Subgroups — C₁₀₁×#17204 #38799355

Order 25856.

1510 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#399×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#396×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#1443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1441	C₂	1	3	yes	maximal, complemented
5	C₁₀₁×#1439	C₂	1	3	yes	maximal, complemented
6	C₁₀₁×#1439	C₂	1	3	yes	maximal, complemented
7	C₁₀₁×#1438	C₂	1	3	yes	maximal
8	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
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	3	yes	—
15	#399×C₁₀₁	—	2	4	no	—
16	#396×C₁₀₁	—	2	4	no	—
17	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
18	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
19	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
24	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
25	C₂²×D₄×C₁₀₁	—	4	3	no	—
26	C₂²×D₄×C₁₀₁	—	4	3	no	—
27	C₂²×D₄×C₁₀₁	Q₈	1	4	yes	—
28	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
29	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
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	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
34	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
35	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
36	C₂×C₄⋊C₄×C₁₀₁	—	4	3	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	4	3	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	4	3	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	—	4	3	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
49	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	4	3	no	—
51	#95×C₁₀₁	—	4	3	no	—
52	#95×C₁₀₁	—	4	3	no	—
53	#95×C₁₀₁	—	4	3	no	—
54	#95×C₁₀₁	—	4	3	no	—
55	#95×C₁₀₁	—	4	3	no	—
56	#95×C₁₀₁	D₄	1	4	yes	complemented
57	C₂⁴×C₁₀₁	—	2	1	no	—
58	C₂⁴×C₁₀₁	—	2	1	no	—
59	C₂⁴×C₁₀₁	—	2	3	no	—
60	C₂⁴×C₁₀₁	—	2	3	no	—
61	C₂⁴×C₁₀₁	—	2	3	no	—
62	C₂⁴×C₁₀₁	—	2	3	no	—
63	C₂⁴×C₁₀₁	—	2	3	no	—
64	C₂⁴×C₁₀₁	—	2	3	no	—
65	C₂⁴×C₁₀₁	—	2	3	no	—
66	C₂⁴×C₁₀₁	—	2	3	no	—
67	C₂⁴×C₁₀₁	—	2	1	no	—
68	C₂⁴×C₁₀₁	—	2	1	no	—
69	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
70	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
71	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
72	C₂×D₄×C₁₀₁	—	4	12	no	—
73	C₂×D₄×C₁₀₁	—	4	4	no	—
74	C₂×D₄×C₁₀₁	—	4	12	no	—
75	C₂²×C₄×C₁₀₁	—	2	3	no	—
76	C₂²×C₄×C₁₀₁	—	2	3	no	—
77	C₂²×C₄×C₁₀₁	—	2	3	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	3	no	—
89	C₂²×C₄×C₁₀₁	—	2	3	no	—
90	C₂²×C₄×C₁₀₁	—	2	3	no	—
91	C₂²×C₄×C₁₀₁	—	2	3	no	—
92	C₂²×C₄×C₁₀₁	—	2	3	no	—
93	C₂²×C₄×C₁₀₁	—	2	3	no	—
94	C₂²×C₄×C₁₀₁	—	2	3	no	—
95	C₂²×C₄×C₁₀₁	—	2	3	no	—
96	C₂²×C₄×C₁₀₁	—	2	3	no	—
97	C₂²×C₄×C₁₀₁	—	2	3	no	—
98	C₂²×C₄×C₁₀₁	—	2	3	no	—
99	C₂²×C₄×C₁₀₁	—	2	3	no	—
100	C₂²×C₄×C₁₀₁	—	2	3	no	—
101	C₂²×C₄×C₁₀₁	—	2	3	no	—
102	C₂²×C₄×C₁₀₁	—	2	3	no	—
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₀₁	#41	1	6	yes	—
106	C₄⋊C₄×C₁₀₁	—	4	12	no	—
107	C₄⋊C₄×C₁₀₁	—	4	12	no	—
108	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
109	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
110	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
111	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
112	C₂³×C₁₀₁	—	2	6	no	—
113	C₂³×C₁₀₁	—	2	6	no	—
114	C₂³×C₁₀₁	—	2	2	no	—
115	C₂³×C₁₀₁	—	2	2	no	—
116	C₂³×C₁₀₁	—	2	6	no	—
117	C₂³×C₁₀₁	—	2	6	no	—
118	C₂³×C₁₀₁	—	4	3	no	—
119	C₂³×C₁₀₁	—	4	3	no	—
120	C₂³×C₁₀₁	—	4	3	no	—
121	C₂³×C₁₀₁	—	4	3	no	—
122	C₂³×C₁₀₁	—	4	3	no	—
123	C₂³×C₁₀₁	—	4	3	no	—
124	C₂³×C₁₀₁	—	4	3	no	—
125	C₂³×C₁₀₁	—	4	3	no	—
126	C₂³×C₁₀₁	—	4	3	no	—
127	C₂³×C₁₀₁	—	4	3	no	—
128	C₂³×C₁₀₁	—	4	3	no	—
129	C₂³×C₁₀₁	—	4	3	no	—
130	C₂³×C₁₀₁	—	4	3	no	—
131	C₂³×C₁₀₁	—	4	1	no	—
132	C₂³×C₁₀₁	—	4	1	no	—
133	C₂³×C₁₀₁	—	4	3	no	—
134	C₂³×C₁₀₁	—	4	3	no	—
135	C₂³×C₁₀₁	—	4	3	no	—
136	C₂³×C₁₀₁	—	4	3	no	—
137	C₂³×C₁₀₁	—	4	3	no	—
138	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
139	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
140	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
141	C₂³×C₁₀₁	H(5,𝔽₂)	1	3	yes	—
142	C₂³×C₁₀₁	H(5,𝔽₂)	1	3	yes	—
143	C₂³×C₁₀₁	H(5,𝔽₂)	1	3	yes	—
144	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
145	D₄×C₁₀₁	—	4	16	no	—
146	C₂×C₄×C₁₀₁	—	2	6	no	—
147	C₂×C₄×C₁₀₁	—	2	6	no	—
148	C₂×C₄×C₁₀₁	—	2	6	no	—
149	C₂×C₄×C₁₀₁	—	2	6	no	—
150	C₂×C₄×C₁₀₁	—	2	6	no	—
151	C₂×C₄×C₁₀₁	—	2	6	no	—
152	C₂×C₄×C₁₀₁	—	2	6	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	3	no	—
157	C₂×C₄×C₁₀₁	—	4	3	no	—
158	C₂×C₄×C₁₀₁	—	4	3	no	—
159	C₂×C₄×C₁₀₁	—	4	3	no	—
160	C₂×C₄×C₁₀₁	—	4	3	no	—
161	C₂×C₄×C₁₀₁	—	4	1	no	—
162	C₂×C₄×C₁₀₁	—	4	3	no	—
163	C₂×C₄×C₁₀₁	—	4	3	no	—
164	C₂×C₄×C₁₀₁	—	4	3	no	—
165	C₂×C₄×C₁₀₁	—	4	3	no	—
166	C₂×C₄×C₁₀₁	—	4	3	no	—
167	C₂×C₄×C₁₀₁	—	4	3	no	—
168	C₂×C₄×C₁₀₁	—	4	3	no	—
169	C₂×C₄×C₁₀₁	—	4	3	no	—
170	C₂×C₄×C₁₀₁	—	4	3	no	—
171	C₂×C₄×C₁₀₁	—	4	3	no	—
172	C₂×C₄×C₁₀₁	—	4	3	no	—
173	C₂×C₄×C₁₀₁	—	4	3	no	—
174	C₂×C₄×C₁₀₁	—	4	3	no	—
175	C₂×C₄×C₁₀₁	—	4	3	no	—
176	C₂×C₄×C₁₀₁	—	4	3	no	—
177	C₂²×C₁₀₁	—	4	2	no	—
178	C₂²×C₁₀₁	—	4	2	no	—
179	C₂²×C₁₀₁	—	4	6	no	—
180	C₂²×C₁₀₁	—	4	6	no	—
181	C₂²×C₁₀₁	—	4	6	no	—
182	C₂²×C₁₀₁	—	4	6	no	—
183	C₂²×C₁₀₁	—	8	1	no	—
184	C₂²×C₁₀₁	—	8	1	no	—
185	C₂²×C₁₀₁	—	8	3	no	—
186	C₂²×C₁₀₁	—	8	3	no	—
187	C₂²×C₁₀₁	—	8	3	no	—
188	C₂²×C₁₀₁	—	8	3	no	—
189	C₂²×C₁₀₁	—	8	1	no	—
190	C₂²×C₁₀₁	—	8	1	no	—
191	C₂²×C₁₀₁	#535	1	3	yes	—
192	C₂²×C₁₀₁	#538	1	3	yes	—
193	C₂²×C₁₀₁	#540	1	3	yes	—
194	C₂²×C₁₀₁	#542	1	3	yes	—
195	C₂²×C₁₀₁	#543	1	3	yes	—
196	C₂²×C₁₀₁	#546	1	3	yes	—
197	C₂²×C₁₀₁	D₄×Q₈	1	1	yes	characteristic
198	C₂²×C₁₀₁	#553	1	3	yes	—
199	C₂²×C₁₀₁	#554	1	3	yes	—
200	C₂²×C₁₀₁	#560	1	3	yes	—
201	C₂²×C₁₀₁	#560	1	1	yes	characteristic
202	C₂²×C₁₀₁	#560	1	3	yes	—
203	C₂²×C₁₀₁	#562	1	3	yes	—
204	C₄×C₁₀₁	—	4	2	no	—
205	C₄×C₁₀₁	—	4	6	no	—
206	C₄×C₁₀₁	—	4	6	no	—
207	C₄×C₁₀₁	—	8	3	no	—
208	C₄×C₁₀₁	—	8	3	no	—
209	#17204	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂×C₁₀₁	—	8	2	no	—
211	C₂×C₁₀₁	—	8	2	no	—
212	C₂×C₁₀₁	#2692	1	3	yes	—
213	C₂×C₁₀₁	#2703	1	3	yes	—
214	C₂×C₁₀₁	#2780	1	3	yes	—
215	C₂×C₁₀₁	#2801	1	1	yes	characteristic
216	C₂×C₁₀₁	#2818	1	1	yes	characteristic
217	C₂×C₁₀₁	#2829	1	3	yes	—
218	C₂×C₁₀₁	#2842	1	1	yes	characteristic
219	C₂×#399	C₂×C₁₀₁	1	1	yes	characteristic, complemented
220	C₂×#396	C₂×C₁₀₁	1	1	yes	characteristic, complemented
221	#1443	C₂×C₁₀₁	1	1	yes	characteristic, complemented
222	#1441	C₂×C₁₀₁	1	3	yes	complemented
223	#1439	C₂×C₁₀₁	1	3	yes	complemented
224	#1439	C₂×C₁₀₁	1	3	yes	complemented
225	#1438	C₂×C₁₀₁	1	3	yes	—
226	C₁₀₁	#17204	1	1	yes	characteristic, direct product factor, Sylow
227	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	3	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	3	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
234	#399	—	2	4	no	—
235	#396	—	2	4	no	—
236	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
237	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
238	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
239	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
240	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
241	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
243	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
244	C₂²×D₄	—	4	3	no	—
245	C₂²×D₄	—	4	3	no	—
246	C₂²×D₄	Q₈×C₁₀₁	1	4	yes	—
247	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
248	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
249	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
250	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
252	C₂×C₄⋊C₄	—	2	6	no	—
253	C₂×C₄⋊C₄	—	2	6	no	—
254	C₂×C₄⋊C₄	—	2	6	no	—
255	C₂×C₄⋊C₄	—	4	3	no	—
256	C₂×C₄⋊C₄	—	4	3	no	—
257	C₂×C₄⋊C₄	—	4	3	no	—
258	C₂×C₂²⋊C₄	—	2	6	no	—
259	C₂×C₂²⋊C₄	—	2	6	no	—
260	C₂×C₂²⋊C₄	—	2	6	no	—
261	C₂×C₂²⋊C₄	—	2	6	no	—
262	C₂×C₂²⋊C₄	—	4	3	no	—
263	C₂×C₂²⋊C₄	—	4	3	no	—
264	C₂×C₂²⋊C₄	—	4	3	no	—
265	C₂×C₂²⋊C₄	—	4	3	no	—
266	C₂×C₂²⋊C₄	—	4	3	no	—
267	C₂×C₂²⋊C₄	—	4	3	no	—
268	C₂×C₂²⋊C₄	—	4	3	no	—
269	C₂×C₂²⋊C₄	—	4	3	no	—
270	#95	—	4	3	no	—
271	#95	—	4	3	no	—
272	#95	—	4	3	no	—
273	#95	—	4	3	no	—
274	#95	—	4	3	no	—
275	#95	D₄×C₁₀₁	1	4	yes	complemented
276	C₂⁴	—	2	1	no	—
277	C₂⁴	—	2	1	no	—
278	C₂⁴	—	2	3	no	—
279	C₂⁴	—	2	3	no	—
280	C₂⁴	—	2	3	no	—
281	C₂⁴	—	2	3	no	—
282	C₂⁴	—	2	3	no	—
283	C₂⁴	—	2	3	no	—
284	C₂⁴	—	2	3	no	—
285	C₂⁴	—	2	3	no	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
289	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
290	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
291	C₂×D₄	—	4	12	no	—
292	C₂×D₄	—	4	12	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂²×C₄	—	2	3	no	—
295	C₂²×C₄	—	2	3	no	—
296	C₂²×C₄	—	2	3	no	—
297	C₂²×C₄	—	2	3	no	—
298	C₂²×C₄	—	2	3	no	—
299	C₂²×C₄	—	2	3	no	—
300	C₂²×C₄	—	2	3	no	—
301	C₂²×C₄	—	2	3	no	—
302	C₂²×C₄	—	2	3	no	—
303	C₂²×C₄	—	2	3	no	—
304	C₂²×C₄	—	2	3	no	—
305	C₂²×C₄	—	2	3	no	—
306	C₂²×C₄	—	2	3	no	—
307	C₂²×C₄	—	2	3	no	—
308	C₂²×C₄	—	2	3	no	—
309	C₂²×C₄	—	2	3	no	—
310	C₂²×C₄	—	2	3	no	—
311	C₂²×C₄	—	2	3	no	—
312	C₂²×C₄	—	2	3	no	—
313	C₂²×C₄	—	2	3	no	—
314	C₂²×C₄	—	2	3	no	—
315	C₂²×C₄	—	2	3	no	—
316	C₂²×C₄	—	2	3	no	—
317	C₂²×C₄	—	2	3	no	—
318	C₂²×C₄	—	2	3	no	—
319	C₂²×C₄	—	2	3	no	—
320	C₂²×C₄	—	2	3	no	—
321	C₂²×C₄	—	2	3	no	—
322	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
323	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
324	C₂²×C₄	#41×C₁₀₁	1	6	yes	—
325	C₄⋊C₄	—	4	12	no	—
326	C₄⋊C₄	—	4	12	no	—
327	C₂²⋊C₄	—	4	12	no	—
328	C₂²⋊C₄	—	4	12	no	—
329	C₂²⋊C₄	—	4	12	no	—
330	C₂²⋊C₄	—	4	12	no	—
331	C₂³	—	2	6	no	—
332	C₂³	—	2	6	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	6	no	—
336	C₂³	—	2	6	no	—
337	C₂³	—	4	3	no	—
338	C₂³	—	4	3	no	—
339	C₂³	—	4	3	no	—
340	C₂³	—	4	3	no	—
341	C₂³	—	4	3	no	—
342	C₂³	—	4	3	no	—
343	C₂³	—	4	3	no	—
344	C₂³	—	4	3	no	—
345	C₂³	—	4	3	no	—
346	C₂³	—	4	3	no	—
347	C₂³	—	4	3	no	—
348	C₂³	—	4	3	no	—
349	C₂³	—	4	3	no	—
350	C₂³	—	4	3	no	—
351	C₂³	—	4	3	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	3	no	—
355	C₂³	—	4	3	no	—
356	C₂³	—	4	3	no	—
357	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
358	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
359	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
360	C₂³	H(5,𝔽₂)×C₁₀₁	1	3	yes	—
361	C₂³	H(5,𝔽₂)×C₁₀₁	1	3	yes	—
362	C₂³	H(5,𝔽₂)×C₁₀₁	1	3	yes	—
363	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
364	D₄	—	4	16	no	—
365	C₂×C₄	—	2	6	no	—
366	C₂×C₄	—	2	6	no	—
367	C₂×C₄	—	2	6	no	—
368	C₂×C₄	—	2	6	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	4	3	no	—
373	C₂×C₄	—	4	3	no	—
374	C₂×C₄	—	4	3	no	—
375	C₂×C₄	—	4	3	no	—
376	C₂×C₄	—	4	3	no	—
377	C₂×C₄	—	4	3	no	—
378	C₂×C₄	—	4	3	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	3	no	—
381	C₂×C₄	—	4	3	no	—
382	C₂×C₄	—	4	3	no	—
383	C₂×C₄	—	4	3	no	—
384	C₂×C₄	—	4	3	no	—
385	C₂×C₄	—	4	3	no	—
386	C₂×C₄	—	4	3	no	—
387	C₂×C₄	—	4	3	no	—
388	C₂×C₄	—	4	3	no	—
389	C₂×C₄	—	4	3	no	—
390	C₂×C₄	—	4	3	no	—
391	C₂×C₄	—	4	3	no	—
392	C₂×C₄	—	4	3	no	—
393	C₂×C₄	—	4	3	no	—
394	C₂×C₄	—	4	3	no	—
395	C₂×C₄	—	4	3	no	—
396	C₂²	—	4	6	no	—
397	C₂²	—	4	6	no	—
398	C₂²	—	4	6	no	—
399	C₂²	—	4	6	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	3	no	—
403	C₂²	—	8	3	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	3	no	—
409	C₂²	—	8	3	no	—
410	C₂²	#535×C₁₀₁	1	3	yes	—
411	C₂²	#538×C₁₀₁	1	3	yes	—
412	C₂²	#540×C₁₀₁	1	3	yes	—
413	C₂²	#542×C₁₀₁	1	3	yes	—
414	C₂²	#543×C₁₀₁	1	3	yes	—
415	C₂²	#546×C₁₀₁	1	3	yes	—
416	C₂²	D₄×Q₈×C₁₀₁	1	1	yes	characteristic
417	C₂²	#553×C₁₀₁	1	3	yes	—
418	C₂²	#554×C₁₀₁	1	3	yes	—
419	C₂²	#560×C₁₀₁	1	3	yes	—
420	C₂²	#560×C₁₀₁	1	3	yes	—
421	C₂²	#560×C₁₀₁	1	1	yes	characteristic
422	C₂²	#562×C₁₀₁	1	3	yes	—
423	C₄	—	4	6	no	—
424	C₄	—	4	6	no	—
425	C₄	—	4	2	no	—
426	C₄	—	8	3	no	—
427	C₄	—	8	3	no	—
428	C₂	—	8	2	no	—
429	C₂	—	8	2	no	—
430	C₂	C₁₀₁×#2692	1	3	yes	—
431	C₂	C₁₀₁×#2703	1	3	yes	—
432	C₂	C₁₀₁×#2780	1	3	yes	—
433	C₂	C₁₀₁×#2801	1	1	yes	characteristic
434	C₂	C₁₀₁×#2818	1	1	yes	characteristic
435	C₂	C₁₀₁×#2829	1	3	yes	—
436	C₂	C₁₀₁×#2842	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
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. C₂×#399×C₁₀₁	C₂	semidirect
2. C₂×#396×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1443	C₂	semidirect
4. C₁₀₁×#1441	C₂	semidirect
5. C₁₀₁×#1439	C₂	semidirect
6. C₁₀₁×#1439	C₂	semidirect
56. #95×C₁₀₁	D₄	semidirect
209. #17204	C₁₀₁	direct (N × H)
219. C₂×#399	C₂×C₁₀₁	semidirect
220. C₂×#396	C₂×C₁₀₁	semidirect
221. #1443	C₂×C₁₀₁	semidirect
222. #1441	C₂×C₁₀₁	semidirect
223. #1439	C₂×C₁₀₁	semidirect
224. #1439	C₂×C₁₀₁	semidirect
226. C₁₀₁	#17204	direct (N × H)
275. #95	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×#399×C₁₀₁	2
C₂×#396×C₁₀₁	2
C₁₀₁×#1443	2
C₁₀₁×#1441	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
#17204	101

Subgroups — C101×#17204 #38799355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17204 #38799355