Subgroups — C₁₀₁×#15259 #38797410

Order 25856.

3670 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#393×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#379×C₁₀₁	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1440	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1438	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1437	C₂	1	2	yes	maximal, complemented
9	C₂⁶×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
11	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₀₁	—	2	4	no	—
14	C₂×#124×C₁₀₁	—	2	8	no	—
15	C₂×#120×C₁₀₁	—	2	4	no	—
16	C₂×#120×C₁₀₁	—	2	8	no	—
17	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
25	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
26	#393×C₁₀₁	—	2	8	no	—
27	#379×C₁₀₁	—	2	8	no	—
28	C₂×#95×C₁₀₁	C₂²	1	2	yes	complemented
29	C₂×#95×C₁₀₁	C₂²	1	4	yes	complemented
30	C₂×#95×C₁₀₁	C₂²	1	4	yes	complemented
31	C₂⁵×C₁₀₁	—	2	2	no	—
32	C₂⁵×C₁₀₁	—	2	4	no	—
33	C₂⁵×C₁₀₁	—	2	4	no	—
34	C₂⁵×C₁₀₁	—	2	8	no	—
35	C₂⁵×C₁₀₁	—	4	4	no	—
36	C₂⁵×C₁₀₁	—	4	2	no	—
37	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
38	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
39	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₀₁	—	2	4	no	—
41	C₂²×Q₈×C₁₀₁	—	2	2	no	—
42	C₂²×Q₈×C₁₀₁	—	2	4	no	—
43	C₂²×Q₈×C₁₀₁	—	4	2	no	—
44	C₂²×D₄×C₁₀₁	—	2	4	no	—
45	C₂²×D₄×C₁₀₁	—	2	4	no	—
46	C₂²×D₄×C₁₀₁	—	2	4	no	—
47	C₂²×D₄×C₁₀₁	—	2	8	no	—
48	C₂²×D₄×C₁₀₁	—	2	4	no	—
49	C₂²×D₄×C₁₀₁	—	2	4	no	—
50	C₂²×D₄×C₁₀₁	—	4	2	no	—
51	C₂²×D₄×C₁₀₁	—	4	4	no	—
52	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
53	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
58	#124×C₁₀₁	—	2	32	no	—
59	#120×C₁₀₁	—	2	32	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	—
80	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	complemented
81	C₂×C₄²×C₁₀₁	—	2	4	no	—
82	C₂×C₄²×C₁₀₁	—	2	2	no	—
83	#95×C₁₀₁	—	2	8	no	—
84	#95×C₁₀₁	—	2	4	no	—
85	#95×C₁₀₁	—	4	4	no	—
86	C₂⁴×C₁₀₁	—	2	4	no	—
87	C₂⁴×C₁₀₁	—	2	2	no	—
88	C₂⁴×C₁₀₁	—	2	2	no	—
89	C₂⁴×C₁₀₁	—	2	2	no	—
90	C₂⁴×C₁₀₁	—	2	4	no	—
91	C₂⁴×C₁₀₁	—	2	4	no	—
92	C₂⁴×C₁₀₁	—	2	4	no	—
93	C₂⁴×C₁₀₁	—	2	4	no	—
94	C₂⁴×C₁₀₁	—	2	4	no	—
95	C₂⁴×C₁₀₁	—	2	2	no	—
96	C₂⁴×C₁₀₁	—	2	4	no	—
97	C₂⁴×C₁₀₁	—	2	8	no	—
98	C₂⁴×C₁₀₁	—	2	16	no	—
99	C₂⁴×C₁₀₁	—	2	2	no	—
100	C₂⁴×C₁₀₁	—	2	2	no	—
101	C₂⁴×C₁₀₁	—	2	4	no	—
102	C₂⁴×C₁₀₁	—	2	2	no	—
103	C₂⁴×C₁₀₁	—	2	4	no	—
104	C₂⁴×C₁₀₁	—	4	16	no	—
105	C₂⁴×C₁₀₁	—	4	16	no	—
106	C₂⁴×C₁₀₁	—	4	16	no	—
107	C₂⁴×C₁₀₁	—	4	16	no	—
108	C₂⁴×C₁₀₁	—	4	8	no	—
109	C₂⁴×C₁₀₁	—	4	4	no	—
110	C₂⁴×C₁₀₁	—	4	8	no	—
111	C₂⁴×C₁₀₁	—	4	8	no	—
112	C₂⁴×C₁₀₁	—	4	16	no	—
113	C₂⁴×C₁₀₁	—	4	8	no	—
114	C₂⁴×C₁₀₁	—	4	4	no	—
115	C₂⁴×C₁₀₁	—	4	8	no	—
116	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
117	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
118	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
119	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
120	C₂⁴×C₁₀₁	#41	1	8	yes	—
121	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
122	C₂×Q₈×C₁₀₁	—	2	8	no	—
123	C₂×Q₈×C₁₀₁	—	4	16	no	—
124	C₂×Q₈×C₁₀₁	—	4	4	no	—
125	C₂×Q₈×C₁₀₁	—	4	4	no	—
126	C₂×D₄×C₁₀₁	—	2	16	no	—
127	C₂×D₄×C₁₀₁	—	2	8	no	—
128	C₂×D₄×C₁₀₁	—	2	8	no	—
129	C₂×D₄×C₁₀₁	—	4	4	no	—
130	C₂×D₄×C₁₀₁	—	4	16	no	—
131	C₂×D₄×C₁₀₁	—	4	16	no	—
132	C₂×D₄×C₁₀₁	—	4	16	no	—
133	C₂×D₄×C₁₀₁	—	4	8	no	—
134	C₂×D₄×C₁₀₁	—	4	8	no	—
135	C₂²×C₄×C₁₀₁	—	2	2	no	—
136	C₂²×C₄×C₁₀₁	—	2	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	4	no	—
138	C₂²×C₄×C₁₀₁	—	2	2	no	—
139	C₂²×C₄×C₁₀₁	—	2	2	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	2	no	—
142	C₂²×C₄×C₁₀₁	—	2	2	no	—
143	C₂²×C₄×C₁₀₁	—	2	2	no	—
144	C₂²×C₄×C₁₀₁	—	2	4	no	—
145	C₂²×C₄×C₁₀₁	—	2	4	no	—
146	C₂²×C₄×C₁₀₁	—	2	4	no	—
147	C₂²×C₄×C₁₀₁	—	2	4	no	—
148	C₂²×C₄×C₁₀₁	—	2	4	no	—
149	C₂²×C₄×C₁₀₁	—	2	4	no	—
150	C₂²×C₄×C₁₀₁	—	2	4	no	—
151	C₂²×C₄×C₁₀₁	—	2	4	no	—
152	C₂²×C₄×C₁₀₁	—	2	4	no	—
153	C₂²×C₄×C₁₀₁	—	2	4	no	—
154	C₂²×C₄×C₁₀₁	—	2	4	no	—
155	C₂²×C₄×C₁₀₁	—	2	4	no	—
156	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
161	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
162	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
163	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
164	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
165	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
166	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
167	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
168	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
169	C₄²×C₁₀₁	—	2	8	no	—
170	C₂³×C₁₀₁	—	2	2	no	—
171	C₂³×C₁₀₁	—	2	4	no	—
172	C₂³×C₁₀₁	—	2	4	no	—
173	C₂³×C₁₀₁	—	2	8	no	—
174	C₂³×C₁₀₁	—	2	2	no	—
175	C₂³×C₁₀₁	—	2	4	no	—
176	C₂³×C₁₀₁	—	2	4	no	—
177	C₂³×C₁₀₁	—	2	8	no	—
178	C₂³×C₁₀₁	—	2	8	no	—
179	C₂³×C₁₀₁	—	2	8	no	—
180	C₂³×C₁₀₁	—	2	8	no	—
181	C₂³×C₁₀₁	—	2	8	no	—
182	C₂³×C₁₀₁	—	2	8	no	—
183	C₂³×C₁₀₁	—	2	8	no	—
184	C₂³×C₁₀₁	—	2	8	no	—
185	C₂³×C₁₀₁	—	2	8	no	—
186	C₂³×C₁₀₁	—	2	8	no	—
187	C₂³×C₁₀₁	—	2	2	no	—
188	C₂³×C₁₀₁	—	2	2	no	—
189	C₂³×C₁₀₁	—	2	2	no	—
190	C₂³×C₁₀₁	—	2	8	no	—
191	C₂³×C₁₀₁	—	4	16	no	—
192	C₂³×C₁₀₁	—	4	32	no	—
193	C₂³×C₁₀₁	—	4	32	no	—
194	C₂³×C₁₀₁	—	4	64	no	—
195	C₂³×C₁₀₁	—	4	64	no	—
196	C₂³×C₁₀₁	—	4	32	no	—
197	C₂³×C₁₀₁	—	4	2	no	—
198	C₂³×C₁₀₁	—	4	2	no	—
199	C₂³×C₁₀₁	—	4	2	no	—
200	C₂³×C₁₀₁	—	4	2	no	—
201	C₂³×C₁₀₁	—	4	4	no	—
202	C₂³×C₁₀₁	—	4	2	no	—
203	C₂³×C₁₀₁	—	4	2	no	—
204	C₂³×C₁₀₁	—	4	4	no	—
205	C₂³×C₁₀₁	—	4	4	no	—
206	C₂³×C₁₀₁	—	4	4	no	—
207	C₂³×C₁₀₁	—	4	4	no	—
208	C₂³×C₁₀₁	—	4	4	no	—
209	C₂³×C₁₀₁	—	4	4	no	—
210	C₂³×C₁₀₁	—	4	2	no	—
211	C₂³×C₁₀₁	—	4	2	no	—
212	C₂³×C₁₀₁	—	4	4	no	—
213	C₂³×C₁₀₁	—	4	2	no	—
214	C₂³×C₁₀₁	—	4	2	no	—
215	C₂³×C₁₀₁	—	4	2	no	—
216	C₂³×C₁₀₁	—	4	2	no	—
217	C₂³×C₁₀₁	—	4	4	no	—
218	C₂³×C₁₀₁	—	4	4	no	—
219	C₂³×C₁₀₁	—	4	4	no	—
220	C₂³×C₁₀₁	—	4	4	no	—
221	C₂³×C₁₀₁	—	4	2	no	—
222	C₂³×C₁₀₁	—	4	2	no	—
223	C₂³×C₁₀₁	#120	1	4	yes	—
224	C₂³×C₁₀₁	#124	1	8	yes	complemented
225	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
226	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
227	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
228	C₂³×C₁₀₁	C₂×#41	1	4	yes	—
229	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
230	C₂³×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
231	Q₈×C₁₀₁	—	4	16	no	—
232	D₄×C₁₀₁	—	4	16	no	—
233	D₄×C₁₀₁	—	4	32	no	—
234	C₂×C₄×C₁₀₁	—	2	2	no	—
235	C₂×C₄×C₁₀₁	—	2	2	no	—
236	C₂×C₄×C₁₀₁	—	2	8	no	—
237	C₂×C₄×C₁₀₁	—	2	4	no	—
238	C₂×C₄×C₁₀₁	—	2	4	no	—
239	C₂×C₄×C₁₀₁	—	2	4	no	—
240	C₂×C₄×C₁₀₁	—	2	8	no	—
241	C₂×C₄×C₁₀₁	—	2	8	no	—
242	C₂×C₄×C₁₀₁	—	2	8	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	—	4	2	no	—
247	C₂×C₄×C₁₀₁	—	4	2	no	—
248	C₂×C₄×C₁₀₁	—	4	2	no	—
249	C₂×C₄×C₁₀₁	—	4	4	no	—
250	C₂×C₄×C₁₀₁	—	4	4	no	—
251	C₂×C₄×C₁₀₁	—	4	4	no	—
252	C₂×C₄×C₁₀₁	—	4	4	no	—
253	C₂×C₄×C₁₀₁	—	4	4	no	—
254	C₂×C₄×C₁₀₁	—	4	4	no	—
255	C₂×C₄×C₁₀₁	—	4	4	no	—
256	C₂×C₄×C₁₀₁	—	4	4	no	—
257	C₂×C₄×C₁₀₁	—	4	4	no	—
258	C₂×C₄×C₁₀₁	—	4	4	no	—
259	C₂×C₄×C₁₀₁	#120	1	4	yes	—
260	C₂²×C₁₀₁	—	2	4	no	—
261	C₂²×C₁₀₁	—	2	8	no	—
262	C₂²×C₁₀₁	—	2	8	no	—
263	C₂²×C₁₀₁	—	2	16	no	—
264	C₂²×C₁₀₁	—	4	64	no	—
265	C₂²×C₁₀₁	—	4	4	no	—
266	C₂²×C₁₀₁	—	4	8	no	—
267	C₂²×C₁₀₁	—	4	8	no	—
268	C₂²×C₁₀₁	—	4	8	no	—
269	C₂²×C₁₀₁	—	4	8	no	—
270	C₂²×C₁₀₁	—	4	4	no	—
271	C₂²×C₁₀₁	—	4	8	no	—
272	C₂²×C₁₀₁	—	4	4	no	—
273	C₂²×C₁₀₁	—	4	4	no	—
274	C₂²×C₁₀₁	—	4	8	no	—
275	C₂²×C₁₀₁	—	4	8	no	—
276	C₂²×C₁₀₁	—	4	2	no	—
277	C₂²×C₁₀₁	—	4	4	no	—
278	C₂²×C₁₀₁	—	4	4	no	—
279	C₂²×C₁₀₁	—	4	4	no	—
280	C₂²×C₁₀₁	—	8	4	no	—
281	C₂²×C₁₀₁	—	8	4	no	—
282	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
283	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
284	C₂²×C₁₀₁	#525	1	2	yes	—
285	C₂²×C₁₀₁	C₂×#124	1	2	yes	—
286	C₂²×C₁₀₁	#534	1	1	yes	characteristic
287	C₂²×C₁₀₁	#535	1	2	yes	—
288	C₂²×C₁₀₁	#535	1	2	yes	—
289	C₂²×C₁₀₁	#538	1	4	yes	—
290	C₂²×C₁₀₁	D₄²	1	4	yes	—
291	C₂²×C₁₀₁	#546	1	4	yes	—
292	C₂²×C₁₀₁	#546	1	4	yes	—
293	C₂²×C₁₀₁	#546	1	4	yes	—
294	C₂²×C₁₀₁	#551	1	2	yes	—
295	C₂²×C₁₀₁	H(3,𝔽₄)	1	2	yes	—
296	C₄×C₁₀₁	—	2	4	no	—
297	C₄×C₁₀₁	—	4	4	no	—
298	C₄×C₁₀₁	—	4	4	no	—
299	C₄×C₁₀₁	—	4	4	no	—
300	C₄×C₁₀₁	—	8	4	no	—
301	#15259	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂×C₁₀₁	—	4	4	no	—
303	C₂×C₁₀₁	—	4	8	no	—
304	C₂×C₁₀₁	—	8	2	no	—
305	C₂×C₁₀₁	#2403	1	1	yes	characteristic
306	C₂×C₁₀₁	#2404	1	2	yes	—
307	C₂×C₁₀₁	#2435	1	2	yes	—
308	C₂×C₁₀₁	#2472	1	4	yes	—
309	C₂×C₁₀₁	#2670	1	4	yes	—
310	C₂×C₁₀₁	#2684	1	2	yes	—
311	C₂²×#124	C₂×C₁₀₁	1	1	yes	characteristic, complemented
312	C₂²×#120	C₂×C₁₀₁	1	1	yes	characteristic
313	C₂×#393	C₂×C₁₀₁	1	2	yes	complemented
314	C₂×#379	C₂×C₁₀₁	1	2	yes	complemented
315	#1440	C₂×C₁₀₁	1	2	yes	complemented
316	#1438	C₂×C₁₀₁	1	4	yes	complemented
317	#1438	C₂×C₁₀₁	1	1	yes	characteristic, complemented
318	#1437	C₂×C₁₀₁	1	2	yes	complemented
319	C₁₀₁	#15259	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁶	C₂²×C₁₀₁	1	1	yes	characteristic
321	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
322	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
323	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
324	C₂×#124	—	2	4	no	—
325	C₂×#124	—	2	8	no	—
326	C₂×#120	—	2	4	no	—
327	C₂×#120	—	2	8	no	—
328	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
330	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
333	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
334	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	complemented
335	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	complemented
336	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
337	#393	—	2	8	no	—
338	#379	—	2	8	no	—
339	C₂×#95	C₂²×C₁₀₁	1	2	yes	complemented
340	C₂×#95	C₂²×C₁₀₁	1	4	yes	complemented
341	C₂×#95	C₂²×C₁₀₁	1	4	yes	complemented
342	C₂⁵	—	2	2	no	—
343	C₂⁵	—	2	4	no	—
344	C₂⁵	—	2	4	no	—
345	C₂⁵	—	2	8	no	—
346	C₂⁵	—	4	4	no	—
347	C₂⁵	—	4	2	no	—
348	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
349	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
350	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
351	C₂²×Q₈	—	2	4	no	—
352	C₂²×Q₈	—	2	2	no	—
353	C₂²×Q₈	—	2	4	no	—
354	C₂²×Q₈	—	4	2	no	—
355	C₂²×D₄	—	2	4	no	—
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	—	2	4	no	—
358	C₂²×D₄	—	2	8	no	—
359	C₂²×D₄	—	2	4	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	4	2	no	—
362	C₂²×D₄	—	4	4	no	—
363	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
365	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
368	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
369	#124	—	2	32	no	—
370	#120	—	2	32	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	—	2	8	no	—
383	C₂×C₂²⋊C₄	—	2	8	no	—
384	C₂×C₂²⋊C₄	—	2	8	no	—
385	C₂×C₂²⋊C₄	—	4	4	no	—
386	C₂×C₂²⋊C₄	—	4	4	no	—
387	C₂×C₂²⋊C₄	—	4	4	no	—
388	C₂×C₂²⋊C₄	—	4	4	no	—
389	C₂×C₂²⋊C₄	—	4	2	no	—
390	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	—
391	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	complemented
392	C₂×C₄²	—	2	4	no	—
393	C₂×C₄²	—	2	2	no	—
394	#95	—	2	8	no	—
395	#95	—	2	4	no	—
396	#95	—	4	4	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	8	no	—
409	C₂⁴	—	2	16	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	4	16	no	—
416	C₂⁴	—	4	16	no	—
417	C₂⁴	—	4	16	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	8	no	—
420	C₂⁴	—	4	4	no	—
421	C₂⁴	—	4	8	no	—
422	C₂⁴	—	4	8	no	—
423	C₂⁴	—	4	16	no	—
424	C₂⁴	—	4	8	no	—
425	C₂⁴	—	4	4	no	—
426	C₂⁴	—	4	8	no	—
427	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
428	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
429	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
430	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
431	C₂⁴	#41×C₁₀₁	1	8	yes	—
432	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
433	C₂×Q₈	—	2	8	no	—
434	C₂×Q₈	—	4	16	no	—
435	C₂×Q₈	—	4	4	no	—
436	C₂×Q₈	—	4	4	no	—
437	C₂×D₄	—	2	16	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	16	no	—
442	C₂×D₄	—	4	16	no	—
443	C₂×D₄	—	4	16	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
468	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
469	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
470	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
471	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	16	no	—
474	C₂²⋊C₄	—	2	16	no	—
475	C₂²⋊C₄	—	2	16	no	—
476	C₂²⋊C₄	—	4	16	no	—
477	C₂²⋊C₄	—	4	16	no	—
478	C₂²⋊C₄	—	4	8	no	—
479	C₂²⋊C₄	—	4	8	no	—
480	C₄²	—	2	8	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	8	no	—
492	C₂³	—	2	8	no	—
493	C₂³	—	2	8	no	—
494	C₂³	—	2	8	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	8	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	4	16	no	—
503	C₂³	—	4	32	no	—
504	C₂³	—	4	32	no	—
505	C₂³	—	4	64	no	—
506	C₂³	—	4	64	no	—
507	C₂³	—	4	32	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	4	4	no	—
518	C₂³	—	4	4	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	4	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	4	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	4	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	2	no	—
534	C₂³	#120×C₁₀₁	1	4	yes	—
535	C₂³	#124×C₁₀₁	1	8	yes	complemented
536	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
537	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
538	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
539	C₂³	C₂×#41×C₁₀₁	1	4	yes	—
540	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
541	C₂³	H(5,𝔽₂)×C₁₀₁	1	4	yes	—
542	Q₈	—	4	16	no	—
543	D₄	—	4	16	no	—
544	D₄	—	4	32	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	#120×C₁₀₁	1	4	yes	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	16	no	—
575	C₂²	—	4	64	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	8	no	—
578	C₂²	—	4	8	no	—
579	C₂²	—	4	8	no	—
580	C₂²	—	4	8	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	8	no	—
586	C₂²	—	4	8	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	8	4	no	—
592	C₂²	—	8	4	no	—
593	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
594	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
595	C₂²	#525×C₁₀₁	1	2	yes	—
596	C₂²	C₂×#124×C₁₀₁	1	2	yes	—
597	C₂²	#534×C₁₀₁	1	1	yes	characteristic
598	C₂²	#535×C₁₀₁	1	2	yes	—
599	C₂²	#535×C₁₀₁	1	2	yes	—
600	C₂²	#538×C₁₀₁	1	4	yes	—
601	C₂²	D₄²×C₁₀₁	1	4	yes	—
602	C₂²	#546×C₁₀₁	1	4	yes	—
603	C₂²	#546×C₁₀₁	1	4	yes	—
604	C₂²	#546×C₁₀₁	1	4	yes	—
605	C₂²	#551×C₁₀₁	1	2	yes	—
606	C₂²	H(3,𝔽₄)×C₁₀₁	1	2	yes	—
607	C₄	—	2	4	no	—
608	C₄	—	4	4	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	4	no	—
611	C₄	—	8	4	no	—
612	C₂	—	4	4	no	—
613	C₂	—	4	8	no	—
614	C₂	—	8	2	no	—
615	C₂	C₁₀₁×#2403	1	1	yes	characteristic
616	C₂	C₁₀₁×#2404	1	2	yes	—
617	C₂	C₁₀₁×#2435	1	2	yes	—
618	C₂	C₁₀₁×#2472	1	4	yes	—
619	C₂	C₁₀₁×#2670	1	4	yes	—
620	C₂	C₁₀₁×#2684	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂²×#120×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×#124×C₁₀₁	C₂	semidirect
3. C₂×#393×C₁₀₁	C₂	semidirect
4. C₂×#379×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1440	C₂	semidirect
6. C₁₀₁×#1438	C₂	semidirect
7. C₁₀₁×#1438	C₂	semidirect
8. C₁₀₁×#1437	C₂	semidirect
10. C₂³×Q₈×C₁₀₁	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
24. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
25. C₂²×C₄²×C₁₀₁	C₂²	semidirect
28. C₂×#95×C₁₀₁	C₂²	semidirect
29. C₂×#95×C₁₀₁	C₂²	semidirect
30. C₂×#95×C₁₀₁	C₂²	semidirect
80. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
224. C₂³×C₁₀₁	#124	semidirect
301. #15259	C₁₀₁	direct (N × H)
311. C₂²×#124	C₂×C₁₀₁	semidirect
313. C₂×#393	C₂×C₁₀₁	semidirect
314. C₂×#379	C₂×C₁₀₁	semidirect
315. #1440	C₂×C₁₀₁	semidirect
316. #1438	C₂×C₁₀₁	semidirect
317. #1438	C₂×C₁₀₁	semidirect
318. #1437	C₂×C₁₀₁	semidirect
319. C₁₀₁	#15259	direct (N × H)
321. C₂³×Q₈	C₂²×C₁₀₁	semidirect
334. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
335. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
336. C₂²×C₄²	C₂²×C₁₀₁	semidirect
339. C₂×#95	C₂²×C₁₀₁	semidirect
340. C₂×#95	C₂²×C₁₀₁	semidirect
341. C₂×#95	C₂²×C₁₀₁	semidirect
391. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
535. C₂³	#124×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#124×C₁₀₁	2
C₂²×#120×C₁₀₁	2
C₂×#393×C₁₀₁	2
C₂×#379×C₁₀₁	2
C₁₀₁×#1440	2
C₁₀₁×#1438	2
C₁₀₁×#1437	2
#15259	101

Subgroups — C101×#15259 #38797410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#15259 #38797410