Subgroups — C₁₀₁×#26253 #38808404

Order 25856.

866 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#495×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2448	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2055	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1970	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1970	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×#1880	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
17	#495×C₁₀₁	—	2	4	no	—
18	C₄×Q₁₆×C₁₀₁	—	2	4	no	—
19	C₂×#107×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
29	#399×C₁₀₁	—	2	2	no	—
30	#397×C₁₀₁	—	2	2	no	—
31	#391×C₁₀₁	C₂²	1	2	yes	—
32	#390×C₁₀₁	C₂²	1	2	yes	—
33	#390×C₁₀₁	C₂²	1	2	yes	—
34	#389×C₁₀₁	C₂²	1	2	yes	—
35	#388×C₁₀₁	—	2	2	no	—
36	#388×C₁₀₁	—	2	2	no	—
37	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
38	#340×C₁₀₁	C₂²	1	2	yes	—
39	#336×C₁₀₁	C₂²	1	1	yes	characteristic
40	#336×C₁₀₁	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
44	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
45	C₂×Q₁₆×C₁₀₁	D₄	1	4	yes	—
46	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
47	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
48	C₂×SD₁₆×C₁₀₁	—	4	2	no	—
49	C₂×D₈×C₁₀₁	—	2	2	no	—
50	C₂×D₈×C₁₀₁	—	2	2	no	—
51	C₂×D₈×C₁₀₁	—	2	2	no	—
52	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
56	#124×C₁₀₁	—	2	4	no	—
57	#124×C₁₀₁	—	4	2	no	—
58	C₄×Q₈×C₁₀₁	—	2	4	no	—
59	C₄×Q₈×C₁₀₁	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
72	C₂×C₄²×C₁₀₁	—	2	2	no	—
73	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
76	#107×C₁₀₁	—	2	2	no	—
77	#107×C₁₀₁	—	2	2	no	—
78	C₄⋊C₈×C₁₀₁	—	2	2	no	—
79	#103×C₁₀₁	—	2	4	no	—
80	#103×C₁₀₁	—	4	2	no	—
81	#102×C₁₀₁	—	4	2	no	—
82	#102×C₁₀₁	—	4	2	no	—
83	C₄×C₈×C₁₀₁	—	2	2	no	—
84	C₄×C₈×C₁₀₁	—	2	2	no	—
85	C₄×C₈×C₁₀₁	—	2	2	no	—
86	#95×C₁₀₁	—	2	2	no	—
87	#95×C₁₀₁	—	2	2	no	—
88	#95×C₁₀₁	—	2	2	no	—
89	#95×C₁₀₁	D₄	1	1	yes	characteristic
90	#95×C₁₀₁	D₄	1	1	yes	characteristic
91	C₂⁴×C₁₀₁	—	2	2	no	—
92	C₂×Q₈×C₁₀₁	—	2	2	no	—
93	C₂×Q₈×C₁₀₁	—	2	2	no	—
94	C₂×Q₈×C₁₀₁	—	2	2	no	—
95	C₂×Q₈×C₁₀₁	—	2	2	no	—
96	C₂×Q₈×C₁₀₁	—	2	2	no	—
97	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
98	C₂×D₄×C₁₀₁	—	2	2	no	—
99	C₂×D₄×C₁₀₁	—	2	2	no	—
100	C₂×D₄×C₁₀₁	—	2	2	no	—
101	C₂×D₄×C₁₀₁	—	2	2	no	—
102	C₂×D₄×C₁₀₁	—	2	2	no	—
103	C₂×D₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₁₀₁	—	2	8	no	—
115	SD₁₆×C₁₀₁	—	4	8	no	—
116	D₈×C₁₀₁	—	4	4	no	—
117	C₂×C₈×C₁₀₁	—	2	1	no	—
118	C₂×C₈×C₁₀₁	—	2	1	no	—
119	C₂×C₈×C₁₀₁	—	2	1	no	—
120	C₂×C₈×C₁₀₁	—	2	1	no	—
121	C₂×C₈×C₁₀₁	—	2	1	no	—
122	C₂×C₈×C₁₀₁	—	2	1	no	—
123	C₂×C₈×C₁₀₁	—	2	1	no	—
124	C₂×C₈×C₁₀₁	—	2	1	no	—
125	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₀₁	#41	1	2	yes	—
127	C₂×C₈×C₁₀₁	#41	1	2	yes	—
128	C₂×C₈×C₁₀₁	#41	1	2	yes	—
129	C₄⋊C₄×C₁₀₁	—	2	2	no	—
130	C₄⋊C₄×C₁₀₁	—	2	2	no	—
131	C₄⋊C₄×C₁₀₁	—	2	2	no	—
132	C₄⋊C₄×C₁₀₁	—	2	2	no	—
133	C₄⋊C₄×C₁₀₁	—	2	2	no	—
134	C₄⋊C₄×C₁₀₁	—	2	2	no	—
135	C₄⋊C₄×C₁₀₁	—	4	4	no	—
136	C₄⋊C₄×C₁₀₁	—	8	2	no	—
137	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
138	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
139	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
140	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
141	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
142	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
143	C₄²×C₁₀₁	—	2	1	no	—
144	C₄²×C₁₀₁	—	2	1	no	—
145	C₄²×C₁₀₁	—	2	1	no	—
146	C₄²×C₁₀₁	—	2	1	no	—
147	C₄²×C₁₀₁	—	2	1	no	—
148	C₄²×C₁₀₁	—	2	1	no	—
149	C₄²×C₁₀₁	—	4	4	no	—
150	C₂³×C₁₀₁	—	4	2	no	—
151	C₂³×C₁₀₁	—	4	2	no	—
152	C₂³×C₁₀₁	—	4	2	no	—
153	C₂³×C₁₀₁	—	4	2	no	—
154	C₂³×C₁₀₁	—	4	2	no	—
155	C₂³×C₁₀₁	—	4	2	no	—
156	C₂³×C₁₀₁	—	4	2	no	—
157	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₀₁	—	2	4	no	—
159	Q₈×C₁₀₁	—	2	4	no	—
160	Q₈×C₁₀₁	—	4	2	no	—
161	Q₈×C₁₀₁	—	4	2	no	—
162	D₄×C₁₀₁	—	4	2	no	—
163	D₄×C₁₀₁	—	4	2	no	—
164	D₄×C₁₀₁	—	4	2	no	—
165	D₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	2	1	no	—
167	C₂×C₄×C₁₀₁	—	2	1	no	—
168	C₂×C₄×C₁₀₁	—	2	1	no	—
169	C₂×C₄×C₁₀₁	—	2	1	no	—
170	C₂×C₄×C₁₀₁	—	2	1	no	—
171	C₂×C₄×C₁₀₁	—	2	1	no	—
172	C₂×C₄×C₁₀₁	—	2	1	no	—
173	C₂×C₄×C₁₀₁	—	2	1	no	—
174	C₂×C₄×C₁₀₁	—	2	4	no	—
175	C₂×C₄×C₁₀₁	—	2	1	no	—
176	C₂×C₄×C₁₀₁	—	2	1	no	—
177	C₂×C₄×C₁₀₁	—	2	1	no	—
178	C₂×C₄×C₁₀₁	—	2	1	no	—
179	C₂×C₄×C₁₀₁	—	2	1	no	—
180	C₂×C₄×C₁₀₁	—	2	1	no	—
181	C₂×C₄×C₁₀₁	—	2	1	no	—
182	C₂×C₄×C₁₀₁	—	2	1	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	4	2	no	—
191	C₂×C₄×C₁₀₁	#135	1	2	yes	—
192	C₂×C₄×C₁₀₁	#135	1	2	yes	—
193	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
199	C₈×C₁₀₁	—	2	2	no	—
200	C₈×C₁₀₁	—	4	1	no	—
201	C₈×C₁₀₁	—	4	1	no	—
202	C₈×C₁₀₁	#123	1	4	yes	—
203	C₂²×C₁₀₁	—	8	2	no	—
204	C₂²×C₁₀₁	—	8	2	no	—
205	C₂²×C₁₀₁	—	8	2	no	—
206	C₂²×C₁₀₁	—	8	2	no	—
207	C₂²×C₁₀₁	—	8	2	no	—
208	C₂²×C₁₀₁	—	8	2	no	—
209	C₂²×C₁₀₁	—	8	2	no	—
210	C₂²×C₁₀₁	#532	1	1	yes	characteristic
211	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
212	C₂²×C₁₀₁	#550	1	1	yes	characteristic
213	C₂²×C₁₀₁	C₂×#135	1	1	yes	characteristic
214	C₂²×C₁₀₁	C₂×#135	1	1	yes	characteristic
215	C₂²×C₁₀₁	#576	1	1	yes	characteristic
216	C₂²×C₁₀₁	#578	1	1	yes	characteristic
217	C₄×C₁₀₁	—	2	2	no	—
218	C₄×C₁₀₁	—	2	2	no	—
219	C₄×C₁₀₁	—	4	1	no	—
220	C₄×C₁₀₁	—	4	4	no	—
221	C₄×C₁₀₁	—	4	1	no	—
222	C₄×C₁₀₁	—	4	1	no	—
223	C₄×C₁₀₁	—	4	1	no	—
224	C₄×C₁₀₁	—	8	2	no	—
225	C₄×C₁₀₁	—	8	2	no	—
226	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
227	C₄×C₁₀₁	#540	1	1	yes	characteristic
228	C₄×C₁₀₁	#546	1	1	yes	characteristic
229	C₄×C₁₀₁	#559	1	1	yes	characteristic
230	#26253	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₁₀₁	—	16	2	no	—
232	C₂×C₁₀₁	#2445	1	1	yes	characteristic
233	C₂×C₁₀₁	#3168	1	1	yes	characteristic
234	C₂×C₁₀₁	#3175	1	1	yes	characteristic
235	C₂×C₁₀₁	#3285	1	1	yes	characteristic
236	C₂×C₁₀₁	#3287	1	1	yes	characteristic
237	C₂×C₁₀₁	#3393	1	1	yes	characteristic
238	C₂×C₁₀₁	#3396	1	1	yes	characteristic
239	C₂×#495	C₂×C₁₀₁	1	1	yes	characteristic
240	C₂×C₄×Q₁₆	C₂×C₁₀₁	1	1	yes	characteristic, complemented
241	#2448	C₂×C₁₀₁	1	2	yes	complemented
242	#2055	C₂×C₁₀₁	1	2	yes	complemented
243	#2042	C₂×C₁₀₁	1	2	yes	complemented
244	#1970	C₂×C₁₀₁	1	1	yes	characteristic
245	#1970	C₂×C₁₀₁	1	1	yes	characteristic
246	#1969	C₂×C₁₀₁	1	1	yes	characteristic, complemented
247	#1942	C₂×C₁₀₁	1	1	yes	characteristic, complemented
248	#1880	C₂×C₁₀₁	1	2	yes	complemented
249	C₈×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic, complemented
250	C₁₀₁	#26253	1	1	yes	characteristic, direct product factor, Sylow
251	C₂²×Q₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
252	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
253	C₂²×D₈	C₂²×C₁₀₁	1	1	yes	characteristic
254	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
255	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
256	#495	—	2	4	no	—
257	C₄×Q₁₆	—	2	4	no	—
258	C₂×#107	C₂²×C₁₀₁	1	1	yes	characteristic
259	C₂×#107	C₂²×C₁₀₁	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
261	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
262	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
263	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
264	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
266	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
268	#399	—	2	2	no	—
269	#397	—	2	2	no	—
270	#391	C₂²×C₁₀₁	1	2	yes	—
271	#390	C₂²×C₁₀₁	1	2	yes	—
272	#390	C₂²×C₁₀₁	1	2	yes	—
273	#389	C₂²×C₁₀₁	1	2	yes	—
274	#388	—	2	2	no	—
275	#388	—	2	2	no	—
276	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
277	#340	C₂²×C₁₀₁	1	2	yes	—
278	#336	C₂²×C₁₀₁	1	1	yes	characteristic
279	#336	C₂²×C₁₀₁	1	1	yes	characteristic
280	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
281	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	D₄×C₁₀₁	1	4	yes	—
285	C₂×SD₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×SD₁₆	—	4	2	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
295	#124	—	2	4	no	—
296	#124	—	4	2	no	—
297	C₄×Q₈	—	2	4	no	—
298	C₄×Q₈	—	4	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
315	#107	—	2	2	no	—
316	#107	—	2	2	no	—
317	C₄⋊C₈	—	2	2	no	—
318	#103	—	2	4	no	—
319	#103	—	4	2	no	—
320	#102	—	4	2	no	—
321	#102	—	4	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	D₄×C₁₀₁	1	1	yes	characteristic
329	#95	D₄×C₁₀₁	1	1	yes	characteristic
330	C₂⁴	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
353	Q₁₆	—	2	8	no	—
354	SD₁₆	—	4	8	no	—
355	D₈	—	4	4	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
365	C₂×C₈	#41×C₁₀₁	1	2	yes	—
366	C₂×C₈	#41×C₁₀₁	1	2	yes	—
367	C₂×C₈	#41×C₁₀₁	1	2	yes	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	4	4	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	#135×C₁₀₁	1	2	yes	—
431	C₂×C₄	#135×C₁₀₁	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
436	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
437	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	1	no	—
441	C₈	#123×C₁₀₁	1	4	yes	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	#532×C₁₀₁	1	1	yes	characteristic
450	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
451	C₂²	#550×C₁₀₁	1	1	yes	characteristic
452	C₂²	C₂×#135×C₁₀₁	1	1	yes	characteristic
453	C₂²	C₂×#135×C₁₀₁	1	1	yes	characteristic
454	C₂²	#576×C₁₀₁	1	1	yes	characteristic
455	C₂²	#578×C₁₀₁	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	8	2	no	—
464	C₄	—	8	2	no	—
465	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
466	C₄	#540×C₁₀₁	1	1	yes	characteristic
467	C₄	#546×C₁₀₁	1	1	yes	characteristic
468	C₄	#559×C₁₀₁	1	1	yes	characteristic
469	C₂	—	16	2	no	—
470	C₂	C₁₀₁×#2445	1	1	yes	characteristic
471	C₂	C₁₀₁×#3168	1	1	yes	characteristic
472	C₂	C₁₀₁×#3175	1	1	yes	characteristic
473	C₂	C₁₀₁×#3285	1	1	yes	characteristic
474	C₂	C₁₀₁×#3287	1	1	yes	characteristic
475	C₂	C₁₀₁×#3393	1	1	yes	characteristic
476	C₂	C₁₀₁×#3396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×D₈×C₁₀₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₄×C₄⋊C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₁₀₁	C₂	semidirect
3. C₁₀₁×#2448	C₂	semidirect
4. C₁₀₁×#2055	C₂	semidirect
5. C₁₀₁×#2042	C₂	semidirect
8. C₁₀₁×#1969	C₂	semidirect
9. C₁₀₁×#1942	C₂	semidirect
10. C₁₀₁×#1880	C₂	semidirect
11. C₈×C₄⋊C₄×C₁₀₁	C₂	semidirect
230. #26253	C₁₀₁	direct (N × H)
240. C₂×C₄×Q₁₆	C₂×C₁₀₁	semidirect
241. #2448	C₂×C₁₀₁	semidirect
242. #2055	C₂×C₁₀₁	semidirect
243. #2042	C₂×C₁₀₁	semidirect
246. #1969	C₂×C₁₀₁	semidirect
247. #1942	C₂×C₁₀₁	semidirect
248. #1880	C₂×C₁₀₁	semidirect
249. C₈×C₄⋊C₄	C₂×C₁₀₁	semidirect
250. C₁₀₁	#26253	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#495×C₁₀₁	2
C₂×C₄×Q₁₆×C₁₀₁	2
C₁₀₁×#2448	2
C₁₀₁×#2055	2
C₁₀₁×#2042	2
C₁₀₁×#1970	2
C₁₀₁×#1969	2
C₁₀₁×#1942	2
C₁₀₁×#1880	2
C₈×C₄⋊C₄×C₁₀₁	2
#26253	101

Subgroups — C101×#26253 #38808404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#26253 #38808404