Subgroups — C₁₀₁×#14900 #38797051

Order 25856.

2210 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#392×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#390×C₁₀₁	C₂	1	3	yes	maximal, complemented
3	C₂×#388×C₁₀₁	C₂	1	3	yes	maximal, complemented
4	C₂×#376×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1444	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#1439	C₂	1	3	yes	maximal, complemented
7	C₁₀₁×#1438	C₂	1	3	yes	maximal, complemented
8	C₂³×D₄×C₁₀₁	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
11	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	6	yes	—
15	C₂²×C₄²×C₁₀₁	C₂²	1	3	yes	—
16	#392×C₁₀₁	—	2	4	no	—
17	#390×C₁₀₁	—	2	12	no	—
18	#388×C₁₀₁	—	2	12	no	—
19	#376×C₁₀₁	—	2	4	no	—
20	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂⁵×C₁₀₁	C₂³	1	3	yes	—
25	C₂²×D₄×C₁₀₁	—	2	12	no	—
26	C₂²×D₄×C₁₀₁	—	2	6	no	—
27	C₂²×D₄×C₁₀₁	—	2	6	no	—
28	C₂²×D₄×C₁₀₁	—	2	6	no	—
29	C₂²×D₄×C₁₀₁	—	4	6	no	—
30	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
31	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
36	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	4	6	no	—
39	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
42	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
43	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	2	12	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	2	12	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	—	4	6	no	—
49	C₂×C₂²⋊C₄×C₁₀₁	—	4	6	no	—
50	C₂×C₄²×C₁₀₁	—	2	6	no	—
51	C₂×C₄²×C₁₀₁	—	2	6	no	—
52	C₂×C₄²×C₁₀₁	D₄	1	12	yes	complemented
53	#95×C₁₀₁	—	2	6	no	—
54	#95×C₁₀₁	—	2	6	no	—
55	#95×C₁₀₁	—	2	6	no	—
56	#95×C₁₀₁	D₄	1	4	yes	—
57	C₂⁴×C₁₀₁	—	2	3	no	—
58	C₂⁴×C₁₀₁	—	2	6	no	—
59	C₂⁴×C₁₀₁	—	2	3	no	—
60	C₂⁴×C₁₀₁	—	2	3	no	—
61	C₂⁴×C₁₀₁	—	2	3	no	—
62	C₂⁴×C₁₀₁	—	2	6	no	—
63	C₂⁴×C₁₀₁	—	2	6	no	—
64	C₂⁴×C₁₀₁	—	2	3	no	—
65	C₂⁴×C₁₀₁	—	2	6	no	—
66	C₂⁴×C₁₀₁	—	2	3	no	—
67	C₂⁴×C₁₀₁	#41	1	6	yes	—
68	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
69	C₂×D₄×C₁₀₁	—	2	24	no	—
70	C₂×D₄×C₁₀₁	—	4	24	no	—
71	C₂×D₄×C₁₀₁	—	4	24	no	—
72	C₂×D₄×C₁₀₁	—	4	12	no	—
73	C₂×D₄×C₁₀₁	—	4	12	no	—
74	C₂²×C₄×C₁₀₁	—	2	1	no	—
75	C₂²×C₄×C₁₀₁	—	2	3	no	—
76	C₂²×C₄×C₁₀₁	—	2	6	no	—
77	C₂²×C₄×C₁₀₁	—	2	6	no	—
78	C₂²×C₄×C₁₀₁	—	2	3	no	—
79	C₂²×C₄×C₁₀₁	—	2	3	no	—
80	C₂²×C₄×C₁₀₁	—	2	3	no	—
81	C₂²×C₄×C₁₀₁	—	2	3	no	—
82	C₂²×C₄×C₁₀₁	—	2	3	no	—
83	C₂²×C₄×C₁₀₁	—	2	3	no	—
84	C₂²×C₄×C₁₀₁	—	2	3	no	—
85	C₂²×C₄×C₁₀₁	—	2	3	no	—
86	C₂²×C₄×C₁₀₁	—	2	3	no	—
87	C₂²×C₄×C₁₀₁	—	2	3	no	—
88	C₂²×C₄×C₁₀₁	—	2	1	no	—
89	C₂²×C₄×C₁₀₁	—	2	6	no	—
90	C₂²×C₄×C₁₀₁	—	2	3	no	—
91	C₂²×C₄×C₁₀₁	—	2	3	no	—
92	C₂²×C₄×C₁₀₁	—	2	6	no	—
93	C₂²×C₄×C₁₀₁	—	2	3	no	—
94	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
95	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
96	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
97	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
98	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
99	C₂²×C₄×C₁₀₁	#41	1	6	yes	—
100	C₄⋊C₄×C₁₀₁	—	4	12	no	—
101	C₄⋊C₄×C₁₀₁	—	4	4	no	—
102	C₂²⋊C₄×C₁₀₁	—	2	24	no	—
103	C₂²⋊C₄×C₁₀₁	—	4	24	no	—
104	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
105	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
106	C₄²×C₁₀₁	—	2	24	no	—
107	C₂³×C₁₀₁	—	2	6	no	—
108	C₂³×C₁₀₁	—	2	12	no	—
109	C₂³×C₁₀₁	—	2	6	no	—
110	C₂³×C₁₀₁	—	2	12	no	—
111	C₂³×C₁₀₁	—	2	6	no	—
112	C₂³×C₁₀₁	—	4	3	no	—
113	C₂³×C₁₀₁	—	4	6	no	—
114	C₂³×C₁₀₁	—	4	3	no	—
115	C₂³×C₁₀₁	—	4	6	no	—
116	C₂³×C₁₀₁	—	4	3	no	—
117	C₂³×C₁₀₁	—	4	6	no	—
118	C₂³×C₁₀₁	—	4	3	no	—
119	C₂³×C₁₀₁	—	4	6	no	—
120	C₂³×C₁₀₁	—	4	6	no	—
121	C₂³×C₁₀₁	—	4	3	no	—
122	C₂³×C₁₀₁	—	4	3	no	—
123	C₂³×C₁₀₁	—	4	6	no	—
124	C₂³×C₁₀₁	—	4	3	no	—
125	C₂³×C₁₀₁	—	4	6	no	—
126	C₂³×C₁₀₁	—	4	6	no	—
127	C₂³×C₁₀₁	—	4	6	no	—
128	C₂³×C₁₀₁	—	4	6	no	—
129	C₂³×C₁₀₁	—	4	3	no	—
130	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
131	C₂³×C₁₀₁	C₂²×D₄	1	3	yes	—
132	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
133	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
134	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
135	C₂³×C₁₀₁	H(5,𝔽₂)	1	3	yes	—
136	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
137	D₄×C₁₀₁	—	4	48	no	—
138	C₂×C₄×C₁₀₁	—	2	6	no	—
139	C₂×C₄×C₁₀₁	—	2	6	no	—
140	C₂×C₄×C₁₀₁	—	2	6	no	—
141	C₂×C₄×C₁₀₁	—	2	6	no	—
142	C₂×C₄×C₁₀₁	—	2	12	no	—
143	C₂×C₄×C₁₀₁	—	2	12	no	—
144	C₂×C₄×C₁₀₁	—	2	6	no	—
145	C₂×C₄×C₁₀₁	—	2	6	no	—
146	C₂×C₄×C₁₀₁	—	2	6	no	—
147	C₂×C₄×C₁₀₁	—	2	6	no	—
148	C₂×C₄×C₁₀₁	—	4	3	no	—
149	C₂×C₄×C₁₀₁	—	4	1	no	—
150	C₂×C₄×C₁₀₁	—	4	3	no	—
151	C₂×C₄×C₁₀₁	—	4	3	no	—
152	C₂×C₄×C₁₀₁	—	4	3	no	—
153	C₂×C₄×C₁₀₁	—	4	3	no	—
154	C₂×C₄×C₁₀₁	—	4	3	no	—
155	C₂×C₄×C₁₀₁	—	4	3	no	—
156	C₂×C₄×C₁₀₁	—	4	1	no	—
157	C₂×C₄×C₁₀₁	—	4	3	no	—
158	C₂×C₄×C₁₀₁	—	4	6	no	—
159	C₂×C₄×C₁₀₁	—	4	6	no	—
160	C₂×C₄×C₁₀₁	—	4	3	no	—
161	C₂×C₄×C₁₀₁	—	4	3	no	—
162	C₂×C₄×C₁₀₁	#121	1	12	yes	—
163	C₂×C₄×C₁₀₁	#127	1	4	yes	—
164	C₂²×C₁₀₁	—	4	12	no	—
165	C₂²×C₁₀₁	—	4	6	no	—
166	C₂²×C₁₀₁	—	4	6	no	—
167	C₂²×C₁₀₁	—	4	12	no	—
168	C₂²×C₁₀₁	—	4	6	no	—
169	C₂²×C₁₀₁	—	8	3	no	—
170	C₂²×C₁₀₁	—	8	3	no	—
171	C₂²×C₁₀₁	—	8	6	no	—
172	C₂²×C₁₀₁	—	8	3	no	—
173	C₂²×C₁₀₁	—	8	3	no	—
174	C₂²×C₁₀₁	—	8	6	no	—
175	C₂²×C₁₀₁	C₂×#121	1	3	yes	—
176	C₂²×C₁₀₁	#525	1	3	yes	—
177	C₂²×C₁₀₁	#525	1	3	yes	—
178	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
179	C₂²×C₁₀₁	#532	1	3	yes	—
180	C₂²×C₁₀₁	#535	1	3	yes	—
181	C₂²×C₁₀₁	#535	1	3	yes	—
182	C₂²×C₁₀₁	#546	1	3	yes	—
183	C₂²×C₁₀₁	#550	1	1	yes	characteristic
184	C₂²×C₁₀₁	#551	1	6	yes	—
185	C₂²×C₁₀₁	#553	1	3	yes	—
186	C₂²×C₁₀₁	#555	1	3	yes	—
187	C₄×C₁₀₁	—	2	4	no	—
188	C₄×C₁₀₁	—	2	12	no	—
189	C₄×C₁₀₁	—	4	2	no	—
190	C₄×C₁₀₁	—	4	6	no	—
191	C₄×C₁₀₁	—	8	1	no	—
192	C₄×C₁₀₁	—	8	3	no	—
193	#14900	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₁₀₁	—	8	6	no	—
195	C₂×C₁₀₁	#2397	1	1	yes	characteristic
196	C₂×C₁₀₁	#2411	1	3	yes	—
197	C₂×C₁₀₁	#2414	1	3	yes	—
198	C₂×C₁₀₁	#2603	1	3	yes	—
199	C₂×C₁₀₁	#2610	1	3	yes	—
200	C₂×C₁₀₁	#2657	1	1	yes	characteristic
201	C₂×C₁₀₁	#2856	1	1	yes	characteristic
202	C₂×#392	C₂×C₁₀₁	1	1	yes	characteristic
203	C₂×#390	C₂×C₁₀₁	1	3	yes	complemented
204	C₂×#388	C₂×C₁₀₁	1	3	yes	complemented
205	C₂×#376	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	#1444	C₂×C₁₀₁	1	1	yes	characteristic, complemented
207	#1439	C₂×C₁₀₁	1	3	yes	complemented
208	#1438	C₂×C₁₀₁	1	3	yes	complemented
209	C₁₀₁	#14900	1	1	yes	characteristic, direct product factor, Sylow
210	C₂³×D₄	C₂²×C₁₀₁	1	3	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	3	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
216	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	6	yes	—
217	C₂²×C₄²	C₂²×C₁₀₁	1	3	yes	—
218	#392	—	2	4	no	—
219	#390	—	2	12	no	—
220	#388	—	2	12	no	—
221	#376	—	2	4	no	—
222	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
223	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
224	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
225	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
226	C₂⁵	C₂³×C₁₀₁	1	3	yes	—
227	C₂²×D₄	—	2	12	no	—
228	C₂²×D₄	—	2	6	no	—
229	C₂²×D₄	—	2	6	no	—
230	C₂²×D₄	—	2	6	no	—
231	C₂²×D₄	—	4	6	no	—
232	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
233	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
235	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
238	C₂×C₄⋊C₄	—	2	6	no	—
239	C₂×C₄⋊C₄	—	2	6	no	—
240	C₂×C₄⋊C₄	—	4	6	no	—
241	C₂×C₂²⋊C₄	—	2	6	no	—
242	C₂×C₂²⋊C₄	—	2	6	no	—
243	C₂×C₂²⋊C₄	—	2	6	no	—
244	C₂×C₂²⋊C₄	—	2	6	no	—
245	C₂×C₂²⋊C₄	—	2	6	no	—
246	C₂×C₂²⋊C₄	—	2	12	no	—
247	C₂×C₂²⋊C₄	—	2	12	no	—
248	C₂×C₂²⋊C₄	—	2	6	no	—
249	C₂×C₂²⋊C₄	—	2	6	no	—
250	C₂×C₂²⋊C₄	—	4	6	no	—
251	C₂×C₂²⋊C₄	—	4	6	no	—
252	C₂×C₄²	—	2	6	no	—
253	C₂×C₄²	—	2	6	no	—
254	C₂×C₄²	D₄×C₁₀₁	1	12	yes	complemented
255	#95	—	2	6	no	—
256	#95	—	2	6	no	—
257	#95	—	2	6	no	—
258	#95	D₄×C₁₀₁	1	4	yes	—
259	C₂⁴	—	2	3	no	—
260	C₂⁴	—	2	6	no	—
261	C₂⁴	—	2	3	no	—
262	C₂⁴	—	2	3	no	—
263	C₂⁴	—	2	3	no	—
264	C₂⁴	—	2	6	no	—
265	C₂⁴	—	2	6	no	—
266	C₂⁴	—	2	3	no	—
267	C₂⁴	—	2	6	no	—
268	C₂⁴	—	2	3	no	—
269	C₂⁴	#41×C₁₀₁	1	6	yes	—
270	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
271	C₂×D₄	—	2	24	no	—
272	C₂×D₄	—	4	24	no	—
273	C₂×D₄	—	4	24	no	—
274	C₂×D₄	—	4	12	no	—
275	C₂×D₄	—	4	12	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	3	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	—	2	6	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	—	2	3	no	—
283	C₂²×C₄	—	2	3	no	—
284	C₂²×C₄	—	2	3	no	—
285	C₂²×C₄	—	2	3	no	—
286	C₂²×C₄	—	2	3	no	—
287	C₂²×C₄	—	2	3	no	—
288	C₂²×C₄	—	2	3	no	—
289	C₂²×C₄	—	2	3	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	6	no	—
292	C₂²×C₄	—	2	3	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	6	no	—
295	C₂²×C₄	—	2	3	no	—
296	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
297	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
298	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
299	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
300	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
301	C₂²×C₄	#41×C₁₀₁	1	6	yes	—
302	C₄⋊C₄	—	4	12	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₂²⋊C₄	—	2	24	no	—
305	C₂²⋊C₄	—	4	24	no	—
306	C₂²⋊C₄	—	4	12	no	—
307	C₂²⋊C₄	—	4	12	no	—
308	C₄²	—	2	24	no	—
309	C₂³	—	2	6	no	—
310	C₂³	—	2	12	no	—
311	C₂³	—	2	6	no	—
312	C₂³	—	2	12	no	—
313	C₂³	—	2	6	no	—
314	C₂³	—	4	3	no	—
315	C₂³	—	4	6	no	—
316	C₂³	—	4	3	no	—
317	C₂³	—	4	6	no	—
318	C₂³	—	4	3	no	—
319	C₂³	—	4	6	no	—
320	C₂³	—	4	3	no	—
321	C₂³	—	4	6	no	—
322	C₂³	—	4	6	no	—
323	C₂³	—	4	3	no	—
324	C₂³	—	4	3	no	—
325	C₂³	—	4	6	no	—
326	C₂³	—	4	3	no	—
327	C₂³	—	4	6	no	—
328	C₂³	—	4	6	no	—
329	C₂³	—	4	6	no	—
330	C₂³	—	4	3	no	—
331	C₂³	—	4	6	no	—
332	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
333	C₂³	C₂²×D₄×C₁₀₁	1	3	yes	—
334	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
335	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
336	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
337	C₂³	H(5,𝔽₂)×C₁₀₁	1	3	yes	—
338	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
339	D₄	—	4	48	no	—
340	C₂×C₄	—	2	6	no	—
341	C₂×C₄	—	2	6	no	—
342	C₂×C₄	—	2	6	no	—
343	C₂×C₄	—	2	6	no	—
344	C₂×C₄	—	2	12	no	—
345	C₂×C₄	—	2	12	no	—
346	C₂×C₄	—	2	6	no	—
347	C₂×C₄	—	2	6	no	—
348	C₂×C₄	—	2	6	no	—
349	C₂×C₄	—	2	6	no	—
350	C₂×C₄	—	4	3	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	3	no	—
353	C₂×C₄	—	4	3	no	—
354	C₂×C₄	—	4	3	no	—
355	C₂×C₄	—	4	3	no	—
356	C₂×C₄	—	4	3	no	—
357	C₂×C₄	—	4	3	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	3	no	—
360	C₂×C₄	—	4	6	no	—
361	C₂×C₄	—	4	6	no	—
362	C₂×C₄	—	4	3	no	—
363	C₂×C₄	—	4	3	no	—
364	C₂×C₄	#121×C₁₀₁	1	12	yes	—
365	C₂×C₄	#127×C₁₀₁	1	4	yes	—
366	C₂²	—	4	6	no	—
367	C₂²	—	4	12	no	—
368	C₂²	—	4	6	no	—
369	C₂²	—	4	12	no	—
370	C₂²	—	4	6	no	—
371	C₂²	—	8	3	no	—
372	C₂²	—	8	3	no	—
373	C₂²	—	8	6	no	—
374	C₂²	—	8	3	no	—
375	C₂²	—	8	3	no	—
376	C₂²	—	8	6	no	—
377	C₂²	C₂×#121×C₁₀₁	1	3	yes	—
378	C₂²	#525×C₁₀₁	1	3	yes	—
379	C₂²	#525×C₁₀₁	1	3	yes	—
380	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
381	C₂²	#532×C₁₀₁	1	3	yes	—
382	C₂²	#535×C₁₀₁	1	3	yes	—
383	C₂²	#535×C₁₀₁	1	3	yes	—
384	C₂²	#546×C₁₀₁	1	3	yes	—
385	C₂²	#550×C₁₀₁	1	1	yes	characteristic
386	C₂²	#551×C₁₀₁	1	6	yes	—
387	C₂²	#553×C₁₀₁	1	3	yes	—
388	C₂²	#555×C₁₀₁	1	3	yes	—
389	C₄	—	2	12	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	6	no	—
393	C₄	—	8	3	no	—
394	C₄	—	8	1	no	—
395	C₂	—	8	6	no	—
396	C₂	C₁₀₁×#2397	1	1	yes	characteristic
397	C₂	C₁₀₁×#2411	1	3	yes	—
398	C₂	C₁₀₁×#2414	1	3	yes	—
399	C₂	C₁₀₁×#2603	1	3	yes	—
400	C₂	C₁₀₁×#2610	1	3	yes	—
401	C₂	C₁₀₁×#2657	1	1	yes	characteristic
402	C₂	C₁₀₁×#2856	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂×#392×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
2. C₂×#390×C₁₀₁	C₂	semidirect
3. C₂×#388×C₁₀₁	C₂	semidirect
4. C₂×#376×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1444	C₂	semidirect
6. C₁₀₁×#1439	C₂	semidirect
7. C₁₀₁×#1438	C₂	semidirect
52. C₂×C₄²×C₁₀₁	D₄	semidirect
193. #14900	C₁₀₁	direct (N × H)
203. C₂×#390	C₂×C₁₀₁	semidirect
204. C₂×#388	C₂×C₁₀₁	semidirect
205. C₂×#376	C₂×C₁₀₁	semidirect
206. #1444	C₂×C₁₀₁	semidirect
207. #1439	C₂×C₁₀₁	semidirect
208. #1438	C₂×C₁₀₁	semidirect
209. C₁₀₁	#14900	direct (N × H)
254. C₂×C₄²	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×#392×C₁₀₁	2
C₂×#390×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₂×#376×C₁₀₁	2
C₁₀₁×#1444	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
#14900	101

Subgroups — C101×#14900 #38797051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14900 #38797051