Subgroups — C₁₀₁×#16260 #38798411

Order 25856.

2790 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#394×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#392×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#392×C₁₀₁	C₂	1	2	yes	maximal, complemented
5	C₂×#386×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#380×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1442	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1439	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1439	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1438	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×#121×C₁₀₁	—	2	4	no	—
18	C₂×#121×C₁₀₁	—	2	8	no	—
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
30	#394×C₁₀₁	—	2	8	no	—
31	#392×C₁₀₁	—	2	8	no	—
32	#392×C₁₀₁	—	2	4	no	—
33	#386×C₁₀₁	—	2	4	no	—
34	#380×C₁₀₁	—	2	4	no	—
35	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
36	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
38	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
39	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
40	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
41	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
42	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
44	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₀₁	—	2	4	no	—
46	C₂²×D₄×C₁₀₁	—	2	4	no	—
47	C₂²×D₄×C₁₀₁	—	2	4	no	—
48	C₂²×D₄×C₁₀₁	—	2	2	no	—
49	C₂²×D₄×C₁₀₁	—	2	2	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	—	2	4	no	—
54	C₂²×D₄×C₁₀₁	—	2	4	no	—
55	C₂²×D₄×C₁₀₁	—	2	2	no	—
56	C₂²×D₄×C₁₀₁	—	2	4	no	—
57	C₂²×D₄×C₁₀₁	—	2	2	no	—
58	C₂²×D₄×C₁₀₁	—	2	2	no	—
59	C₂²×D₄×C₁₀₁	—	4	2	no	—
60	C₂²×D₄×C₁₀₁	—	4	2	no	—
61	C₂²×D₄×C₁₀₁	—	4	2	no	—
62	C₂²×D₄×C₁₀₁	—	4	2	no	—
63	C₂²×D₄×C₁₀₁	—	4	2	no	—
64	C₂²×D₄×C₁₀₁	—	4	2	no	—
65	C₂²×D₄×C₁₀₁	—	4	2	no	—
66	C₂²×D₄×C₁₀₁	—	4	2	no	—
67	C₂²×D₄×C₁₀₁	—	4	2	no	—
68	C₂²×D₄×C₁₀₁	D₄	1	4	yes	complemented
69	C₂³×C₄×C₁₀₁	—	2	4	no	—
70	C₂³×C₄×C₁₀₁	—	2	2	no	—
71	C₂³×C₄×C₁₀₁	—	2	2	no	—
72	C₂³×C₄×C₁₀₁	—	4	2	no	—
73	C₂³×C₄×C₁₀₁	D₄	1	4	yes	complemented
74	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
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	2	yes	—
79	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
82	#121×C₁₀₁	—	2	32	no	—
83	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
88	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	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	—	4	2	no	—
104	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
105	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
106	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
107	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	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	8	yes	complemented
113	#95×C₁₀₁	—	2	2	no	—
114	#95×C₁₀₁	—	2	2	no	—
115	#95×C₁₀₁	—	2	2	no	—
116	#95×C₁₀₁	—	2	4	no	—
117	#95×C₁₀₁	—	2	4	no	—
118	#95×C₁₀₁	—	4	2	no	—
119	#95×C₁₀₁	D₄	1	4	yes	complemented
120	C₂⁴×C₁₀₁	—	2	1	no	—
121	C₂⁴×C₁₀₁	—	2	2	no	—
122	C₂⁴×C₁₀₁	—	2	1	no	—
123	C₂⁴×C₁₀₁	—	2	1	no	—
124	C₂⁴×C₁₀₁	—	2	2	no	—
125	C₂⁴×C₁₀₁	—	2	2	no	—
126	C₂⁴×C₁₀₁	—	2	2	no	—
127	C₂⁴×C₁₀₁	—	2	1	no	—
128	C₂⁴×C₁₀₁	—	2	1	no	—
129	C₂⁴×C₁₀₁	—	2	2	no	—
130	C₂⁴×C₁₀₁	—	2	2	no	—
131	C₂⁴×C₁₀₁	—	2	2	no	—
132	C₂⁴×C₁₀₁	—	2	1	no	—
133	C₂⁴×C₁₀₁	—	2	2	no	—
134	C₂⁴×C₁₀₁	—	2	2	no	—
135	C₂⁴×C₁₀₁	—	2	1	no	—
136	C₂⁴×C₁₀₁	—	2	1	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	—	2	2	no	—
142	C₂⁴×C₁₀₁	—	2	2	no	—
143	C₂⁴×C₁₀₁	—	2	2	no	—
144	C₂⁴×C₁₀₁	—	2	2	no	—
145	C₂⁴×C₁₀₁	—	2	2	no	—
146	C₂⁴×C₁₀₁	—	2	2	no	—
147	C₂⁴×C₁₀₁	—	2	2	no	—
148	C₂⁴×C₁₀₁	—	2	1	no	—
149	C₂⁴×C₁₀₁	—	2	2	no	—
150	C₂⁴×C₁₀₁	—	2	2	no	—
151	C₂⁴×C₁₀₁	—	2	1	no	—
152	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
153	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
154	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
155	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
156	C₂⁴×C₁₀₁	#41	1	2	yes	—
157	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
158	C₂×D₄×C₁₀₁	—	2	8	no	—
159	C₂×D₄×C₁₀₁	—	2	16	no	—
160	C₂×D₄×C₁₀₁	—	2	8	no	—
161	C₂×D₄×C₁₀₁	—	4	8	no	—
162	C₂×D₄×C₁₀₁	—	4	8	no	—
163	C₂×D₄×C₁₀₁	—	4	8	no	—
164	C₂×D₄×C₁₀₁	—	4	8	no	—
165	C₂×D₄×C₁₀₁	—	4	8	no	—
166	C₂×D₄×C₁₀₁	—	4	8	no	—
167	C₂×D₄×C₁₀₁	—	4	8	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	4	no	—
174	C₂×D₄×C₁₀₁	—	4	8	no	—
175	C₂×D₄×C₁₀₁	—	4	4	no	—
176	C₂×D₄×C₁₀₁	—	4	8	no	—
177	C₂×D₄×C₁₀₁	—	4	8	no	—
178	C₂×D₄×C₁₀₁	—	4	8	no	—
179	C₂×D₄×C₁₀₁	—	4	8	no	—
180	C₂×D₄×C₁₀₁	—	4	8	no	—
181	C₂×D₄×C₁₀₁	—	4	4	no	—
182	C₂²×C₄×C₁₀₁	—	2	1	no	—
183	C₂²×C₄×C₁₀₁	—	2	2	no	—
184	C₂²×C₄×C₁₀₁	—	2	1	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	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	1	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	8	no	—
204	C₂²×C₄×C₁₀₁	—	2	8	no	—
205	C₂²×C₄×C₁₀₁	—	2	1	no	—
206	C₂²×C₄×C₁₀₁	—	2	2	no	—
207	C₂²×C₄×C₁₀₁	—	2	1	no	—
208	C₂²×C₄×C₁₀₁	—	2	2	no	—
209	C₂²×C₄×C₁₀₁	—	2	1	no	—
210	C₂²×C₄×C₁₀₁	—	2	2	no	—
211	C₂²×C₄×C₁₀₁	—	2	2	no	—
212	C₂²×C₄×C₁₀₁	—	2	1	no	—
213	C₂²×C₄×C₁₀₁	—	2	2	no	—
214	C₂²×C₄×C₁₀₁	—	2	2	no	—
215	C₂²×C₄×C₁₀₁	—	2	2	no	—
216	C₂²×C₄×C₁₀₁	—	2	2	no	—
217	C₂²×C₄×C₁₀₁	—	2	1	no	—
218	C₂²×C₄×C₁₀₁	—	2	2	no	—
219	C₂²×C₄×C₁₀₁	—	2	2	no	—
220	C₂²×C₄×C₁₀₁	—	2	2	no	—
221	C₂²×C₄×C₁₀₁	—	2	1	no	—
222	C₂²×C₄×C₁₀₁	—	4	4	no	—
223	C₂²×C₄×C₁₀₁	—	4	8	no	—
224	C₂²×C₄×C₁₀₁	—	4	8	no	—
225	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
227	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
228	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
233	C₄⋊C₄×C₁₀₁	—	2	8	no	—
234	C₄⋊C₄×C₁₀₁	—	4	8	no	—
235	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
236	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
237	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
238	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
239	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
240	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
241	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
242	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
243	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
244	C₂³×C₁₀₁	—	2	2	no	—
245	C₂³×C₁₀₁	—	2	2	no	—
246	C₂³×C₁₀₁	—	2	2	no	—
247	C₂³×C₁₀₁	—	2	4	no	—
248	C₂³×C₁₀₁	—	2	2	no	—
249	C₂³×C₁₀₁	—	2	2	no	—
250	C₂³×C₁₀₁	—	2	2	no	—
251	C₂³×C₁₀₁	—	2	4	no	—
252	C₂³×C₁₀₁	—	2	2	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	2	no	—
260	C₂³×C₁₀₁	—	2	4	no	—
261	C₂³×C₁₀₁	—	2	4	no	—
262	C₂³×C₁₀₁	—	2	4	no	—
263	C₂³×C₁₀₁	—	2	4	no	—
264	C₂³×C₁₀₁	—	2	4	no	—
265	C₂³×C₁₀₁	—	2	4	no	—
266	C₂³×C₁₀₁	—	2	2	no	—
267	C₂³×C₁₀₁	—	2	4	no	—
268	C₂³×C₁₀₁	—	2	4	no	—
269	C₂³×C₁₀₁	—	2	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	2	no	—
282	C₂³×C₁₀₁	—	4	2	no	—
283	C₂³×C₁₀₁	—	4	1	no	—
284	C₂³×C₁₀₁	—	4	2	no	—
285	C₂³×C₁₀₁	—	4	2	no	—
286	C₂³×C₁₀₁	—	4	2	no	—
287	C₂³×C₁₀₁	—	4	1	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	—	4	1	no	—
295	C₂³×C₁₀₁	—	4	2	no	—
296	C₂³×C₁₀₁	—	4	2	no	—
297	C₂³×C₁₀₁	—	4	2	no	—
298	C₂³×C₁₀₁	—	4	1	no	—
299	C₂³×C₁₀₁	—	4	2	no	—
300	C₂³×C₁₀₁	—	4	2	no	—
301	C₂³×C₁₀₁	—	4	2	no	—
302	C₂³×C₁₀₁	—	4	2	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	2	no	—
309	C₂³×C₁₀₁	—	4	2	no	—
310	C₂³×C₁₀₁	—	4	2	no	—
311	C₂³×C₁₀₁	—	4	2	no	—
312	C₂³×C₁₀₁	—	4	2	no	—
313	C₂³×C₁₀₁	—	4	2	no	—
314	C₂³×C₁₀₁	—	4	1	no	—
315	C₂³×C₁₀₁	—	4	2	no	—
316	C₂³×C₁₀₁	—	4	1	no	—
317	C₂³×C₁₀₁	—	4	2	no	—
318	C₂³×C₁₀₁	—	4	2	no	—
319	C₂³×C₁₀₁	—	4	2	no	—
320	C₂³×C₁₀₁	—	4	2	no	—
321	C₂³×C₁₀₁	—	4	2	no	—
322	C₂³×C₁₀₁	—	4	2	no	—
323	C₂³×C₁₀₁	—	4	2	no	—
324	C₂³×C₁₀₁	#121	1	4	yes	—
325	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
328	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
330	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
331	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
332	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
333	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
336	D₄×C₁₀₁	—	4	16	no	—
337	D₄×C₁₀₁	—	4	16	no	—
338	D₄×C₁₀₁	—	4	32	no	—
339	D₄×C₁₀₁	—	4	32	no	—
340	C₂×C₄×C₁₀₁	—	2	2	no	—
341	C₂×C₄×C₁₀₁	—	2	2	no	—
342	C₂×C₄×C₁₀₁	—	2	2	no	—
343	C₂×C₄×C₁₀₁	—	2	2	no	—
344	C₂×C₄×C₁₀₁	—	2	4	no	—
345	C₂×C₄×C₁₀₁	—	2	4	no	—
346	C₂×C₄×C₁₀₁	—	2	4	no	—
347	C₂×C₄×C₁₀₁	—	2	4	no	—
348	C₂×C₄×C₁₀₁	—	2	4	no	—
349	C₂×C₄×C₁₀₁	—	2	2	no	—
350	C₂×C₄×C₁₀₁	—	2	4	no	—
351	C₂×C₄×C₁₀₁	—	2	4	no	—
352	C₂×C₄×C₁₀₁	—	2	4	no	—
353	C₂×C₄×C₁₀₁	—	2	4	no	—
354	C₂×C₄×C₁₀₁	—	2	4	no	—
355	C₂×C₄×C₁₀₁	—	2	4	no	—
356	C₂×C₄×C₁₀₁	—	4	16	no	—
357	C₂×C₄×C₁₀₁	—	4	2	no	—
358	C₂×C₄×C₁₀₁	—	4	1	no	—
359	C₂×C₄×C₁₀₁	—	4	2	no	—
360	C₂×C₄×C₁₀₁	—	4	1	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	—	4	2	no	—
365	C₂×C₄×C₁₀₁	—	4	2	no	—
366	C₂×C₄×C₁₀₁	—	4	2	no	—
367	C₂×C₄×C₁₀₁	—	4	2	no	—
368	C₂×C₄×C₁₀₁	—	4	1	no	—
369	C₂×C₄×C₁₀₁	—	4	1	no	—
370	C₂×C₄×C₁₀₁	—	4	2	no	—
371	C₂×C₄×C₁₀₁	—	4	1	no	—
372	C₂×C₄×C₁₀₁	—	4	2	no	—
373	C₂×C₄×C₁₀₁	—	4	1	no	—
374	C₂×C₄×C₁₀₁	—	4	2	no	—
375	C₂×C₄×C₁₀₁	—	4	2	no	—
376	C₂×C₄×C₁₀₁	—	4	1	no	—
377	C₂×C₄×C₁₀₁	—	4	2	no	—
378	C₂×C₄×C₁₀₁	—	4	2	no	—
379	C₂×C₄×C₁₀₁	—	4	1	no	—
380	C₂×C₄×C₁₀₁	—	4	2	no	—
381	C₂×C₄×C₁₀₁	—	4	2	no	—
382	C₂×C₄×C₁₀₁	—	4	2	no	—
383	C₂×C₄×C₁₀₁	—	4	2	no	—
384	C₂×C₄×C₁₀₁	—	4	2	no	—
385	C₂×C₄×C₁₀₁	#120	1	4	yes	—
386	C₂×C₄×C₁₀₁	#121	1	4	yes	—
387	C₂²×C₁₀₁	—	2	4	no	—
388	C₂²×C₁₀₁	—	2	4	no	—
389	C₂²×C₁₀₁	—	2	4	no	—
390	C₂²×C₁₀₁	—	4	2	no	—
391	C₂²×C₁₀₁	—	4	2	no	—
392	C₂²×C₁₀₁	—	4	2	no	—
393	C₂²×C₁₀₁	—	4	4	no	—
394	C₂²×C₁₀₁	—	4	4	no	—
395	C₂²×C₁₀₁	—	4	4	no	—
396	C₂²×C₁₀₁	—	4	4	no	—
397	C₂²×C₁₀₁	—	4	2	no	—
398	C₂²×C₁₀₁	—	4	4	no	—
399	C₂²×C₁₀₁	—	4	2	no	—
400	C₂²×C₁₀₁	—	4	4	no	—
401	C₂²×C₁₀₁	—	4	2	no	—
402	C₂²×C₁₀₁	—	4	4	no	—
403	C₂²×C₁₀₁	—	4	4	no	—
404	C₂²×C₁₀₁	—	4	4	no	—
405	C₂²×C₁₀₁	—	4	4	no	—
406	C₂²×C₁₀₁	—	4	4	no	—
407	C₂²×C₁₀₁	—	4	2	no	—
408	C₂²×C₁₀₁	—	4	4	no	—
409	C₂²×C₁₀₁	—	4	4	no	—
410	C₂²×C₁₀₁	—	8	1	no	—
411	C₂²×C₁₀₁	—	8	2	no	—
412	C₂²×C₁₀₁	—	8	1	no	—
413	C₂²×C₁₀₁	—	8	2	no	—
414	C₂²×C₁₀₁	—	8	1	no	—
415	C₂²×C₁₀₁	—	8	2	no	—
416	C₂²×C₁₀₁	—	8	2	no	—
417	C₂²×C₁₀₁	—	8	2	no	—
418	C₂²×C₁₀₁	—	8	2	no	—
419	C₂²×C₁₀₁	—	8	2	no	—
420	C₂²×C₁₀₁	—	8	2	no	—
421	C₂²×C₁₀₁	—	8	2	no	—
422	C₂²×C₁₀₁	—	8	2	no	—
423	C₂²×C₁₀₁	—	8	1	no	—
424	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
425	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
426	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
427	C₂²×C₁₀₁	#534	1	1	yes	characteristic
428	C₂²×C₁₀₁	#534	1	2	yes	—
429	C₂²×C₁₀₁	#535	1	1	yes	characteristic
430	C₂²×C₁₀₁	#535	1	2	yes	—
431	C₂²×C₁₀₁	#535	1	1	yes	characteristic
432	C₂²×C₁₀₁	#535	1	2	yes	—
433	C₂²×C₁₀₁	#537	1	2	yes	—
434	C₂²×C₁₀₁	#537	1	1	yes	characteristic
435	C₂²×C₁₀₁	#538	1	2	yes	—
436	C₂²×C₁₀₁	#540	1	2	yes	—
437	C₂²×C₁₀₁	D₄²	1	2	yes	—
438	C₂²×C₁₀₁	D₄²	1	2	yes	—
439	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
440	C₂²×C₁₀₁	#546	1	2	yes	—
441	C₂²×C₁₀₁	#546	1	2	yes	—
442	C₂²×C₁₀₁	#547	1	1	yes	characteristic
443	C₂²×C₁₀₁	#548	1	1	yes	characteristic
444	C₂²×C₁₀₁	#553	1	1	yes	characteristic
445	C₂²×C₁₀₁	#560	1	2	yes	—
446	C₂²×C₁₀₁	#562	1	2	yes	—
447	C₄×C₁₀₁	—	2	4	no	—
448	C₄×C₁₀₁	—	2	4	no	—
449	C₄×C₁₀₁	—	4	2	no	—
450	C₄×C₁₀₁	—	4	4	no	—
451	C₄×C₁₀₁	—	4	4	no	—
452	C₄×C₁₀₁	—	8	1	no	—
453	C₄×C₁₀₁	—	8	1	no	—
454	C₄×C₁₀₁	—	8	2	no	—
455	#16260	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂×C₁₀₁	—	4	4	no	—
457	C₂×C₁₀₁	—	8	4	no	—
458	C₂×C₁₀₁	—	8	2	no	—
459	C₂×C₁₀₁	#2408	1	1	yes	characteristic
460	C₂×C₁₀₁	#2410	1	1	yes	characteristic
461	C₂×C₁₀₁	#2416	1	1	yes	characteristic
462	C₂×C₁₀₁	#2615	1	1	yes	characteristic
463	C₂×C₁₀₁	#2617	1	1	yes	characteristic
464	C₂×C₁₀₁	#2619	1	1	yes	characteristic
465	C₂×C₁₀₁	#2669	1	2	yes	—
466	C₂×C₁₀₁	#2671	1	2	yes	—
467	C₂×C₁₀₁	#2676	1	2	yes	—
468	C₂×C₁₀₁	#2703	1	2	yes	—
469	C₂×C₁₀₁	#2813	1	1	yes	characteristic
470	C₂²×#121	C₂×C₁₀₁	1	1	yes	characteristic, complemented
471	C₂×#394	C₂×C₁₀₁	1	2	yes	complemented
472	C₂×#392	C₂×C₁₀₁	1	1	yes	characteristic, complemented
473	C₂×#392	C₂×C₁₀₁	1	2	yes	complemented
474	C₂×#386	C₂×C₁₀₁	1	1	yes	characteristic, complemented
475	C₂×#380	C₂×C₁₀₁	1	1	yes	characteristic, complemented
476	#1442	C₂×C₁₀₁	1	1	yes	characteristic, complemented
477	#1439	C₂×C₁₀₁	1	1	yes	characteristic, complemented
478	#1439	C₂×C₁₀₁	1	2	yes	complemented
479	#1438	C₂×C₁₀₁	1	2	yes	complemented
480	#1438	C₂×C₁₀₁	1	1	yes	characteristic, complemented
481	C₁₀₁	#16260	1	1	yes	characteristic, direct product factor, Sylow
482	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
483	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
484	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
485	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
486	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
487	C₂×#121	—	2	4	no	—
488	C₂×#121	—	2	8	no	—
489	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
490	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
491	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
492	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
493	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
494	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
495	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
496	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
497	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
498	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
499	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
500	#394	—	2	8	no	—
501	#392	—	2	8	no	—
502	#392	—	2	4	no	—
503	#386	—	2	4	no	—
504	#380	—	2	4	no	—
505	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
506	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
507	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
508	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
509	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
510	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
511	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
512	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
513	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
514	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
515	C₂²×D₄	—	2	4	no	—
516	C₂²×D₄	—	2	4	no	—
517	C₂²×D₄	—	2	4	no	—
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	—	2	2	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	4	no	—
523	C₂²×D₄	—	2	4	no	—
524	C₂²×D₄	—	2	4	no	—
525	C₂²×D₄	—	2	2	no	—
526	C₂²×D₄	—	2	4	no	—
527	C₂²×D₄	—	2	2	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	4	2	no	—
530	C₂²×D₄	—	4	2	no	—
531	C₂²×D₄	—	4	2	no	—
532	C₂²×D₄	—	4	2	no	—
533	C₂²×D₄	—	4	2	no	—
534	C₂²×D₄	—	4	2	no	—
535	C₂²×D₄	—	4	2	no	—
536	C₂²×D₄	—	4	2	no	—
537	C₂²×D₄	—	4	2	no	—
538	C₂²×D₄	D₄×C₁₀₁	1	4	yes	complemented
539	C₂³×C₄	—	2	4	no	—
540	C₂³×C₄	—	2	2	no	—
541	C₂³×C₄	—	2	2	no	—
542	C₂³×C₄	—	4	2	no	—
543	C₂³×C₄	D₄×C₁₀₁	1	4	yes	complemented
544	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
545	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
552	#121	—	2	32	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	4	no	—
556	C₂×C₄⋊C₄	—	2	4	no	—
557	C₂×C₄⋊C₄	—	4	2	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	2	no	—
561	C₂×C₂²⋊C₄	—	2	4	no	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	2	no	—
566	C₂×C₂²⋊C₄	—	2	2	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	—	2	2	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₂²⋊C₄	—	2	4	no	—
572	C₂×C₂²⋊C₄	—	2	2	no	—
573	C₂×C₂²⋊C₄	—	4	2	no	—
574	C₂×C₂²⋊C₄	—	4	2	no	—
575	C₂×C₂²⋊C₄	—	4	2	no	—
576	C₂×C₂²⋊C₄	—	4	2	no	—
577	C₂×C₂²⋊C₄	—	4	2	no	—
578	C₂×C₂²⋊C₄	—	4	2	no	—
579	C₂×C₂²⋊C₄	—	4	2	no	—
580	C₂×C₂²⋊C₄	—	4	2	no	—
581	C₂×C₂²⋊C₄	—	4	2	no	—
582	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	complemented
583	#95	—	2	2	no	—
584	#95	—	2	2	no	—
585	#95	—	2	2	no	—
586	#95	—	2	4	no	—
587	#95	—	2	4	no	—
588	#95	—	4	2	no	—
589	#95	D₄×C₁₀₁	1	4	yes	complemented
590	C₂⁴	—	2	1	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	1	no	—
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	1	no	—
599	C₂⁴	—	2	2	no	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	1	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	—	2	2	no	—
617	C₂⁴	—	2	2	no	—
618	C₂⁴	—	2	1	no	—
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	1	no	—
622	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
623	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
624	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
625	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
626	C₂⁴	#41×C₁₀₁	1	2	yes	—
627	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	16	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	4	8	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	4	8	no	—
634	C₂×D₄	—	4	8	no	—
635	C₂×D₄	—	4	8	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	8	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	8	no	—
640	C₂×D₄	—	4	8	no	—
641	C₂×D₄	—	4	8	no	—
642	C₂×D₄	—	4	8	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	8	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	8	no	—
647	C₂×D₄	—	4	8	no	—
648	C₂×D₄	—	4	8	no	—
649	C₂×D₄	—	4	8	no	—
650	C₂×D₄	—	4	8	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	8	no	—
674	C₂²×C₄	—	2	8	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	4	8	no	—
694	C₂²×C₄	—	4	8	no	—
695	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
697	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
698	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
700	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
701	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
702	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
703	C₄⋊C₄	—	2	8	no	—
704	C₄⋊C₄	—	4	8	no	—
705	C₂²⋊C₄	—	2	16	no	—
706	C₂²⋊C₄	—	4	8	no	—
707	C₂²⋊C₄	—	4	8	no	—
708	C₂²⋊C₄	—	4	8	no	—
709	C₂²⋊C₄	—	4	8	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	8	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	4	no	—
735	C₂³	—	2	4	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	4	no	—
738	C₂³	—	2	4	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	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	2	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	2	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	—	4	2	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	2	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	2	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	4	2	no	—
790	C₂³	—	4	2	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	#121×C₁₀₁	1	4	yes	—
795	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
796	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
797	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
798	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
799	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
800	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
801	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
802	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
803	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
804	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
805	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
806	D₄	—	4	16	no	—
807	D₄	—	4	32	no	—
808	D₄	—	4	16	no	—
809	D₄	—	4	32	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	4	16	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	#120×C₁₀₁	1	4	yes	—
856	C₂×C₄	#121×C₁₀₁	1	4	yes	—
857	C₂²	—	2	4	no	—
858	C₂²	—	2	4	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	4	4	no	—
878	C₂²	—	4	4	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	8	1	no	—
881	C₂²	—	8	2	no	—
882	C₂²	—	8	2	no	—
883	C₂²	—	8	2	no	—
884	C₂²	—	8	2	no	—
885	C₂²	—	8	2	no	—
886	C₂²	—	8	2	no	—
887	C₂²	—	8	2	no	—
888	C₂²	—	8	2	no	—
889	C₂²	—	8	1	no	—
890	C₂²	—	8	1	no	—
891	C₂²	—	8	2	no	—
892	C₂²	—	8	1	no	—
893	C₂²	—	8	2	no	—
894	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
895	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
896	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
897	C₂²	#534×C₁₀₁	1	1	yes	characteristic
898	C₂²	#534×C₁₀₁	1	2	yes	—
899	C₂²	#535×C₁₀₁	1	1	yes	characteristic
900	C₂²	#535×C₁₀₁	1	2	yes	—
901	C₂²	#535×C₁₀₁	1	2	yes	—
902	C₂²	#535×C₁₀₁	1	1	yes	characteristic
903	C₂²	#537×C₁₀₁	1	2	yes	—
904	C₂²	#537×C₁₀₁	1	1	yes	characteristic
905	C₂²	#538×C₁₀₁	1	2	yes	—
906	C₂²	#540×C₁₀₁	1	2	yes	—
907	C₂²	D₄²×C₁₀₁	1	2	yes	—
908	C₂²	D₄²×C₁₀₁	1	2	yes	—
909	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
910	C₂²	#546×C₁₀₁	1	2	yes	—
911	C₂²	#546×C₁₀₁	1	2	yes	—
912	C₂²	#547×C₁₀₁	1	1	yes	characteristic
913	C₂²	#548×C₁₀₁	1	1	yes	characteristic
914	C₂²	#553×C₁₀₁	1	1	yes	characteristic
915	C₂²	#560×C₁₀₁	1	2	yes	—
916	C₂²	#562×C₁₀₁	1	2	yes	—
917	C₄	—	2	4	no	—
918	C₄	—	2	4	no	—
919	C₄	—	4	4	no	—
920	C₄	—	4	4	no	—
921	C₄	—	4	2	no	—
922	C₄	—	8	2	no	—
923	C₄	—	8	1	no	—
924	C₄	—	8	1	no	—
925	C₂	—	4	4	no	—
926	C₂	—	8	4	no	—
927	C₂	—	8	2	no	—
928	C₂	C₁₀₁×#2408	1	1	yes	characteristic
929	C₂	C₁₀₁×#2410	1	1	yes	characteristic
930	C₂	C₁₀₁×#2416	1	1	yes	characteristic
931	C₂	C₁₀₁×#2615	1	1	yes	characteristic
932	C₂	C₁₀₁×#2617	1	1	yes	characteristic
933	C₂	C₁₀₁×#2619	1	1	yes	characteristic
934	C₂	C₁₀₁×#2669	1	2	yes	—
935	C₂	C₁₀₁×#2671	1	2	yes	—
936	C₂	C₁₀₁×#2676	1	2	yes	—
937	C₂	C₁₀₁×#2703	1	2	yes	—
938	C₂	C₁₀₁×#2813	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
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×#121×C₁₀₁	C₂	semidirect
2. C₂×#394×C₁₀₁	C₂	semidirect
3. C₂×#392×C₁₀₁	C₂	semidirect
4. C₂×#392×C₁₀₁	C₂	semidirect
5. C₂×#386×C₁₀₁	C₂	semidirect
6. C₂×#380×C₁₀₁	C₂	semidirect
7. C₁₀₁×#1442	C₂	semidirect
8. C₁₀₁×#1439	C₂	semidirect
9. C₁₀₁×#1439	C₂	semidirect
10. C₁₀₁×#1438	C₂	semidirect
11. C₁₀₁×#1438	C₂	semidirect
68. C₂²×D₄×C₁₀₁	D₄	semidirect
73. C₂³×C₄×C₁₀₁	D₄	semidirect
112. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
119. #95×C₁₀₁	D₄	semidirect
455. #16260	C₁₀₁	direct (N × H)
470. C₂²×#121	C₂×C₁₀₁	semidirect
471. C₂×#394	C₂×C₁₀₁	semidirect
472. C₂×#392	C₂×C₁₀₁	semidirect
473. C₂×#392	C₂×C₁₀₁	semidirect
474. C₂×#386	C₂×C₁₀₁	semidirect
475. C₂×#380	C₂×C₁₀₁	semidirect
476. #1442	C₂×C₁₀₁	semidirect
477. #1439	C₂×C₁₀₁	semidirect
478. #1439	C₂×C₁₀₁	semidirect
479. #1438	C₂×C₁₀₁	semidirect
480. #1438	C₂×C₁₀₁	semidirect
481. C₁₀₁	#16260	direct (N × H)
538. C₂²×D₄	D₄×C₁₀₁	semidirect
543. C₂³×C₄	D₄×C₁₀₁	semidirect
582. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
589. #95	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₀₁	2
C₂×#394×C₁₀₁	2
C₂×#392×C₁₀₁	2
C₂×#386×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₁₀₁×#1442	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
#16260	101

Subgroups — C101×#16260 #38798411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#16260 #38798411