Subgroups — C₁₀₁×#22330 #38804481

Order 25856.

832 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#2392	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#1954	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1924	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1916	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1869	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1869	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1818	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₂²⋊C₄×C₁₀₁	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
24	#398×C₁₀₁	C₄	1	1	yes	characteristic
25	#397×C₁₀₁	C₄	1	1	yes	characteristic
26	#396×C₁₀₁	C₄	1	2	yes	—
27	#394×C₁₀₁	C₄	1	1	yes	characteristic
28	#394×C₁₀₁	C₄	1	2	yes	—
29	#392×C₁₀₁	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
32	#336×C₁₀₁	C₂²	1	2	yes	—
33	#336×C₁₀₁	C₂²	1	2	yes	—
34	#336×C₁₀₁	C₂²	1	2	yes	—
35	#336×C₁₀₁	C₂²	1	2	yes	—
36	#336×C₁₀₁	C₂²	1	2	yes	—
37	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₀₁	—	2	4	no	—
42	C₂²×C₈×C₁₀₁	—	4	2	no	—
43	C₂²×C₈×C₁₀₁	—	4	2	no	—
44	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
48	C₄×D₄×C₁₀₁	—	4	2	no	—
49	C₄×D₄×C₁₀₁	—	4	2	no	—
50	C₄×D₄×C₁₀₁	—	4	1	no	—
51	C₄×D₄×C₁₀₁	—	4	1	no	—
52	#117×C₁₀₁	—	4	1	no	—
53	#117×C₁₀₁	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₁₀₁	—	4	2	no	—
70	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
71	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
72	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
73	C₂²⋊C₈×C₁₀₁	—	4	1	no	—
74	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
75	C₂²⋊C₈×C₁₀₁	—	4	1	no	—
76	#97×C₁₀₁	—	4	1	no	—
77	C₄×C₈×C₁₀₁	—	4	1	no	—
78	C₄×C₈×C₁₀₁	—	4	2	no	—
79	#95×C₁₀₁	C₂×C₄	1	2	yes	—
80	#95×C₁₀₁	C₂×C₄	1	1	yes	characteristic
81	#95×C₁₀₁	C₂×C₄	1	2	yes	—
82	#95×C₁₀₁	C₂×C₄	1	1	yes	characteristic
83	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
84	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₁₀₁	—	2	4	no	—
86	C₂×D₄×C₁₀₁	—	2	4	no	—
87	C₂×D₄×C₁₀₁	—	2	4	no	—
88	C₂×D₄×C₁₀₁	—	4	2	no	—
89	C₂×D₄×C₁₀₁	—	4	1	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	1	no	—
94	C₂²×C₄×C₁₀₁	—	2	1	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₀₁	—	2	2	no	—
110	C₂×C₈×C₁₀₁	—	2	2	no	—
111	C₂×C₈×C₁₀₁	—	2	2	no	—
112	C₂×C₈×C₁₀₁	—	2	2	no	—
113	C₂×C₈×C₁₀₁	—	2	2	no	—
114	C₂×C₈×C₁₀₁	—	2	2	no	—
115	C₂×C₈×C₁₀₁	—	2	2	no	—
116	C₂×C₈×C₁₀₁	—	2	2	no	—
117	C₂×C₈×C₁₀₁	—	2	2	no	—
118	C₂×C₈×C₁₀₁	—	2	2	no	—
119	C₂×C₈×C₁₀₁	—	2	2	no	—
120	C₂×C₈×C₁₀₁	—	4	8	no	—
121	C₂×C₈×C₁₀₁	#41	1	4	yes	—
122	C₄⋊C₄×C₁₀₁	—	2	4	no	—
123	C₄⋊C₄×C₁₀₁	—	4	1	no	—
124	C₄⋊C₄×C₁₀₁	—	4	1	no	—
125	C₄⋊C₄×C₁₀₁	—	4	2	no	—
126	C₄⋊C₄×C₁₀₁	—	4	1	no	—
127	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
128	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
129	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
130	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
131	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
132	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
133	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
134	C₄²×C₁₀₁	—	2	1	no	—
135	C₄²×C₁₀₁	—	2	2	no	—
136	C₄²×C₁₀₁	—	2	1	no	—
137	C₄²×C₁₀₁	—	2	2	no	—
138	C₄²×C₁₀₁	—	2	1	no	—
139	C₄²×C₁₀₁	—	2	1	no	—
140	C₂³×C₁₀₁	—	2	2	no	—
141	C₂³×C₁₀₁	—	2	2	no	—
142	C₂³×C₁₀₁	—	2	2	no	—
143	C₂³×C₁₀₁	—	2	2	no	—
144	C₂³×C₁₀₁	—	2	2	no	—
145	C₂³×C₁₀₁	—	2	2	no	—
146	C₂³×C₁₀₁	—	2	1	no	—
147	C₂³×C₁₀₁	—	2	1	no	—
148	C₂³×C₁₀₁	—	2	1	no	—
149	C₂³×C₁₀₁	—	2	2	no	—
150	C₂³×C₁₀₁	—	2	2	no	—
151	C₂³×C₁₀₁	#131	1	4	yes	—
152	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
153	D₄×C₁₀₁	—	4	8	no	—
154	D₄×C₁₀₁	—	4	4	no	—
155	C₂×C₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	1	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	1	no	—
160	C₂×C₄×C₁₀₁	—	2	2	no	—
161	C₂×C₄×C₁₀₁	—	2	1	no	—
162	C₂×C₄×C₁₀₁	—	2	1	no	—
163	C₂×C₄×C₁₀₁	—	2	1	no	—
164	C₂×C₄×C₁₀₁	—	2	1	no	—
165	C₂×C₄×C₁₀₁	—	2	2	no	—
166	C₂×C₄×C₁₀₁	—	2	2	no	—
167	C₂×C₄×C₁₀₁	—	2	1	no	—
168	C₂×C₄×C₁₀₁	—	2	2	no	—
169	C₂×C₄×C₁₀₁	—	2	2	no	—
170	C₂×C₄×C₁₀₁	—	2	2	no	—
171	C₂×C₄×C₁₀₁	—	2	2	no	—
172	C₂×C₄×C₁₀₁	—	2	2	no	—
173	C₂×C₄×C₁₀₁	—	2	2	no	—
174	C₂×C₄×C₁₀₁	—	4	2	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	2	no	—
177	C₂×C₄×C₁₀₁	—	4	2	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	2	no	—
180	C₂×C₄×C₁₀₁	#131	1	4	yes	—
181	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
184	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
185	C₈×C₁₀₁	—	2	4	no	—
186	C₈×C₁₀₁	—	4	2	no	—
187	C₈×C₁₀₁	—	4	2	no	—
188	C₈×C₁₀₁	—	4	2	no	—
189	C₂²×C₁₀₁	—	2	4	no	—
190	C₂²×C₁₀₁	—	2	4	no	—
191	C₂²×C₁₀₁	—	2	4	no	—
192	C₂²×C₁₀₁	—	4	2	no	—
193	C₂²×C₁₀₁	—	4	2	no	—
194	C₂²×C₁₀₁	—	4	2	no	—
195	C₂²×C₁₀₁	—	4	2	no	—
196	C₂²×C₁₀₁	—	4	1	no	—
197	C₂²×C₁₀₁	—	4	2	no	—
198	C₂²×C₁₀₁	—	4	2	no	—
199	C₂²×C₁₀₁	—	4	1	no	—
200	C₂²×C₁₀₁	—	4	1	no	—
201	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
202	C₂²×C₁₀₁	#518	1	1	yes	characteristic
203	C₂²×C₁₀₁	#518	1	1	yes	characteristic
204	C₂²×C₁₀₁	C₂×#131	1	2	yes	—
205	C₂²×C₁₀₁	C₂×#131	1	2	yes	—
206	C₄×C₁₀₁	—	2	4	no	—
207	C₄×C₁₀₁	—	4	1	no	—
208	C₄×C₁₀₁	—	4	2	no	—
209	C₄×C₁₀₁	—	4	2	no	—
210	C₄×C₁₀₁	—	4	1	no	—
211	C₄×C₁₀₁	—	4	1	no	—
212	C₄×C₁₀₁	—	4	1	no	—
213	C₄×C₁₀₁	—	4	1	no	—
214	C₄×C₁₀₁	#538	1	2	yes	—
215	C₄×C₁₀₁	#540	1	2	yes	—
216	#22330	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₁₀₁	—	4	4	no	—
218	C₂×C₁₀₁	—	8	1	no	—
219	C₂×C₁₀₁	#2333	1	1	yes	characteristic
220	C₂×C₁₀₁	#2966	1	2	yes	—
221	C₂×C₁₀₁	#2977	1	2	yes	—
222	C₂×C₁₀₁	#2977	1	1	yes	characteristic
223	C₂×C₁₀₁	#2979	1	1	yes	characteristic
224	#2392	C₂×C₁₀₁	1	1	yes	characteristic
225	#1954	C₂×C₁₀₁	1	2	yes	complemented
226	#1924	C₂×C₁₀₁	1	2	yes	complemented
227	#1916	C₂×C₁₀₁	1	2	yes	complemented
228	#1869	C₂×C₁₀₁	1	2	yes	complemented
229	#1869	C₂×C₁₀₁	1	2	yes	complemented
230	#1818	C₂×C₁₀₁	1	1	yes	characteristic, complemented
231	C₈×C₂²⋊C₄	C₂×C₁₀₁	1	2	yes	complemented
232	#1750	C₂×C₁₀₁	1	1	yes	characteristic, complemented
233	C₁₀₁	#22330	1	1	yes	characteristic, direct product factor, Sylow
234	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
235	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
237	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
244	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
245	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
248	#398	C₄×C₁₀₁	1	1	yes	characteristic
249	#397	C₄×C₁₀₁	1	1	yes	characteristic
250	#396	C₄×C₁₀₁	1	2	yes	—
251	#394	C₄×C₁₀₁	1	2	yes	—
252	#394	C₄×C₁₀₁	1	1	yes	characteristic
253	#392	C₄×C₁₀₁	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
255	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
256	#336	C₂²×C₁₀₁	1	2	yes	—
257	#336	C₂²×C₁₀₁	1	2	yes	—
258	#336	C₂²×C₁₀₁	1	2	yes	—
259	#336	C₂²×C₁₀₁	1	2	yes	—
260	#336	C₂²×C₁₀₁	1	2	yes	—
261	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
262	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
263	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	4	2	no	—
267	C₂²×C₈	—	4	2	no	—
268	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
272	C₄×D₄	—	4	2	no	—
273	C₄×D₄	—	4	2	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	4	1	no	—
276	#117	—	4	1	no	—
277	#117	—	4	1	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
282	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
293	C₄⋊C₈	—	4	2	no	—
294	C₂²⋊C₈	—	2	4	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	C₂²⋊C₈	—	4	2	no	—
297	C₂²⋊C₈	—	4	1	no	—
298	C₂²⋊C₈	—	4	2	no	—
299	C₂²⋊C₈	—	4	1	no	—
300	#97	—	4	1	no	—
301	C₄×C₈	—	4	1	no	—
302	C₄×C₈	—	4	2	no	—
303	#95	C₂×C₄×C₁₀₁	1	2	yes	—
304	#95	C₂×C₄×C₁₀₁	1	2	yes	—
305	#95	C₂×C₄×C₁₀₁	1	1	yes	characteristic
306	#95	C₂×C₄×C₁₀₁	1	1	yes	characteristic
307	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
308	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	4	8	no	—
345	C₂×C₈	#41×C₁₀₁	1	4	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	#131×C₁₀₁	1	4	yes	—
376	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
377	D₄	—	4	8	no	—
378	D₄	—	4	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	#131×C₁₀₁	1	4	yes	—
405	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
406	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
407	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
408	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
426	C₂²	#518×C₁₀₁	1	1	yes	characteristic
427	C₂²	#518×C₁₀₁	1	1	yes	characteristic
428	C₂²	C₂×#131×C₁₀₁	1	2	yes	—
429	C₂²	C₂×#131×C₁₀₁	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	2	no	—
438	C₄	#538×C₁₀₁	1	2	yes	—
439	C₄	#540×C₁₀₁	1	2	yes	—
440	C₂	—	4	4	no	—
441	C₂	—	8	1	no	—
442	C₂	C₁₀₁×#2333	1	1	yes	characteristic
443	C₂	C₁₀₁×#2966	1	2	yes	—
444	C₂	C₁₀₁×#2977	1	2	yes	—
445	C₂	C₁₀₁×#2977	1	1	yes	characteristic
446	C₂	C₁₀₁×#2979	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂³×C₄
prime radical	#392×C₁₀₁	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#1954	C₂	semidirect
3. C₁₀₁×#1924	C₂	semidirect
4. C₁₀₁×#1916	C₂	semidirect
5. C₁₀₁×#1869	C₂	semidirect
6. C₁₀₁×#1869	C₂	semidirect
7. C₁₀₁×#1818	C₂	semidirect
8. C₈×C₂²⋊C₄×C₁₀₁	C₂	semidirect
9. C₁₀₁×#1750	C₂	semidirect
216. #22330	C₁₀₁	direct (N × H)
225. #1954	C₂×C₁₀₁	semidirect
226. #1924	C₂×C₁₀₁	semidirect
227. #1916	C₂×C₁₀₁	semidirect
228. #1869	C₂×C₁₀₁	semidirect
229. #1869	C₂×C₁₀₁	semidirect
230. #1818	C₂×C₁₀₁	semidirect
231. C₈×C₂²⋊C₄	C₂×C₁₀₁	semidirect
232. #1750	C₂×C₁₀₁	semidirect
233. C₁₀₁	#22330	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₁×#2392	2
C₁₀₁×#1954	2
C₁₀₁×#1924	2
C₁₀₁×#1916	2
C₁₀₁×#1869	2
C₁₀₁×#1818	2
C₈×C₂²⋊C₄×C₁₀₁	2
C₁₀₁×#1750	2
#22330	101

Subgroups — C101×#22330 #38804481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#22330 #38804481