Subgroups — C₁₀₁×#25866 #38808017

Order 25856.

1238 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#489×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#487×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2043	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1788	C₂	1	2	yes	maximal
10	C₁₀₁×#1787	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	#536×C₁₀₁	—	2	4	no	—
15	#536×C₁₀₁	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×#124×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₁₀₁	—	2	1	no	—
22	C₂×#123×C₁₀₁	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
25	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
26	#489×C₁₀₁	—	2	4	no	—
27	#487×C₁₀₁	—	2	4	no	—
28	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
35	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
37	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
39	#400×C₁₀₁	—	2	1	no	—
40	#399×C₁₀₁	—	2	1	no	—
41	#395×C₁₀₁	—	2	1	no	—
42	#393×C₁₀₁	—	2	1	no	—
43	#389×C₁₀₁	C₂²	1	2	yes	—
44	#382×C₁₀₁	C₂²	1	1	yes	characteristic
45	#380×C₁₀₁	C₂²	1	2	yes	—
46	#336×C₁₀₁	C₂²	1	2	yes	—
47	C₂×#41×C₁₀₁	—	2	2	no	—
48	C₂×#41×C₁₀₁	—	2	2	no	—
49	C₂×#41×C₁₀₁	—	2	4	no	—
50	C₂×#41×C₁₀₁	—	4	2	no	—
51	C₂²×Q₈×C₁₀₁	—	2	2	no	—
52	C₂²×Q₈×C₁₀₁	—	2	2	no	—
53	C₂²×Q₈×C₁₀₁	—	2	1	no	—
54	C₂²×Q₈×C₁₀₁	—	2	1	no	—
55	C₂²×Q₈×C₁₀₁	—	2	4	no	—
56	C₂²×Q₈×C₁₀₁	—	4	2	no	—
57	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₀₁	—	2	1	no	—
61	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₀₁	—	2	1	no	—
63	C₂³×C₄×C₁₀₁	—	2	1	no	—
64	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
68	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
69	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
70	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
71	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
72	C₄⋊Q₈×C₁₀₁	D₄	1	4	yes	—
73	#124×C₁₀₁	—	2	2	no	—
74	#124×C₁₀₁	—	2	2	no	—
75	#124×C₁₀₁	—	2	2	no	—
76	#124×C₁₀₁	D₄	1	4	yes	—
77	#123×C₁₀₁	—	2	8	no	—
78	#123×C₁₀₁	—	2	8	no	—
79	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
80	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
81	#117×C₁₀₁	—	2	2	no	—
82	#117×C₁₀₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
102	#103×C₁₀₁	—	2	4	no	—
103	#103×C₁₀₁	—	2	4	no	—
104	#103×C₁₀₁	—	2	4	no	—
105	#103×C₁₀₁	—	4	2	no	—
106	#103×C₁₀₁	—	4	2	no	—
107	#103×C₁₀₁	—	4	2	no	—
108	#102×C₁₀₁	—	2	4	no	—
109	#102×C₁₀₁	—	4	2	no	—
110	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
111	#97×C₁₀₁	—	2	2	no	—
112	C₄×C₈×C₁₀₁	—	2	2	no	—
113	#95×C₁₀₁	—	2	2	no	—
114	#95×C₁₀₁	—	2	1	no	—
115	#95×C₁₀₁	—	2	1	no	—
116	#95×C₁₀₁	—	2	2	no	—
117	C₂⁴×C₁₀₁	—	2	1	no	—
118	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
119	#41×C₁₀₁	—	4	8	no	—
120	#41×C₁₀₁	—	4	8	no	—
121	C₂×Q₈×C₁₀₁	—	2	4	no	—
122	C₂×Q₈×C₁₀₁	—	2	1	no	—
123	C₂×Q₈×C₁₀₁	—	2	1	no	—
124	C₂×Q₈×C₁₀₁	—	2	1	no	—
125	C₂×Q₈×C₁₀₁	—	2	2	no	—
126	C₂×Q₈×C₁₀₁	—	2	2	no	—
127	C₂×Q₈×C₁₀₁	—	2	2	no	—
128	C₂×Q₈×C₁₀₁	—	2	2	no	—
129	C₂×Q₈×C₁₀₁	—	2	2	no	—
130	C₂×Q₈×C₁₀₁	—	2	2	no	—
131	C₂×Q₈×C₁₀₁	—	4	8	no	—
132	C₂×Q₈×C₁₀₁	—	4	8	no	—
133	C₂×Q₈×C₁₀₁	—	4	2	no	—
134	C₂×Q₈×C₁₀₁	—	4	2	no	—
135	C₂×Q₈×C₁₀₁	—	4	2	no	—
136	C₂×Q₈×C₁₀₁	—	8	2	no	—
137	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₁₀₁	—	2	4	no	—
141	C₂×D₄×C₁₀₁	—	2	1	no	—
142	C₂×D₄×C₁₀₁	—	2	2	no	—
143	C₂×D₄×C₁₀₁	—	2	2	no	—
144	C₂×D₄×C₁₀₁	—	4	2	no	—
145	C₂×D₄×C₁₀₁	—	4	2	no	—
146	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₀₁	—	2	1	no	—
148	C₂²×C₄×C₁₀₁	—	2	1	no	—
149	C₂²×C₄×C₁₀₁	—	2	2	no	—
150	C₂²×C₄×C₁₀₁	—	2	4	no	—
151	C₂²×C₄×C₁₀₁	—	2	4	no	—
152	C₂²×C₄×C₁₀₁	—	2	1	no	—
153	C₂²×C₄×C₁₀₁	—	2	1	no	—
154	C₂²×C₄×C₁₀₁	—	2	1	no	—
155	C₂²×C₄×C₁₀₁	—	2	2	no	—
156	C₂²×C₄×C₁₀₁	—	2	2	no	—
157	C₂²×C₄×C₁₀₁	—	4	2	no	—
158	C₂²×C₄×C₁₀₁	—	4	2	no	—
159	C₂²×C₄×C₁₀₁	—	4	2	no	—
160	C₂²×C₄×C₁₀₁	—	4	2	no	—
161	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
167	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₁₀₁	—	2	2	no	—
169	C₂×C₈×C₁₀₁	—	2	2	no	—
170	C₂×C₈×C₁₀₁	—	2	2	no	—
171	C₂×C₈×C₁₀₁	—	2	2	no	—
172	C₂×C₈×C₁₀₁	—	2	2	no	—
173	C₂×C₈×C₁₀₁	—	2	2	no	—
174	C₄⋊C₄×C₁₀₁	—	2	4	no	—
175	C₄⋊C₄×C₁₀₁	—	2	4	no	—
176	C₄⋊C₄×C₁₀₁	—	2	4	no	—
177	C₄⋊C₄×C₁₀₁	—	2	4	no	—
178	C₄⋊C₄×C₁₀₁	—	2	2	no	—
179	C₄⋊C₄×C₁₀₁	—	2	2	no	—
180	C₄⋊C₄×C₁₀₁	—	2	2	no	—
181	C₄⋊C₄×C₁₀₁	—	2	2	no	—
182	C₄⋊C₄×C₁₀₁	—	2	2	no	—
183	C₄⋊C₄×C₁₀₁	—	2	2	no	—
184	C₄⋊C₄×C₁₀₁	—	4	2	no	—
185	C₄⋊C₄×C₁₀₁	—	8	2	no	—
186	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
187	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
188	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
189	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
190	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
191	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
192	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
193	C₄²×C₁₀₁	—	2	1	no	—
194	C₄²×C₁₀₁	—	2	1	no	—
195	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
196	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
197	C₂³×C₁₀₁	—	2	1	no	—
198	C₂³×C₁₀₁	—	2	1	no	—
199	C₂³×C₁₀₁	—	2	2	no	—
200	C₂³×C₁₀₁	—	2	2	no	—
201	C₂³×C₁₀₁	—	2	2	no	—
202	C₂³×C₁₀₁	—	4	1	no	—
203	C₂³×C₁₀₁	—	4	1	no	—
204	C₂³×C₁₀₁	—	4	2	no	—
205	C₂³×C₁₀₁	—	4	2	no	—
206	C₂³×C₁₀₁	#124	1	2	yes	—
207	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₀₁	—	2	4	no	—
209	Q₈×C₁₀₁	—	2	4	no	—
210	Q₈×C₁₀₁	—	2	4	no	—
211	Q₈×C₁₀₁	—	4	8	no	—
212	Q₈×C₁₀₁	—	4	2	no	—
213	Q₈×C₁₀₁	—	4	2	no	—
214	Q₈×C₁₀₁	—	4	2	no	—
215	Q₈×C₁₀₁	—	8	4	no	—
216	D₄×C₁₀₁	—	2	4	no	—
217	D₄×C₁₀₁	—	4	8	no	—
218	D₄×C₁₀₁	—	4	2	no	—
219	C₂×C₄×C₁₀₁	—	2	1	no	—
220	C₂×C₄×C₁₀₁	—	2	1	no	—
221	C₂×C₄×C₁₀₁	—	2	2	no	—
222	C₂×C₄×C₁₀₁	—	2	2	no	—
223	C₂×C₄×C₁₀₁	—	2	4	no	—
224	C₂×C₄×C₁₀₁	—	2	4	no	—
225	C₂×C₄×C₁₀₁	—	2	1	no	—
226	C₂×C₄×C₁₀₁	—	2	1	no	—
227	C₂×C₄×C₁₀₁	—	2	2	no	—
228	C₂×C₄×C₁₀₁	—	2	2	no	—
229	C₂×C₄×C₁₀₁	—	2	2	no	—
230	C₂×C₄×C₁₀₁	—	2	2	no	—
231	C₂×C₄×C₁₀₁	—	2	2	no	—
232	C₂×C₄×C₁₀₁	—	4	8	no	—
233	C₂×C₄×C₁₀₁	—	4	8	no	—
234	C₂×C₄×C₁₀₁	—	4	1	no	—
235	C₂×C₄×C₁₀₁	—	4	1	no	—
236	C₂×C₄×C₁₀₁	—	4	1	no	—
237	C₂×C₄×C₁₀₁	—	4	1	no	—
238	C₂×C₄×C₁₀₁	—	4	1	no	—
239	C₂×C₄×C₁₀₁	—	4	1	no	—
240	C₂×C₄×C₁₀₁	—	4	2	no	—
241	C₂×C₄×C₁₀₁	—	4	2	no	—
242	C₂×C₄×C₁₀₁	—	4	2	no	—
243	C₂×C₄×C₁₀₁	—	4	2	no	—
244	C₂×C₄×C₁₀₁	—	4	2	no	—
245	C₂×C₄×C₁₀₁	—	4	2	no	—
246	C₂×C₄×C₁₀₁	#120	1	2	yes	—
247	C₂×C₄×C₁₀₁	#120	1	2	yes	—
248	C₂×C₄×C₁₀₁	#124	1	2	yes	—
249	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
252	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
253	C₈×C₁₀₁	—	4	2	no	—
254	C₈×C₁₀₁	—	4	2	no	—
255	C₂²×C₁₀₁	—	2	4	no	—
256	C₂²×C₁₀₁	—	2	2	no	—
257	C₂²×C₁₀₁	—	4	2	no	—
258	C₂²×C₁₀₁	—	4	1	no	—
259	C₂²×C₁₀₁	—	4	1	no	—
260	C₂²×C₁₀₁	—	4	2	no	—
261	C₂²×C₁₀₁	—	4	2	no	—
262	C₂²×C₁₀₁	—	4	2	no	—
263	C₂²×C₁₀₁	—	8	2	no	—
264	C₂²×C₁₀₁	—	8	2	no	—
265	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
266	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
267	C₂²×C₁₀₁	#535	1	1	yes	characteristic
268	C₂²×C₁₀₁	#577	1	2	yes	—
269	C₂²×C₁₀₁	#578	1	2	yes	—
270	C₄×C₁₀₁	—	2	2	no	—
271	C₄×C₁₀₁	—	2	2	no	—
272	C₄×C₁₀₁	—	2	2	no	—
273	C₄×C₁₀₁	—	4	2	no	—
274	C₄×C₁₀₁	—	4	2	no	—
275	C₄×C₁₀₁	—	4	2	no	—
276	C₄×C₁₀₁	—	4	1	no	—
277	C₄×C₁₀₁	—	4	1	no	—
278	C₄×C₁₀₁	—	8	2	no	—
279	C₄×C₁₀₁	—	8	2	no	—
280	C₄×C₁₀₁	#546	1	2	yes	—
281	C₄×C₁₀₁	#546	1	2	yes	—
282	#25866	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂×C₁₀₁	—	4	2	no	—
284	C₂×C₁₀₁	—	8	2	no	—
285	C₂×C₁₀₁	#2435	1	1	yes	characteristic
286	C₂×C₁₀₁	#3010	1	1	yes	characteristic
287	C₂×C₁₀₁	#3011	1	1	yes	characteristic
288	C₂×C₁₀₁	#3137	1	2	yes	—
289	C₂×C₁₀₁	#3225	1	2	yes	—
290	C₂×#536	C₂×C₁₀₁	1	1	yes	characteristic
291	C₂×#489	C₂×C₁₀₁	1	1	yes	characteristic, complemented
292	C₂×#487	C₂×C₁₀₁	1	1	yes	characteristic, complemented
293	#2628	C₂×C₁₀₁	1	1	yes	characteristic, complemented
294	#2043	C₂×C₁₀₁	1	2	yes	complemented
295	#2042	C₂×C₁₀₁	1	2	yes	complemented
296	#1960	C₂×C₁₀₁	1	1	yes	characteristic, complemented
297	#1958	C₂×C₁₀₁	1	1	yes	characteristic, complemented
298	#1788	C₂×C₁₀₁	1	2	yes	—
299	#1787	C₂×C₁₀₁	1	2	yes	complemented
300	#1750	C₂×C₁₀₁	1	1	yes	characteristic, complemented
301	C₁₀₁	#25866	1	1	yes	characteristic, direct product factor, Sylow
302	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
303	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
304	#536	—	2	4	no	—
305	#536	—	2	4	no	—
306	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
307	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
308	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
309	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
310	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
311	C₂×#123	—	2	1	no	—
312	C₂×#123	—	2	1	no	—
313	C₂×C₂²⋊Q₈	—	2	1	no	—
314	C₂×C₂²⋊Q₈	—	2	1	no	—
315	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
316	#489	—	2	4	no	—
317	#487	—	2	4	no	—
318	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
319	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
320	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
321	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
322	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
323	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
324	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
325	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
326	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
327	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
328	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
329	#400	—	2	1	no	—
330	#399	—	2	1	no	—
331	#395	—	2	1	no	—
332	#393	—	2	1	no	—
333	#389	C₂²×C₁₀₁	1	2	yes	—
334	#382	C₂²×C₁₀₁	1	1	yes	characteristic
335	#380	C₂²×C₁₀₁	1	2	yes	—
336	#336	C₂²×C₁₀₁	1	2	yes	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	—	4	2	no	—
341	C₂²×Q₈	—	2	2	no	—
342	C₂²×Q₈	—	2	2	no	—
343	C₂²×Q₈	—	2	1	no	—
344	C₂²×Q₈	—	2	1	no	—
345	C₂²×Q₈	—	2	4	no	—
346	C₂²×Q₈	—	4	2	no	—
347	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
348	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
356	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
357	C₄⋊Q₈	—	2	2	no	—
358	C₄⋊Q₈	—	2	2	no	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	D₄×C₁₀₁	1	4	yes	—
363	#124	—	2	2	no	—
364	#124	—	2	2	no	—
365	#124	—	2	2	no	—
366	#124	D₄×C₁₀₁	1	4	yes	—
367	#123	—	2	8	no	—
368	#123	—	2	8	no	—
369	C₂²⋊Q₈	—	2	8	no	—
370	C₂²⋊Q₈	—	2	8	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
380	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
392	#103	—	2	4	no	—
393	#103	—	2	4	no	—
394	#103	—	2	4	no	—
395	#103	—	4	2	no	—
396	#103	—	4	2	no	—
397	#103	—	4	2	no	—
398	#102	—	2	4	no	—
399	#102	—	4	2	no	—
400	C₂²⋊C₈	—	2	4	no	—
401	#97	—	2	2	no	—
402	C₄×C₈	—	2	2	no	—
403	#95	—	2	2	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	2	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
409	#41	—	4	8	no	—
410	#41	—	4	8	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	4	8	no	—
422	C₂×Q₈	—	4	8	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	—	4	2	no	—
425	C₂×Q₈	—	4	2	no	—
426	C₂×Q₈	—	8	2	no	—
427	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
428	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
429	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
456	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	8	2	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	8	2	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
486	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	#124×C₁₀₁	1	2	yes	—
497	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
498	Q₈	—	2	4	no	—
499	Q₈	—	2	4	no	—
500	Q₈	—	2	4	no	—
501	Q₈	—	4	8	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	8	4	no	—
506	D₄	—	2	4	no	—
507	D₄	—	4	8	no	—
508	D₄	—	4	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	#120×C₁₀₁	1	2	yes	—
537	C₂×C₄	#120×C₁₀₁	1	2	yes	—
538	C₂×C₄	#124×C₁₀₁	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
542	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
543	C₈	—	4	2	no	—
544	C₈	—	4	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
556	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
557	C₂²	#535×C₁₀₁	1	1	yes	characteristic
558	C₂²	#577×C₁₀₁	1	2	yes	—
559	C₂²	#578×C₁₀₁	1	2	yes	—
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	#546×C₁₀₁	1	2	yes	—
571	C₄	#546×C₁₀₁	1	2	yes	—
572	C₂	—	4	2	no	—
573	C₂	—	8	2	no	—
574	C₂	C₁₀₁×#2435	1	1	yes	characteristic
575	C₂	C₁₀₁×#3010	1	1	yes	characteristic
576	C₂	C₁₀₁×#3011	1	1	yes	characteristic
577	C₂	C₁₀₁×#3137	1	2	yes	—
578	C₂	C₁₀₁×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×#41×C₁₀₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×#117×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#489×C₁₀₁	C₂	semidirect
3. C₂×#487×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2628	C₂	semidirect
5. C₁₀₁×#2043	C₂	semidirect
6. C₁₀₁×#2042	C₂	semidirect
7. C₁₀₁×#1960	C₂	semidirect
8. C₁₀₁×#1958	C₂	semidirect
10. C₁₀₁×#1787	C₂	semidirect
11. C₁₀₁×#1750	C₂	semidirect
282. #25866	C₁₀₁	direct (N × H)
291. C₂×#489	C₂×C₁₀₁	semidirect
292. C₂×#487	C₂×C₁₀₁	semidirect
293. #2628	C₂×C₁₀₁	semidirect
294. #2043	C₂×C₁₀₁	semidirect
295. #2042	C₂×C₁₀₁	semidirect
296. #1960	C₂×C₁₀₁	semidirect
297. #1958	C₂×C₁₀₁	semidirect
299. #1787	C₂×C₁₀₁	semidirect
300. #1750	C₂×C₁₀₁	semidirect
301. C₁₀₁	#25866	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#536×C₁₀₁	2
C₂×#489×C₁₀₁	2
C₂×#487×C₁₀₁	2
C₁₀₁×#2628	2
C₁₀₁×#2043	2
C₁₀₁×#2042	2
C₁₀₁×#1960	2
C₁₀₁×#1958	2
C₁₀₁×#1788	2
C₁₀₁×#1787	2
C₁₀₁×#1750	2
#25866	101

Subgroups — C101×#25866 #38808017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25866 #38808017