Subgroups — C₁₀₁×#16560 #38798711

Order 25856.

1510 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#400×C₁₀₁	C₂	1	2	yes	maximal
3	C₂×#387×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1446	C₂	1	2	yes	maximal
5	C₁₀₁×#1446	C₂	1	2	yes	maximal
6	C₁₀₁×#1445	C₂	1	2	yes	maximal
7	C₁₀₁×#1442	C₂	1	2	yes	maximal
8	C₁₀₁×#1441	C₂	1	2	yes	maximal
9	C₁₀₁×#1434	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₀₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₁₀₁	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₁₀₁	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
18	#400×C₁₀₁	—	2	8	no	—
19	#387×C₁₀₁	—	2	4	no	—
20	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
30	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₀₁	—	2	8	no	—
32	C₂²×Q₈×C₁₀₁	—	2	4	no	—
33	C₂²×Q₈×C₁₀₁	—	2	4	no	—
34	C₂²×Q₈×C₁₀₁	—	2	4	no	—
35	C₂²×Q₈×C₁₀₁	—	4	4	no	—
36	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₄⋊Q₈×C₁₀₁	—	2	32	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	8	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	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₀₁	D₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₀₁	Q₈	1	4	yes	complemented
56	C₂×C₄²×C₁₀₁	—	2	4	no	—
57	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
58	#95×C₁₀₁	—	2	8	no	—
59	#95×C₁₀₁	—	2	4	no	—
60	#95×C₁₀₁	—	2	8	no	—
61	#95×C₁₀₁	—	2	2	no	—
62	#95×C₁₀₁	—	2	2	no	—
63	#95×C₁₀₁	—	2	2	no	—
64	#95×C₁₀₁	—	2	2	no	—
65	#95×C₁₀₁	—	2	4	no	—
66	#95×C₁₀₁	—	2	4	no	—
67	#95×C₁₀₁	—	4	4	no	—
68	#95×C₁₀₁	—	4	4	no	—
69	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
70	C₂×Q₈×C₁₀₁	—	2	16	no	—
71	C₂×Q₈×C₁₀₁	—	4	16	no	—
72	C₂×Q₈×C₁₀₁	—	4	16	no	—
73	C₂×Q₈×C₁₀₁	—	4	8	no	—
74	C₂×Q₈×C₁₀₁	—	4	8	no	—
75	C₂²×C₄×C₁₀₁	—	2	2	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	2	no	—
81	C₂²×C₄×C₁₀₁	—	2	1	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	1	no	—
84	C₂²×C₄×C₁₀₁	—	2	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	4	no	—
86	C₂²×C₄×C₁₀₁	—	2	1	no	—
87	C₂²×C₄×C₁₀₁	—	2	1	no	—
88	C₂²×C₄×C₁₀₁	—	2	4	no	—
89	C₂²×C₄×C₁₀₁	—	2	4	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	4	no	—
92	C₂²×C₄×C₁₀₁	—	2	4	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	4	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	4	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	4	no	—
106	C₂²×C₄×C₁₀₁	—	2	4	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	2	4	no	—
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
119	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
120	C₄⋊C₄×C₁₀₁	—	2	16	no	—
121	C₄⋊C₄×C₁₀₁	—	2	16	no	—
122	C₄⋊C₄×C₁₀₁	—	2	8	no	—
123	C₄⋊C₄×C₁₀₁	—	4	4	no	—
124	C₄²×C₁₀₁	—	2	8	no	—
125	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
126	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
127	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
128	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
129	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
130	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
131	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
132	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
133	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
134	Q₈×C₁₀₁	—	4	32	no	—
135	C₂×C₄×C₁₀₁	—	2	2	no	—
136	C₂×C₄×C₁₀₁	—	2	2	no	—
137	C₂×C₄×C₁₀₁	—	2	2	no	—
138	C₂×C₄×C₁₀₁	—	2	2	no	—
139	C₂×C₄×C₁₀₁	—	2	2	no	—
140	C₂×C₄×C₁₀₁	—	2	8	no	—
141	C₂×C₄×C₁₀₁	—	2	2	no	—
142	C₂×C₄×C₁₀₁	—	2	8	no	—
143	C₂×C₄×C₁₀₁	—	2	4	no	—
144	C₂×C₄×C₁₀₁	—	2	4	no	—
145	C₂×C₄×C₁₀₁	—	2	8	no	—
146	C₂×C₄×C₁₀₁	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	—	2	4	no	—
149	C₂×C₄×C₁₀₁	—	2	8	no	—
150	C₂×C₄×C₁₀₁	—	2	8	no	—
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	4	1	no	—
153	C₂×C₄×C₁₀₁	—	4	4	no	—
154	C₂×C₄×C₁₀₁	—	4	1	no	—
155	C₂×C₄×C₁₀₁	—	4	4	no	—
156	C₂×C₄×C₁₀₁	—	4	1	no	—
157	C₂×C₄×C₁₀₁	—	4	1	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	4	no	—
160	C₂×C₄×C₁₀₁	—	4	4	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	—	4	1	no	—
163	C₂×C₄×C₁₀₁	—	4	1	no	—
164	C₂×C₄×C₁₀₁	—	4	1	no	—
165	C₂×C₄×C₁₀₁	—	4	1	no	—
166	C₂×C₄×C₁₀₁	—	4	1	no	—
167	C₂×C₄×C₁₀₁	—	4	1	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	—	4	4	no	—
177	C₂×C₄×C₁₀₁	#120	1	4	yes	—
178	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
179	C₂×C₄×C₁₀₁	#124	1	4	yes	—
180	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
181	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
183	C₂²×C₁₀₁	#535	1	1	yes	characteristic
184	C₂²×C₁₀₁	#536	1	1	yes	characteristic
185	C₂²×C₁₀₁	#536	1	1	yes	characteristic
186	C₂²×C₁₀₁	#536	1	1	yes	characteristic
187	C₂²×C₁₀₁	#536	1	4	yes	—
188	C₂²×C₁₀₁	#541	1	4	yes	—
189	C₂²×C₁₀₁	#542	1	2	yes	—
190	C₂²×C₁₀₁	#544	1	2	yes	—
191	C₂²×C₁₀₁	#546	1	4	yes	—
192	C₂²×C₁₀₁	#548	1	2	yes	—
193	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
194	C₂²×C₁₀₁	#556	1	2	yes	—
195	C₂²×C₁₀₁	#557	1	2	yes	—
196	C₂²×C₁₀₁	#563	1	4	yes	—
197	C₄×C₁₀₁	—	2	4	no	—
198	C₄×C₁₀₁	—	2	4	no	—
199	C₄×C₁₀₁	—	2	4	no	—
200	C₄×C₁₀₁	—	4	2	no	—
201	C₄×C₁₀₁	—	4	2	no	—
202	C₄×C₁₀₁	—	4	8	no	—
203	C₄×C₁₀₁	—	8	1	no	—
204	C₄×C₁₀₁	—	8	1	no	—
205	C₄×C₁₀₁	—	8	4	no	—
206	#16560	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₁₀₁	#2409	1	1	yes	characteristic
208	C₂×C₁₀₁	#2435	1	1	yes	characteristic
209	C₂×C₁₀₁	#2568	1	1	yes	characteristic
210	C₂×C₁₀₁	#2614	1	1	yes	characteristic
211	C₂×C₁₀₁	#2628	1	1	yes	characteristic
212	C₂×C₁₀₁	#2642	1	1	yes	characteristic
213	C₂×C₁₀₁	#2713	1	4	yes	—
214	C₂×C₁₀₁	#2716	1	4	yes	—
215	C₂×C₁₀₁	#2821	1	1	yes	characteristic
216	C₂²×C₄⋊Q₈	C₂×C₁₀₁	1	1	yes	characteristic
217	C₂×#400	C₂×C₁₀₁	1	2	yes	—
218	C₂×#387	C₂×C₁₀₁	1	1	yes	characteristic
219	#1446	C₂×C₁₀₁	1	2	yes	—
220	#1446	C₂×C₁₀₁	1	2	yes	—
221	#1445	C₂×C₁₀₁	1	2	yes	—
222	#1442	C₂×C₁₀₁	1	2	yes	—
223	#1441	C₂×C₁₀₁	1	2	yes	—
224	#1434	C₂×C₁₀₁	1	1	yes	characteristic
225	C₁₀₁	#16560	1	1	yes	characteristic, direct product factor, Sylow
226	C₂³×Q₈	C₂²×C₁₀₁	1	2	yes	—
227	C₂×C₄⋊Q₈	—	2	8	no	—
228	C₂×C₄⋊Q₈	—	2	4	no	—
229	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
231	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
233	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
234	#400	—	2	8	no	—
235	#387	—	2	4	no	—
236	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
237	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
238	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
239	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
240	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
241	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
243	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
244	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
245	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
246	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	2	4	no	—
249	C₂²×Q₈	—	2	4	no	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	—	4	4	no	—
252	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
256	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	32	no	—
262	C₂×C₄⋊C₄	—	2	8	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	D₄×C₁₀₁	1	8	yes	—
271	C₂×C₄⋊C₄	Q₈×C₁₀₁	1	4	yes	complemented
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	8	no	—
279	#95	—	2	4	no	—
280	#95	—	2	8	no	—
281	#95	—	2	4	no	—
282	#95	—	2	4	no	—
283	#95	—	4	4	no	—
284	#95	—	4	4	no	—
285	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
286	C₂×Q₈	—	2	16	no	—
287	C₂×Q₈	—	4	16	no	—
288	C₂×Q₈	—	4	16	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×Q₈	—	4	8	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
327	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
331	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
332	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
333	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
334	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
335	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
336	C₄⋊C₄	—	2	16	no	—
337	C₄⋊C₄	—	2	16	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄²	—	2	8	no	—
341	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
342	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
343	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
344	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
345	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
346	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
347	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
348	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
349	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
350	Q₈	—	4	32	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	#120×C₁₀₁	1	4	yes	—
394	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
395	C₂×C₄	#124×C₁₀₁	1	4	yes	—
396	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
397	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
398	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
399	C₂²	#535×C₁₀₁	1	1	yes	characteristic
400	C₂²	#536×C₁₀₁	1	1	yes	characteristic
401	C₂²	#536×C₁₀₁	1	4	yes	—
402	C₂²	#536×C₁₀₁	1	1	yes	characteristic
403	C₂²	#536×C₁₀₁	1	1	yes	characteristic
404	C₂²	#541×C₁₀₁	1	4	yes	—
405	C₂²	#542×C₁₀₁	1	2	yes	—
406	C₂²	#544×C₁₀₁	1	2	yes	—
407	C₂²	#546×C₁₀₁	1	4	yes	—
408	C₂²	#548×C₁₀₁	1	2	yes	—
409	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
410	C₂²	#556×C₁₀₁	1	2	yes	—
411	C₂²	#557×C₁₀₁	1	2	yes	—
412	C₂²	#563×C₁₀₁	1	4	yes	—
413	C₄	—	2	4	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	4	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	8	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	4	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₂	C₁₀₁×#2409	1	1	yes	characteristic
423	C₂	C₁₀₁×#2435	1	1	yes	characteristic
424	C₂	C₁₀₁×#2568	1	1	yes	characteristic
425	C₂	C₁₀₁×#2614	1	1	yes	characteristic
426	C₂	C₁₀₁×#2628	1	1	yes	characteristic
427	C₂	C₁₀₁×#2642	1	1	yes	characteristic
428	C₂	C₁₀₁×#2713	1	4	yes	—
429	C₂	C₁₀₁×#2716	1	4	yes	—
430	C₂	C₁₀₁×#2821	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
55. C₂×C₄⋊C₄×C₁₀₁	Q₈	semidirect
206. #16560	C₁₀₁	direct (N × H)
225. C₁₀₁	#16560	direct (N × H)
271. 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
C₂²×C₄⋊Q₈×C₁₀₁	2
C₂×#400×C₁₀₁	2
C₂×#387×C₁₀₁	2
C₁₀₁×#1446	2
C₁₀₁×#1445	2
C₁₀₁×#1442	2
C₁₀₁×#1441	2
C₁₀₁×#1434	2
#16560	101

Subgroups — C101×#16560 #38798711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#16560 #38798711