Subgroups — C₁₀₁×#15260 #38797411

Order 25856.

2662 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#394×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#386×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#385×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#1444	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1440	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1439	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₁×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×#123×C₁₀₁	—	2	4	no	—
18	C₂×#123×C₁₀₁	—	2	8	no	—
19	C₂×#121×C₁₀₁	—	2	4	no	—
20	C₂×#121×C₁₀₁	—	2	4	no	—
21	C₂×#121×C₁₀₁	—	2	4	no	—
22	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
34	#394×C₁₀₁	—	2	8	no	—
35	#386×C₁₀₁	—	2	4	no	—
36	#385×C₁₀₁	—	2	4	no	—
37	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
38	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
39	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
40	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
41	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
42	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
43	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
44	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
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	2	no	—
50	C₂²×D₄×C₁₀₁	—	2	2	no	—
51	C₂²×D₄×C₁₀₁	—	2	2	no	—
52	C₂²×D₄×C₁₀₁	—	2	4	no	—
53	C₂²×D₄×C₁₀₁	—	2	4	no	—
54	C₂²×D₄×C₁₀₁	—	2	2	no	—
55	C₂²×D₄×C₁₀₁	—	2	4	no	—
56	C₂²×D₄×C₁₀₁	—	4	2	no	—
57	C₂²×D₄×C₁₀₁	—	4	2	no	—
58	C₂²×D₄×C₁₀₁	—	4	2	no	—
59	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
60	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
61	C₂³×C₄×C₁₀₁	—	2	2	no	—
62	C₂³×C₄×C₁₀₁	—	2	2	no	—
63	C₂³×C₄×C₁₀₁	—	2	2	no	—
64	C₂³×C₄×C₁₀₁	—	2	2	no	—
65	C₂³×C₄×C₁₀₁	—	2	4	no	—
66	C₂³×C₄×C₁₀₁	—	2	2	no	—
67	C₂³×C₄×C₁₀₁	—	2	2	no	—
68	C₂³×C₄×C₁₀₁	—	2	4	no	—
69	C₂³×C₄×C₁₀₁	—	4	2	no	—
70	C₂³×C₄×C₁₀₁	—	4	2	no	—
71	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
79	#123×C₁₀₁	—	2	32	no	—
80	#121×C₁₀₁	—	2	32	no	—
81	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
85	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
88	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
90	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
100	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
104	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
106	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
108	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
109	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
110	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
111	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
112	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	complemented
114	#95×C₁₀₁	—	2	4	no	—
115	#95×C₁₀₁	—	2	4	no	—
116	#95×C₁₀₁	—	2	4	no	—
117	#95×C₁₀₁	—	2	4	no	—
118	#95×C₁₀₁	—	4	2	no	—
119	#95×C₁₀₁	—	4	2	no	—
120	C₂⁴×C₁₀₁	—	2	2	no	—
121	C₂⁴×C₁₀₁	—	2	1	no	—
122	C₂⁴×C₁₀₁	—	2	1	no	—
123	C₂⁴×C₁₀₁	—	2	2	no	—
124	C₂⁴×C₁₀₁	—	2	2	no	—
125	C₂⁴×C₁₀₁	—	2	2	no	—
126	C₂⁴×C₁₀₁	—	2	2	no	—
127	C₂⁴×C₁₀₁	—	2	2	no	—
128	C₂⁴×C₁₀₁	—	2	2	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	—	2	2	no	—
138	C₂⁴×C₁₀₁	—	2	2	no	—
139	C₂⁴×C₁₀₁	—	2	2	no	—
140	C₂⁴×C₁₀₁	—	2	2	no	—
141	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
142	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
143	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
144	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
145	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
146	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
147	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
148	C₂×D₄×C₁₀₁	—	2	8	no	—
149	C₂×D₄×C₁₀₁	—	2	8	no	—
150	C₂×D₄×C₁₀₁	—	2	8	no	—
151	C₂×D₄×C₁₀₁	—	2	8	no	—
152	C₂×D₄×C₁₀₁	—	2	8	no	—
153	C₂×D₄×C₁₀₁	—	4	4	no	—
154	C₂×D₄×C₁₀₁	—	4	4	no	—
155	C₂×D₄×C₁₀₁	—	4	8	no	—
156	C₂×D₄×C₁₀₁	—	4	8	no	—
157	C₂×D₄×C₁₀₁	—	4	8	no	—
158	C₂×D₄×C₁₀₁	—	4	8	no	—
159	C₂×D₄×C₁₀₁	—	4	8	no	—
160	C₂×D₄×C₁₀₁	—	4	8	no	—
161	C₂×D₄×C₁₀₁	—	4	4	no	—
162	C₂×D₄×C₁₀₁	—	4	4	no	—
163	C₂²×C₄×C₁₀₁	—	2	1	no	—
164	C₂²×C₄×C₁₀₁	—	2	1	no	—
165	C₂²×C₄×C₁₀₁	—	2	2	no	—
166	C₂²×C₄×C₁₀₁	—	2	8	no	—
167	C₂²×C₄×C₁₀₁	—	2	8	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	1	no	—
176	C₂²×C₄×C₁₀₁	—	2	1	no	—
177	C₂²×C₄×C₁₀₁	—	2	2	no	—
178	C₂²×C₄×C₁₀₁	—	2	2	no	—
179	C₂²×C₄×C₁₀₁	—	2	1	no	—
180	C₂²×C₄×C₁₀₁	—	2	1	no	—
181	C₂²×C₄×C₁₀₁	—	2	1	no	—
182	C₂²×C₄×C₁₀₁	—	2	1	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	2	no	—
188	C₂²×C₄×C₁₀₁	—	2	2	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	—	4	8	no	—
206	C₂²×C₄×C₁₀₁	—	4	8	no	—
207	C₂²×C₄×C₁₀₁	—	4	8	no	—
208	C₂²×C₄×C₁₀₁	—	4	8	no	—
209	C₂²×C₄×C₁₀₁	—	4	4	no	—
210	C₂²×C₄×C₁₀₁	—	4	4	no	—
211	C₂²×C₄×C₁₀₁	—	4	4	no	—
212	C₂²×C₄×C₁₀₁	—	4	4	no	—
213	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
220	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
221	C₄⋊C₄×C₁₀₁	—	2	8	no	—
222	C₄⋊C₄×C₁₀₁	—	2	16	no	—
223	C₄⋊C₄×C₁₀₁	—	4	8	no	—
224	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
225	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
226	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
227	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
228	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
229	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
230	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
231	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
232	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
233	C₂³×C₁₀₁	—	2	2	no	—
234	C₂³×C₁₀₁	—	2	2	no	—
235	C₂³×C₁₀₁	—	2	2	no	—
236	C₂³×C₁₀₁	—	2	2	no	—
237	C₂³×C₁₀₁	—	2	4	no	—
238	C₂³×C₁₀₁	—	2	2	no	—
239	C₂³×C₁₀₁	—	2	2	no	—
240	C₂³×C₁₀₁	—	2	2	no	—
241	C₂³×C₁₀₁	—	2	2	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	2	no	—
256	C₂³×C₁₀₁	—	2	2	no	—
257	C₂³×C₁₀₁	—	2	2	no	—
258	C₂³×C₁₀₁	—	2	4	no	—
259	C₂³×C₁₀₁	—	2	4	no	—
260	C₂³×C₁₀₁	—	4	1	no	—
261	C₂³×C₁₀₁	—	4	1	no	—
262	C₂³×C₁₀₁	—	4	2	no	—
263	C₂³×C₁₀₁	—	4	1	no	—
264	C₂³×C₁₀₁	—	4	1	no	—
265	C₂³×C₁₀₁	—	4	2	no	—
266	C₂³×C₁₀₁	—	4	2	no	—
267	C₂³×C₁₀₁	—	4	2	no	—
268	C₂³×C₁₀₁	—	4	2	no	—
269	C₂³×C₁₀₁	—	4	2	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	1	no	—
279	C₂³×C₁₀₁	—	4	1	no	—
280	C₂³×C₁₀₁	—	4	2	no	—
281	C₂³×C₁₀₁	—	4	1	no	—
282	C₂³×C₁₀₁	—	4	1	no	—
283	C₂³×C₁₀₁	—	4	2	no	—
284	C₂³×C₁₀₁	—	4	2	no	—
285	C₂³×C₁₀₁	—	4	2	no	—
286	C₂³×C₁₀₁	—	4	2	no	—
287	C₂³×C₁₀₁	—	4	2	no	—
288	C₂³×C₁₀₁	—	4	2	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	2	no	—
294	C₂³×C₁₀₁	#120	1	4	yes	—
295	C₂³×C₁₀₁	#120	1	4	yes	—
296	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
300	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
301	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
302	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
303	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
304	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
305	D₄×C₁₀₁	—	4	16	no	—
306	D₄×C₁₀₁	—	4	16	no	—
307	D₄×C₁₀₁	—	4	16	no	—
308	C₂×C₄×C₁₀₁	—	2	2	no	—
309	C₂×C₄×C₁₀₁	—	2	2	no	—
310	C₂×C₄×C₁₀₁	—	2	4	no	—
311	C₂×C₄×C₁₀₁	—	2	4	no	—
312	C₂×C₄×C₁₀₁	—	2	4	no	—
313	C₂×C₄×C₁₀₁	—	2	2	no	—
314	C₂×C₄×C₁₀₁	—	2	4	no	—
315	C₂×C₄×C₁₀₁	—	2	2	no	—
316	C₂×C₄×C₁₀₁	—	2	2	no	—
317	C₂×C₄×C₁₀₁	—	2	2	no	—
318	C₂×C₄×C₁₀₁	—	2	4	no	—
319	C₂×C₄×C₁₀₁	—	2	2	no	—
320	C₂×C₄×C₁₀₁	—	2	4	no	—
321	C₂×C₄×C₁₀₁	—	2	4	no	—
322	C₂×C₄×C₁₀₁	—	2	4	no	—
323	C₂×C₄×C₁₀₁	—	2	4	no	—
324	C₂×C₄×C₁₀₁	—	2	4	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	—	4	16	no	—
329	C₂×C₄×C₁₀₁	—	4	16	no	—
330	C₂×C₄×C₁₀₁	—	4	2	no	—
331	C₂×C₄×C₁₀₁	—	4	1	no	—
332	C₂×C₄×C₁₀₁	—	4	1	no	—
333	C₂×C₄×C₁₀₁	—	4	2	no	—
334	C₂×C₄×C₁₀₁	—	4	2	no	—
335	C₂×C₄×C₁₀₁	—	4	2	no	—
336	C₂×C₄×C₁₀₁	—	4	1	no	—
337	C₂×C₄×C₁₀₁	—	4	1	no	—
338	C₂×C₄×C₁₀₁	—	4	2	no	—
339	C₂×C₄×C₁₀₁	—	4	2	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	#123	1	4	yes	complemented
358	C₂²×C₁₀₁	—	2	4	no	—
359	C₂²×C₁₀₁	—	2	4	no	—
360	C₂²×C₁₀₁	—	2	4	no	—
361	C₂²×C₁₀₁	—	2	4	no	—
362	C₂²×C₁₀₁	—	2	8	no	—
363	C₂²×C₁₀₁	—	4	2	no	—
364	C₂²×C₁₀₁	—	4	2	no	—
365	C₂²×C₁₀₁	—	4	4	no	—
366	C₂²×C₁₀₁	—	4	4	no	—
367	C₂²×C₁₀₁	—	4	4	no	—
368	C₂²×C₁₀₁	—	4	4	no	—
369	C₂²×C₁₀₁	—	4	4	no	—
370	C₂²×C₁₀₁	—	4	4	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	4	no	—
376	C₂²×C₁₀₁	—	4	2	no	—
377	C₂²×C₁₀₁	—	4	2	no	—
378	C₂²×C₁₀₁	—	4	2	no	—
379	C₂²×C₁₀₁	—	4	4	no	—
380	C₂²×C₁₀₁	—	4	4	no	—
381	C₂²×C₁₀₁	—	8	2	no	—
382	C₂²×C₁₀₁	—	8	2	no	—
383	C₂²×C₁₀₁	—	8	2	no	—
384	C₂²×C₁₀₁	—	8	2	no	—
385	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
386	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
387	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
388	C₂²×C₁₀₁	#525	1	1	yes	characteristic
389	C₂²×C₁₀₁	#532	1	2	yes	—
390	C₂²×C₁₀₁	#534	1	1	yes	characteristic
391	C₂²×C₁₀₁	#534	1	1	yes	characteristic
392	C₂²×C₁₀₁	#536	1	1	yes	characteristic
393	C₂²×C₁₀₁	#537	1	2	yes	—
394	C₂²×C₁₀₁	#540	1	2	yes	—
395	C₂²×C₁₀₁	#542	1	2	yes	—
396	C₂²×C₁₀₁	D₄²	1	2	yes	—
397	C₂²×C₁₀₁	D₄²	1	2	yes	—
398	C₂²×C₁₀₁	#546	1	2	yes	—
399	C₂²×C₁₀₁	#546	1	2	yes	—
400	C₂²×C₁₀₁	#546	1	2	yes	—
401	C₂²×C₁₀₁	#547	1	2	yes	—
402	C₂²×C₁₀₁	#547	1	2	yes	—
403	C₂²×C₁₀₁	#547	1	2	yes	—
404	C₂²×C₁₀₁	#553	1	2	yes	—
405	C₂²×C₁₀₁	#562	1	2	yes	—
406	C₄×C₁₀₁	—	2	4	no	—
407	C₄×C₁₀₁	—	4	4	no	—
408	C₄×C₁₀₁	—	4	2	no	—
409	C₄×C₁₀₁	—	4	2	no	—
410	C₄×C₁₀₁	—	4	2	no	—
411	C₄×C₁₀₁	—	4	4	no	—
412	C₄×C₁₀₁	—	4	4	no	—
413	C₄×C₁₀₁	—	8	2	no	—
414	#15260	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₁₀₁	—	4	4	no	—
416	C₂×C₁₀₁	—	4	4	no	—
417	C₂×C₁₀₁	—	8	2	no	—
418	C₂×C₁₀₁	#2403	1	1	yes	characteristic
419	C₂×C₁₀₁	#2405	1	1	yes	characteristic
420	C₂×C₁₀₁	#2406	1	1	yes	characteristic
421	C₂×C₁₀₁	#2422	1	2	yes	—
422	C₂×C₁₀₁	#2430	1	2	yes	—
423	C₂×C₁₀₁	#2464	1	2	yes	—
424	C₂×C₁₀₁	#2671	1	2	yes	—
425	C₂×C₁₀₁	#2672	1	2	yes	—
426	C₂×C₁₀₁	#2701	1	2	yes	—
427	C₂²×#123	C₂×C₁₀₁	1	1	yes	characteristic, complemented
428	C₂²×#121	C₂×C₁₀₁	1	1	yes	characteristic
429	C₂×#394	C₂×C₁₀₁	1	2	yes	complemented
430	C₂×#386	C₂×C₁₀₁	1	1	yes	characteristic, complemented
431	C₂×#385	C₂×C₁₀₁	1	1	yes	characteristic, complemented
432	#1444	C₂×C₁₀₁	1	2	yes	complemented
433	#1440	C₂×C₁₀₁	1	1	yes	characteristic, complemented
434	#1439	C₂×C₁₀₁	1	2	yes	complemented
435	#1438	C₂×C₁₀₁	1	1	yes	characteristic, complemented
436	#1438	C₂×C₁₀₁	1	1	yes	characteristic, complemented
437	C₂²⋊#95	C₂×C₁₀₁	1	2	yes	complemented
438	C₁₀₁	#15260	1	1	yes	characteristic, direct product factor, Sylow
439	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
440	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
441	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
442	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
443	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
444	C₂×#123	—	2	4	no	—
445	C₂×#123	—	2	8	no	—
446	C₂×#121	—	2	4	no	—
447	C₂×#121	—	2	4	no	—
448	C₂×#121	—	2	4	no	—
449	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
450	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
451	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
452	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
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	1	yes	characteristic
459	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
460	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
461	#394	—	2	8	no	—
462	#386	—	2	4	no	—
463	#385	—	2	4	no	—
464	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
465	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
466	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
467	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
468	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
469	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
470	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
471	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
472	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	—	2	2	no	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	4	no	—
480	C₂²×D₄	—	2	4	no	—
481	C₂²×D₄	—	2	2	no	—
482	C₂²×D₄	—	2	4	no	—
483	C₂²×D₄	—	4	2	no	—
484	C₂²×D₄	—	4	2	no	—
485	C₂²×D₄	—	4	2	no	—
486	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
487	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
488	C₂³×C₄	—	2	2	no	—
489	C₂³×C₄	—	2	2	no	—
490	C₂³×C₄	—	2	2	no	—
491	C₂³×C₄	—	2	2	no	—
492	C₂³×C₄	—	2	4	no	—
493	C₂³×C₄	—	2	2	no	—
494	C₂³×C₄	—	2	2	no	—
495	C₂³×C₄	—	2	4	no	—
496	C₂³×C₄	—	4	2	no	—
497	C₂³×C₄	—	4	2	no	—
498	C₂³×C₄	C₂³×C₁₀₁	1	2	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	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
506	#123	—	2	32	no	—
507	#121	—	2	32	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	—	2	2	no	—
511	C₂×C₄⋊C₄	—	2	4	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	—	2	4	no	—
514	C₂×C₄⋊C₄	—	2	4	no	—
515	C₂×C₄⋊C₄	—	2	4	no	—
516	C₂×C₄⋊C₄	—	4	2	no	—
517	C₂×C₂²⋊C₄	—	2	2	no	—
518	C₂×C₂²⋊C₄	—	2	2	no	—
519	C₂×C₂²⋊C₄	—	2	2	no	—
520	C₂×C₂²⋊C₄	—	2	2	no	—
521	C₂×C₂²⋊C₄	—	2	4	no	—
522	C₂×C₂²⋊C₄	—	2	4	no	—
523	C₂×C₂²⋊C₄	—	2	2	no	—
524	C₂×C₂²⋊C₄	—	2	2	no	—
525	C₂×C₂²⋊C₄	—	2	2	no	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	C₂×C₂²⋊C₄	—	2	4	no	—
528	C₂×C₂²⋊C₄	—	2	4	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	—	2	4	no	—
533	C₂×C₂²⋊C₄	—	2	4	no	—
534	C₂×C₂²⋊C₄	—	2	4	no	—
535	C₂×C₂²⋊C₄	—	4	2	no	—
536	C₂×C₂²⋊C₄	—	4	2	no	—
537	C₂×C₂²⋊C₄	—	4	2	no	—
538	C₂×C₂²⋊C₄	—	4	2	no	—
539	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	4	yes	—
540	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	complemented
541	#95	—	2	4	no	—
542	#95	—	2	4	no	—
543	#95	—	2	4	no	—
544	#95	—	2	4	no	—
545	#95	—	4	2	no	—
546	#95	—	4	2	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	2	1	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	1	no	—
562	C₂⁴	—	2	1	no	—
563	C₂⁴	—	2	2	no	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	2	no	—
566	C₂⁴	—	2	2	no	—
567	C₂⁴	—	2	2	no	—
568	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
569	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
570	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
571	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
572	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
573	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
574	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	—	4	4	no	—
582	C₂×D₄	—	4	8	no	—
583	C₂×D₄	—	4	8	no	—
584	C₂×D₄	—	4	8	no	—
585	C₂×D₄	—	4	8	no	—
586	C₂×D₄	—	4	8	no	—
587	C₂×D₄	—	4	8	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	8	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	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	2	no	—
627	C₂²×C₄	—	2	2	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	—	4	8	no	—
633	C₂²×C₄	—	4	8	no	—
634	C₂²×C₄	—	4	8	no	—
635	C₂²×C₄	—	4	8	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	4	no	—
640	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
641	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
642	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
643	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
644	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
645	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
646	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
647	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
648	C₄⋊C₄	—	2	8	no	—
649	C₄⋊C₄	—	2	16	no	—
650	C₄⋊C₄	—	4	8	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	8	no	—
655	C₂²⋊C₄	—	2	16	no	—
656	C₂²⋊C₄	—	4	8	no	—
657	C₂²⋊C₄	—	4	8	no	—
658	C₂²⋊C₄	—	4	8	no	—
659	C₂²⋊C₄	—	4	4	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	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	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	2	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	—	4	2	no	—
703	C₂³	—	4	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	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	#120×C₁₀₁	1	4	yes	—
722	C₂³	#120×C₁₀₁	1	4	yes	—
723	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
724	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
725	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
726	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
727	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
728	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
729	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
730	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
731	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
732	D₄	—	4	16	no	—
733	D₄	—	4	16	no	—
734	D₄	—	4	16	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	4	16	no	—
756	C₂×C₄	—	4	16	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	2	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	#123×C₁₀₁	1	4	yes	complemented
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	4	4	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	4	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	8	2	no	—
809	C₂²	—	8	2	no	—
810	C₂²	—	8	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
813	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
814	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
815	C₂²	#525×C₁₀₁	1	1	yes	characteristic
816	C₂²	#532×C₁₀₁	1	2	yes	—
817	C₂²	#534×C₁₀₁	1	1	yes	characteristic
818	C₂²	#534×C₁₀₁	1	1	yes	characteristic
819	C₂²	#536×C₁₀₁	1	1	yes	characteristic
820	C₂²	#537×C₁₀₁	1	2	yes	—
821	C₂²	#540×C₁₀₁	1	2	yes	—
822	C₂²	#542×C₁₀₁	1	2	yes	—
823	C₂²	D₄²×C₁₀₁	1	2	yes	—
824	C₂²	D₄²×C₁₀₁	1	2	yes	—
825	C₂²	#546×C₁₀₁	1	2	yes	—
826	C₂²	#546×C₁₀₁	1	2	yes	—
827	C₂²	#546×C₁₀₁	1	2	yes	—
828	C₂²	#547×C₁₀₁	1	2	yes	—
829	C₂²	#547×C₁₀₁	1	2	yes	—
830	C₂²	#547×C₁₀₁	1	2	yes	—
831	C₂²	#553×C₁₀₁	1	2	yes	—
832	C₂²	#562×C₁₀₁	1	2	yes	—
833	C₄	—	2	4	no	—
834	C₄	—	4	4	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	4	no	—
840	C₄	—	8	2	no	—
841	C₂	—	4	4	no	—
842	C₂	—	4	4	no	—
843	C₂	—	8	2	no	—
844	C₂	C₁₀₁×#2403	1	1	yes	characteristic
845	C₂	C₁₀₁×#2405	1	1	yes	characteristic
846	C₂	C₁₀₁×#2406	1	1	yes	characteristic
847	C₂	C₁₀₁×#2422	1	2	yes	—
848	C₂	C₁₀₁×#2430	1	2	yes	—
849	C₂	C₁₀₁×#2464	1	2	yes	—
850	C₂	C₁₀₁×#2671	1	2	yes	—
851	C₂	C₁₀₁×#2672	1	2	yes	—
852	C₂	C₁₀₁×#2701	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂²×#121×C₁₀₁	C₂
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#123×C₁₀₁	C₂	semidirect
3. C₂×#394×C₁₀₁	C₂	semidirect
4. C₂×#386×C₁₀₁	C₂	semidirect
5. C₂×#385×C₁₀₁	C₂	semidirect
6. C₁₀₁×#1444	C₂	semidirect
7. C₁₀₁×#1440	C₂	semidirect
8. C₁₀₁×#1439	C₂	semidirect
9. C₁₀₁×#1438	C₂	semidirect
10. C₁₀₁×#1438	C₂	semidirect
11. C₁₀₁×C₂²⋊#95	C₂	semidirect
113. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
357. C₂×C₄×C₁₀₁	#123	semidirect
414. #15260	C₁₀₁	direct (N × H)
427. C₂²×#123	C₂×C₁₀₁	semidirect
429. C₂×#394	C₂×C₁₀₁	semidirect
430. C₂×#386	C₂×C₁₀₁	semidirect
431. C₂×#385	C₂×C₁₀₁	semidirect
432. #1444	C₂×C₁₀₁	semidirect
433. #1440	C₂×C₁₀₁	semidirect
434. #1439	C₂×C₁₀₁	semidirect
435. #1438	C₂×C₁₀₁	semidirect
436. #1438	C₂×C₁₀₁	semidirect
437. C₂²⋊#95	C₂×C₁₀₁	semidirect
438. C₁₀₁	#15260	direct (N × H)
540. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
784. C₂×C₄	#123×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#123×C₁₀₁	2
C₂²×#121×C₁₀₁	2
C₂×#394×C₁₀₁	2
C₂×#386×C₁₀₁	2
C₂×#385×C₁₀₁	2
C₁₀₁×#1444	2
C₁₀₁×#1440	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
C₁₀₁×C₂²⋊#95	2
#15260	101

Subgroups — C101×#15260 #38797411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#15260 #38797411