Subgroups — C₁₀₁×#16109 #38798260

Order 25856.

1198 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#391×C₁₀₁	C₂	1	2	yes	maximal
2	C₁₀₁×#1446	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#1445	C₂	1	2	yes	maximal
4	C₁₀₁×#1445	C₂	1	2	yes	maximal
5	C₁₀₁×#1445	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1443	C₂	1	2	yes	maximal
7	C₁₀₁×#1442	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1436	C₂	1	2	yes	maximal
9	C₁₀₁×#1436	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
15	#391×C₁₀₁	—	2	8	no	—
16	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
17	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
19	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
30	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂²×Q₈×C₁₀₁	—	2	4	no	—
33	C₂²×Q₈×C₁₀₁	—	2	4	no	—
34	C₂²×Q₈×C₁₀₁	—	4	1	no	—
35	C₂²×Q₈×C₁₀₁	—	4	1	no	—
36	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
37	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
53	C₂×C₄⋊C₄×C₁₀₁	Q₈	1	4	yes	complemented
54	C₂×C₄²×C₁₀₁	—	2	4	no	—
55	C₂×C₄²×C₁₀₁	—	4	2	no	—
56	C₂×C₄²×C₁₀₁	—	4	2	no	—
57	#95×C₁₀₁	—	2	4	no	—
58	#95×C₁₀₁	—	2	4	no	—
59	#95×C₁₀₁	—	2	4	no	—
60	#95×C₁₀₁	—	2	4	no	—
61	#95×C₁₀₁	—	2	4	no	—
62	#95×C₁₀₁	—	2	4	no	—
63	#95×C₁₀₁	—	2	4	no	—
64	#95×C₁₀₁	—	2	4	no	—
65	#95×C₁₀₁	—	2	2	no	—
66	#95×C₁₀₁	—	2	4	no	—
67	#95×C₁₀₁	—	4	2	no	—
68	#95×C₁₀₁	—	4	1	no	—
69	#95×C₁₀₁	—	4	2	no	—
70	#95×C₁₀₁	—	4	1	no	—
71	#95×C₁₀₁	—	4	1	no	—
72	#95×C₁₀₁	—	4	2	no	—
73	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
74	C₂×Q₈×C₁₀₁	—	2	16	no	—
75	C₂×Q₈×C₁₀₁	—	4	4	no	—
76	C₂×Q₈×C₁₀₁	—	4	8	no	—
77	C₂×Q₈×C₁₀₁	—	4	4	no	—
78	C₂×Q₈×C₁₀₁	—	4	4	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	2	no	—
81	C₂²×C₄×C₁₀₁	—	2	2	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	2	no	—
84	C₂²×C₄×C₁₀₁	—	2	2	no	—
85	C₂²×C₄×C₁₀₁	—	2	2	no	—
86	C₂²×C₄×C₁₀₁	—	2	2	no	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	1	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	1	no	—
99	C₂²×C₄×C₁₀₁	—	2	1	no	—
100	C₂²×C₄×C₁₀₁	—	2	1	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	1	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	2	no	—
113	C₂²×C₄×C₁₀₁	—	2	2	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
132	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
133	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
134	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
135	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
136	C₄⋊C₄×C₁₀₁	—	4	4	no	—
137	C₄⋊C₄×C₁₀₁	—	4	4	no	—
138	C₄⋊C₄×C₁₀₁	—	4	8	no	—
139	C₄²×C₁₀₁	—	4	8	no	—
140	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
141	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
142	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
143	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
144	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
145	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
146	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
147	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
150	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
151	Q₈×C₁₀₁	—	4	16	no	—
152	C₂×C₄×C₁₀₁	—	2	4	no	—
153	C₂×C₄×C₁₀₁	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	4	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	—	2	4	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	4	no	—
159	C₂×C₄×C₁₀₁	—	2	4	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	—	2	2	no	—
162	C₂×C₄×C₁₀₁	—	2	4	no	—
163	C₂×C₄×C₁₀₁	—	2	2	no	—
164	C₂×C₄×C₁₀₁	—	2	2	no	—
165	C₂×C₄×C₁₀₁	—	2	4	no	—
166	C₂×C₄×C₁₀₁	—	2	4	no	—
167	C₂×C₄×C₁₀₁	—	2	4	no	—
168	C₂×C₄×C₁₀₁	—	2	4	no	—
169	C₂×C₄×C₁₀₁	—	2	4	no	—
170	C₂×C₄×C₁₀₁	—	4	2	no	—
171	C₂×C₄×C₁₀₁	—	4	2	no	—
172	C₂×C₄×C₁₀₁	—	4	2	no	—
173	C₂×C₄×C₁₀₁	—	4	2	no	—
174	C₂×C₄×C₁₀₁	—	4	2	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	1	no	—
177	C₂×C₄×C₁₀₁	—	4	1	no	—
178	C₂×C₄×C₁₀₁	—	4	1	no	—
179	C₂×C₄×C₁₀₁	—	4	1	no	—
180	C₂×C₄×C₁₀₁	—	4	2	no	—
181	C₂×C₄×C₁₀₁	—	4	1	no	—
182	C₂×C₄×C₁₀₁	—	4	1	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	4	2	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	—	4	2	no	—
193	C₂×C₄×C₁₀₁	—	4	2	no	—
194	C₂×C₄×C₁₀₁	—	4	2	no	—
195	C₂×C₄×C₁₀₁	—	4	2	no	—
196	C₂×C₄×C₁₀₁	—	4	2	no	—
197	C₂×C₄×C₁₀₁	—	4	2	no	—
198	C₂×C₄×C₁₀₁	—	4	2	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	4	2	no	—
202	C₂×C₄×C₁₀₁	—	4	2	no	—
203	C₂×C₄×C₁₀₁	—	4	2	no	—
204	C₂×C₄×C₁₀₁	—	4	2	no	—
205	C₂×C₄×C₁₀₁	—	4	2	no	—
206	C₂×C₄×C₁₀₁	—	4	2	no	—
207	C₂×C₄×C₁₀₁	—	4	2	no	—
208	C₂×C₄×C₁₀₁	#123	1	8	yes	—
209	C₂²×C₁₀₁	C₂×#123	1	2	yes	—
210	C₂²×C₁₀₁	#529	1	2	yes	—
211	C₂²×C₁₀₁	#533	1	2	yes	—
212	C₂²×C₁₀₁	#534	1	1	yes	characteristic
213	C₂²×C₁₀₁	#539	1	2	yes	—
214	C₂²×C₁₀₁	#539	1	1	yes	characteristic
215	C₂²×C₁₀₁	#541	1	2	yes	—
216	C₂²×C₁₀₁	#542	1	2	yes	—
217	C₂²×C₁₀₁	#543	1	1	yes	characteristic
218	C₂²×C₁₀₁	#548	1	2	yes	—
219	C₂²×C₁₀₁	D₄×Q₈	1	1	yes	characteristic
220	C₂²×C₁₀₁	#550	1	1	yes	characteristic
221	C₂²×C₁₀₁	#551	1	2	yes	—
222	C₂²×C₁₀₁	#551	1	1	yes	characteristic
223	C₂²×C₁₀₁	#551	1	1	yes	characteristic
224	C₂²×C₁₀₁	#551	1	1	yes	characteristic
225	C₂²×C₁₀₁	#554	1	1	yes	characteristic
226	C₂²×C₁₀₁	#556	1	2	yes	—
227	C₂²×C₁₀₁	#556	1	2	yes	—
228	C₂²×C₁₀₁	#557	1	2	yes	—
229	C₂²×C₁₀₁	#559	1	2	yes	—
230	C₂²×C₁₀₁	#562	1	1	yes	characteristic
231	C₂²×C₁₀₁	#563	1	1	yes	characteristic
232	C₄×C₁₀₁	—	2	8	no	—
233	C₄×C₁₀₁	—	4	2	no	—
234	C₄×C₁₀₁	—	4	4	no	—
235	C₄×C₁₀₁	—	4	4	no	—
236	C₄×C₁₀₁	—	4	2	no	—
237	C₄×C₁₀₁	—	4	2	no	—
238	C₄×C₁₀₁	—	8	2	no	—
239	C₄×C₁₀₁	—	8	2	no	—
240	C₄×C₁₀₁	—	8	2	no	—
241	#16109	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₁₀₁	#2446	1	2	yes	—
243	C₂×C₁₀₁	#2448	1	2	yes	—
244	C₂×C₁₀₁	#2483	1	1	yes	characteristic
245	C₂×C₁₀₁	#2523	1	1	yes	characteristic
246	C₂×C₁₀₁	#2588	1	2	yes	—
247	C₂×C₁₀₁	#2607	1	1	yes	characteristic
248	C₂×C₁₀₁	#2728	1	1	yes	characteristic
249	C₂×C₁₀₁	#2732	1	1	yes	characteristic
250	C₂×C₁₀₁	#2789	1	1	yes	characteristic
251	C₂×C₁₀₁	#2798	1	2	yes	—
252	C₂×C₁₀₁	#2799	1	1	yes	characteristic
253	C₂×#391	C₂×C₁₀₁	1	2	yes	—
254	#1446	C₂×C₁₀₁	1	1	yes	characteristic
255	#1445	C₂×C₁₀₁	1	2	yes	—
256	#1445	C₂×C₁₀₁	1	2	yes	—
257	#1445	C₂×C₁₀₁	1	1	yes	characteristic
258	#1443	C₂×C₁₀₁	1	2	yes	—
259	#1442	C₂×C₁₀₁	1	1	yes	characteristic
260	#1436	C₂×C₁₀₁	1	2	yes	—
261	#1436	C₂×C₁₀₁	1	2	yes	—
262	C₁₀₁	#16109	1	1	yes	characteristic, direct product factor, Sylow
263	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
268	#391	—	2	8	no	—
269	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
270	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
271	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
272	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
273	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
274	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
275	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
276	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
277	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
278	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
279	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
280	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
281	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
282	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
283	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
284	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
285	C₂²×Q₈	—	2	4	no	—
286	C₂²×Q₈	—	2	4	no	—
287	C₂²×Q₈	—	4	1	no	—
288	C₂²×Q₈	—	4	1	no	—
289	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
290	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
293	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	4	1	no	—
304	C₂×C₄⋊C₄	—	4	1	no	—
305	C₂×C₄⋊C₄	—	4	1	no	—
306	C₂×C₄⋊C₄	Q₈×C₁₀₁	1	4	yes	complemented
307	C₂×C₄²	—	2	4	no	—
308	C₂×C₄²	—	4	2	no	—
309	C₂×C₄²	—	4	2	no	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	4	no	—
313	#95	—	2	4	no	—
314	#95	—	2	4	no	—
315	#95	—	2	4	no	—
316	#95	—	2	4	no	—
317	#95	—	2	4	no	—
318	#95	—	2	2	no	—
319	#95	—	2	4	no	—
320	#95	—	4	2	no	—
321	#95	—	4	1	no	—
322	#95	—	4	2	no	—
323	#95	—	4	1	no	—
324	#95	—	4	1	no	—
325	#95	—	4	2	no	—
326	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
327	C₂×Q₈	—	2	16	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	—	4	8	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
383	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
384	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
385	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
386	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
387	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
388	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	8	no	—
392	C₄²	—	4	8	no	—
393	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
394	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
395	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
396	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
397	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
398	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
399	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
400	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
401	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
402	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
403	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
404	Q₈	—	4	16	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	#123×C₁₀₁	1	8	yes	—
462	C₂²	C₂×#123×C₁₀₁	1	2	yes	—
463	C₂²	#529×C₁₀₁	1	2	yes	—
464	C₂²	#533×C₁₀₁	1	2	yes	—
465	C₂²	#534×C₁₀₁	1	1	yes	characteristic
466	C₂²	#539×C₁₀₁	1	2	yes	—
467	C₂²	#539×C₁₀₁	1	1	yes	characteristic
468	C₂²	#541×C₁₀₁	1	2	yes	—
469	C₂²	#542×C₁₀₁	1	2	yes	—
470	C₂²	#543×C₁₀₁	1	1	yes	characteristic
471	C₂²	#548×C₁₀₁	1	2	yes	—
472	C₂²	D₄×Q₈×C₁₀₁	1	1	yes	characteristic
473	C₂²	#550×C₁₀₁	1	1	yes	characteristic
474	C₂²	#551×C₁₀₁	1	1	yes	characteristic
475	C₂²	#551×C₁₀₁	1	1	yes	characteristic
476	C₂²	#551×C₁₀₁	1	1	yes	characteristic
477	C₂²	#551×C₁₀₁	1	2	yes	—
478	C₂²	#554×C₁₀₁	1	1	yes	characteristic
479	C₂²	#556×C₁₀₁	1	2	yes	—
480	C₂²	#556×C₁₀₁	1	2	yes	—
481	C₂²	#557×C₁₀₁	1	2	yes	—
482	C₂²	#559×C₁₀₁	1	2	yes	—
483	C₂²	#562×C₁₀₁	1	1	yes	characteristic
484	C₂²	#563×C₁₀₁	1	1	yes	characteristic
485	C₄	—	2	8	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	2	no	—
494	C₂	C₁₀₁×#2446	1	2	yes	—
495	C₂	C₁₀₁×#2448	1	2	yes	—
496	C₂	C₁₀₁×#2483	1	1	yes	characteristic
497	C₂	C₁₀₁×#2523	1	1	yes	characteristic
498	C₂	C₁₀₁×#2588	1	2	yes	—
499	C₂	C₁₀₁×#2607	1	1	yes	characteristic
500	C₂	C₁₀₁×#2728	1	1	yes	characteristic
501	C₂	C₁₀₁×#2732	1	1	yes	characteristic
502	C₂	C₁₀₁×#2789	1	1	yes	characteristic
503	C₂	C₁₀₁×#2798	1	2	yes	—
504	C₂	C₁₀₁×#2799	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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
53. C₂×C₄⋊C₄×C₁₀₁	Q₈	semidirect
241. #16109	C₁₀₁	direct (N × H)
262. C₁₀₁	#16109	direct (N × H)
306. C₂×C₄⋊C₄	Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#391×C₁₀₁	2
C₁₀₁×#1446	2
C₁₀₁×#1445	2
C₁₀₁×#1443	2
C₁₀₁×#1442	2
C₁₀₁×#1436	2
#16109	101

Subgroups — C101×#16109 #38798260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#16109 #38798260