Subgroups — C₁₀₁×#21877 #38804028

Order 25856.

1098 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2316	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1996	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1964	C₂	1	2	yes	maximal
6	C₁₀₁×#1899	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1799	C₂	1	4	yes	maximal, complemented
8	#539×C₁₀₁	—	2	4	no	—
9	#539×C₁₀₁	—	2	4	no	—
10	C₂×#126×C₁₀₁	C₄	1	2	yes	complemented
11	C₂×#125×C₁₀₁	C₄	1	2	yes	complemented
12	C₂×#123×C₁₀₁	C₄	1	2	yes	complemented
13	C₂×#123×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₀₁	C₄	1	2	yes	complemented
15	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#99×C₁₀₁	C₂²	1	8	yes	—
21	#389×C₁₀₁	—	2	4	no	—
22	#387×C₁₀₁	—	2	4	no	—
23	#381×C₁₀₁	C₂²	1	2	yes	—
24	#380×C₁₀₁	C₂²	1	2	yes	—
25	#380×C₁₀₁	C₂²	1	2	yes	—
26	#380×C₁₀₁	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
28	#342×C₁₀₁	C₂²	1	8	yes	—
29	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	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	1	yes	characteristic
36	#126×C₁₀₁	—	2	8	no	—
37	#125×C₁₀₁	—	2	8	no	—
38	#123×C₁₀₁	—	2	4	no	—
39	#123×C₁₀₁	—	2	4	no	—
40	#123×C₁₀₁	—	2	8	no	—
41	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
42	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
43	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
44	#121×C₁₀₁	—	2	2	no	—
45	#121×C₁₀₁	—	2	2	no	—
46	C₄×D₄×C₁₀₁	—	2	4	no	—
47	C₄×D₄×C₁₀₁	—	2	4	no	—
48	#117×C₁₀₁	—	4	4	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₀₁	—	2	2	no	—
71	C₂×C₄²×C₁₀₁	—	2	2	no	—
72	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
73	#99×C₁₀₁	—	4	8	no	—
74	#95×C₁₀₁	—	2	2	no	—
75	#95×C₁₀₁	—	2	2	no	—
76	#95×C₁₀₁	—	2	2	no	—
77	#95×C₁₀₁	—	2	2	no	—
78	#95×C₁₀₁	—	2	4	no	—
79	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
80	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
81	C₂×Q₈×C₁₀₁	—	2	2	no	—
82	C₂×Q₈×C₁₀₁	—	8	1	no	—
83	C₂×D₄×C₁₀₁	—	2	2	no	—
84	C₂×D₄×C₁₀₁	—	2	2	no	—
85	C₂×D₄×C₁₀₁	—	2	4	no	—
86	C₂×D₄×C₁₀₁	—	2	4	no	—
87	C₂×D₄×C₁₀₁	—	2	2	no	—
88	C₂×D₄×C₁₀₁	—	8	1	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	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	4	no	—
94	C₂²×C₄×C₁₀₁	—	8	1	no	—
95	C₂²×C₄×C₁₀₁	—	8	1	no	—
96	C₂²×C₄×C₁₀₁	—	8	2	no	—
97	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
110	C₄⋊C₄×C₁₀₁	—	2	4	no	—
111	C₄⋊C₄×C₁₀₁	—	2	2	no	—
112	C₄⋊C₄×C₁₀₁	—	2	4	no	—
113	C₄⋊C₄×C₁₀₁	—	2	4	no	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	2	4	no	—
116	C₄⋊C₄×C₁₀₁	—	4	4	no	—
117	C₄⋊C₄×C₁₀₁	—	8	2	no	—
118	C₄⋊C₄×C₁₀₁	—	8	2	no	—
119	C₄⋊C₄×C₁₀₁	—	8	2	no	—
120	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	8	yes	—
121	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	8	yes	—
122	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
123	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
124	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
125	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
126	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
128	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
129	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
130	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
131	C₄²×C₁₀₁	—	2	4	no	—
132	C₄²×C₁₀₁	—	4	4	no	—
133	C₄²×C₁₀₁	—	8	2	no	—
134	C₂³×C₁₀₁	—	2	2	no	—
135	C₂³×C₁₀₁	—	2	4	no	—
136	C₂³×C₁₀₁	—	4	1	no	—
137	C₂³×C₁₀₁	—	4	1	no	—
138	C₂³×C₁₀₁	—	4	2	no	—
139	C₂³×C₁₀₁	—	4	2	no	—
140	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
141	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
142	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
143	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
144	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
145	Q₈×C₁₀₁	—	8	2	no	—
146	D₄×C₁₀₁	—	4	2	no	—
147	D₄×C₁₀₁	—	4	2	no	—
148	D₄×C₁₀₁	—	4	4	no	—
149	D₄×C₁₀₁	—	8	2	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	2	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	1	no	—
164	C₂×C₄×C₁₀₁	—	4	1	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	4	2	no	—
167	C₂×C₄×C₁₀₁	—	4	4	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	—	8	4	no	—
174	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
175	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂²×C₁₀₁	—	2	1	no	—
179	C₂²×C₁₀₁	—	2	1	no	—
180	C₂²×C₁₀₁	—	2	1	no	—
181	C₂²×C₁₀₁	—	2	1	no	—
182	C₂²×C₁₀₁	—	2	1	no	—
183	C₂²×C₁₀₁	—	2	1	no	—
184	C₂²×C₁₀₁	—	4	2	no	—
185	C₂²×C₁₀₁	—	4	2	no	—
186	C₂²×C₁₀₁	—	4	2	no	—
187	C₂²×C₁₀₁	—	4	2	no	—
188	C₂²×C₁₀₁	—	4	2	no	—
189	C₂²×C₁₀₁	—	8	4	no	—
190	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₁₀₁	#520	1	2	yes	—
192	C₂²×C₁₀₁	#535	1	1	yes	characteristic
193	C₂²×C₁₀₁	#536	1	1	yes	characteristic
194	C₂²×C₁₀₁	#537	1	2	yes	—
195	C₄×C₁₀₁	—	2	4	no	—
196	C₄×C₁₀₁	—	2	4	no	—
197	C₄×C₁₀₁	—	2	2	no	—
198	C₄×C₁₀₁	—	2	2	no	—
199	C₄×C₁₀₁	—	4	2	no	—
200	C₄×C₁₀₁	—	4	2	no	—
201	C₄×C₁₀₁	—	4	2	no	—
202	C₄×C₁₀₁	—	8	4	no	—
203	C₄×C₁₀₁	—	8	4	no	—
204	#21877	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₁₀₁	—	2	1	no	—
206	C₂×C₁₀₁	—	2	2	no	—
207	C₂×C₁₀₁	—	2	2	no	—
208	C₂×C₁₀₁	—	2	1	no	—
209	C₂×C₁₀₁	—	8	2	no	—
210	C₂×C₁₀₁	#2311	1	1	yes	characteristic
211	C₂×C₁₀₁	#2883	1	1	yes	characteristic
212	C₂×C₁₀₁	#2884	1	1	yes	characteristic
213	C₂×#539	C₂×C₁₀₁	1	1	yes	characteristic
214	#2316	C₂×C₁₀₁	1	1	yes	characteristic, complemented
215	#2313	C₂×C₁₀₁	1	1	yes	characteristic, complemented
216	#1996	C₂×C₁₀₁	1	2	yes	complemented
217	#1964	C₂×C₁₀₁	1	2	yes	—
218	#1899	C₂×C₁₀₁	1	4	yes	complemented
219	#1799	C₂×C₁₀₁	1	4	yes	complemented
220	C₁₀₁	#21877	1	1	yes	characteristic, direct product factor, Sylow
221	#539	—	2	4	no	—
222	#539	—	2	4	no	—
223	C₂×#126	C₄×C₁₀₁	1	2	yes	complemented
224	C₂×#125	C₄×C₁₀₁	1	2	yes	complemented
225	C₂×#123	C₄×C₁₀₁	1	2	yes	complemented
226	C₂×#123	C₂²×C₁₀₁	1	2	yes	—
227	C₂×C₂²⋊Q₈	C₄×C₁₀₁	1	2	yes	complemented
228	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
229	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
231	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
233	C₂×#99	C₂²×C₁₀₁	1	8	yes	—
234	#389	—	2	4	no	—
235	#387	—	2	4	no	—
236	#381	C₂²×C₁₀₁	1	2	yes	—
237	#380	C₂²×C₁₀₁	1	2	yes	—
238	#380	C₂²×C₁₀₁	1	2	yes	—
239	#380	C₂²×C₁₀₁	1	2	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
241	#342	C₂²×C₁₀₁	1	8	yes	—
242	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
243	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
244	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
245	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
249	#126	—	2	8	no	—
250	#125	—	2	8	no	—
251	#123	—	2	4	no	—
252	#123	—	2	4	no	—
253	#123	—	2	8	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	2	8	no	—
257	#121	—	2	2	no	—
258	#121	—	2	2	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	#117	—	4	4	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
274	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
275	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
286	#99	—	4	8	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	4	no	—
292	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
293	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	8	1	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	8	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	8	1	no	—
308	C₂²×C₄	—	8	1	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	8	2	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	8	yes	—
334	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	8	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	4	4	no	—
346	C₄²	—	8	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
354	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
355	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
356	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
357	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
358	Q₈	—	8	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
404	C₂²	#520×C₁₀₁	1	2	yes	—
405	C₂²	#535×C₁₀₁	1	1	yes	characteristic
406	C₂²	#536×C₁₀₁	1	1	yes	characteristic
407	C₂²	#537×C₁₀₁	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	4	no	—
416	C₄	—	8	4	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	2	no	—
419	C₂	—	2	2	no	—
420	C₂	—	2	1	no	—
421	C₂	—	8	2	no	—
422	C₂	C₁₀₁×#2311	1	1	yes	characteristic
423	C₂	C₁₀₁×#2883	1	1	yes	characteristic
424	C₂	C₁₀₁×#2884	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂×#121×C₁₀₁	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂²×C₄⋊C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2316	C₂	semidirect
3. C₁₀₁×#2313	C₂	semidirect
4. C₁₀₁×#1996	C₂	semidirect
6. C₁₀₁×#1899	C₂	semidirect
7. C₁₀₁×#1799	C₂	semidirect
10. C₂×#126×C₁₀₁	C₄	semidirect
11. C₂×#125×C₁₀₁	C₄	semidirect
12. C₂×#123×C₁₀₁	C₄	semidirect
14. C₂×C₂²⋊Q₈×C₁₀₁	C₄	semidirect
204. #21877	C₁₀₁	direct (N × H)
214. #2316	C₂×C₁₀₁	semidirect
215. #2313	C₂×C₁₀₁	semidirect
216. #1996	C₂×C₁₀₁	semidirect
218. #1899	C₂×C₁₀₁	semidirect
219. #1799	C₂×C₁₀₁	semidirect
220. C₁₀₁	#21877	direct (N × H)
223. C₂×#126	C₄×C₁₀₁	semidirect
224. C₂×#125	C₄×C₁₀₁	semidirect
225. C₂×#123	C₄×C₁₀₁	semidirect
227. C₂×C₂²⋊Q₈	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₁₀₁	2
C₁₀₁×#2316	2
C₁₀₁×#2313	2
C₁₀₁×#1996	2
C₁₀₁×#1964	2
C₁₀₁×#1899	2
C₁₀₁×#1799	2
#21877	101

Subgroups — C101×#21877 #38804028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#21877 #38804028