₁	—	2	2	no	—
232	C₂³×C₁₀₁	—	2	2	no	—
233	C₂³×C₁₀₁	—	2	4	no	—
234	C₂³×C₁₀₁	—	2	4	no	—
235	C₂³×C₁₀₁	—	2	4	no	—
236	C₂³×C₁₀₁	—	2	4	no	—
237	C₂³×C₁₀₁	—	2	4	no	—
238	C₂³×C₁₀₁	—	2	4	no	—
239	C₂³×C₁₀₁	—	2	4	no	—
240	C₂³×C₁₀₁	—	2	4	no	—
241	C₂³×C₁₀₁	—	2	4	no	—
242	C₂³×C₁₀₁	—	2	4	no	—
243	C₂³×C₁₀₁	—	2	4	no	—
244	C₂³×C₁₀₁	—	2	4	no	—
245	C₂³×C₁₀₁	—	2	4	no	—
246	C₂³×C₁₀₁	—	2	4	no	—
247	C₂³×C₁₀₁	—	2	4	no	—
248	C₂³×C₁₀₁	—	2	4	no	—
249	C₂³×C₁₀₁	—	2	4	no	—
250	C₂³×C₁₀₁	—	2	4	no	—
251	C₂³×C₁₀₁	—	2	4	no	—
252	C₂³×C₁₀₁	—	2	4	no	—
253	C₂³×C₁₀₁	—	2	4	no	—
254	C₂³×C₁₀₁	—	2	4	no	—
255	C₂³×C₁₀₁	—	2	4	no	—
256	C₂³×C₁₀₁	—	2	2	no	—
257	C₂³×C₁₀₁	—	2	4	no	—
258	C₂³×C₁₀₁	—	2	2	no	—
259	C₂³×C₁₀₁	—	2	2	no	—
260	C₂³×C₁₀₁	—	2	4	no	—
261	C₂³×C₁₀₁	—	4	32	no	—
262	C₂³×C₁₀₁	—	4	16	no	—
263	C₂³×C₁₀₁	—	4	16	no	—
264	C₂³×C₁₀₁	—	4	32	no	—
265	C₂³×C₁₀₁	—	4	16	no	—
266	C₂³×C₁₀₁	—	4	32	no	—
267	C₂³×C₁₀₁	—	4	32	no	—
268	C₂³×C₁₀₁	—	4	32	no	—
269	C₂³×C₁₀₁	—	4	32	no	—
270	C₂³×C₁₀₁	—	4	2	no	—
271	C₂³×C₁₀₁	—	4	2	no	—
272	C₂³×C₁₀₁	—	4	2	no	—
273	C₂³×C₁₀₁	—	4	2	no	—
274	C₂³×C₁₀₁	—	4	2	no	—
275	C₂³×C₁₀₁	—	4	2	no	—
276	C₂³×C₁₀₁	—	4	2	no	—
277	C₂³×C₁₀₁	—	4	2	no	—
278	C₂³×C₁₀₁	—	4	2	no	—
279	C₂³×C₁₀₁	—	4	2	no	—
280	C₂³×C₁₀₁	—	4	2	no	—
281	C₂³×C₁₀₁	—	4	2	no	—
282	C₂³×C₁₀₁	—	4	2	no	—
283	C₂³×C₁₀₁	—	4	2	no	—
284	C₂³×C₁₀₁	—	4	1	no	—
285	C₂³×C₁₀₁	—	4	2	no	—
286	C₂³×C₁₀₁	—	4	2	no	—
287	C₂³×C₁₀₁	—	4	2	no	—
288	C₂³×C₁₀₁	—	4	1	no	—
289	C₂³×C₁₀₁	—	4	2	no	—
290	C₂³×C₁₀₁	—	4	2	no	—
291	C₂³×C₁₀₁	—	4	2	no	—
292	C₂³×C₁₀₁	—	4	2	no	—
293	C₂³×C₁₀₁	—	4	1	no	—
294	C₂³×C₁₀₁	—	4	2	no	—
295	C₂³×C₁₀₁	—	4	1	no	—
296	C₂³×C₁₀₁	—	4	2	no	—
297	C₂³×C₁₀₁	—	4	2	no	—
298	C₂³×C₁₀₁	—	4	2	no	—
299	C₂³×C₁₀₁	—	4	2	no	—
300	C₂³×C₁₀₁	—	4	2	no	—
301	C₂³×C₁₀₁	—	4	2	no	—
302	C₂³×C₁₀₁	—	4	1	no	—
303	C₂³×C₁₀₁	—	4	2	no	—
304	C₂³×C₁₀₁	—	4	2	no	—
305	C₂³×C₁₀₁	—	4	2	no	—
306	C₂³×C₁₀₁	—	4	2	no	—
307	C₂³×C₁₀₁	—	4	2	no	—
308	C₂³×C₁₀₁	—	4	1	no	—
309	C₂³×C₁₀₁	—	4	2	no	—
310	C₂³×C₁₀₁	—	4	1	no	—
311	C₂³×C₁₀₁	—	4	1	no	—
312	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
313	C₂³×C₁₀₁	C₄×D₄	1	8	yes	—
314	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
315	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
316	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
317	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
318	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
319	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
320	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
323	D₄×C₁₀₁	—	4	32	no	—
324	D₄×C₁₀₁	—	4	16	no	—
325	C₂×C₄×C₁₀₁	—	2	4	no	—
326	C₂×C₄×C₁₀₁	—	2	4	no	—
327	C₂×C₄×C₁₀₁	—	2	4	no	—
328	C₂×C₄×C₁₀₁	—	2	4	no	—
329	C₂×C₄×C₁₀₁	—	2	4	no	—
330	C₂×C₄×C₁₀₁	—	2	4	no	—
331	C₂×C₄×C₁₀₁	—	2	2	no	—
332	C₂×C₄×C₁₀₁	—	2	2	no	—
333	C₂×C₄×C₁₀₁	—	2	2	no	—
334	C₂×C₄×C₁₀₁	—	2	4	no	—
335	C₂×C₄×C₁₀₁	—	2	4	no	—
336	C₂×C₄×C₁₀₁	—	2	4	no	—
337	C₂×C₄×C₁₀₁	—	2	4	no	—
338	C₂×C₄×C₁₀₁	—	2	4	no	—
339	C₂×C₄×C₁₀₁	—	2	4	no	—
340	C₂×C₄×C₁₀₁	—	4	2	no	—
341	C₂×C₄×C₁₀₁	—	4	2	no	—
342	C₂×C₄×C₁₀₁	—	4	2	no	—
343	C₂×C₄×C₁₀₁	—	4	2	no	—
344	C₂×C₄×C₁₀₁	—	4	2	no	—
345	C₂×C₄×C₁₀₁	—	4	2	no	—
346	C₂×C₄×C₁₀₁	—	4	2	no	—
347	C₂×C₄×C₁₀₁	—	4	2	no	—
348	C₂×C₄×C₁₀₁	—	4	2	no	—
349	C₂×C₄×C₁₀₁	—	4	2	no	—
350	C₂×C₄×C₁₀₁	—	4	2	no	—
351	C₂×C₄×C₁₀₁	—	4	2	no	—
352	C₂×C₄×C₁₀₁	—	4	2	no	—
353	C₂×C₄×C₁₀₁	—	4	2	no	—
354	C₂×C₄×C₁₀₁	—	4	2	no	—
355	C₂×C₄×C₁₀₁	—	4	2	no	—
356	C₂×C₄×C₁₀₁	—	4	2	no	—
357	C₂×C₄×C₁₀₁	—	4	2	no	—
358	C₂×C₄×C₁₀₁	—	4	2	no	—
359	C₂×C₄×C₁₀₁	—	4	2	no	—
360	C₂×C₄×C₁₀₁	—	4	2	no	—
361	C₂×C₄×C₁₀₁	—	4	2	no	—
362	C₂×C₄×C₁₀₁	—	4	2	no	—
363	C₂×C₄×C₁₀₁	—	4	2	no	—
364	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
365	C₂²×C₁₀₁	—	2	4	no	—
366	C₂²×C₁₀₁	—	2	8	no	—
367	C₂²×C₁₀₁	—	2	8	no	—
368	C₂²×C₁₀₁	—	2	8	no	—
369	C₂²×C₁₀₁	—	2	8	no	—
370	C₂²×C₁₀₁	—	4	64	no	—
371	C₂²×C₁₀₁	—	4	4	no	—
372	C₂²×C₁₀₁	—	4	4	no	—
373	C₂²×C₁₀₁	—	4	4	no	—
374	C₂²×C₁₀₁	—	4	4	no	—
375	C₂²×C₁₀₁	—	4	2	no	—
376	C₂²×C₁₀₁	—	4	2	no	—
377	C₂²×C₁₀₁	—	4	4	no	—
378	C₂²×C₁₀₁	—	4	4	no	—
379	C₂²×C₁₀₁	—	4	4	no	—
380	C₂²×C₁₀₁	—	4	4	no	—
381	C₂²×C₁₀₁	—	4	4	no	—
382	C₂²×C₁₀₁	—	4	4	no	—
383	C₂²×C₁₀₁	—	4	4	no	—
384	C₂²×C₁₀₁	—	4	4	no	—
385	C₂²×C₁₀₁	—	4	4	no	—
386	C₂²×C₁₀₁	—	4	4	no	—
387	C₂²×C₁₀₁	—	4	4	no	—
388	C₂²×C₁₀₁	—	4	4	no	—
389	C₂²×C₁₀₁	—	4	4	no	—
390	C₂²×C₁₀₁	—	4	2	no	—
391	C₂²×C₁₀₁	—	4	4	no	—
392	C₂²×C₁₀₁	—	4	4	no	—
393	C₂²×C₁₀₁	—	4	2	no	—
394	C₂²×C₁₀₁	—	4	2	no	—
395	C₂²×C₁₀₁	—	8	2	no	—
396	C₂²×C₁₀₁	—	8	2	no	—
397	C₂²×C₁₀₁	—	8	2	no	—
398	C₂²×C₁₀₁	—	8	2	no	—
399	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
400	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
401	C₂²×C₁₀₁	#518	1	1	yes	characteristic
402	C₂²×C₁₀₁	#518	1	1	yes	characteristic
403	C₂²×C₁₀₁	#518	1	2	yes	—
404	C₂²×C₁₀₁	#534	1	2	yes	—
405	C₂²×C₁₀₁	#535	1	2	yes	—
406	C₂²×C₁₀₁	#535	1	2	yes	—
407	C₂²×C₁₀₁	#535	1	2	yes	—
408	C₂²×C₁₀₁	#538	1	2	yes	—
409	C₂²×C₁₀₁	#538	1	2	yes	—
410	C₂²×C₁₀₁	D₄²	1	2	yes	—
411	C₂²×C₁₀₁	D₄²	1	2	yes	—
412	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
413	C₂²×C₁₀₁	#546	1	2	yes	—
414	C₂²×C₁₀₁	#546	1	2	yes	—
415	C₂²×C₁₀₁	#546	1	2	yes	—
416	C₂²×C₁₀₁	#551	1	1	yes	characteristic
417	C₂²×C₁₀₁	#560	1	2	yes	—
418	C₂²×C₁₀₁	#560	1	1	yes	characteristic
419	C₂²×C₁₀₁	H(3,𝔽₄)	1	1	yes	characteristic
420	C₄×C₁₀₁	—	2	8	no	—
421	C₄×C₁₀₁	—	4	2	no	—
422	C₄×C₁₀₁	—	4	4	no	—
423	C₄×C₁₀₁	—	4	4	no	—
424	C₄×C₁₀₁	—	8	2	no	—
425	C₄×C₁₀₁	—	8	2	no	—
426	#14358	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂×C₁₀₁	—	4	4	no	—
428	C₂×C₁₀₁	—	4	8	no	—
429	C₂×C₁₀₁	—	8	2	no	—
430	C₂×C₁₀₁	#2309	1	1	yes	characteristic
431	C₂×C₁₀₁	#2321	1	2	yes	—
432	C₂×C₁₀₁	D₄×C₂²⋊C₄	1	2	yes	—
433	C₂×C₁₀₁	#2358	1	1	yes	characteristic
434	C₂×C₁₀₁	#2375	1	1	yes	characteristic
435	C₂×C₁₀₁	#2669	1	2	yes	—
436	C₂×C₁₀₁	#2670	1	2	yes	—
437	C₂×C₁₀₁	#2678	1	2	yes	—
438	C₂×C₁₀₁	#2685	1	2	yes	—
439	C₂²×#120	C₂×C₁₀₁	1	1	yes	characteristic
440	C₂×#390	C₂×C₁₀₁	1	2	yes	complemented
441	C₂×#388	C₂×C₁₀₁	1	2	yes	complemented
442	C₂×#379	C₂×C₁₀₁	1	2	yes	complemented
443	#1439	C₂×C₁₀₁	1	2	yes	complemented
444	#1438	C₂×C₁₀₁	1	2	yes	complemented
445	#1438	C₂×C₁₀₁	1	1	yes	characteristic, complemented
446	#1438	C₂×C₁₀₁	1	1	yes	characteristic, complemented
447	#1437	C₂×C₁₀₁	1	2	yes	complemented
448	C₁₀₁	#14358	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁶	C₂²×C₁₀₁	1	1	yes	characteristic
450	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
451	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
452	C₂×#120	—	2	8	no	—
453	C₂×#120	C₄×C₁₀₁	1	8	yes	complemented
454	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	complemented
455	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
456	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
457	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
458	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
459	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
460	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
461	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
462	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
463	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
464	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	complemented
465	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
466	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	complemented
467	#390	—	2	8	no	—
468	#388	—	2	8	no	—
469	#379	—	2	8	no	—
470	C₂×#95	C₂²×C₁₀₁	1	2	yes	complemented
471	C₂×#95	C₂²×C₁₀₁	1	2	yes	complemented
472	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
473	C₂×#95	C₂²×C₁₀₁	1	2	yes	complemented
474	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
475	C₂⁵	—	2	4	no	—
476	C₂⁵	—	2	4	no	—
477	C₂⁵	—	2	4	no	—
478	C₂⁵	—	4	2	no	—
479	C₂⁵	—	4	2	no	—
480	C₂⁵	—	4	1	no	—
481	C₂⁵	—	4	1	no	—
482	C₂⁵	—	4	2	no	—
483	C₂⁵	C₂×C₄×C₁₀₁	1	4	yes	—
484	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
485	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
486	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
487	C₂²×D₄	—	2	4	no	—
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	—	2	4	no	—
490	C₂²×D₄	—	2	4	no	—
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	—	4	2	no	—
493	C₂²×D₄	—	4	2	no	—
494	C₂²×D₄	—	4	2	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	C₂×C₄×C₁₀₁	1	8	yes	—
498	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
499	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
503	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
504	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
505	#120	—	2	32	no	—
506	C₂×C₄⋊C₄	—	2	4	no	—
507	C₂×C₄⋊C₄	—	2	4	no	—
508	C₂×C₄⋊C₄	—	4	2	no	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₂²⋊C₄	—	2	4	no	—
518	C₂×C₂²⋊C₄	—	2	4	no	—
519	C₂×C₂²⋊C₄	—	2	4	no	—
520	C₂×C₂²⋊C₄	—	2	4	no	—
521	C₂×C₂²⋊C₄	—	2	4	no	—
522	C₂×C₂²⋊C₄	—	4	2	no	—
523	C₂×C₂²⋊C₄	—	4	2	no	—
524	C₂×C₂²⋊C₄	—	4	2	no	—
525	C₂×C₂²⋊C₄	—	4	2	no	—
526	C₂×C₂²⋊C₄	—	4	2	no	—
527	C₂×C₂²⋊C₄	—	4	2	no	—
528	C₂×C₂²⋊C₄	—	4	2	no	—
529	C₂×C₂²⋊C₄	—	4	2	no	—
530	C₂×C₂²⋊C₄	—	4	1	no	—
531	C₂×C₂²⋊C₄	—	4	2	no	—
532	C₂×C₂²⋊C₄	—	4	2	no	—
533	C₂×C₂²⋊C₄	—	4	2	no	—
534	C₂×C₂²⋊C₄	—	4	1	no	—
535	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
536	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
537	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	—
538	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	complemented
539	C₂×C₄²	—	2	4	no	—
540	C₂×C₄²	—	2	4	no	—
541	C₂×C₄²	—	4	2	no	—
542	#95	—	2	4	no	—
543	#95	—	2	4	no	—
544	#95	—	4	1	no	—
545	#95	—	4	2	no	—
546	#95	—	4	1	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	1	no	—
563	C₂⁴	—	2	1	no	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	2	no	—
566	C₂⁴	—	2	8	no	—
567	C₂⁴	—	2	16	no	—
568	C₂⁴	—	2	2	no	—
569	C₂⁴	—	2	2	no	—
570	C₂⁴	—	2	2	no	—
571	C₂⁴	—	2	2	no	—
572	C₂⁴	—	2	2	no	—
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	4	4	no	—
577	C₂⁴	—	4	8	no	—
578	C₂⁴	—	4	4	no	—
579	C₂⁴	—	4	4	no	—
580	C₂⁴	—	4	8	no	—
581	C₂⁴	—	4	8	no	—
582	C₂⁴	—	4	8	no	—
583	C₂⁴	—	4	8	no	—
584	C₂⁴	—	4	8	no	—
585	C₂⁴	—	4	4	no	—
586	C₂⁴	—	4	8	no	—
587	C₂⁴	—	4	8	no	—
588	C₂⁴	—	4	8	no	—
589	C₂⁴	—	4	8	no	—
590	C₂⁴	—	4	8	no	—
591	C₂⁴	—	4	8	no	—
592	C₂⁴	—	4	8	no	—
593	C₂⁴	—	4	4	no	—
594	C₂⁴	—	4	4	no	—
595	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
596	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
597	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
598	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
599	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
600	C₂⁴	#41×C₁₀₁	1	4	yes	—
601	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
602	C₂×D₄	—	2	8	no	—
603	C₂×D₄	—	2	16	no	—
604	C₂×D₄	—	2	16	no	—
605	C₂×D₄	—	4	8	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	8	no	—
609	C₂×D₄	—	4	8	no	—
610	C₂×D₄	—	4	8	no	—
611	C₂×D₄	—	4	8	no	—
612	C₂×D₄	—	4	8	no	—
613	C₂×D₄	—	4	8	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
649	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
650	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
651	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
652	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
653	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
654	C₄⋊C₄	—	4	8	no	—
655	C₂²⋊C₄	—	2	16	no	—
656	C₂²⋊C₄	—	4	8	no	—
657	C₂²⋊C₄	—	4	4	no	—
658	C₂²⋊C₄	—	4	8	no	—
659	C₂²⋊C₄	—	4	8	no	—
660	C₂²⋊C₄	—	4	8	no	—
661	C₂²⋊C₄	—	4	8	no	—
662	C₂²⋊C₄	—	4	8	no	—
663	C₂²⋊C₄	—	4	8	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
666	C₄²	—	4	8	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	4	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	4	32	no	—
701	C₂³	—	4	16	no	—
702	C₂³	—	4	16	no	—
703	C₂³	—	4	32	no	—
704	C₂³	—	4	32	no	—
705	C₂³	—	4	32	no	—
706	C₂³	—	4	32	no	—
707	C₂³	—	4	32	no	—
708	C₂³	—	4	16	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	4	2	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	4	2	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	2	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
752	C₂³	C₄×D₄×C₁₀₁	1	8	yes	—
753	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
754	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
755	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
756	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
757	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
758	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
759	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
760	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
761	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
762	D₄	—	4	32	no	—
763	D₄	—	4	16	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	8	no	—
806	C₂²	—	2	8	no	—
807	C₂²	—	2	8	no	—
808	C₂²	—	2	8	no	—
809	C₂²	—	4	64	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	4	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	8	2	no	—
835	C₂²	—	8	2	no	—
836	C₂²	—	8	2	no	—
837	C₂²	—	8	2	no	—
838	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
839	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
840	C₂²	#518×C₁₀₁	1	1	yes	characteristic
841	C₂²	#518×C₁₀₁	1	1	yes	characteristic
842	C₂²	#518×C₁₀₁	1	2	yes	—
843	C₂²	#534×C₁₀₁	1	2	yes	—
844	C₂²	#535×C₁₀₁	1	2	yes	—
845	C₂²	#535×C₁₀₁	1	2	yes	—
846	C₂²	#535×C₁₀₁	1	2	yes	—
847	C₂²	#538×C₁₀₁	1	2	yes	—
848	C₂²	#538×C₁₀₁	1	2	yes	—
849	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
850	C₂²	D₄²×C₁₀₁	1	2	yes	—
851	C₂²	D₄²×C₁₀₁	1	2	yes	—
852	C₂²	#546×C₁₀₁	1	2	yes	—
853	C₂²	#546×C₁₀₁	1	2	yes	—
854	C₂²	#546×C₁₀₁	1	2	yes	—
855	C₂²	#551×C₁₀₁	1	1	yes	characteristic
856	C₂²	#560×C₁₀₁	1	2	yes	—
857	C₂²	#560×C₁₀₁	1	1	yes	characteristic
858	C₂²	H(3,𝔽₄)×C₁₀₁	1	1	yes	characteristic
859	C₄	—	2	8	no	—
860	C₄	—	4	4	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	2	no	—
863	C₄	—	8	2	no	—
864	C₄	—	8	2	no	—
865	C₂	—	4	4	no	—
866	C₂	—	4	8	no	—
867	C₂	—	8	2	no	—
868	C₂	C₁₀₁×#2309	1	1	yes	characteristic
869	C₂	C₁₀₁×#2321	1	2	yes	—
870	C₂	D₄×C₂²⋊C₄×C₁₀₁	1	2	yes	—
871	C₂	C₁₀₁×#2358	1	1	yes	characteristic
872	C₂	C₁₀₁×#2375	1	1	yes	characteristic
873	C₂	C₁₀₁×#2669	1	2	yes	—
874	C₂	C₁₀₁×#2670	1	2	yes	—
875	C₂	C₁₀₁×#2678	1	2	yes	—
876	C₂	C₁₀₁×#2685	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂²×#120×C₁₀₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#390×C₁₀₁	C₂	semidirect
3. C₂×#388×C₁₀₁	C₂	semidirect
4. C₂×#379×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1439	C₂	semidirect
6. C₁₀₁×#1438	C₂	semidirect
7. C₁₀₁×#1438	C₂	semidirect
8. C₁₀₁×#1438	C₂	semidirect
9. C₁₀₁×#1437	C₂	semidirect
14. C₂×#120×C₁₀₁	C₄	semidirect
15. C₂²×C₄⋊C₄×C₁₀₁	C₂²	semidirect
24. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
25. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
26. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
27. C₂²×C₄²×C₁₀₁	C₂²	semidirect
31. C₂×#95×C₁₀₁	C₂²	semidirect
32. C₂×#95×C₁₀₁	C₂²	semidirect
33. C₂×#95×C₁₀₁	C₂²	semidirect
34. C₂×#95×C₁₀₁	C₂²	semidirect
35. C₂×#95×C₁₀₁	C₂²	semidirect
99. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
226. C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	semidirect
426. #14358	C₁₀₁	direct (N × H)
440. C₂×#390	C₂×C₁₀₁	semidirect
441. C₂×#388	C₂×C₁₀₁	semidirect
442. C₂×#379	C₂×C₁₀₁	semidirect
443. #1439	C₂×C₁₀₁	semidirect
444. #1438	C₂×C₁₀₁	semidirect
445. #1438	C₂×C₁₀₁	semidirect
446. #1438	C₂×C₁₀₁	semidirect
447. #1437	C₂×C₁₀₁	semidirect
448. C₁₀₁	#14358	direct (N × H)
453. C₂×#120	C₄×C₁₀₁	semidirect
454. C₂²×C₄⋊C₄	C₂²×C₁₀₁	semidirect
463. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
464. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
465. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
466. C₂²×C₄²	C₂²×C₁₀₁	semidirect
470. C₂×#95	C₂²×C₁₀₁	semidirect
471. C₂×#95	C₂²×C₁₀₁	semidirect
472. C₂×#95	C₂²×C₁₀₁	semidirect
473. C₂×#95	C₂²×C₁₀₁	semidirect
474. C₂×#95	C₂²×C₁₀₁	semidirect
538. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
665. C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#120×C₁₀₁	2
C₂×#390×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₂×#379×C₁₀₁	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
C₁₀₁×#1437	2
#14358	101

Subgroups — C101×#14358 #38796509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14358 #38796509