Subgroups — C₁₀₁×#14338 #38796489

Order 25856.

3390 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#380×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#379×C₁₀₁	C₂	1	2	yes	maximal
4	C₁₀₁×#1439	C₂	1	8	yes	maximal, complemented
5	C₁₀₁×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
6	C₂⁶×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	4	yes	complemented
10	C₂²×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
11	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	8	yes	complemented
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	8	yes	—
15	#380×C₁₀₁	—	2	8	no	—
16	#379×C₁₀₁	—	2	8	no	—
17	C₂×#95×C₁₀₁	C₂²	1	4	yes	complemented
18	C₂×#95×C₁₀₁	C₂²	1	8	yes	complemented
19	C₂⁵×C₁₀₁	—	2	4	no	—
20	C₂⁵×C₁₀₁	—	2	4	no	—
21	C₂⁵×C₁₀₁	—	4	4	no	—
22	C₂⁵×C₁₀₁	—	4	4	no	—
23	C₂⁵×C₁₀₁	C₂×C₄	1	4	yes	—
24	C₂⁵×C₁₀₁	D₄	1	4	yes	—
25	C₂⁵×C₁₀₁	Q₈	1	4	yes	—
26	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
27	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
28	C₂³×C₄×C₁₀₁	—	2	4	no	—
29	C₂³×C₄×C₁₀₁	—	4	4	no	—
30	C₂³×C₄×C₁₀₁	—	4	4	no	—
31	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₁₀₁	D₄	1	8	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	8	yes	—
35	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	4	8	no	—
39	C₂×C₂²⋊C₄×C₁₀₁	—	2	32	no	—
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
42	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
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	—	4	8	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	—	4	8	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	16	yes	—
49	#95×C₁₀₁	—	2	8	no	—
50	#95×C₁₀₁	—	4	8	no	—
51	C₂⁴×C₁₀₁	—	2	4	no	—
52	C₂⁴×C₁₀₁	—	2	4	no	—
53	C₂⁴×C₁₀₁	—	2	8	no	—
54	C₂⁴×C₁₀₁	—	2	8	no	—
55	C₂⁴×C₁₀₁	—	2	16	no	—
56	C₂⁴×C₁₀₁	—	2	16	no	—
57	C₂⁴×C₁₀₁	—	2	4	no	—
58	C₂⁴×C₁₀₁	—	2	4	no	—
59	C₂⁴×C₁₀₁	—	2	8	no	—
60	C₂⁴×C₁₀₁	—	2	8	no	—
61	C₂⁴×C₁₀₁	—	4	8	no	—
62	C₂⁴×C₁₀₁	—	4	8	no	—
63	C₂⁴×C₁₀₁	—	4	16	no	—
64	C₂⁴×C₁₀₁	—	4	16	no	—
65	C₂⁴×C₁₀₁	—	4	16	no	—
66	C₂⁴×C₁₀₁	—	4	16	no	—
67	C₂⁴×C₁₀₁	—	4	32	no	—
68	C₂⁴×C₁₀₁	C₄⋊C₄	1	16	yes	complemented
69	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
70	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
72	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
73	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
74	C₂⁴×C₁₀₁	C₂×Q₈	1	4	yes	—
75	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
76	C₂⁴×C₁₀₁	#41	1	4	yes	—
77	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₁	—	2	8	no	—
79	C₂²×C₄×C₁₀₁	—	2	8	no	—
80	C₂²×C₄×C₁₀₁	—	2	4	no	—
81	C₂²×C₄×C₁₀₁	—	2	8	no	—
82	C₂²×C₄×C₁₀₁	—	2	8	no	—
83	C₂²×C₄×C₁₀₁	—	2	8	no	—
84	C₂²×C₄×C₁₀₁	—	2	8	no	—
85	C₂²×C₄×C₁₀₁	—	2	16	no	—
86	C₂²×C₄×C₁₀₁	—	2	16	no	—
87	C₂²×C₄×C₁₀₁	—	4	8	no	—
88	C₂²×C₄×C₁₀₁	—	4	8	no	—
89	C₂²×C₄×C₁₀₁	—	4	16	no	—
90	C₂²×C₄×C₁₀₁	—	4	16	no	—
91	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
92	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
96	C₄⋊C₄×C₁₀₁	—	4	16	no	—
97	C₂²⋊C₄×C₁₀₁	—	2	32	no	—
98	C₂²⋊C₄×C₁₀₁	—	4	32	no	—
99	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
100	C₂³×C₁₀₁	—	2	4	no	—
101	C₂³×C₁₀₁	—	2	4	no	—
102	C₂³×C₁₀₁	—	2	8	no	—
103	C₂³×C₁₀₁	—	2	8	no	—
104	C₂³×C₁₀₁	—	2	8	no	—
105	C₂³×C₁₀₁	—	2	16	no	—
106	C₂³×C₁₀₁	—	2	8	no	—
107	C₂³×C₁₀₁	—	2	4	no	—
108	C₂³×C₁₀₁	—	2	4	no	—
109	C₂³×C₁₀₁	—	2	8	no	—
110	C₂³×C₁₀₁	—	2	8	no	—
111	C₂³×C₁₀₁	—	2	8	no	—
112	C₂³×C₁₀₁	—	2	8	no	—
113	C₂³×C₁₀₁	—	2	16	no	—
114	C₂³×C₁₀₁	—	2	16	no	—
115	C₂³×C₁₀₁	—	2	32	no	—
116	C₂³×C₁₀₁	—	4	32	no	—
117	C₂³×C₁₀₁	—	4	16	no	—
118	C₂³×C₁₀₁	—	4	16	no	—
119	C₂³×C₁₀₁	—	4	32	no	—
120	C₂³×C₁₀₁	—	4	64	no	—
121	C₂³×C₁₀₁	—	4	64	no	—
122	C₂³×C₁₀₁	—	4	8	no	—
123	C₂³×C₁₀₁	—	4	8	no	—
124	C₂³×C₁₀₁	—	4	16	no	—
125	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	8	yes	—
127	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
128	C₂³×C₁₀₁	#117	1	4	yes	—
129	C₂³×C₁₀₁	#121	1	8	yes	—
130	C₂³×C₁₀₁	C₂²⋊Q₈	1	8	yes	—
131	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
132	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
133	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
134	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
135	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
136	C₂³×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
137	C₂³×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
138	C₂×C₄×C₁₀₁	—	2	8	no	—
139	C₂×C₄×C₁₀₁	—	2	8	no	—
140	C₂×C₄×C₁₀₁	—	2	8	no	—
141	C₂×C₄×C₁₀₁	—	2	4	no	—
142	C₂×C₄×C₁₀₁	—	2	8	no	—
143	C₂×C₄×C₁₀₁	—	4	16	no	—
144	C₂×C₄×C₁₀₁	—	4	16	no	—
145	C₂×C₄×C₁₀₁	—	4	8	no	—
146	C₂×C₄×C₁₀₁	—	4	8	no	—
147	C₂×C₄×C₁₀₁	—	4	16	no	—
148	C₂×C₄×C₁₀₁	—	4	8	no	—
149	C₂×C₄×C₁₀₁	—	4	8	no	—
150	C₂×C₄×C₁₀₁	—	4	16	no	—
151	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
152	C₂²×C₁₀₁	—	2	4	no	—
153	C₂²×C₁₀₁	—	2	4	no	—
154	C₂²×C₁₀₁	—	2	8	no	—
155	C₂²×C₁₀₁	—	2	8	no	—
156	C₂²×C₁₀₁	—	2	16	no	—
157	C₂²×C₁₀₁	—	2	16	no	—
158	C₂²×C₁₀₁	—	2	16	no	—
159	C₂²×C₁₀₁	—	2	8	no	—
160	C₂²×C₁₀₁	—	4	64	no	—
161	C₂²×C₁₀₁	—	4	4	no	—
162	C₂²×C₁₀₁	—	4	4	no	—
163	C₂²×C₁₀₁	—	4	8	no	—
164	C₂²×C₁₀₁	—	4	16	no	—
165	C₂²×C₁₀₁	—	4	16	no	—
166	C₂²×C₁₀₁	#380	1	8	yes	—
167	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
170	C₂²×C₁₀₁	#518	1	2	yes	—
171	C₂²×C₁₀₁	#518	1	2	yes	—
172	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
173	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
174	C₂²×C₁₀₁	#534	1	4	yes	—
175	C₂²×C₁₀₁	#534	1	4	yes	—
176	C₂²×C₁₀₁	#535	1	4	yes	—
177	C₂²×C₁₀₁	#538	1	8	yes	—
178	C₂²×C₁₀₁	#543	1	4	yes	—
179	C₄×C₁₀₁	—	2	8	no	—
180	C₄×C₁₀₁	—	4	4	no	—
181	C₄×C₁₀₁	—	8	8	no	—
182	#14338	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₁₀₁	—	2	8	no	—
184	C₂×C₁₀₁	—	4	8	no	—
185	C₂×C₁₀₁	C₂×#380	1	1	yes	characteristic
186	C₂×C₁₀₁	#2308	1	1	yes	characteristic
187	C₂×C₁₀₁	#2309	1	1	yes	characteristic
188	C₂×C₁₀₁	#2312	1	2	yes	—
189	C₂×C₁₀₁	#2315	1	2	yes	—
190	C₂×C₁₀₁	#2617	1	4	yes	—
191	C₂×C₁₀₁	#2626	1	4	yes	—
192	C₂³×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
193	C₂×#380	C₂×C₁₀₁	1	2	yes	complemented
194	C₂×#379	C₂×C₁₀₁	1	2	yes	—
195	#1439	C₂×C₁₀₁	1	8	yes	complemented
196	C₂²⋊#95	C₂×C₁₀₁	1	2	yes	complemented
197	C₁₀₁	#14338	1	1	yes	characteristic, direct product factor, Sylow
198	C₂⁶	C₂²×C₁₀₁	1	1	yes	characteristic
199	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	complemented
202	C₂²×C₂²⋊C₄	—	2	8	no	—
203	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	8	yes	complemented
204	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	8	yes	—
207	#380	—	2	8	no	—
208	#379	—	2	8	no	—
209	C₂×#95	C₂²×C₁₀₁	1	4	yes	complemented
210	C₂×#95	C₂²×C₁₀₁	1	8	yes	complemented
211	C₂⁵	—	2	4	no	—
212	C₂⁵	—	2	4	no	—
213	C₂⁵	—	4	4	no	—
214	C₂⁵	—	4	4	no	—
215	C₂⁵	C₂×C₄×C₁₀₁	1	4	yes	—
216	C₂⁵	D₄×C₁₀₁	1	4	yes	—
217	C₂⁵	Q₈×C₁₀₁	1	4	yes	—
218	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
219	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	4	4	no	—
222	C₂³×C₄	—	4	4	no	—
223	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
224	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
225	C₂³×C₄	D₄×C₁₀₁	1	8	yes	—
226	C₂³×C₄	C₂³×C₁₀₁	1	8	yes	—
227	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
228	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
229	C₂×C₄⋊C₄	—	2	8	no	—
230	C₂×C₄⋊C₄	—	4	8	no	—
231	C₂×C₂²⋊C₄	—	2	32	no	—
232	C₂×C₂²⋊C₄	—	2	8	no	—
233	C₂×C₂²⋊C₄	—	2	8	no	—
234	C₂×C₂²⋊C₄	—	2	16	no	—
235	C₂×C₂²⋊C₄	—	2	8	no	—
236	C₂×C₂²⋊C₄	—	2	8	no	—
237	C₂×C₂²⋊C₄	—	2	8	no	—
238	C₂×C₂²⋊C₄	—	4	8	no	—
239	C₂×C₂²⋊C₄	—	4	8	no	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	16	yes	—
241	#95	—	2	8	no	—
242	#95	—	4	8	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	8	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	2	16	no	—
248	C₂⁴	—	2	16	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	8	no	—
252	C₂⁴	—	2	8	no	—
253	C₂⁴	—	4	8	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	—	4	16	no	—
256	C₂⁴	—	4	16	no	—
257	C₂⁴	—	4	16	no	—
258	C₂⁴	—	4	16	no	—
259	C₂⁴	—	4	32	no	—
260	C₂⁴	C₄⋊C₄×C₁₀₁	1	16	yes	complemented
261	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
262	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
263	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
264	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
265	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
266	C₂⁴	C₂×Q₈×C₁₀₁	1	4	yes	—
267	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
268	C₂⁴	#41×C₁₀₁	1	4	yes	—
269	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	16	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	—	4	8	no	—
281	C₂²×C₄	—	4	16	no	—
282	C₂²×C₄	—	4	16	no	—
283	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
284	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
286	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
287	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
288	C₄⋊C₄	—	4	16	no	—
289	C₂²⋊C₄	—	2	32	no	—
290	C₂²⋊C₄	—	4	32	no	—
291	C₂²⋊C₄	—	4	16	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	8	no	—
295	C₂³	—	2	8	no	—
296	C₂³	—	2	8	no	—
297	C₂³	—	2	16	no	—
298	C₂³	—	2	8	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	2	8	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	2	16	no	—
306	C₂³	—	2	16	no	—
307	C₂³	—	2	32	no	—
308	C₂³	—	4	32	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	32	no	—
312	C₂³	—	4	64	no	—
313	C₂³	—	4	64	no	—
314	C₂³	—	4	8	no	—
315	C₂³	—	4	8	no	—
316	C₂³	—	4	16	no	—
317	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
318	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	8	yes	—
319	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
320	C₂³	#117×C₁₀₁	1	4	yes	—
321	C₂³	#121×C₁₀₁	1	8	yes	—
322	C₂³	C₂²⋊Q₈×C₁₀₁	1	8	yes	—
323	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
324	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
325	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
326	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
327	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
328	C₂³	H(5,𝔽₂)×C₁₀₁	1	4	yes	—
329	C₂³	H(5,𝔽₂)×C₁₀₁	1	4	yes	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	4	16	no	—
336	C₂×C₄	—	4	16	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	8	no	—
339	C₂×C₄	—	4	16	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	16	no	—
349	C₂²	—	2	16	no	—
350	C₂²	—	2	8	no	—
351	C₂²	—	2	16	no	—
352	C₂²	—	4	64	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	16	no	—
357	C₂²	—	4	16	no	—
358	C₂²	#380×C₁₀₁	1	8	yes	—
359	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
360	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
361	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
362	C₂²	#518×C₁₀₁	1	2	yes	—
363	C₂²	#518×C₁₀₁	1	2	yes	—
364	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
365	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
366	C₂²	#534×C₁₀₁	1	4	yes	—
367	C₂²	#534×C₁₀₁	1	4	yes	—
368	C₂²	#535×C₁₀₁	1	4	yes	—
369	C₂²	#538×C₁₀₁	1	8	yes	—
370	C₂²	#543×C₁₀₁	1	4	yes	—
371	C₄	—	2	8	no	—
372	C₄	—	4	4	no	—
373	C₄	—	8	8	no	—
374	C₂	—	2	8	no	—
375	C₂	—	4	8	no	—
376	C₂	C₂×#380×C₁₀₁	1	1	yes	characteristic
377	C₂	C₁₀₁×#2308	1	1	yes	characteristic
378	C₂	C₁₀₁×#2309	1	1	yes	characteristic
379	C₂	C₁₀₁×#2312	1	2	yes	—
380	C₂	C₁₀₁×#2315	1	2	yes	—
381	C₂	C₁₀₁×#2617	1	4	yes	—
382	C₂	C₁₀₁×#2626	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂⁶×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×#380×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1439	C₂	semidirect
5. C₁₀₁×C₂²⋊#95	C₂	semidirect
9. C₂²×C₄⋊C₄×C₁₀₁	C₂²	semidirect
11. C₂²×C₂²⋊C₄×C₁₀₁	C₄	semidirect
17. C₂×#95×C₁₀₁	C₂²	semidirect
18. C₂×#95×C₁₀₁	C₂²	semidirect
68. C₂⁴×C₁₀₁	C₄⋊C₄	semidirect
91. C₂²×C₄×C₁₀₁	C₂²⋊C₄	semidirect
182. #14338	C₁₀₁	direct (N × H)
193. C₂×#380	C₂×C₁₀₁	semidirect
195. #1439	C₂×C₁₀₁	semidirect
196. C₂²⋊#95	C₂×C₁₀₁	semidirect
197. C₁₀₁	#14338	direct (N × H)
201. C₂²×C₄⋊C₄	C₂²×C₁₀₁	semidirect
203. C₂²×C₂²⋊C₄	C₄×C₁₀₁	semidirect
209. C₂×#95	C₂²×C₁₀₁	semidirect
210. C₂×#95	C₂²×C₁₀₁	semidirect
260. C₂⁴	C₄⋊C₄×C₁₀₁	semidirect
283. C₂²×C₄	C₂²⋊C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₂×#379×C₁₀₁	2
C₁₀₁×#1439	2
C₁₀₁×C₂²⋊#95	2
#14338	101

Subgroups — C101×#14338 #38796489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14338 #38796489