Subgroups — C₁₀₁×#25865 #38808016

Order 25856.

1430 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#489×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#486×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2041	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1961	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, complemented
10	C₁₀₁×#1786	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×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	#535×C₁₀₁	—	2	4	no	—
15	#535×C₁₀₁	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×#127×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×#121×C₁₀₁	—	2	1	no	—
22	C₂×#121×C₁₀₁	—	2	1	no	—
23	C₂×#120×C₁₀₁	—	2	1	no	—
24	C₂×#120×C₁₀₁	—	2	1	no	—
25	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
26	#489×C₁₀₁	—	2	4	no	—
27	#486×C₁₀₁	—	2	4	no	—
28	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
29	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
30	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#102×C₁₀₁	C₂²	1	2	yes	complemented
35	C₂×#102×C₁₀₁	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
37	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
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	complemented
44	#382×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
45	#380×C₁₀₁	C₂²	1	2	yes	—
46	#336×C₁₀₁	C₂²	1	2	yes	complemented
47	C₂⁵×C₁₀₁	—	2	1	no	—
48	C₂×#41×C₁₀₁	—	2	2	no	—
49	C₂×#41×C₁₀₁	—	2	2	no	—
50	C₂×#41×C₁₀₁	—	2	4	no	—
51	C₂×#41×C₁₀₁	—	4	2	no	—
52	C₂²×Q₈×C₁₀₁	—	2	1	no	—
53	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₀₁	—	2	1	no	—
55	C₂²×D₄×C₁₀₁	—	2	2	no	—
56	C₂²×D₄×C₁₀₁	—	2	2	no	—
57	C₂²×D₄×C₁₀₁	—	2	1	no	—
58	C₂²×D₄×C₁₀₁	—	2	1	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	4	no	—
63	C₂²×D₄×C₁₀₁	—	4	2	no	—
64	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₀₁	—	2	1	no	—
68	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
72	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
73	#127×C₁₀₁	—	2	2	no	—
74	#127×C₁₀₁	—	2	2	no	—
75	#127×C₁₀₁	—	2	2	no	—
76	#127×C₁₀₁	D₄	1	4	yes	—
77	#124×C₁₀₁	—	2	2	no	—
78	#124×C₁₀₁	—	2	2	no	—
79	#124×C₁₀₁	—	2	2	no	—
80	#124×C₁₀₁	D₄	1	4	yes	—
81	#121×C₁₀₁	—	2	8	no	—
82	#121×C₁₀₁	—	2	8	no	—
83	#120×C₁₀₁	—	2	8	no	—
84	#120×C₁₀₁	—	2	8	no	—
85	#117×C₁₀₁	—	2	2	no	—
86	#117×C₁₀₁	—	2	2	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	—	4	2	no	—
104	#102×C₁₀₁	—	2	4	no	—
105	#102×C₁₀₁	—	2	4	no	—
106	#102×C₁₀₁	—	2	4	no	—
107	#102×C₁₀₁	—	4	2	no	—
108	#102×C₁₀₁	—	4	2	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	4	no	—
118	C₂⁴×C₁₀₁	—	2	1	no	—
119	C₂⁴×C₁₀₁	—	2	1	no	—
120	C₂⁴×C₁₀₁	—	2	1	no	—
121	C₂⁴×C₁₀₁	—	4	2	no	—
122	C₂⁴×C₁₀₁	—	4	2	no	—
123	C₂⁴×C₁₀₁	—	8	2	no	—
124	C₂⁴×C₁₀₁	—	8	2	no	—
125	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
126	#41×C₁₀₁	—	4	8	no	—
127	#41×C₁₀₁	—	4	8	no	—
128	C₂×Q₈×C₁₀₁	—	2	1	no	—
129	C₂×Q₈×C₁₀₁	—	2	2	no	—
130	C₂×Q₈×C₁₀₁	—	2	2	no	—
131	C₂×Q₈×C₁₀₁	—	4	2	no	—
132	C₂×Q₈×C₁₀₁	—	8	2	no	—
133	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₀₁	—	2	4	no	—
135	C₂×D₄×C₁₀₁	—	2	4	no	—
136	C₂×D₄×C₁₀₁	—	2	4	no	—
137	C₂×D₄×C₁₀₁	—	2	4	no	—
138	C₂×D₄×C₁₀₁	—	2	4	no	—
139	C₂×D₄×C₁₀₁	—	2	4	no	—
140	C₂×D₄×C₁₀₁	—	2	1	no	—
141	C₂×D₄×C₁₀₁	—	2	1	no	—
142	C₂×D₄×C₁₀₁	—	2	1	no	—
143	C₂×D₄×C₁₀₁	—	2	2	no	—
144	C₂×D₄×C₁₀₁	—	2	2	no	—
145	C₂×D₄×C₁₀₁	—	2	2	no	—
146	C₂×D₄×C₁₀₁	—	2	2	no	—
147	C₂×D₄×C₁₀₁	—	2	2	no	—
148	C₂×D₄×C₁₀₁	—	2	2	no	—
149	C₂×D₄×C₁₀₁	—	4	8	no	—
150	C₂×D₄×C₁₀₁	—	4	8	no	—
151	C₂×D₄×C₁₀₁	—	4	2	no	—
152	C₂×D₄×C₁₀₁	—	4	2	no	—
153	C₂×D₄×C₁₀₁	—	4	2	no	—
154	C₂×D₄×C₁₀₁	—	4	2	no	—
155	C₂×D₄×C₁₀₁	—	8	2	no	—
156	C₂×D₄×C₁₀₁	—	8	2	no	—
157	C₂×D₄×C₁₀₁	—	8	2	no	—
158	C₂×D₄×C₁₀₁	—	8	2	no	—
159	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₀₁	—	2	1	no	—
163	C₂²×C₄×C₁₀₁	—	2	1	no	—
164	C₂²×C₄×C₁₀₁	—	2	2	no	—
165	C₂²×C₄×C₁₀₁	—	2	4	no	—
166	C₂²×C₄×C₁₀₁	—	2	1	no	—
167	C₂²×C₄×C₁₀₁	—	2	2	no	—
168	C₂²×C₄×C₁₀₁	—	2	2	no	—
169	C₂²×C₄×C₁₀₁	—	4	2	no	—
170	C₂²×C₄×C₁₀₁	—	4	2	no	—
171	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
177	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₀₁	—	2	2	no	—
179	C₂×C₈×C₁₀₁	—	2	2	no	—
180	C₂×C₈×C₁₀₁	—	2	2	no	—
181	C₂×C₈×C₁₀₁	—	2	2	no	—
182	C₂×C₈×C₁₀₁	—	2	2	no	—
183	C₂×C₈×C₁₀₁	—	2	2	no	—
184	C₄⋊C₄×C₁₀₁	—	2	2	no	—
185	C₄⋊C₄×C₁₀₁	—	2	2	no	—
186	C₄⋊C₄×C₁₀₁	—	2	2	no	—
187	C₄⋊C₄×C₁₀₁	—	2	2	no	—
188	C₄⋊C₄×C₁₀₁	—	2	2	no	—
189	C₄⋊C₄×C₁₀₁	—	2	2	no	—
190	C₄⋊C₄×C₁₀₁	—	4	2	no	—
191	C₄⋊C₄×C₁₀₁	—	8	2	no	—
192	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
193	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
194	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
195	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
196	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
197	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
198	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
199	C₄²×C₁₀₁	—	2	1	no	—
200	C₄²×C₁₀₁	—	2	1	no	—
201	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
202	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
203	C₂³×C₁₀₁	—	2	1	no	—
204	C₂³×C₁₀₁	—	2	1	no	—
205	C₂³×C₁₀₁	—	2	2	no	—
206	C₂³×C₁₀₁	—	2	2	no	—
207	C₂³×C₁₀₁	—	2	2	no	—
208	C₂³×C₁₀₁	—	2	2	no	—
209	C₂³×C₁₀₁	—	2	2	no	—
210	C₂³×C₁₀₁	—	4	8	no	—
211	C₂³×C₁₀₁	—	4	1	no	—
212	C₂³×C₁₀₁	—	4	1	no	—
213	C₂³×C₁₀₁	—	4	1	no	—
214	C₂³×C₁₀₁	—	4	1	no	—
215	C₂³×C₁₀₁	—	4	1	no	—
216	C₂³×C₁₀₁	—	4	1	no	—
217	C₂³×C₁₀₁	—	4	2	no	—
218	C₂³×C₁₀₁	—	4	2	no	—
219	C₂³×C₁₀₁	—	4	2	no	—
220	C₂³×C₁₀₁	—	4	2	no	—
221	C₂³×C₁₀₁	—	4	2	no	—
222	C₂³×C₁₀₁	—	4	2	no	—
223	C₂³×C₁₀₁	—	8	8	no	—
224	C₂³×C₁₀₁	—	8	4	no	—
225	C₂³×C₁₀₁	—	8	4	no	—
226	C₂³×C₁₀₁	—	8	8	no	—
227	C₂³×C₁₀₁	#124	1	2	yes	—
228	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₁₀₁	—	2	4	no	—
230	Q₈×C₁₀₁	—	4	2	no	—
231	Q₈×C₁₀₁	—	8	4	no	—
232	D₄×C₁₀₁	—	2	4	no	—
233	D₄×C₁₀₁	—	2	4	no	—
234	D₄×C₁₀₁	—	2	4	no	—
235	D₄×C₁₀₁	—	4	8	no	—
236	D₄×C₁₀₁	—	4	8	no	—
237	D₄×C₁₀₁	—	4	2	no	—
238	D₄×C₁₀₁	—	4	2	no	—
239	D₄×C₁₀₁	—	4	2	no	—
240	D₄×C₁₀₁	—	8	4	no	—
241	D₄×C₁₀₁	—	8	4	no	—
242	D₄×C₁₀₁	—	8	4	no	—
243	D₄×C₁₀₁	—	8	4	no	—
244	C₂×C₄×C₁₀₁	—	2	1	no	—
245	C₂×C₄×C₁₀₁	—	2	1	no	—
246	C₂×C₄×C₁₀₁	—	2	2	no	—
247	C₂×C₄×C₁₀₁	—	2	2	no	—
248	C₂×C₄×C₁₀₁	—	2	4	no	—
249	C₂×C₄×C₁₀₁	—	2	4	no	—
250	C₂×C₄×C₁₀₁	—	2	1	no	—
251	C₂×C₄×C₁₀₁	—	2	1	no	—
252	C₂×C₄×C₁₀₁	—	2	2	no	—
253	C₂×C₄×C₁₀₁	—	2	2	no	—
254	C₂×C₄×C₁₀₁	—	2	2	no	—
255	C₂×C₄×C₁₀₁	—	4	8	no	—
256	C₂×C₄×C₁₀₁	—	4	1	no	—
257	C₂×C₄×C₁₀₁	—	4	1	no	—
258	C₂×C₄×C₁₀₁	—	4	2	no	—
259	C₂×C₄×C₁₀₁	—	4	2	no	—
260	C₂×C₄×C₁₀₁	—	4	2	no	—
261	C₂×C₄×C₁₀₁	—	4	2	no	—
262	C₂×C₄×C₁₀₁	—	4	2	no	—
263	C₂×C₄×C₁₀₁	—	4	2	no	—
264	C₂×C₄×C₁₀₁	#120	1	2	yes	—
265	C₂×C₄×C₁₀₁	#120	1	2	yes	—
266	C₂×C₄×C₁₀₁	#124	1	2	yes	—
267	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
270	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
271	C₈×C₁₀₁	—	4	2	no	—
272	C₈×C₁₀₁	—	4	2	no	—
273	C₂²×C₁₀₁	—	2	4	no	—
274	C₂²×C₁₀₁	—	2	2	no	—
275	C₂²×C₁₀₁	—	4	2	no	—
276	C₂²×C₁₀₁	—	4	1	no	—
277	C₂²×C₁₀₁	—	4	1	no	—
278	C₂²×C₁₀₁	—	4	2	no	—
279	C₂²×C₁₀₁	—	4	2	no	—
280	C₂²×C₁₀₁	—	4	2	no	—
281	C₂²×C₁₀₁	—	4	2	no	—
282	C₂²×C₁₀₁	—	4	2	no	—
283	C₂²×C₁₀₁	—	4	2	no	—
284	C₂²×C₁₀₁	—	4	2	no	—
285	C₂²×C₁₀₁	—	4	2	no	—
286	C₂²×C₁₀₁	—	4	2	no	—
287	C₂²×C₁₀₁	—	8	16	no	—
288	C₂²×C₁₀₁	—	8	2	no	—
289	C₂²×C₁₀₁	—	8	2	no	—
290	C₂²×C₁₀₁	—	8	2	no	—
291	C₂²×C₁₀₁	—	8	2	no	—
292	C₂²×C₁₀₁	—	8	2	no	—
293	C₂²×C₁₀₁	—	8	2	no	—
294	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
295	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
296	C₂²×C₁₀₁	#535	1	1	yes	characteristic
297	C₂²×C₁₀₁	#576	1	2	yes	—
298	C₂²×C₁₀₁	#577	1	2	yes	—
299	C₄×C₁₀₁	—	2	2	no	—
300	C₄×C₁₀₁	—	2	2	no	—
301	C₄×C₁₀₁	—	2	2	no	—
302	C₄×C₁₀₁	—	4	2	no	—
303	C₄×C₁₀₁	—	4	1	no	—
304	C₄×C₁₀₁	—	4	1	no	—
305	C₄×C₁₀₁	—	8	2	no	—
306	C₄×C₁₀₁	—	8	2	no	—
307	C₄×C₁₀₁	#546	1	2	yes	—
308	C₄×C₁₀₁	#546	1	2	yes	—
309	#25865	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₂×C₁₀₁	—	4	2	no	—
311	C₂×C₁₀₁	—	8	2	no	—
312	C₂×C₁₀₁	—	8	2	no	—
313	C₂×C₁₀₁	—	8	2	no	—
314	C₂×C₁₀₁	#2435	1	1	yes	characteristic
315	C₂×C₁₀₁	#3008	1	1	yes	characteristic
316	C₂×C₁₀₁	#3009	1	1	yes	characteristic
317	C₂×C₁₀₁	#3136	1	2	yes	—
318	C₂×C₁₀₁	#3224	1	2	yes	—
319	C₂×#535	C₂×C₁₀₁	1	1	yes	characteristic
320	C₂×#489	C₂×C₁₀₁	1	1	yes	characteristic, complemented
321	C₂×#486	C₂×C₁₀₁	1	1	yes	characteristic, complemented
322	#2628	C₂×C₁₀₁	1	1	yes	characteristic, complemented
323	#2042	C₂×C₁₀₁	1	2	yes	complemented
324	#2041	C₂×C₁₀₁	1	2	yes	complemented
325	#1961	C₂×C₁₀₁	1	1	yes	characteristic, complemented
326	#1958	C₂×C₁₀₁	1	1	yes	characteristic, complemented
327	#1788	C₂×C₁₀₁	1	2	yes	complemented
328	#1786	C₂×C₁₀₁	1	2	yes	complemented
329	#1750	C₂×C₁₀₁	1	1	yes	characteristic, complemented
330	C₁₀₁	#25865	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
332	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
333	#535	—	2	4	no	—
334	#535	—	2	4	no	—
335	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
336	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
337	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
338	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
339	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
340	C₂×#121	—	2	1	no	—
341	C₂×#121	—	2	1	no	—
342	C₂×#120	—	2	1	no	—
343	C₂×#120	—	2	1	no	—
344	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
345	#489	—	2	4	no	—
346	#486	—	2	4	no	—
347	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
348	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
349	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
350	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
351	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
352	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
353	C₂×#102	C₂²×C₁₀₁	1	2	yes	complemented
354	C₂×#102	C₂²×C₁₀₁	1	2	yes	complemented
355	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
356	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
357	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
358	#400	—	2	1	no	—
359	#399	—	2	1	no	—
360	#395	—	2	1	no	—
361	#393	—	2	1	no	—
362	#389	C₂²×C₁₀₁	1	2	yes	complemented
363	#382	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
364	#380	C₂²×C₁₀₁	1	2	yes	—
365	#336	C₂²×C₁₀₁	1	2	yes	complemented
366	C₂⁵	—	2	1	no	—
367	C₂×#41	—	2	2	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	4	no	—
370	C₂×#41	—	4	2	no	—
371	C₂²×Q₈	—	2	1	no	—
372	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	—	2	2	no	—
375	C₂²×D₄	—	2	2	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	4	no	—
382	C₂²×D₄	—	4	2	no	—
383	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
389	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
390	C₄⋊Q₈	—	2	2	no	—
391	C₄⋊Q₈	—	2	2	no	—
392	#127	—	2	2	no	—
393	#127	—	2	2	no	—
394	#127	—	2	2	no	—
395	#127	D₄×C₁₀₁	1	4	yes	—
396	#124	—	2	2	no	—
397	#124	—	2	2	no	—
398	#124	—	2	2	no	—
399	#124	D₄×C₁₀₁	1	4	yes	—
400	#121	—	2	8	no	—
401	#121	—	2	8	no	—
402	#120	—	2	8	no	—
403	#120	—	2	8	no	—
404	#117	—	2	2	no	—
405	#117	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
409	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
421	#103	—	2	4	no	—
422	#103	—	4	2	no	—
423	#102	—	2	4	no	—
424	#102	—	2	4	no	—
425	#102	—	2	4	no	—
426	#102	—	4	2	no	—
427	#102	—	4	2	no	—
428	#102	—	4	2	no	—
429	C₂²⋊C₈	—	2	4	no	—
430	#97	—	2	2	no	—
431	C₄×C₈	—	2	2	no	—
432	#95	—	2	2	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	2	no	—
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	2	1	no	—
438	C₂⁴	—	2	1	no	—
439	C₂⁴	—	2	1	no	—
440	C₂⁴	—	4	2	no	—
441	C₂⁴	—	4	2	no	—
442	C₂⁴	—	8	2	no	—
443	C₂⁴	—	8	2	no	—
444	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
445	#41	—	4	8	no	—
446	#41	—	4	8	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	4	2	no	—
451	C₂×Q₈	—	8	2	no	—
452	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	4	8	no	—
469	C₂×D₄	—	4	8	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	8	2	no	—
475	C₂×D₄	—	8	2	no	—
476	C₂×D₄	—	8	2	no	—
477	C₂×D₄	—	8	2	no	—
478	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
479	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
480	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
495	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	8	2	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	8	2	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
521	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	8	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	8	8	no	—
543	C₂³	—	8	4	no	—
544	C₂³	—	8	4	no	—
545	C₂³	—	8	8	no	—
546	C₂³	#124×C₁₀₁	1	2	yes	—
547	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
548	Q₈	—	2	4	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	8	4	no	—
551	D₄	—	2	4	no	—
552	D₄	—	2	4	no	—
553	D₄	—	2	4	no	—
554	D₄	—	4	8	no	—
555	D₄	—	4	8	no	—
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	8	4	no	—
560	D₄	—	8	4	no	—
561	D₄	—	8	4	no	—
562	D₄	—	8	4	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	#120×C₁₀₁	1	2	yes	—
584	C₂×C₄	#120×C₁₀₁	1	2	yes	—
585	C₂×C₄	#124×C₁₀₁	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
588	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
589	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
590	C₈	—	4	2	no	—
591	C₈	—	4	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	8	16	no	—
607	C₂²	—	8	2	no	—
608	C₂²	—	8	2	no	—
609	C₂²	—	8	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
614	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
615	C₂²	#535×C₁₀₁	1	1	yes	characteristic
616	C₂²	#576×C₁₀₁	1	2	yes	—
617	C₂²	#577×C₁₀₁	1	2	yes	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	8	2	no	—
625	C₄	—	8	2	no	—
626	C₄	#546×C₁₀₁	1	2	yes	—
627	C₄	#546×C₁₀₁	1	2	yes	—
628	C₂	—	4	2	no	—
629	C₂	—	8	2	no	—
630	C₂	—	8	2	no	—
631	C₂	—	8	2	no	—
632	C₂	C₁₀₁×#2435	1	1	yes	characteristic
633	C₂	C₁₀₁×#3008	1	1	yes	characteristic
634	C₂	C₁₀₁×#3009	1	1	yes	characteristic
635	C₂	C₁₀₁×#3136	1	2	yes	—
636	C₂	C₁₀₁×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#535×C₁₀₁	C₂
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×#486×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2628	C₂	semidirect
5. C₁₀₁×#2042	C₂	semidirect
6. C₁₀₁×#2041	C₂	semidirect
7. C₁₀₁×#1961	C₂	semidirect
8. C₁₀₁×#1958	C₂	semidirect
9. C₁₀₁×#1788	C₂	semidirect
10. C₁₀₁×#1786	C₂	semidirect
11. C₁₀₁×#1750	C₂	semidirect
16. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
28. C₂×#103×C₁₀₁	C₂²	semidirect
29. C₂×#103×C₁₀₁	C₂²	semidirect
34. C₂×#102×C₁₀₁	C₂²	semidirect
35. C₂×#102×C₁₀₁	C₂²	semidirect
37. C₂×#97×C₁₀₁	C₂²	semidirect
38. C₂×C₄×C₈×C₁₀₁	C₂²	semidirect
43. #389×C₁₀₁	C₂²	semidirect
44. #382×C₁₀₁	C₂²	semidirect
46. #336×C₁₀₁	C₂²	semidirect
309. #25865	C₁₀₁	direct (N × H)
320. C₂×#489	C₂×C₁₀₁	semidirect
321. C₂×#486	C₂×C₁₀₁	semidirect
322. #2628	C₂×C₁₀₁	semidirect
323. #2042	C₂×C₁₀₁	semidirect
324. #2041	C₂×C₁₀₁	semidirect
325. #1961	C₂×C₁₀₁	semidirect
326. #1958	C₂×C₁₀₁	semidirect
327. #1788	C₂×C₁₀₁	semidirect
328. #1786	C₂×C₁₀₁	semidirect
329. #1750	C₂×C₁₀₁	semidirect
330. C₁₀₁	#25865	direct (N × H)
335. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
347. C₂×#103	C₂²×C₁₀₁	semidirect
348. C₂×#103	C₂²×C₁₀₁	semidirect
353. C₂×#102	C₂²×C₁₀₁	semidirect
354. C₂×#102	C₂²×C₁₀₁	semidirect
356. C₂×#97	C₂²×C₁₀₁	semidirect
357. C₂×C₄×C₈	C₂²×C₁₀₁	semidirect
362. #389	C₂²×C₁₀₁	semidirect
363. #382	C₂²×C₁₀₁	semidirect
365. #336	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₁₀₁	2
C₂×#489×C₁₀₁	2
C₂×#486×C₁₀₁	2
C₁₀₁×#2628	2
C₁₀₁×#2042	2
C₁₀₁×#2041	2
C₁₀₁×#1961	2
C₁₀₁×#1958	2
C₁₀₁×#1788	2
C₁₀₁×#1786	2
C₁₀₁×#1750	2
#25865	101

Subgroups — C101×#25865 #38808016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25865 #38808016