Subgroups — C₁₀₁×#23903 #38806054

Order 25856.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#534×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#458×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×B(4,𝔽₂)×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2613	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2022	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2021	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1898	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1890	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×#1889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₁×#1781	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
15	#546×C₁₀₁	—	2	4	no	—
16	D₄²×C₁₀₁	—	2	4	no	—
17	#535×C₁₀₁	—	2	1	no	—
18	#534×C₁₀₁	—	2	1	no	—
19	#534×C₁₀₁	—	2	4	no	—
20	#534×C₁₀₁	—	2	4	no	—
21	#534×C₁₀₁	C₂²	1	2	yes	—
22	#525×C₁₀₁	—	2	1	no	—
23	C₂×#123×C₁₀₁	—	2	1	no	—
24	C₂×#123×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×#123×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×#123×C₁₀₁	C₂²	1	2	yes	complemented
27	C₂×#121×C₁₀₁	—	2	1	no	—
28	C₂×#121×C₁₀₁	—	2	1	no	—
29	C₂×#120×C₁₀₁	—	2	1	no	—
30	C₂×#120×C₁₀₁	—	2	1	no	—
31	C₂×#120×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂×#120×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#120×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×#120×C₁₀₁	C₂²	1	2	yes	complemented
35	#518×C₁₀₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
37	#458×C₁₀₁	—	2	4	no	—
38	B(4,𝔽₂)×C₁₀₁	—	2	4	no	—
39	C₂×#99×C₁₀₁	C₂²	1	1	yes	characteristic
40	C₂×#99×C₁₀₁	C₂²	1	1	yes	characteristic
41	C₂×#99×C₁₀₁	C₂²	1	2	yes	complemented
42	C₂×#99×C₁₀₁	C₂²	1	2	yes	complemented
43	C₂×#99×C₁₀₁	C₂²	1	2	yes	complemented
44	#394×C₁₀₁	—	2	4	no	—
45	#392×C₁₀₁	—	2	4	no	—
46	#381×C₁₀₁	C₂²	1	2	yes	complemented
47	#379×C₁₀₁	C₂²	1	2	yes	complemented
48	#379×C₁₀₁	C₂²	1	2	yes	complemented
49	#342×C₁₀₁	C₂²	1	2	yes	complemented
50	#342×C₁₀₁	C₂²	1	2	yes	complemented
51	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic, complemented
52	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
54	H(5,𝔽₂)×C₁₀₁	—	2	2	no	—
55	H(5,𝔽₂)×C₁₀₁	—	2	2	no	—
56	H(5,𝔽₂)×C₁₀₁	—	4	2	no	—
57	C₂×#41×C₁₀₁	—	2	1	no	—
58	C₂×#41×C₁₀₁	—	2	2	no	—
59	C₂²×D₄×C₁₀₁	—	2	1	no	—
60	C₂²×D₄×C₁₀₁	—	2	1	no	—
61	C₂²×D₄×C₁₀₁	—	2	1	no	—
62	C₂²×D₄×C₁₀₁	—	2	2	no	—
63	C₂²×D₄×C₁₀₁	—	2	4	no	—
64	C₂²×D₄×C₁₀₁	—	2	2	no	—
65	C₂²×D₄×C₁₀₁	—	2	2	no	—
66	C₂²×D₄×C₁₀₁	—	2	1	no	—
67	C₂²×D₄×C₁₀₁	—	2	1	no	—
68	C₂²×D₄×C₁₀₁	—	2	2	no	—
69	C₂²×D₄×C₁₀₁	—	2	2	no	—
70	C₂²×D₄×C₁₀₁	—	2	4	no	—
71	C₂²×D₄×C₁₀₁	—	2	2	no	—
72	C₂²×D₄×C₁₀₁	—	2	2	no	—
73	C₂²×D₄×C₁₀₁	—	4	2	no	—
74	C₂²×D₄×C₁₀₁	—	4	2	no	—
75	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic, complemented
76	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic, complemented
77	C₂²×D₄×C₁₀₁	D₄	1	4	yes	complemented
78	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₀₁	—	2	1	no	—
82	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic, complemented
83	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
84	#127×C₁₀₁	—	2	2	no	—
85	#124×C₁₀₁	—	2	2	no	—
86	#123×C₁₀₁	—	2	8	no	—
87	#123×C₁₀₁	—	2	2	no	—
88	#123×C₁₀₁	—	2	2	no	—
89	#123×C₁₀₁	—	2	2	no	—
90	#123×C₁₀₁	—	2	2	no	—
91	#123×C₁₀₁	—	2	2	no	—
92	#123×C₁₀₁	—	2	2	no	—
93	#123×C₁₀₁	—	2	4	no	—
94	#123×C₁₀₁	—	4	2	no	—
95	#123×C₁₀₁	D₄	1	4	yes	complemented
96	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
97	#121×C₁₀₁	—	2	8	no	—
98	#121×C₁₀₁	—	2	8	no	—
99	#121×C₁₀₁	—	2	2	no	—
100	#121×C₁₀₁	—	2	4	no	—
101	#121×C₁₀₁	—	2	4	no	—
102	#121×C₁₀₁	—	2	4	no	—
103	#120×C₁₀₁	—	2	8	no	—
104	#120×C₁₀₁	—	2	4	no	—
105	#120×C₁₀₁	—	2	2	no	—
106	#120×C₁₀₁	—	2	2	no	—
107	#120×C₁₀₁	—	2	2	no	—
108	#120×C₁₀₁	—	2	2	no	—
109	#120×C₁₀₁	—	2	4	no	—
110	#120×C₁₀₁	—	2	2	no	—
111	#120×C₁₀₁	—	2	2	no	—
112	#120×C₁₀₁	—	2	2	no	—
113	#120×C₁₀₁	—	2	2	no	—
114	#120×C₁₀₁	—	2	4	no	—
115	#120×C₁₀₁	—	4	2	no	—
116	#120×C₁₀₁	D₄	1	4	yes	complemented
117	C₄×D₄×C₁₀₁	—	2	4	no	—
118	C₄×D₄×C₁₀₁	—	2	4	no	—
119	#117×C₁₀₁	—	2	1	no	—
120	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
121	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
122	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
134	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	4	yes	complemented
137	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
142	#99×C₁₀₁	—	2	2	no	—
143	#99×C₁₀₁	—	2	2	no	—
144	#99×C₁₀₁	—	2	4	no	—
145	#99×C₁₀₁	—	2	4	no	—
146	#99×C₁₀₁	—	4	2	no	—
147	#95×C₁₀₁	—	2	4	no	—
148	C₂⁴×C₁₀₁	—	2	1	no	—
149	C₂⁴×C₁₀₁	—	2	1	no	—
150	C₂⁴×C₁₀₁	—	2	2	no	—
151	C₂⁴×C₁₀₁	—	2	1	no	—
152	C₂⁴×C₁₀₁	—	2	2	no	—
153	C₂⁴×C₁₀₁	—	2	1	no	—
154	C₂⁴×C₁₀₁	—	2	2	no	—
155	C₂⁴×C₁₀₁	—	2	2	no	—
156	C₂⁴×C₁₀₁	—	2	1	no	—
157	C₂⁴×C₁₀₁	—	2	2	no	—
158	C₂⁴×C₁₀₁	—	4	1	no	—
159	C₂⁴×C₁₀₁	—	8	2	no	—
160	C₂⁴×C₁₀₁	—	8	2	no	—
161	C₂⁴×C₁₀₁	—	8	2	no	—
162	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
164	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
165	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
166	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	complemented
169	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
170	#41×C₁₀₁	—	4	4	no	—
171	#41×C₁₀₁	—	4	4	no	—
172	#41×C₁₀₁	—	4	2	no	—
173	#41×C₁₀₁	—	4	2	no	—
174	C₂×Q₈×C₁₀₁	—	2	1	no	—
175	C₂×D₄×C₁₀₁	—	2	2	no	—
176	C₂×D₄×C₁₀₁	—	2	2	no	—
177	C₂×D₄×C₁₀₁	—	2	2	no	—
178	C₂×D₄×C₁₀₁	—	2	4	no	—
179	C₂×D₄×C₁₀₁	—	2	4	no	—
180	C₂×D₄×C₁₀₁	—	2	1	no	—
181	C₂×D₄×C₁₀₁	—	2	4	no	—
182	C₂×D₄×C₁₀₁	—	2	2	no	—
183	C₂×D₄×C₁₀₁	—	2	2	no	—
184	C₂×D₄×C₁₀₁	—	2	2	no	—
185	C₂×D₄×C₁₀₁	—	2	2	no	—
186	C₂×D₄×C₁₀₁	—	2	2	no	—
187	C₂×D₄×C₁₀₁	—	2	2	no	—
188	C₂×D₄×C₁₀₁	—	2	2	no	—
189	C₂×D₄×C₁₀₁	—	2	1	no	—
190	C₂×D₄×C₁₀₁	—	2	1	no	—
191	C₂×D₄×C₁₀₁	—	2	2	no	—
192	C₂×D₄×C₁₀₁	—	2	2	no	—
193	C₂×D₄×C₁₀₁	—	2	2	no	—
194	C₂×D₄×C₁₀₁	—	2	2	no	—
195	C₂×D₄×C₁₀₁	—	2	4	no	—
196	C₂×D₄×C₁₀₁	—	2	4	no	—
197	C₂×D₄×C₁₀₁	—	2	4	no	—
198	C₂×D₄×C₁₀₁	—	2	4	no	—
199	C₂×D₄×C₁₀₁	—	2	2	no	—
200	C₂×D₄×C₁₀₁	—	4	1	no	—
201	C₂×D₄×C₁₀₁	—	4	1	no	—
202	C₂×D₄×C₁₀₁	—	4	8	no	—
203	C₂×D₄×C₁₀₁	—	4	8	no	—
204	C₂×D₄×C₁₀₁	—	4	8	no	—
205	C₂×D₄×C₁₀₁	—	4	4	no	—
206	C₂×D₄×C₁₀₁	—	4	4	no	—
207	C₂×D₄×C₁₀₁	—	4	8	no	—
208	C₂×D₄×C₁₀₁	—	4	2	no	—
209	C₂×D₄×C₁₀₁	—	4	2	no	—
210	C₂×D₄×C₁₀₁	—	4	2	no	—
211	C₂×D₄×C₁₀₁	—	4	2	no	—
212	C₂×D₄×C₁₀₁	—	4	2	no	—
213	C₂×D₄×C₁₀₁	—	4	2	no	—
214	C₂×D₄×C₁₀₁	—	4	4	no	—
215	C₂×D₄×C₁₀₁	—	8	4	no	—
216	C₂×D₄×C₁₀₁	—	8	2	no	—
217	C₂×D₄×C₁₀₁	—	8	2	no	—
218	C₂×D₄×C₁₀₁	—	8	4	no	—
219	C₂×D₄×C₁₀₁	—	8	4	no	—
220	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₀₁	—	2	1	no	—
223	C₂²×C₄×C₁₀₁	—	2	2	no	—
224	C₂²×C₄×C₁₀₁	—	2	2	no	—
225	C₂²×C₄×C₁₀₁	—	2	2	no	—
226	C₂²×C₄×C₁₀₁	—	2	1	no	—
227	C₂²×C₄×C₁₀₁	—	2	1	no	—
228	C₂²×C₄×C₁₀₁	—	2	1	no	—
229	C₂²×C₄×C₁₀₁	—	2	1	no	—
230	C₂²×C₄×C₁₀₁	—	2	2	no	—
231	C₂²×C₄×C₁₀₁	—	2	2	no	—
232	C₂²×C₄×C₁₀₁	—	2	4	no	—
233	C₂²×C₄×C₁₀₁	—	2	2	no	—
234	C₂²×C₄×C₁₀₁	—	2	2	no	—
235	C₂²×C₄×C₁₀₁	—	2	2	no	—
236	C₂²×C₄×C₁₀₁	—	4	1	no	—
237	C₂²×C₄×C₁₀₁	—	8	2	no	—
238	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	complemented
243	C₄⋊C₄×C₁₀₁	—	2	4	no	—
244	C₄⋊C₄×C₁₀₁	—	2	2	no	—
245	C₄⋊C₄×C₁₀₁	—	2	4	no	—
246	C₄⋊C₄×C₁₀₁	—	2	4	no	—
247	C₄⋊C₄×C₁₀₁	—	4	4	no	—
248	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
249	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
250	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
251	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
252	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
253	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
254	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
255	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
256	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
257	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
258	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
259	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
260	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
261	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
262	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
263	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
264	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
265	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
266	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
267	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
268	C₂²⋊C₄×C₁₀₁	—	8	4	no	—
269	C₂²⋊C₄×C₁₀₁	—	8	4	no	—
270	C₂²⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	complemented
271	C₂²⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	complemented
272	C₄²×C₁₀₁	—	2	2	no	—
273	C₂³×C₁₀₁	—	2	1	no	—
274	C₂³×C₁₀₁	—	2	1	no	—
275	C₂³×C₁₀₁	—	2	1	no	—
276	C₂³×C₁₀₁	—	2	1	no	—
277	C₂³×C₁₀₁	—	2	1	no	—
278	C₂³×C₁₀₁	—	2	1	no	—
279	C₂³×C₁₀₁	—	2	4	no	—
280	C₂³×C₁₀₁	—	2	4	no	—
281	C₂³×C₁₀₁	—	2	1	no	—
282	C₂³×C₁₀₁	—	2	2	no	—
283	C₂³×C₁₀₁	—	2	1	no	—
284	C₂³×C₁₀₁	—	2	2	no	—
285	C₂³×C₁₀₁	—	2	4	no	—
286	C₂³×C₁₀₁	—	2	1	no	—
287	C₂³×C₁₀₁	—	2	2	no	—
288	C₂³×C₁₀₁	—	2	2	no	—
289	C₂³×C₁₀₁	—	4	2	no	—
290	C₂³×C₁₀₁	—	4	2	no	—
291	C₂³×C₁₀₁	—	4	2	no	—
292	C₂³×C₁₀₁	—	4	4	no	—
293	C₂³×C₁₀₁	—	4	4	no	—
294	C₂³×C₁₀₁	—	4	4	no	—
295	C₂³×C₁₀₁	—	4	2	no	—
296	C₂³×C₁₀₁	—	4	2	no	—
297	C₂³×C₁₀₁	—	4	4	no	—
298	C₂³×C₁₀₁	—	4	4	no	—
299	C₂³×C₁₀₁	—	4	2	no	—
300	C₂³×C₁₀₁	—	4	2	no	—
301	C₂³×C₁₀₁	—	4	4	no	—
302	C₂³×C₁₀₁	—	4	2	no	—
303	C₂³×C₁₀₁	—	4	4	no	—
304	C₂³×C₁₀₁	—	4	1	no	—
305	C₂³×C₁₀₁	—	4	1	no	—
306	C₂³×C₁₀₁	—	4	2	no	—
307	C₂³×C₁₀₁	—	8	2	no	—
308	C₂³×C₁₀₁	—	8	2	no	—
309	C₂³×C₁₀₁	—	8	2	no	—
310	C₂³×C₁₀₁	—	8	2	no	—
311	C₂³×C₁₀₁	—	8	2	no	—
312	C₂³×C₁₀₁	—	8	4	no	—
313	C₂³×C₁₀₁	—	8	4	no	—
314	C₂³×C₁₀₁	—	8	4	no	—
315	C₂³×C₁₀₁	—	8	2	no	—
316	C₂³×C₁₀₁	—	8	4	no	—
317	C₂³×C₁₀₁	#120	1	2	yes	—
318	C₂³×C₁₀₁	#120	1	2	yes	—
319	C₂³×C₁₀₁	#120	1	2	yes	—
320	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
322	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
324	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
325	Q₈×C₁₀₁	—	4	2	no	—
326	D₄×C₁₀₁	—	2	4	no	—
327	D₄×C₁₀₁	—	2	4	no	—
328	D₄×C₁₀₁	—	4	4	no	—
329	D₄×C₁₀₁	—	4	2	no	—
330	D₄×C₁₀₁	—	4	4	no	—
331	D₄×C₁₀₁	—	4	8	no	—
332	D₄×C₁₀₁	—	4	8	no	—
333	D₄×C₁₀₁	—	4	4	no	—
334	D₄×C₁₀₁	—	4	8	no	—
335	D₄×C₁₀₁	—	4	2	no	—
336	D₄×C₁₀₁	—	4	2	no	—
337	D₄×C₁₀₁	—	4	2	no	—
338	D₄×C₁₀₁	—	4	2	no	—
339	D₄×C₁₀₁	—	4	2	no	—
340	D₄×C₁₀₁	—	4	2	no	—
341	D₄×C₁₀₁	—	8	4	no	—
342	D₄×C₁₀₁	—	8	4	no	—
343	D₄×C₁₀₁	—	8	4	no	—
344	D₄×C₁₀₁	—	8	4	no	—
345	D₄×C₁₀₁	—	8	8	no	—
346	C₂×C₄×C₁₀₁	—	2	1	no	—
347	C₂×C₄×C₁₀₁	—	2	1	no	—
348	C₂×C₄×C₁₀₁	—	2	2	no	—
349	C₂×C₄×C₁₀₁	—	2	2	no	—
350	C₂×C₄×C₁₀₁	—	2	1	no	—
351	C₂×C₄×C₁₀₁	—	2	2	no	—
352	C₂×C₄×C₁₀₁	—	2	4	no	—
353	C₂×C₄×C₁₀₁	—	2	2	no	—
354	C₂×C₄×C₁₀₁	—	2	1	no	—
355	C₂×C₄×C₁₀₁	—	2	1	no	—
356	C₂×C₄×C₁₀₁	—	2	2	no	—
357	C₂×C₄×C₁₀₁	—	2	4	no	—
358	C₂×C₄×C₁₀₁	—	2	2	no	—
359	C₂×C₄×C₁₀₁	—	4	4	no	—
360	C₂×C₄×C₁₀₁	—	4	4	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	1	no	—
365	C₂×C₄×C₁₀₁	—	4	1	no	—
366	C₂×C₄×C₁₀₁	—	4	2	no	—
367	C₂×C₄×C₁₀₁	—	4	4	no	—
368	C₂×C₄×C₁₀₁	—	4	4	no	—
369	C₂×C₄×C₁₀₁	—	4	4	no	—
370	C₂×C₄×C₁₀₁	—	4	2	no	—
371	C₂×C₄×C₁₀₁	—	4	2	no	—
372	C₂×C₄×C₁₀₁	—	8	4	no	—
373	C₂×C₄×C₁₀₁	—	8	2	no	—
374	C₂×C₄×C₁₀₁	#120	1	2	yes	—
375	C₂²×C₁₀₁	—	2	4	no	—
376	C₂²×C₁₀₁	—	2	2	no	—
377	C₂²×C₁₀₁	—	2	2	no	—
378	C₂²×C₁₀₁	—	2	2	no	—
379	C₂²×C₁₀₁	—	2	2	no	—
380	C₂²×C₁₀₁	—	2	2	no	—
381	C₂²×C₁₀₁	—	2	4	no	—
382	C₂²×C₁₀₁	—	2	2	no	—
383	C₂²×C₁₀₁	—	4	1	no	—
384	C₂²×C₁₀₁	—	4	1	no	—
385	C₂²×C₁₀₁	—	4	2	no	—
386	C₂²×C₁₀₁	—	4	2	no	—
387	C₂²×C₁₀₁	—	4	2	no	—
388	C₂²×C₁₀₁	—	4	2	no	—
389	C₂²×C₁₀₁	—	4	2	no	—
390	C₂²×C₁₀₁	—	4	2	no	—
391	C₂²×C₁₀₁	—	4	2	no	—
392	C₂²×C₁₀₁	—	4	2	no	—
393	C₂²×C₁₀₁	—	4	2	no	—
394	C₂²×C₁₀₁	—	4	4	no	—
395	C₂²×C₁₀₁	—	4	4	no	—
396	C₂²×C₁₀₁	—	4	2	no	—
397	C₂²×C₁₀₁	—	4	2	no	—
398	C₂²×C₁₀₁	—	4	2	no	—
399	C₂²×C₁₀₁	—	4	1	no	—
400	C₂²×C₁₀₁	—	4	4	no	—
401	C₂²×C₁₀₁	—	4	2	no	—
402	C₂²×C₁₀₁	—	8	4	no	—
403	C₂²×C₁₀₁	—	8	4	no	—
404	C₂²×C₁₀₁	—	8	1	no	—
405	C₂²×C₁₀₁	—	8	2	no	—
406	C₂²×C₁₀₁	—	8	2	no	—
407	C₂²×C₁₀₁	—	8	1	no	—
408	C₂²×C₁₀₁	—	8	4	no	—
409	C₂²×C₁₀₁	—	8	2	no	—
410	C₂²×C₁₀₁	—	8	8	no	—
411	C₂²×C₁₀₁	—	8	2	no	—
412	C₂²×C₁₀₁	—	16	2	no	—
413	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
414	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
415	C₂²×C₁₀₁	#534	1	1	yes	characteristic
416	C₂²×C₁₀₁	D₄²	1	2	yes	—
417	C₂²×C₁₀₁	D₄²	1	2	yes	—
418	C₄×C₁₀₁	—	2	2	no	—
419	C₄×C₁₀₁	—	4	2	no	—
420	C₄×C₁₀₁	—	4	2	no	—
421	C₄×C₁₀₁	—	4	1	no	—
422	C₄×C₁₀₁	—	4	2	no	—
423	C₄×C₁₀₁	—	4	2	no	—
424	C₄×C₁₀₁	—	4	4	no	—
425	C₄×C₁₀₁	—	8	2	no	—
426	C₄×C₁₀₁	—	8	2	no	—
427	#23903	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂×C₁₀₁	—	2	1	no	—
429	C₂×C₁₀₁	—	2	2	no	—
430	C₂×C₁₀₁	—	2	2	no	—
431	C₂×C₁₀₁	—	2	1	no	—
432	C₂×C₁₀₁	—	4	2	no	—
433	C₂×C₁₀₁	—	4	2	no	—
434	C₂×C₁₀₁	—	4	2	no	—
435	C₂×C₁₀₁	—	8	2	no	—
436	C₂×C₁₀₁	—	8	1	no	—
437	C₂×C₁₀₁	—	8	2	no	—
438	C₂×C₁₀₁	#2403	1	1	yes	characteristic
439	C₂×C₁₀₁	#3026	1	2	yes	—
440	#3484	C₂×C₁₀₁	1	1	yes	characteristic, complemented
441	C₂×#534	C₂×C₁₀₁	1	1	yes	characteristic, complemented
442	C₂×#458	C₂×C₁₀₁	1	1	yes	characteristic, complemented
443	C₂×B(4,𝔽₂)	C₂×C₁₀₁	1	1	yes	characteristic, complemented
444	#2613	C₂×C₁₀₁	1	2	yes	complemented
445	#2022	C₂×C₁₀₁	1	2	yes	complemented
446	#2021	C₂×C₁₀₁	1	2	yes	complemented
447	#1898	C₂×C₁₀₁	1	2	yes	complemented
448	#1890	C₂×C₁₀₁	1	1	yes	characteristic, complemented
449	#1889	C₂×C₁₀₁	1	1	yes	characteristic, complemented
450	#1781	C₂×C₁₀₁	1	1	yes	characteristic, complemented
451	C₁₀₁	#23903	1	1	yes	characteristic, direct product factor, Sylow
452	C₂×H(5,𝔽₂)	C₂²×C₁₀₁	1	1	yes	characteristic
453	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
454	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
455	#546	—	2	4	no	—
456	D₄²	—	2	4	no	—
457	#535	—	2	1	no	—
458	#534	—	2	1	no	—
459	#534	—	2	4	no	—
460	#534	—	2	4	no	—
461	#534	C₂²×C₁₀₁	1	2	yes	—
462	#525	—	2	1	no	—
463	C₂×#123	—	2	1	no	—
464	C₂×#123	C₂²×C₁₀₁	1	1	yes	characteristic
465	C₂×#123	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
466	C₂×#123	C₂²×C₁₀₁	1	2	yes	complemented
467	C₂×#121	—	2	1	no	—
468	C₂×#121	—	2	1	no	—
469	C₂×#120	—	2	1	no	—
470	C₂×#120	—	2	1	no	—
471	C₂×#120	C₂²×C₁₀₁	1	1	yes	characteristic
472	C₂×#120	C₂²×C₁₀₁	1	2	yes	—
473	C₂×#120	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
474	C₂×#120	C₂²×C₁₀₁	1	2	yes	complemented
475	#518	C₂²×C₁₀₁	1	1	yes	characteristic
476	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
477	#458	—	2	4	no	—
478	B(4,𝔽₂)	—	2	4	no	—
479	C₂×#99	C₂²×C₁₀₁	1	1	yes	characteristic
480	C₂×#99	C₂²×C₁₀₁	1	1	yes	characteristic
481	C₂×#99	C₂²×C₁₀₁	1	2	yes	complemented
482	C₂×#99	C₂²×C₁₀₁	1	2	yes	complemented
483	C₂×#99	C₂²×C₁₀₁	1	2	yes	complemented
484	#394	—	2	4	no	—
485	#392	—	2	4	no	—
486	#381	C₂²×C₁₀₁	1	2	yes	complemented
487	#379	C₂²×C₁₀₁	1	2	yes	complemented
488	#379	C₂²×C₁₀₁	1	2	yes	complemented
489	#342	C₂²×C₁₀₁	1	2	yes	complemented
490	#342	C₂²×C₁₀₁	1	2	yes	complemented
491	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic, complemented
492	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
493	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
494	H(5,𝔽₂)	—	2	2	no	—
495	H(5,𝔽₂)	—	2	2	no	—
496	H(5,𝔽₂)	—	4	2	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	—	2	2	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	4	no	—
504	C₂²×D₄	—	2	2	no	—
505	C₂²×D₄	—	2	2	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	2	4	no	—
511	C₂²×D₄	—	2	2	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	—	4	2	no	—
514	C₂²×D₄	—	4	2	no	—
515	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic, complemented
516	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic, complemented
517	C₂²×D₄	D₄×C₁₀₁	1	4	yes	complemented
518	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
519	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic, complemented
523	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
524	#127	—	2	2	no	—
525	#124	—	2	2	no	—
526	#123	—	2	8	no	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	#123	—	2	2	no	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	4	no	—
534	#123	—	4	2	no	—
535	#123	D₄×C₁₀₁	1	4	yes	complemented
536	C₂²⋊Q₈	—	2	2	no	—
537	#121	—	2	8	no	—
538	#121	—	2	8	no	—
539	#121	—	2	2	no	—
540	#121	—	2	4	no	—
541	#121	—	2	4	no	—
542	#121	—	2	4	no	—
543	#120	—	2	8	no	—
544	#120	—	2	4	no	—
545	#120	—	2	2	no	—
546	#120	—	2	2	no	—
547	#120	—	2	2	no	—
548	#120	—	2	2	no	—
549	#120	—	2	4	no	—
550	#120	—	2	2	no	—
551	#120	—	2	2	no	—
552	#120	—	2	2	no	—
553	#120	—	2	2	no	—
554	#120	—	2	4	no	—
555	#120	—	4	2	no	—
556	#120	D₄×C₁₀₁	1	4	yes	complemented
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	4	no	—
559	#117	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₂²⋊C₄	—	2	2	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	2	no	—
571	C₂×C₂²⋊C₄	—	2	2	no	—
572	C₂×C₂²⋊C₄	—	2	2	no	—
573	C₂×C₂²⋊C₄	—	2	2	no	—
574	C₂×C₂²⋊C₄	—	2	4	no	—
575	C₂×C₂²⋊C₄	—	2	4	no	—
576	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	4	yes	complemented
577	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
582	#99	—	2	2	no	—
583	#99	—	2	2	no	—
584	#99	—	2	4	no	—
585	#99	—	2	4	no	—
586	#99	—	4	2	no	—
587	#95	—	2	4	no	—
588	C₂⁴	—	2	1	no	—
589	C₂⁴	—	2	1	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	1	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	4	1	no	—
599	C₂⁴	—	8	2	no	—
600	C₂⁴	—	8	2	no	—
601	C₂⁴	—	8	2	no	—
602	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
604	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
605	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
606	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
607	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
608	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	complemented
609	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	2	no	—
613	#41	—	4	2	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	4	1	no	—
641	C₂×D₄	—	4	1	no	—
642	C₂×D₄	—	4	8	no	—
643	C₂×D₄	—	4	8	no	—
644	C₂×D₄	—	4	8	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	4	8	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	8	4	no	—
656	C₂×D₄	—	8	2	no	—
657	C₂×D₄	—	8	2	no	—
658	C₂×D₄	—	8	4	no	—
659	C₂×D₄	—	8	4	no	—
660	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
661	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	8	2	no	—
678	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
682	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	complemented
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	8	4	no	—
709	C₂²⋊C₄	—	8	4	no	—
710	C₂²⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	complemented
711	C₂²⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	complemented
712	C₄²	—	2	2	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	4	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	4	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	8	2	no	—
748	C₂³	—	8	2	no	—
749	C₂³	—	8	2	no	—
750	C₂³	—	8	2	no	—
751	C₂³	—	8	2	no	—
752	C₂³	—	8	4	no	—
753	C₂³	—	8	4	no	—
754	C₂³	—	8	4	no	—
755	C₂³	—	8	2	no	—
756	C₂³	—	8	4	no	—
757	C₂³	#120×C₁₀₁	1	2	yes	—
758	C₂³	#120×C₁₀₁	1	2	yes	—
759	C₂³	#120×C₁₀₁	1	2	yes	—
760	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
761	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
762	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
763	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
764	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
765	Q₈	—	4	2	no	—
766	D₄	—	2	4	no	—
767	D₄	—	2	4	no	—
768	D₄	—	4	4	no	—
769	D₄	—	4	2	no	—
770	D₄	—	4	4	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	2	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	D₄	—	8	4	no	—
785	D₄	—	8	8	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	#120×C₁₀₁	1	2	yes	—
815	C₂²	—	2	4	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	8	4	no	—
843	C₂²	—	8	4	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	2	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	2	no	—
848	C₂²	—	8	4	no	—
849	C₂²	—	8	2	no	—
850	C₂²	—	8	8	no	—
851	C₂²	—	8	2	no	—
852	C₂²	—	16	2	no	—
853	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
854	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
855	C₂²	#534×C₁₀₁	1	1	yes	characteristic
856	C₂²	D₄²×C₁₀₁	1	2	yes	—
857	C₂²	D₄²×C₁₀₁	1	2	yes	—
858	C₄	—	2	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	4	no	—
865	C₄	—	8	2	no	—
866	C₄	—	8	2	no	—
867	C₂	—	2	1	no	—
868	C₂	—	2	2	no	—
869	C₂	—	2	2	no	—
870	C₂	—	2	1	no	—
871	C₂	—	4	2	no	—
872	C₂	—	4	2	no	—
873	C₂	—	4	2	no	—
874	C₂	—	8	2	no	—
875	C₂	—	8	1	no	—
876	C₂	—	8	2	no	—
877	C₂	C₁₀₁×#2403	1	1	yes	characteristic
878	C₂	C₁₀₁×#3026	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂⁵×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×#3484	C₂	semidirect
2. C₂×#534×C₁₀₁	C₂	semidirect
3. C₂×#458×C₁₀₁	C₂	semidirect
4. C₂×B(4,𝔽₂)×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2613	C₂	semidirect
6. C₁₀₁×#2022	C₂	semidirect
7. C₁₀₁×#2021	C₂	semidirect
8. C₁₀₁×#1898	C₂	semidirect
9. C₁₀₁×#1890	C₂	semidirect
10. C₁₀₁×#1889	C₂	semidirect
11. C₁₀₁×#1781	C₂	semidirect
14. C₂³×D₄×C₁₀₁	C₂²	semidirect
25. C₂×#123×C₁₀₁	C₂²	semidirect
26. C₂×#123×C₁₀₁	C₂²	semidirect
33. C₂×#120×C₁₀₁	C₂²	semidirect
34. C₂×#120×C₁₀₁	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
41. C₂×#99×C₁₀₁	C₂²	semidirect
42. C₂×#99×C₁₀₁	C₂²	semidirect
43. C₂×#99×C₁₀₁	C₂²	semidirect
46. #381×C₁₀₁	C₂²	semidirect
47. #379×C₁₀₁	C₂²	semidirect
48. #379×C₁₀₁	C₂²	semidirect
49. #342×C₁₀₁	C₂²	semidirect
50. #342×C₁₀₁	C₂²	semidirect
51. C₂⁵×C₁₀₁	D₄	semidirect
75. C₂²×D₄×C₁₀₁	D₄	semidirect
76. C₂²×D₄×C₁₀₁	D₄	semidirect
77. C₂²×D₄×C₁₀₁	D₄	semidirect
82. C₂³×C₄×C₁₀₁	D₄	semidirect
95. #123×C₁₀₁	D₄	semidirect
116. #120×C₁₀₁	D₄	semidirect
136. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
168. C₂⁴×C₁₀₁	C₂×D₄	semidirect
242. C₂²×C₄×C₁₀₁	C₂×D₄	semidirect
270. C₂²⋊C₄×C₁₀₁	C₂×D₄	semidirect
271. C₂²⋊C₄×C₁₀₁	C₂×D₄	semidirect
427. #23903	C₁₀₁	direct (N × H)
440. #3484	C₂×C₁₀₁	semidirect
441. C₂×#534	C₂×C₁₀₁	semidirect
442. C₂×#458	C₂×C₁₀₁	semidirect
443. C₂×B(4,𝔽₂)	C₂×C₁₀₁	semidirect
444. #2613	C₂×C₁₀₁	semidirect
445. #2022	C₂×C₁₀₁	semidirect
446. #2021	C₂×C₁₀₁	semidirect
447. #1898	C₂×C₁₀₁	semidirect
448. #1890	C₂×C₁₀₁	semidirect
449. #1889	C₂×C₁₀₁	semidirect
450. #1781	C₂×C₁₀₁	semidirect
451. C₁₀₁	#23903	direct (N × H)
454. C₂³×D₄	C₂²×C₁₀₁	semidirect
465. C₂×#123	C₂²×C₁₀₁	semidirect
466. C₂×#123	C₂²×C₁₀₁	semidirect
473. C₂×#120	C₂²×C₁₀₁	semidirect
474. C₂×#120	C₂²×C₁₀₁	semidirect
476. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
481. C₂×#99	C₂²×C₁₀₁	semidirect
482. C₂×#99	C₂²×C₁₀₁	semidirect
483. C₂×#99	C₂²×C₁₀₁	semidirect
486. #381	C₂²×C₁₀₁	semidirect
487. #379	C₂²×C₁₀₁	semidirect
488. #379	C₂²×C₁₀₁	semidirect
489. #342	C₂²×C₁₀₁	semidirect
490. #342	C₂²×C₁₀₁	semidirect
491. C₂⁵	D₄×C₁₀₁	semidirect
515. C₂²×D₄	D₄×C₁₀₁	semidirect
516. C₂²×D₄	D₄×C₁₀₁	semidirect
517. C₂²×D₄	D₄×C₁₀₁	semidirect
522. C₂³×C₄	D₄×C₁₀₁	semidirect
535. #123	D₄×C₁₀₁	semidirect
556. #120	D₄×C₁₀₁	semidirect
576. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
608. C₂⁴	C₂×D₄×C₁₀₁	semidirect
682. C₂²×C₄	C₂×D₄×C₁₀₁	semidirect
710. C₂²⋊C₄	C₂×D₄×C₁₀₁	semidirect
711. C₂²⋊C₄	C₂×D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3484	2
C₂×#534×C₁₀₁	2
C₂×#458×C₁₀₁	2
C₂×B(4,𝔽₂)×C₁₀₁	2
C₁₀₁×#2613	2
C₁₀₁×#2022	2
C₁₀₁×#2021	2
C₁₀₁×#1898	2
C₁₀₁×#1890	2
C₁₀₁×#1889	2
C₁₀₁×#1781	2
#23903	101

Subgroups — C101×#23903 #38806054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23903 #38806054