Subgroups — C₁₀₁×#13912 #38796063

Order 25856.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#388×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#381×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#380×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1441	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1438	C₂	1	2	yes	maximal
7	C₁₀₁×#1437	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1434	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₀₁	—	2	8	no	—
16	C₂×C₄×D₄×C₁₀₁	C₄	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
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
25	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
27	#388×C₁₀₁	—	2	8	no	—
28	#381×C₁₀₁	—	2	4	no	—
29	#380×C₁₀₁	—	2	4	no	—
30	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
33	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
34	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
35	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
36	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
37	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
38	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
39	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
40	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₁₀₁	—	2	4	no	—
43	C₂²×D₄×C₁₀₁	—	2	2	no	—
44	C₂²×D₄×C₁₀₁	—	2	2	no	—
45	C₂²×D₄×C₁₀₁	—	2	4	no	—
46	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
47	C₂³×C₄×C₁₀₁	—	2	4	no	—
48	C₂³×C₄×C₁₀₁	—	2	4	no	—
49	C₂³×C₄×C₁₀₁	—	2	2	no	—
50	C₂³×C₄×C₁₀₁	—	2	2	no	—
51	C₂³×C₄×C₁₀₁	—	2	2	no	—
52	C₂³×C₄×C₁₀₁	—	2	2	no	—
53	C₂³×C₄×C₁₀₁	—	4	2	no	—
54	C₂³×C₄×C₁₀₁	—	4	2	no	—
55	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
56	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
57	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
64	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₄×D₄×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	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
71	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
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	—	4	2	no	—
82	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
83	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
85	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	—
88	C₂×C₄²×C₁₀₁	—	2	4	no	—
89	C₂×C₄²×C₁₀₁	—	2	4	no	—
90	C₂×C₄²×C₁₀₁	—	2	4	no	—
91	C₂×C₄²×C₁₀₁	—	4	2	no	—
92	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
93	#95×C₁₀₁	—	2	2	no	—
94	#95×C₁₀₁	—	2	4	no	—
95	#95×C₁₀₁	—	2	2	no	—
96	#95×C₁₀₁	—	2	4	no	—
97	#95×C₁₀₁	—	2	4	no	—
98	#95×C₁₀₁	—	2	4	no	—
99	#95×C₁₀₁	—	2	2	no	—
100	#95×C₁₀₁	—	2	4	no	—
101	#95×C₁₀₁	—	4	2	no	—
102	#95×C₁₀₁	D₄	1	4	yes	complemented
103	C₂⁴×C₁₀₁	—	2	1	no	—
104	C₂⁴×C₁₀₁	—	2	1	no	—
105	C₂⁴×C₁₀₁	—	2	2	no	—
106	C₂⁴×C₁₀₁	—	2	2	no	—
107	C₂⁴×C₁₀₁	—	2	2	no	—
108	C₂⁴×C₁₀₁	—	2	1	no	—
109	C₂⁴×C₁₀₁	—	2	1	no	—
110	C₂⁴×C₁₀₁	—	2	2	no	—
111	C₂⁴×C₁₀₁	—	2	1	no	—
112	C₂⁴×C₁₀₁	—	2	1	no	—
113	C₂⁴×C₁₀₁	—	2	2	no	—
114	C₂⁴×C₁₀₁	—	2	1	no	—
115	C₂⁴×C₁₀₁	—	2	1	no	—
116	C₂⁴×C₁₀₁	—	2	2	no	—
117	C₂⁴×C₁₀₁	—	2	2	no	—
118	C₂⁴×C₁₀₁	—	2	1	no	—
119	C₂⁴×C₁₀₁	—	2	1	no	—
120	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
121	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
122	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₂⁴×C₁₀₁	#41	1	2	yes	—
124	C₂⁴×C₁₀₁	#41	1	2	yes	—
125	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
126	C₂×D₄×C₁₀₁	—	2	16	no	—
127	C₂×D₄×C₁₀₁	—	2	16	no	—
128	C₂×D₄×C₁₀₁	—	2	8	no	—
129	C₂×D₄×C₁₀₁	—	2	8	no	—
130	C₂×D₄×C₁₀₁	—	2	8	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	2	1	no	—
134	C₂²×C₄×C₁₀₁	—	2	2	no	—
135	C₂²×C₄×C₁₀₁	—	2	1	no	—
136	C₂²×C₄×C₁₀₁	—	2	1	no	—
137	C₂²×C₄×C₁₀₁	—	2	1	no	—
138	C₂²×C₄×C₁₀₁	—	2	1	no	—
139	C₂²×C₄×C₁₀₁	—	2	2	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	1	no	—
142	C₂²×C₄×C₁₀₁	—	2	8	no	—
143	C₂²×C₄×C₁₀₁	—	2	1	no	—
144	C₂²×C₄×C₁₀₁	—	2	2	no	—
145	C₂²×C₄×C₁₀₁	—	2	2	no	—
146	C₂²×C₄×C₁₀₁	—	2	2	no	—
147	C₂²×C₄×C₁₀₁	—	2	2	no	—
148	C₂²×C₄×C₁₀₁	—	2	2	no	—
149	C₂²×C₄×C₁₀₁	—	2	2	no	—
150	C₂²×C₄×C₁₀₁	—	2	2	no	—
151	C₂²×C₄×C₁₀₁	—	2	2	no	—
152	C₂²×C₄×C₁₀₁	—	2	2	no	—
153	C₂²×C₄×C₁₀₁	—	2	1	no	—
154	C₂²×C₄×C₁₀₁	—	2	2	no	—
155	C₂²×C₄×C₁₀₁	—	2	2	no	—
156	C₂²×C₄×C₁₀₁	—	2	2	no	—
157	C₂²×C₄×C₁₀₁	—	2	2	no	—
158	C₂²×C₄×C₁₀₁	—	2	2	no	—
159	C₂²×C₄×C₁₀₁	—	2	8	no	—
160	C₂²×C₄×C₁₀₁	—	2	8	no	—
161	C₂²×C₄×C₁₀₁	—	2	8	no	—
162	C₂²×C₄×C₁₀₁	—	2	2	no	—
163	C₂²×C₄×C₁₀₁	—	2	2	no	—
164	C₂²×C₄×C₁₀₁	—	2	2	no	—
165	C₂²×C₄×C₁₀₁	—	2	2	no	—
166	C₂²×C₄×C₁₀₁	—	2	2	no	—
167	C₂²×C₄×C₁₀₁	—	2	2	no	—
168	C₂²×C₄×C₁₀₁	—	2	2	no	—
169	C₂²×C₄×C₁₀₁	—	2	2	no	—
170	C₂²×C₄×C₁₀₁	—	2	2	no	—
171	C₂²×C₄×C₁₀₁	—	2	2	no	—
172	C₂²×C₄×C₁₀₁	—	2	2	no	—
173	C₂²×C₄×C₁₀₁	—	2	2	no	—
174	C₂²×C₄×C₁₀₁	—	2	2	no	—
175	C₂²×C₄×C₁₀₁	—	2	2	no	—
176	C₂²×C₄×C₁₀₁	—	4	4	no	—
177	C₂²×C₄×C₁₀₁	—	4	4	no	—
178	C₂²×C₄×C₁₀₁	—	4	8	no	—
179	C₂²×C₄×C₁₀₁	—	4	8	no	—
180	C₂²×C₄×C₁₀₁	—	4	8	no	—
181	C₂²×C₄×C₁₀₁	—	4	8	no	—
182	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
184	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
185	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
192	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
193	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
194	C₄⋊C₄×C₁₀₁	—	2	8	no	—
195	C₄⋊C₄×C₁₀₁	—	4	8	no	—
196	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
197	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
198	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
199	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
200	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
201	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
202	C₄²×C₁₀₁	—	2	8	no	—
203	C₄²×C₁₀₁	—	4	8	no	—
204	C₂³×C₁₀₁	—	2	2	no	—
205	C₂³×C₁₀₁	—	2	2	no	—
206	C₂³×C₁₀₁	—	2	2	no	—
207	C₂³×C₁₀₁	—	2	2	no	—
208	C₂³×C₁₀₁	—	2	2	no	—
209	C₂³×C₁₀₁	—	2	2	no	—
210	C₂³×C₁₀₁	—	2	2	no	—
211	C₂³×C₁₀₁	—	2	2	no	—
212	C₂³×C₁₀₁	—	2	2	no	—
213	C₂³×C₁₀₁	—	2	2	no	—
214	C₂³×C₁₀₁	—	2	2	no	—
215	C₂³×C₁₀₁	—	2	2	no	—
216	C₂³×C₁₀₁	—	2	4	no	—
217	C₂³×C₁₀₁	—	2	4	no	—
218	C₂³×C₁₀₁	—	2	4	no	—
219	C₂³×C₁₀₁	—	2	4	no	—
220	C₂³×C₁₀₁	—	2	4	no	—
221	C₂³×C₁₀₁	—	2	2	no	—
222	C₂³×C₁₀₁	—	2	4	no	—
223	C₂³×C₁₀₁	—	2	4	no	—
224	C₂³×C₁₀₁	—	2	4	no	—
225	C₂³×C₁₀₁	—	2	2	no	—
226	C₂³×C₁₀₁	—	2	4	no	—
227	C₂³×C₁₀₁	—	2	2	no	—
228	C₂³×C₁₀₁	—	2	2	no	—
229	C₂³×C₁₀₁	—	2	4	no	—
230	C₂³×C₁₀₁	—	4	2	no	—
231	C₂³×C₁₀₁	—	4	2	no	—
232	C₂³×C₁₀₁	—	4	2	no	—
233	C₂³×C₁₀₁	—	4	2	no	—
234	C₂³×C₁₀₁	—	4	2	no	—
235	C₂³×C₁₀₁	—	4	2	no	—
236	C₂³×C₁₀₁	—	4	2	no	—
237	C₂³×C₁₀₁	—	4	2	no	—
238	C₂³×C₁₀₁	—	4	2	no	—
239	C₂³×C₁₀₁	—	4	2	no	—
240	C₂³×C₁₀₁	—	4	2	no	—
241	C₂³×C₁₀₁	—	4	1	no	—
242	C₂³×C₁₀₁	—	4	2	no	—
243	C₂³×C₁₀₁	—	4	1	no	—
244	C₂³×C₁₀₁	—	4	2	no	—
245	C₂³×C₁₀₁	—	4	1	no	—
246	C₂³×C₁₀₁	—	4	1	no	—
247	C₂³×C₁₀₁	—	4	2	no	—
248	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
249	C₂³×C₁₀₁	#117	1	4	yes	—
250	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
251	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
252	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
253	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
254	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
255	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
256	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
257	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
258	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
259	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
261	D₄×C₁₀₁	—	2	32	no	—
262	C₂×C₄×C₁₀₁	—	2	2	no	—
263	C₂×C₄×C₁₀₁	—	2	2	no	—
264	C₂×C₄×C₁₀₁	—	2	2	no	—
265	C₂×C₄×C₁₀₁	—	2	2	no	—
266	C₂×C₄×C₁₀₁	—	2	2	no	—
267	C₂×C₄×C₁₀₁	—	2	2	no	—
268	C₂×C₄×C₁₀₁	—	2	2	no	—
269	C₂×C₄×C₁₀₁	—	2	2	no	—
270	C₂×C₄×C₁₀₁	—	2	4	no	—
271	C₂×C₄×C₁₀₁	—	2	4	no	—
272	C₂×C₄×C₁₀₁	—	2	4	no	—
273	C₂×C₄×C₁₀₁	—	2	4	no	—
274	C₂×C₄×C₁₀₁	—	2	4	no	—
275	C₂×C₄×C₁₀₁	—	2	4	no	—
276	C₂×C₄×C₁₀₁	—	2	4	no	—
277	C₂×C₄×C₁₀₁	—	2	4	no	—
278	C₂×C₄×C₁₀₁	—	2	2	no	—
279	C₂×C₄×C₁₀₁	—	2	2	no	—
280	C₂×C₄×C₁₀₁	—	2	2	no	—
281	C₂×C₄×C₁₀₁	—	2	4	no	—
282	C₂×C₄×C₁₀₁	—	2	4	no	—
283	C₂×C₄×C₁₀₁	—	2	4	no	—
284	C₂×C₄×C₁₀₁	—	2	4	no	—
285	C₂×C₄×C₁₀₁	—	2	4	no	—
286	C₂×C₄×C₁₀₁	—	2	4	no	—
287	C₂×C₄×C₁₀₁	—	4	16	no	—
288	C₂×C₄×C₁₀₁	—	4	16	no	—
289	C₂×C₄×C₁₀₁	—	4	2	no	—
290	C₂×C₄×C₁₀₁	—	4	2	no	—
291	C₂×C₄×C₁₀₁	—	4	2	no	—
292	C₂×C₄×C₁₀₁	—	4	2	no	—
293	C₂×C₄×C₁₀₁	—	4	2	no	—
294	C₂×C₄×C₁₀₁	—	4	2	no	—
295	C₂×C₄×C₁₀₁	—	4	2	no	—
296	C₂×C₄×C₁₀₁	—	4	2	no	—
297	C₂×C₄×C₁₀₁	—	4	2	no	—
298	C₂×C₄×C₁₀₁	—	4	2	no	—
299	C₂×C₄×C₁₀₁	—	4	2	no	—
300	C₂×C₄×C₁₀₁	—	4	2	no	—
301	C₂×C₄×C₁₀₁	—	4	2	no	—
302	C₂×C₄×C₁₀₁	—	4	2	no	—
303	C₂×C₄×C₁₀₁	—	4	2	no	—
304	C₂×C₄×C₁₀₁	—	4	2	no	—
305	C₂×C₄×C₁₀₁	—	4	2	no	—
306	C₂×C₄×C₁₀₁	—	4	2	no	—
307	C₂×C₄×C₁₀₁	—	4	2	no	—
308	C₂×C₄×C₁₀₁	—	4	2	no	—
309	C₂×C₄×C₁₀₁	—	4	2	no	—
310	C₂×C₄×C₁₀₁	—	4	2	no	—
311	C₂×C₄×C₁₀₁	—	4	2	no	—
312	C₂×C₄×C₁₀₁	—	4	2	no	—
313	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
314	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
315	C₂×C₄×C₁₀₁	#117	1	4	yes	—
316	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
317	C₂²×C₁₀₁	—	2	4	no	—
318	C₂²×C₁₀₁	—	2	4	no	—
319	C₂²×C₁₀₁	—	2	4	no	—
320	C₂²×C₁₀₁	—	2	4	no	—
321	C₂²×C₁₀₁	—	2	4	no	—
322	C₂²×C₁₀₁	—	2	4	no	—
323	C₂²×C₁₀₁	—	4	2	no	—
324	C₂²×C₁₀₁	—	4	2	no	—
325	C₂²×C₁₀₁	—	4	2	no	—
326	C₂²×C₁₀₁	—	4	2	no	—
327	C₂²×C₁₀₁	—	4	2	no	—
328	C₂²×C₁₀₁	—	4	2	no	—
329	C₂²×C₁₀₁	—	4	4	no	—
330	C₂²×C₁₀₁	—	4	4	no	—
331	C₂²×C₁₀₁	—	4	4	no	—
332	C₂²×C₁₀₁	—	4	4	no	—
333	C₂²×C₁₀₁	—	4	4	no	—
334	C₂²×C₁₀₁	—	4	4	no	—
335	C₂²×C₁₀₁	—	4	4	no	—
336	C₂²×C₁₀₁	—	4	4	no	—
337	C₂²×C₁₀₁	—	4	2	no	—
338	C₂²×C₁₀₁	—	4	2	no	—
339	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
341	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
342	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
343	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
344	C₂²×C₁₀₁	#518	1	1	yes	characteristic
345	C₂²×C₁₀₁	#520	1	1	yes	characteristic
346	C₂²×C₁₀₁	#525	1	2	yes	—
347	C₂²×C₁₀₁	#525	1	2	yes	—
348	C₂²×C₁₀₁	#529	1	2	yes	—
349	C₂²×C₁₀₁	#532	1	2	yes	—
350	C₂²×C₁₀₁	#540	1	2	yes	—
351	C₂²×C₁₀₁	#542	1	2	yes	—
352	C₂²×C₁₀₁	D₄²	1	2	yes	—
353	C₂²×C₁₀₁	#546	1	2	yes	—
354	C₂²×C₁₀₁	#546	1	2	yes	—
355	C₂²×C₁₀₁	#546	1	1	yes	characteristic
356	C₂²×C₁₀₁	#547	1	2	yes	—
357	C₂²×C₁₀₁	#548	1	1	yes	characteristic
358	C₂²×C₁₀₁	#551	1	2	yes	—
359	C₂²×C₁₀₁	#552	1	1	yes	characteristic
360	C₂²×C₁₀₁	#553	1	1	yes	characteristic
361	C₂²×C₁₀₁	#553	1	2	yes	—
362	C₄×C₁₀₁	—	2	4	no	—
363	C₄×C₁₀₁	—	2	4	no	—
364	C₄×C₁₀₁	—	2	4	no	—
365	C₄×C₁₀₁	—	2	4	no	—
366	C₄×C₁₀₁	—	4	2	no	—
367	C₄×C₁₀₁	—	4	4	no	—
368	C₄×C₁₀₁	—	4	4	no	—
369	C₄×C₁₀₁	—	8	2	no	—
370	C₄×C₁₀₁	—	8	2	no	—
371	#13912	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₁₀₁	—	4	4	no	—
373	C₂×C₁₀₁	—	4	4	no	—
374	C₂×C₁₀₁	#2280	1	1	yes	characteristic
375	C₂×C₁₀₁	#2293	1	1	yes	characteristic
376	C₂×C₁₀₁	#2319	1	1	yes	characteristic
377	C₂×C₁₀₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₁₀₁	#2339	1	1	yes	characteristic
379	C₂×C₁₀₁	#2352	1	1	yes	characteristic
380	C₂×C₁₀₁	#2353	1	1	yes	characteristic
381	C₂×C₁₀₁	#2457	1	2	yes	—
382	C₂×C₁₀₁	#2461	1	2	yes	—
383	C₂×C₁₀₁	#2464	1	2	yes	—
384	C₂×C₁₀₁	#2468	1	2	yes	—
385	C₂²×C₄×D₄	C₂×C₁₀₁	1	1	yes	characteristic
386	C₂×#388	C₂×C₁₀₁	1	2	yes	complemented
387	C₂×#381	C₂×C₁₀₁	1	1	yes	characteristic, complemented
388	C₂×#380	C₂×C₁₀₁	1	1	yes	characteristic, complemented
389	#1441	C₂×C₁₀₁	1	2	yes	complemented
390	#1438	C₂×C₁₀₁	1	2	yes	—
391	#1437	C₂×C₁₀₁	1	2	yes	complemented
392	#1434	C₂×C₁₀₁	1	1	yes	characteristic, complemented
393	C₂²⋊#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
394	C₂²⋊#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
395	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
396	C₁₀₁	#13912	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
398	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
399	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
400	C₂×C₄×D₄	—	2	8	no	—
401	C₂×C₄×D₄	C₄×C₁₀₁	1	8	yes	complemented
402	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
403	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
405	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
406	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
407	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
408	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
410	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
411	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
412	#388	—	2	8	no	—
413	#381	—	2	4	no	—
414	#380	—	2	4	no	—
415	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
416	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
417	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
418	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
419	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
420	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
421	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
422	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
423	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
424	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
425	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
426	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
427	C₂²×D₄	—	2	4	no	—
428	C₂²×D₄	—	2	2	no	—
429	C₂²×D₄	—	2	2	no	—
430	C₂²×D₄	—	2	4	no	—
431	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	2	4	no	—
434	C₂³×C₄	—	2	2	no	—
435	C₂³×C₄	—	2	2	no	—
436	C₂³×C₄	—	2	2	no	—
437	C₂³×C₄	—	2	2	no	—
438	C₂³×C₄	—	4	2	no	—
439	C₂³×C₄	—	4	2	no	—
440	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
441	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
442	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
443	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
444	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
446	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
447	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
451	C₄×D₄	—	2	32	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	—	2	4	no	—
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₄⋊C₄	—	4	2	no	—
456	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
457	C₂×C₂²⋊C₄	—	2	4	no	—
458	C₂×C₂²⋊C₄	—	2	4	no	—
459	C₂×C₂²⋊C₄	—	2	4	no	—
460	C₂×C₂²⋊C₄	—	2	4	no	—
461	C₂×C₂²⋊C₄	—	2	4	no	—
462	C₂×C₂²⋊C₄	—	2	4	no	—
463	C₂×C₂²⋊C₄	—	2	4	no	—
464	C₂×C₂²⋊C₄	—	2	4	no	—
465	C₂×C₂²⋊C₄	—	2	4	no	—
466	C₂×C₂²⋊C₄	—	4	2	no	—
467	C₂×C₂²⋊C₄	—	4	2	no	—
468	C₂×C₂²⋊C₄	—	4	2	no	—
469	C₂×C₂²⋊C₄	—	4	2	no	—
470	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
472	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	—
473	C₂×C₄²	—	2	4	no	—
474	C₂×C₄²	—	2	4	no	—
475	C₂×C₄²	—	2	4	no	—
476	C₂×C₄²	—	4	2	no	—
477	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
478	#95	—	2	2	no	—
479	#95	—	2	4	no	—
480	#95	—	2	2	no	—
481	#95	—	2	4	no	—
482	#95	—	2	4	no	—
483	#95	—	2	4	no	—
484	#95	—	2	2	no	—
485	#95	—	2	4	no	—
486	#95	—	4	2	no	—
487	#95	D₄×C₁₀₁	1	4	yes	complemented
488	C₂⁴	—	2	1	no	—
489	C₂⁴	—	2	1	no	—
490	C₂⁴	—	2	2	no	—
491	C₂⁴	—	2	2	no	—
492	C₂⁴	—	2	2	no	—
493	C₂⁴	—	2	1	no	—
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	2	no	—
496	C₂⁴	—	2	1	no	—
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	2	no	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	—	2	2	no	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	—	2	1	no	—
504	C₂⁴	—	2	1	no	—
505	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
506	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
507	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
508	C₂⁴	#41×C₁₀₁	1	2	yes	—
509	C₂⁴	#41×C₁₀₁	1	2	yes	—
510	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
511	C₂×D₄	—	2	16	no	—
512	C₂×D₄	—	2	16	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	8	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	8	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	2	8	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	—	4	4	no	—
563	C₂²×C₄	—	4	8	no	—
564	C₂²×C₄	—	4	8	no	—
565	C₂²×C₄	—	4	8	no	—
566	C₂²×C₄	—	4	8	no	—
567	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
568	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
569	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
570	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
571	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
572	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
573	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
574	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
575	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
576	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
577	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
578	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
579	C₄⋊C₄	—	2	8	no	—
580	C₄⋊C₄	—	4	8	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	4	8	no	—
583	C₂²⋊C₄	—	4	8	no	—
584	C₂²⋊C₄	—	4	8	no	—
585	C₂²⋊C₄	—	4	8	no	—
586	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
587	C₄²	—	2	8	no	—
588	C₄²	—	4	8	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	4	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	4	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	4	2	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	2	no	—
623	C₂³	—	4	2	no	—
624	C₂³	—	4	2	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	2	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	2	no	—
633	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
634	C₂³	#117×C₁₀₁	1	4	yes	—
635	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
636	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
637	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
638	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
639	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
640	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
641	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
642	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
643	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
644	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
645	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
646	D₄	—	2	32	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	4	16	no	—
673	C₂×C₄	—	4	16	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
699	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
700	C₂×C₄	#117×C₁₀₁	1	4	yes	—
701	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
725	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
726	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
727	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
728	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
729	C₂²	#518×C₁₀₁	1	1	yes	characteristic
730	C₂²	#520×C₁₀₁	1	1	yes	characteristic
731	C₂²	#525×C₁₀₁	1	2	yes	—
732	C₂²	#525×C₁₀₁	1	2	yes	—
733	C₂²	#529×C₁₀₁	1	2	yes	—
734	C₂²	#532×C₁₀₁	1	2	yes	—
735	C₂²	#540×C₁₀₁	1	2	yes	—
736	C₂²	#542×C₁₀₁	1	2	yes	—
737	C₂²	D₄²×C₁₀₁	1	2	yes	—
738	C₂²	#546×C₁₀₁	1	2	yes	—
739	C₂²	#546×C₁₀₁	1	2	yes	—
740	C₂²	#546×C₁₀₁	1	1	yes	characteristic
741	C₂²	#547×C₁₀₁	1	2	yes	—
742	C₂²	#548×C₁₀₁	1	1	yes	characteristic
743	C₂²	#551×C₁₀₁	1	2	yes	—
744	C₂²	#552×C₁₀₁	1	1	yes	characteristic
745	C₂²	#553×C₁₀₁	1	1	yes	characteristic
746	C₂²	#553×C₁₀₁	1	2	yes	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	2	no	—
754	C₄	—	8	2	no	—
755	C₄	—	8	2	no	—
756	C₂	—	4	4	no	—
757	C₂	—	4	4	no	—
758	C₂	C₁₀₁×#2280	1	1	yes	characteristic
759	C₂	C₁₀₁×#2293	1	1	yes	characteristic
760	C₂	C₁₀₁×#2319	1	1	yes	characteristic
761	C₂	D₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
762	C₂	C₁₀₁×#2339	1	1	yes	characteristic
763	C₂	C₁₀₁×#2352	1	1	yes	characteristic
764	C₂	C₁₀₁×#2353	1	1	yes	characteristic
765	C₂	C₁₀₁×#2457	1	2	yes	—
766	C₂	C₁₀₁×#2461	1	2	yes	—
767	C₂	C₁₀₁×#2464	1	2	yes	—
768	C₂	C₁₀₁×#2468	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
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×#388×C₁₀₁	C₂	semidirect
3. C₂×#381×C₁₀₁	C₂	semidirect
4. C₂×#380×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1441	C₂	semidirect
7. C₁₀₁×#1437	C₂	semidirect
8. C₁₀₁×#1434	C₂	semidirect
9. C₁₀₁×C₂²⋊#95	C₂	semidirect
10. C₁₀₁×C₂²⋊#95	C₂	semidirect
11. C₄×#95×C₁₀₁	C₂	semidirect
16. C₂×C₄×D₄×C₁₀₁	C₄	semidirect
102. #95×C₁₀₁	D₄	semidirect
201. C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	semidirect
371. #13912	C₁₀₁	direct (N × H)
386. C₂×#388	C₂×C₁₀₁	semidirect
387. C₂×#381	C₂×C₁₀₁	semidirect
388. C₂×#380	C₂×C₁₀₁	semidirect
389. #1441	C₂×C₁₀₁	semidirect
391. #1437	C₂×C₁₀₁	semidirect
392. #1434	C₂×C₁₀₁	semidirect
393. C₂²⋊#95	C₂×C₁₀₁	semidirect
394. C₂²⋊#95	C₂×C₁₀₁	semidirect
395. C₄×#95	C₂×C₁₀₁	semidirect
396. C₁₀₁	#13912	direct (N × H)
401. C₂×C₄×D₄	C₄×C₁₀₁	semidirect
487. #95	D₄×C₁₀₁	semidirect
586. 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×C₄×D₄×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₂×#381×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₁₀₁×#1441	2
C₁₀₁×#1438	2
C₁₀₁×#1437	2
C₁₀₁×#1434	2
C₁₀₁×C₂²⋊#95	2
C₄×#95×C₁₀₁	2
#13912	101

Subgroups — C101×#13912 #38796063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13912 #38796063