Subgroups — C₁₀₁×#14445 #38796596

Order 25856.

1758 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#390×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#388×C₁₀₁	C₂	1	4	yes	maximal, complemented
3	C₁₀₁×#1439	C₂	1	4	yes	maximal, complemented
4	C₁₀₁×#1438	C₂	1	2	yes	maximal
5	C₁₀₁×#1436	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
11	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
17	#390×C₁₀₁	C₄	1	8	yes	complemented
18	#388×C₁₀₁	—	2	16	no	—
19	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
23	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
24	C₂²×D₄×C₁₀₁	—	2	4	no	—
25	C₂²×D₄×C₁₀₁	—	4	2	no	—
26	C₂²×D₄×C₁₀₁	—	4	1	no	—
27	C₂²×D₄×C₁₀₁	—	4	1	no	—
28	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
29	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
30	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
32	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
35	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
36	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
40	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
41	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₁₀₁	D₄	1	8	yes	complemented
43	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
49	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
51	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
52	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	16	yes	—
53	C₂×C₄²×C₁₀₁	—	2	8	no	—
54	C₂×C₄²×C₁₀₁	—	4	2	no	—
55	C₂×C₄²×C₁₀₁	—	4	2	no	—
56	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
57	#95×C₁₀₁	—	2	8	no	—
58	#95×C₁₀₁	—	2	8	no	—
59	#95×C₁₀₁	—	2	8	no	—
60	#95×C₁₀₁	—	4	2	no	—
61	C₂⁴×C₁₀₁	—	2	4	no	—
62	C₂⁴×C₁₀₁	—	2	4	no	—
63	C₂⁴×C₁₀₁	—	2	4	no	—
64	C₂⁴×C₁₀₁	—	2	4	no	—
65	C₂⁴×C₁₀₁	—	2	4	no	—
66	C₂⁴×C₁₀₁	—	2	2	no	—
67	C₂⁴×C₁₀₁	—	2	2	no	—
68	C₂⁴×C₁₀₁	—	2	4	no	—
69	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
70	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
71	C₂×D₄×C₁₀₁	—	2	8	no	—
72	C₂×D₄×C₁₀₁	—	4	4	no	—
73	C₂×D₄×C₁₀₁	—	4	4	no	—
74	C₂×D₄×C₁₀₁	—	4	8	no	—
75	C₂×D₄×C₁₀₁	—	4	8	no	—
76	C₂²×C₄×C₁₀₁	—	2	2	no	—
77	C₂²×C₄×C₁₀₁	—	2	2	no	—
78	C₂²×C₄×C₁₀₁	—	2	2	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	1	no	—
81	C₂²×C₄×C₁₀₁	—	2	1	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	4	no	—
84	C₂²×C₄×C₁₀₁	—	2	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	4	no	—
86	C₂²×C₄×C₁₀₁	—	2	4	no	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	2	4	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	4	no	—
91	C₂²×C₄×C₁₀₁	—	2	4	no	—
92	C₂²×C₄×C₁₀₁	—	2	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	4	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	no	—
96	C₂²×C₄×C₁₀₁	—	2	4	no	—
97	C₂²×C₄×C₁₀₁	—	2	4	no	—
98	C₂²×C₄×C₁₀₁	—	2	4	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
106	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
107	C₄⋊C₄×C₁₀₁	—	4	4	no	—
108	C₄⋊C₄×C₁₀₁	—	4	8	no	—
109	C₄⋊C₄×C₁₀₁	—	4	8	no	—
110	C₂²⋊C₄×C₁₀₁	—	2	32	no	—
111	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
112	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
113	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
114	C₄²×C₁₀₁	—	4	4	no	—
115	C₄²×C₁₀₁	—	4	8	no	—
116	C₂³×C₁₀₁	—	2	4	no	—
117	C₂³×C₁₀₁	—	2	8	no	—
118	C₂³×C₁₀₁	—	2	4	no	—
119	C₂³×C₁₀₁	—	2	4	no	—
120	C₂³×C₁₀₁	—	2	8	no	—
121	C₂³×C₁₀₁	—	4	4	no	—
122	C₂³×C₁₀₁	—	4	4	no	—
123	C₂³×C₁₀₁	—	4	4	no	—
124	C₂³×C₁₀₁	—	4	4	no	—
125	C₂³×C₁₀₁	—	4	4	no	—
126	C₂³×C₁₀₁	—	4	4	no	—
127	C₂³×C₁₀₁	—	4	2	no	—
128	C₂³×C₁₀₁	—	4	4	no	—
129	C₂³×C₁₀₁	—	4	4	no	—
130	C₂³×C₁₀₁	—	4	4	no	—
131	C₂³×C₁₀₁	—	4	4	no	—
132	C₂³×C₁₀₁	—	4	4	no	—
133	C₂³×C₁₀₁	—	4	2	no	—
134	C₂³×C₁₀₁	—	4	2	no	—
135	C₂³×C₁₀₁	—	4	4	no	—
136	C₂³×C₁₀₁	—	4	2	no	—
137	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
138	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
139	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
140	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
141	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
142	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
144	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
145	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
146	D₄×C₁₀₁	—	4	16	no	—
147	C₂×C₄×C₁₀₁	—	2	4	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	4	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	8	no	—
158	C₂×C₄×C₁₀₁	—	2	4	no	—
159	C₂×C₄×C₁₀₁	—	2	8	no	—
160	C₂×C₄×C₁₀₁	—	2	8	no	—
161	C₂×C₄×C₁₀₁	—	2	8	no	—
162	C₂×C₄×C₁₀₁	—	4	4	no	—
163	C₂×C₄×C₁₀₁	—	4	4	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	4	4	no	—
166	C₂×C₄×C₁₀₁	—	4	4	no	—
167	C₂×C₄×C₁₀₁	—	4	2	no	—
168	C₂×C₄×C₁₀₁	—	4	4	no	—
169	C₂×C₄×C₁₀₁	—	4	4	no	—
170	C₂×C₄×C₁₀₁	—	4	4	no	—
171	C₂×C₄×C₁₀₁	—	4	4	no	—
172	C₂×C₄×C₁₀₁	—	4	4	no	—
173	C₂×C₄×C₁₀₁	—	4	4	no	—
174	C₂×C₄×C₁₀₁	—	4	4	no	—
175	C₂×C₄×C₁₀₁	—	4	4	no	—
176	C₂×C₄×C₁₀₁	#117	1	4	yes	—
177	C₂×C₄×C₁₀₁	C₄×D₄	1	8	yes	—
178	C₂²×C₁₀₁	—	4	4	no	—
179	C₂²×C₁₀₁	—	4	8	no	—
180	C₂²×C₁₀₁	—	4	8	no	—
181	C₂²×C₁₀₁	—	4	4	no	—
182	C₂²×C₁₀₁	—	4	4	no	—
183	C₂²×C₁₀₁	—	8	4	no	—
184	C₂²×C₁₀₁	—	8	4	no	—
185	C₂²×C₁₀₁	—	8	4	no	—
186	C₂²×C₁₀₁	—	8	4	no	—
187	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
188	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
189	C₂²×C₁₀₁	#518	1	1	yes	characteristic
190	C₂²×C₁₀₁	#518	1	1	yes	characteristic
191	C₂²×C₁₀₁	#520	1	2	yes	—
192	C₂²×C₁₀₁	#534	1	2	yes	—
193	C₂²×C₁₀₁	#537	1	2	yes	—
194	C₂²×C₁₀₁	#538	1	2	yes	—
195	C₂²×C₁₀₁	#538	1	2	yes	—
196	C₂²×C₁₀₁	#538	1	2	yes	—
197	C₂²×C₁₀₁	#539	1	2	yes	—
198	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
199	C₂²×C₁₀₁	#547	1	2	yes	—
200	C₂²×C₁₀₁	#550	1	2	yes	—
201	C₂²×C₁₀₁	#550	1	2	yes	—
202	C₂²×C₁₀₁	#555	1	2	yes	—
203	C₂²×C₁₀₁	#556	1	2	yes	—
204	C₂²×C₁₀₁	#559	1	1	yes	characteristic
205	C₂²×C₁₀₁	H(3,𝔽₄)	1	1	yes	characteristic
206	C₂²×C₁₀₁	#562	1	2	yes	—
207	C₂²×C₁₀₁	#563	1	1	yes	characteristic
208	C₄×C₁₀₁	—	2	4	no	—
209	C₄×C₁₀₁	—	2	8	no	—
210	C₄×C₁₀₁	—	4	4	no	—
211	C₄×C₁₀₁	—	4	8	no	—
212	C₄×C₁₀₁	—	8	4	no	—
213	#14445	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₁₀₁	—	8	4	no	—
215	C₂×C₁₀₁	#2312	1	1	yes	characteristic
216	C₂×C₁₀₁	#2325	1	2	yes	—
217	C₂×C₁₀₁	#2354	1	2	yes	—
218	C₂×C₁₀₁	#2366	1	1	yes	characteristic
219	C₂×C₁₀₁	#2379	1	1	yes	characteristic
220	C₂×C₁₀₁	#2682	1	2	yes	—
221	C₂×C₁₀₁	#2727	1	2	yes	—
222	C₂×C₁₀₁	#2733	1	2	yes	—
223	C₂×C₁₀₁	#2808	1	2	yes	—
224	C₂×#390	C₂×C₁₀₁	1	1	yes	characteristic
225	C₂×#388	C₂×C₁₀₁	1	4	yes	complemented
226	#1439	C₂×C₁₀₁	1	4	yes	complemented
227	#1438	C₂×C₁₀₁	1	2	yes	—
228	#1436	C₂×C₁₀₁	1	2	yes	complemented
229	C₄⋊#95	C₂×C₁₀₁	1	2	yes	complemented
230	C₁₀₁	#14445	1	1	yes	characteristic, direct product factor, Sylow
231	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
239	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
240	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
241	#390	C₄×C₁₀₁	1	8	yes	complemented
242	#388	—	2	16	no	—
243	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
244	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
245	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
246	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
247	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
248	C₂²×D₄	—	2	4	no	—
249	C₂²×D₄	—	4	2	no	—
250	C₂²×D₄	—	4	1	no	—
251	C₂²×D₄	—	4	1	no	—
252	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
253	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
256	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	4	1	no	—
260	C₂×C₄⋊C₄	—	4	1	no	—
261	C₂×C₄⋊C₄	—	4	2	no	—
262	C₂×C₄⋊C₄	—	4	2	no	—
263	C₂×C₄⋊C₄	—	4	2	no	—
264	C₂×C₄⋊C₄	—	4	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
266	C₂×C₄⋊C₄	D₄×C₁₀₁	1	8	yes	complemented
267	C₂×C₂²⋊C₄	—	2	8	no	—
268	C₂×C₂²⋊C₄	—	2	8	no	—
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	4	2	no	—
272	C₂×C₂²⋊C₄	—	4	4	no	—
273	C₂×C₂²⋊C₄	—	4	4	no	—
274	C₂×C₂²⋊C₄	—	4	2	no	—
275	C₂×C₂²⋊C₄	—	4	4	no	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	16	yes	—
277	C₂×C₄²	—	2	8	no	—
278	C₂×C₄²	—	4	2	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
281	#95	—	2	8	no	—
282	#95	—	2	8	no	—
283	#95	—	2	8	no	—
284	#95	—	4	2	no	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	—	2	2	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
294	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
327	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
328	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
329	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
330	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	8	no	—
333	C₄⋊C₄	—	4	8	no	—
334	C₂²⋊C₄	—	2	32	no	—
335	C₂²⋊C₄	—	4	8	no	—
336	C₂²⋊C₄	—	4	16	no	—
337	C₂²⋊C₄	—	4	8	no	—
338	C₄²	—	4	4	no	—
339	C₄²	—	4	8	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	4	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
362	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
363	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
364	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
365	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
366	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
367	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
368	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
369	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
370	D₄	—	4	16	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	#117×C₁₀₁	1	4	yes	—
401	C₂×C₄	C₄×D₄×C₁₀₁	1	8	yes	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	4	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	4	no	—
411	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
412	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
413	C₂²	#518×C₁₀₁	1	1	yes	characteristic
414	C₂²	#518×C₁₀₁	1	1	yes	characteristic
415	C₂²	#520×C₁₀₁	1	2	yes	—
416	C₂²	#534×C₁₀₁	1	2	yes	—
417	C₂²	#537×C₁₀₁	1	2	yes	—
418	C₂²	#538×C₁₀₁	1	2	yes	—
419	C₂²	#538×C₁₀₁	1	2	yes	—
420	C₂²	#538×C₁₀₁	1	2	yes	—
421	C₂²	#539×C₁₀₁	1	2	yes	—
422	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
423	C₂²	#547×C₁₀₁	1	2	yes	—
424	C₂²	#550×C₁₀₁	1	2	yes	—
425	C₂²	#550×C₁₀₁	1	2	yes	—
426	C₂²	#555×C₁₀₁	1	2	yes	—
427	C₂²	#556×C₁₀₁	1	2	yes	—
428	C₂²	#559×C₁₀₁	1	1	yes	characteristic
429	C₂²	H(3,𝔽₄)×C₁₀₁	1	1	yes	characteristic
430	C₂²	#562×C₁₀₁	1	2	yes	—
431	C₂²	#563×C₁₀₁	1	1	yes	characteristic
432	C₄	—	2	4	no	—
433	C₄	—	2	8	no	—
434	C₄	—	4	8	no	—
435	C₄	—	4	4	no	—
436	C₄	—	8	4	no	—
437	C₂	—	8	4	no	—
438	C₂	C₁₀₁×#2312	1	1	yes	characteristic
439	C₂	C₁₀₁×#2325	1	2	yes	—
440	C₂	C₁₀₁×#2354	1	2	yes	—
441	C₂	C₁₀₁×#2366	1	1	yes	characteristic
442	C₂	C₁₀₁×#2379	1	1	yes	characteristic
443	C₂	C₁₀₁×#2682	1	2	yes	—
444	C₂	C₁₀₁×#2727	1	2	yes	—
445	C₂	C₁₀₁×#2733	1	2	yes	—
446	C₂	C₁₀₁×#2808	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#388×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1439	C₂	semidirect
5. C₁₀₁×#1436	C₂	semidirect
6. C₁₀₁×C₄⋊#95	C₂	semidirect
17. #390×C₁₀₁	C₄	semidirect
42. C₂×C₄⋊C₄×C₁₀₁	D₄	semidirect
213. #14445	C₁₀₁	direct (N × H)
225. C₂×#388	C₂×C₁₀₁	semidirect
226. #1439	C₂×C₁₀₁	semidirect
228. #1436	C₂×C₁₀₁	semidirect
229. C₄⋊#95	C₂×C₁₀₁	semidirect
230. C₁₀₁	#14445	direct (N × H)
241. #390	C₄×C₁₀₁	semidirect
266. C₂×C₄⋊C₄	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#390×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
C₁₀₁×#1436	2
C₁₀₁×C₄⋊#95	2
#14445	101

Subgroups — C101×#14445 #38796596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14445 #38796596