Subgroups — C₁₀₁×#22049 #38804200

Order 25856.

1212 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#450×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#390×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1973	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1936	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1925	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1880	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×#1786	C₂	1	1	yes	maximal, characteristic
11	C₁₀₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
18	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
20	#450×C₁₀₁	C₄	1	8	yes	complemented
21	C₂×#107×C₁₀₁	C₂²	1	2	yes	complemented
22	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
23	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₁₀₁	C₂²	1	2	yes	complemented
29	#391×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
30	#390×C₁₀₁	—	2	1	no	—
31	#390×C₁₀₁	—	2	1	no	—
32	#390×C₁₀₁	C₂²	1	2	yes	—
33	#390×C₁₀₁	C₂²	1	2	yes	—
34	#389×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
35	#387×C₁₀₁	—	2	1	no	—
36	#385×C₁₀₁	—	2	1	no	—
37	#380×C₁₀₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₀₁	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
41	#340×C₁₀₁	C₂²	1	2	yes	complemented
42	#340×C₁₀₁	C₂²	1	2	yes	complemented
43	#336×C₁₀₁	C₂²	1	2	yes	complemented
44	C₂⁵×C₁₀₁	—	2	1	no	—
45	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₀₁	—	2	1	no	—
47	C₂²×D₄×C₁₀₁	—	2	2	no	—
48	C₂²×D₄×C₁₀₁	—	4	2	no	—
49	C₂²×D₄×C₁₀₁	—	4	2	no	—
50	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
51	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₀₁	—	2	1	no	—
53	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₁₀₁	—	4	2	no	—
57	C₂×SD₁₆×C₁₀₁	—	4	2	no	—
58	C₂×SD₁₆×C₁₀₁	C₂×C₄	1	8	yes	complemented
59	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
61	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
62	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₁₀₁	—	4	2	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
69	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
80	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
81	C₂×C₄²×C₁₀₁	—	2	1	no	—
82	C₂×C₄²×C₁₀₁	—	2	1	no	—
83	C₂×C₄²×C₁₀₁	—	4	2	no	—
84	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
88	#107×C₁₀₁	—	4	2	no	—
89	#103×C₁₀₁	—	4	2	no	—
90	#102×C₁₀₁	—	4	2	no	—
91	#102×C₁₀₁	—	4	2	no	—
92	#102×C₁₀₁	C₂×C₄	1	8	yes	complemented
93	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
94	C₂²⋊C₈×C₁₀₁	C₂×C₄	1	4	yes	—
95	#97×C₁₀₁	—	4	2	no	—
96	#95×C₁₀₁	—	2	1	no	—
97	#95×C₁₀₁	—	2	1	no	—
98	#95×C₁₀₁	—	2	1	no	—
99	#95×C₁₀₁	—	2	1	no	—
100	#95×C₁₀₁	—	2	1	no	—
101	C₂⁴×C₁₀₁	—	2	4	no	—
102	C₂⁴×C₁₀₁	—	2	2	no	—
103	C₂⁴×C₁₀₁	—	4	2	no	—
104	C₂⁴×C₁₀₁	—	4	2	no	—
105	C₂⁴×C₁₀₁	—	4	2	no	—
106	C₂⁴×C₁₀₁	—	4	2	no	—
107	C₂⁴×C₁₀₁	—	4	2	no	—
108	C₂⁴×C₁₀₁	—	4	2	no	—
109	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₀₁	—	2	1	no	—
111	C₂×Q₈×C₁₀₁	—	2	2	no	—
112	C₂×Q₈×C₁₀₁	—	2	2	no	—
113	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
114	C₂×D₄×C₁₀₁	—	2	4	no	—
115	C₂×D₄×C₁₀₁	—	2	2	no	—
116	C₂×D₄×C₁₀₁	—	2	2	no	—
117	C₂×D₄×C₁₀₁	—	2	2	no	—
118	C₂×D₄×C₁₀₁	—	2	2	no	—
119	C₂×D₄×C₁₀₁	—	2	2	no	—
120	C₂×D₄×C₁₀₁	—	4	8	no	—
121	C₂×D₄×C₁₀₁	—	4	2	no	—
122	C₂×D₄×C₁₀₁	—	4	2	no	—
123	C₂×D₄×C₁₀₁	—	4	8	no	—
124	C₂×D₄×C₁₀₁	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	—	2	2	no	—
129	C₂²×C₄×C₁₀₁	—	2	1	no	—
130	C₂²×C₄×C₁₀₁	—	2	1	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	1	no	—
133	C₂²×C₄×C₁₀₁	—	2	1	no	—
134	C₂²×C₄×C₁₀₁	—	2	2	no	—
135	C₂²×C₄×C₁₀₁	—	4	1	no	—
136	C₂²×C₄×C₁₀₁	—	4	1	no	—
137	C₂²×C₄×C₁₀₁	—	4	1	no	—
138	C₂²×C₄×C₁₀₁	—	4	2	no	—
139	C₂²×C₄×C₁₀₁	—	4	2	no	—
140	C₂²×C₄×C₁₀₁	—	4	2	no	—
141	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
148	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₁₀₁	—	4	8	no	—
150	C₂×C₈×C₁₀₁	—	2	2	no	—
151	C₂×C₈×C₁₀₁	—	2	2	no	—
152	C₂×C₈×C₁₀₁	—	2	2	no	—
153	C₂×C₈×C₁₀₁	—	2	2	no	—
154	C₂×C₈×C₁₀₁	—	2	2	no	—
155	C₂×C₈×C₁₀₁	C₂²×C₄	1	4	yes	—
156	C₄⋊C₄×C₁₀₁	—	2	4	no	—
157	C₄⋊C₄×C₁₀₁	—	2	1	no	—
158	C₄⋊C₄×C₁₀₁	—	2	2	no	—
159	C₄⋊C₄×C₁₀₁	—	2	2	no	—
160	C₄⋊C₄×C₁₀₁	—	2	2	no	—
161	C₄⋊C₄×C₁₀₁	—	2	2	no	—
162	C₄⋊C₄×C₁₀₁	—	4	2	no	—
163	C₄⋊C₄×C₁₀₁	—	4	2	no	—
164	C₄⋊C₄×C₁₀₁	—	4	2	no	—
165	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
166	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
167	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
168	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
169	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
170	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
171	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
172	C₄²×C₁₀₁	—	2	2	no	—
173	C₄²×C₁₀₁	—	2	2	no	—
174	C₄²×C₁₀₁	—	4	1	no	—
175	C₄²×C₁₀₁	—	4	1	no	—
176	C₄²×C₁₀₁	—	4	2	no	—
177	C₄²×C₁₀₁	—	4	2	no	—
178	C₂³×C₁₀₁	—	2	1	no	—
179	C₂³×C₁₀₁	—	2	1	no	—
180	C₂³×C₁₀₁	—	2	1	no	—
181	C₂³×C₁₀₁	—	2	1	no	—
182	C₂³×C₁₀₁	—	2	4	no	—
183	C₂³×C₁₀₁	—	4	8	no	—
184	C₂³×C₁₀₁	—	4	8	no	—
185	C₂³×C₁₀₁	—	4	2	no	—
186	C₂³×C₁₀₁	—	4	2	no	—
187	C₂³×C₁₀₁	—	4	2	no	—
188	C₂³×C₁₀₁	—	4	2	no	—
189	C₂³×C₁₀₁	—	4	2	no	—
190	C₂³×C₁₀₁	—	4	2	no	—
191	C₂³×C₁₀₁	—	4	8	no	—
192	C₂³×C₁₀₁	—	8	4	no	—
193	C₂³×C₁₀₁	—	8	4	no	—
194	C₂³×C₁₀₁	—	8	4	no	—
195	C₂³×C₁₀₁	—	8	4	no	—
196	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
197	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
198	C₂³×C₁₀₁	#137	1	2	yes	—
199	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₀₁	—	2	4	no	—
201	Q₈×C₁₀₁	—	4	2	no	—
202	D₄×C₁₀₁	—	2	4	no	—
203	D₄×C₁₀₁	—	2	4	no	—
204	D₄×C₁₀₁	—	4	8	no	—
205	D₄×C₁₀₁	—	4	2	no	—
206	D₄×C₁₀₁	—	4	2	no	—
207	C₂×C₄×C₁₀₁	—	2	1	no	—
208	C₂×C₄×C₁₀₁	—	2	1	no	—
209	C₂×C₄×C₁₀₁	—	2	1	no	—
210	C₂×C₄×C₁₀₁	—	2	1	no	—
211	C₂×C₄×C₁₀₁	—	2	4	no	—
212	C₂×C₄×C₁₀₁	—	2	4	no	—
213	C₂×C₄×C₁₀₁	—	2	2	no	—
214	C₂×C₄×C₁₀₁	—	2	2	no	—
215	C₂×C₄×C₁₀₁	—	2	1	no	—
216	C₂×C₄×C₁₀₁	—	2	1	no	—
217	C₂×C₄×C₁₀₁	—	2	1	no	—
218	C₂×C₄×C₁₀₁	—	2	1	no	—
219	C₂×C₄×C₁₀₁	—	2	1	no	—
220	C₂×C₄×C₁₀₁	—	2	1	no	—
221	C₂×C₄×C₁₀₁	—	2	1	no	—
222	C₂×C₄×C₁₀₁	—	2	1	no	—
223	C₂×C₄×C₁₀₁	—	2	1	no	—
224	C₂×C₄×C₁₀₁	—	4	4	no	—
225	C₂×C₄×C₁₀₁	—	4	4	no	—
226	C₂×C₄×C₁₀₁	—	4	1	no	—
227	C₂×C₄×C₁₀₁	—	4	1	no	—
228	C₂×C₄×C₁₀₁	—	4	1	no	—
229	C₂×C₄×C₁₀₁	—	4	1	no	—
230	C₂×C₄×C₁₀₁	—	4	1	no	—
231	C₂×C₄×C₁₀₁	—	4	2	no	—
232	C₂×C₄×C₁₀₁	—	4	1	no	—
233	C₂×C₄×C₁₀₁	—	4	1	no	—
234	C₂×C₄×C₁₀₁	—	4	2	no	—
235	C₂×C₄×C₁₀₁	—	4	2	no	—
236	C₂×C₄×C₁₀₁	—	4	1	no	—
237	C₂×C₄×C₁₀₁	—	4	1	no	—
238	C₂×C₄×C₁₀₁	—	4	1	no	—
239	C₂×C₄×C₁₀₁	—	8	4	no	—
240	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
245	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
246	C₈×C₁₀₁	—	2	4	no	—
247	C₈×C₁₀₁	—	4	2	no	—
248	C₂²×C₁₀₁	—	2	2	no	—
249	C₂²×C₁₀₁	—	2	2	no	—
250	C₂²×C₁₀₁	—	2	2	no	—
251	C₂²×C₁₀₁	—	2	2	no	—
252	C₂²×C₁₀₁	—	2	2	no	—
253	C₂²×C₁₀₁	—	2	2	no	—
254	C₂²×C₁₀₁	—	4	4	no	—
255	C₂²×C₁₀₁	—	4	4	no	—
256	C₂²×C₁₀₁	—	4	4	no	—
257	C₂²×C₁₀₁	—	8	16	no	—
258	C₂²×C₁₀₁	—	8	2	no	—
259	C₂²×C₁₀₁	—	8	2	no	—
260	C₂²×C₁₀₁	—	8	2	no	—
261	C₂²×C₁₀₁	—	8	2	no	—
262	C₂²×C₁₀₁	#440	1	4	yes	—
263	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂²×C₁₀₁	#534	1	1	yes	characteristic
265	C₂²×C₁₀₁	#535	1	1	yes	characteristic
266	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₂²×C₁₀₁	C₂×#137	1	1	yes	characteristic
269	C₂²×C₁₀₁	#575	1	1	yes	characteristic
270	C₄×C₁₀₁	—	2	2	no	—
271	C₄×C₁₀₁	—	2	2	no	—
272	C₄×C₁₀₁	—	4	2	no	—
273	C₄×C₁₀₁	—	4	1	no	—
274	C₄×C₁₀₁	—	4	1	no	—
275	C₄×C₁₀₁	—	4	1	no	—
276	C₄×C₁₀₁	—	4	2	no	—
277	C₄×C₁₀₁	—	8	1	no	—
278	C₄×C₁₀₁	—	8	1	no	—
279	C₄×C₁₀₁	—	8	2	no	—
280	C₄×C₁₀₁	#518	1	2	yes	—
281	C₄×C₁₀₁	#538	1	2	yes	—
282	#22049	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂×C₁₀₁	—	2	4	no	—
284	C₂×C₁₀₁	—	8	4	no	—
285	C₂×C₁₀₁	#2321	1	1	yes	characteristic
286	C₂×C₁₀₁	C₂×#440	1	1	yes	characteristic
287	C₂×C₁₀₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂×C₁₀₁	#3193	1	1	yes	characteristic
289	C₂×C₁₀₁	#3194	1	1	yes	characteristic
290	C₂×C₁₀₁	#3215	1	1	yes	characteristic
291	C₂×C₁₀₁	#3217	1	1	yes	characteristic
292	C₂×#450	C₂×C₁₀₁	1	1	yes	characteristic
293	C₄×C₂²⋊Q₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
294	C₂×#390	C₂×C₁₀₁	1	1	yes	characteristic
295	#1973	C₂×C₁₀₁	1	2	yes	complemented
296	#1936	C₂×C₁₀₁	1	2	yes	complemented
297	#1925	C₂×C₁₀₁	1	2	yes	complemented
298	#1880	C₂×C₁₀₁	1	2	yes	complemented
299	#1872	C₂×C₁₀₁	1	1	yes	characteristic, complemented
300	#1852	C₂×C₁₀₁	1	1	yes	characteristic, complemented
301	#1786	C₂×C₁₀₁	1	1	yes	characteristic
302	#1749	C₂×C₁₀₁	1	1	yes	characteristic, complemented
303	C₁₀₁	#22049	1	1	yes	characteristic, direct product factor, Sylow
304	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
305	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
306	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
308	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	—	2	1	no	—
310	C₂²×C₂²⋊C₄	—	2	1	no	—
311	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
312	#450	C₄×C₁₀₁	1	8	yes	complemented
313	C₂×#107	C₂²×C₁₀₁	1	2	yes	complemented
314	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
315	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
316	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
317	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
318	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
320	C₂×#97	C₂²×C₁₀₁	1	2	yes	complemented
321	#391	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
322	#390	—	2	1	no	—
323	#390	—	2	1	no	—
324	#390	C₂²×C₁₀₁	1	2	yes	—
325	#390	C₂²×C₁₀₁	1	2	yes	—
326	#389	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
327	#387	—	2	1	no	—
328	#385	—	2	1	no	—
329	#380	C₂²×C₁₀₁	1	1	yes	characteristic
330	C₄×C₄⋊C₄	—	2	1	no	—
331	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
332	C₄×C₂²⋊C₄	—	2	1	no	—
333	#340	C₂²×C₁₀₁	1	2	yes	complemented
334	#340	C₂²×C₁₀₁	1	2	yes	complemented
335	#336	C₂²×C₁₀₁	1	2	yes	complemented
336	C₂⁵	—	2	1	no	—
337	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	4	2	no	—
341	C₂²×D₄	—	4	2	no	—
342	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
343	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
346	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
348	C₂×SD₁₆	—	4	2	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂×SD₁₆	C₂×C₄×C₁₀₁	1	8	yes	complemented
351	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
352	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
355	C₄×Q₈	—	4	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	4	2	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	4	4	no	—
372	C₂×C₂²⋊C₄	—	4	4	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	4	2	no	—
376	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
377	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
380	#107	—	4	2	no	—
381	#103	—	4	2	no	—
382	#102	—	4	2	no	—
383	#102	—	4	2	no	—
384	#102	C₂×C₄×C₁₀₁	1	8	yes	complemented
385	C₂²⋊C₈	—	2	2	no	—
386	C₂²⋊C₈	C₂×C₄×C₁₀₁	1	4	yes	—
387	#97	—	4	2	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	C₂⁴	—	2	4	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	2	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	C₂²×C₄×C₁₀₁	1	4	yes	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
439	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
441	SD₁₆	—	4	8	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	C₂²×C₄×C₁₀₁	1	4	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	4	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	4	1	no	—
467	C₄²	—	4	1	no	—
468	C₄²	—	4	2	no	—
469	C₄²	—	4	2	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	4	8	no	—
476	C₂³	—	4	8	no	—
477	C₂³	—	4	8	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	4	no	—
487	C₂³	—	8	4	no	—
488	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
489	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
490	C₂³	#137×C₁₀₁	1	2	yes	—
491	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
492	Q₈	—	2	4	no	—
493	Q₈	—	4	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	4	8	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
533	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
534	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
536	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
537	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
538	C₈	—	2	4	no	—
539	C₈	—	4	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	8	16	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	#440×C₁₀₁	1	4	yes	—
555	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
556	C₂²	#534×C₁₀₁	1	1	yes	characteristic
557	C₂²	#535×C₁₀₁	1	1	yes	characteristic
558	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
559	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
560	C₂²	C₂×#137×C₁₀₁	1	1	yes	characteristic
561	C₂²	#575×C₁₀₁	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	1	no	—
572	C₄	#518×C₁₀₁	1	2	yes	—
573	C₄	#538×C₁₀₁	1	2	yes	—
574	C₂	—	2	4	no	—
575	C₂	—	8	4	no	—
576	C₂	C₁₀₁×#2321	1	1	yes	characteristic
577	C₂	C₂×#440×C₁₀₁	1	1	yes	characteristic
578	C₂	C₄×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
579	C₂	C₁₀₁×#3193	1	1	yes	characteristic
580	C₂	C₁₀₁×#3194	1	1	yes	characteristic
581	C₂	C₁₀₁×#3215	1	1	yes	characteristic
582	C₂	C₁₀₁×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂²⋊Q₈×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1973	C₂	semidirect
5. C₁₀₁×#1936	C₂	semidirect
6. C₁₀₁×#1925	C₂	semidirect
7. C₁₀₁×#1880	C₂	semidirect
8. C₁₀₁×#1872	C₂	semidirect
9. C₁₀₁×#1852	C₂	semidirect
11. C₁₀₁×#1749	C₂	semidirect
15. C₂×C₄×Q₈×C₁₀₁	C₂²	semidirect
20. #450×C₁₀₁	C₄	semidirect
21. C₂×#107×C₁₀₁	C₂²	semidirect
22. C₂×#103×C₁₀₁	C₂²	semidirect
28. C₂×#97×C₁₀₁	C₂²	semidirect
29. #391×C₁₀₁	C₂²	semidirect
34. #389×C₁₀₁	C₂²	semidirect
39. C₄×C₄⋊C₄×C₁₀₁	C₂²	semidirect
41. #340×C₁₀₁	C₂²	semidirect
42. #340×C₁₀₁	C₂²	semidirect
43. #336×C₁₀₁	C₂²	semidirect
58. C₂×SD₁₆×C₁₀₁	C₂×C₄	semidirect
92. #102×C₁₀₁	C₂×C₄	semidirect
282. #22049	C₁₀₁	direct (N × H)
293. C₄×C₂²⋊Q₈	C₂×C₁₀₁	semidirect
295. #1973	C₂×C₁₀₁	semidirect
296. #1936	C₂×C₁₀₁	semidirect
297. #1925	C₂×C₁₀₁	semidirect
298. #1880	C₂×C₁₀₁	semidirect
299. #1872	C₂×C₁₀₁	semidirect
300. #1852	C₂×C₁₀₁	semidirect
302. #1749	C₂×C₁₀₁	semidirect
303. C₁₀₁	#22049	direct (N × H)
307. C₂×C₄×Q₈	C₂²×C₁₀₁	semidirect
312. #450	C₄×C₁₀₁	semidirect
313. C₂×#107	C₂²×C₁₀₁	semidirect
314. C₂×#103	C₂²×C₁₀₁	semidirect
320. C₂×#97	C₂²×C₁₀₁	semidirect
321. #391	C₂²×C₁₀₁	semidirect
326. #389	C₂²×C₁₀₁	semidirect
331. C₄×C₄⋊C₄	C₂²×C₁₀₁	semidirect
333. #340	C₂²×C₁₀₁	semidirect
334. #340	C₂²×C₁₀₁	semidirect
335. #336	C₂²×C₁₀₁	semidirect
350. C₂×SD₁₆	C₂×C₄×C₁₀₁	semidirect
384. #102	C₂×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×#450×C₁₀₁	2
C₄×C₂²⋊Q₈×C₁₀₁	2
C₂×#390×C₁₀₁	2
C₁₀₁×#1973	2
C₁₀₁×#1936	2
C₁₀₁×#1925	2
C₁₀₁×#1880	2
C₁₀₁×#1872	2
C₁₀₁×#1852	2
C₁₀₁×#1786	2
C₁₀₁×#1749	2
#22049	101

Subgroups — C101×#22049 #38804200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#22049 #38804200