Subgroups — #400×C₁₃₁ #22552844

Order 8384.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#95×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#95×C₁₃₁	C₂	1	2	yes	maximal
5	#95×C₁₃₁	C₂	1	2	yes	maximal
6	C₂²×C₄×C₁₃₁	C₂²	1	2	yes	—
7	C₂²×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₁₃₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₃₁	—	2	2	no	—
12	C₄⋊C₄×C₁₃₁	—	2	2	no	—
13	C₂³×C₁₃₁	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₁₃₁	—	2	1	no	—
15	C₂×C₄×C₁₃₁	—	2	1	no	—
16	C₂×C₄×C₁₃₁	—	2	2	no	—
17	C₂×C₄×C₁₃₁	—	2	1	no	—
18	C₂×C₄×C₁₃₁	—	2	2	no	—
19	C₂×C₄×C₁₃₁	—	2	2	no	—
20	C₂×C₄×C₁₃₁	—	2	4	no	—
21	C₂×C₄×C₁₃₁	—	2	2	no	—
22	C₂×C₄×C₁₃₁	—	2	2	no	—
23	C₂×C₄×C₁₃₁	—	2	2	no	—
24	C₂×C₄×C₁₃₁	D₄	1	2	yes	—
25	C₂×C₄×C₁₃₁	Q₈	1	2	yes	—
26	C₂²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
28	C₂²×C₁₃₁	#41	1	1	yes	characteristic
29	C₂²×C₁₃₁	#41	1	2	yes	—
30	C₂²×C₁₃₁	#41	1	2	yes	—
31	C₄×C₁₃₁	—	2	2	no	—
32	C₄×C₁₃₁	—	2	2	no	—
33	C₄×C₁₃₁	—	4	1	no	—
34	C₄×C₁₃₁	—	4	2	no	—
35	C₄×C₁₃₁	—	4	2	no	—
36	C₂×C₁₃₁	C₂²⋊Q₈	1	1	yes	characteristic
37	C₂×C₁₃₁	#123	1	1	yes	characteristic
38	C₂×C₁₃₁	#124	1	1	yes	characteristic
39	C₂×C₁₃₁	#125	1	2	yes	—
40	C₂×C₁₃₁	#126	1	2	yes	—
41	C₁₃₁	#400	1	1	yes	characteristic, direct product factor, Sylow
42	#400	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
44	C₂×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
45	#95	C₂×C₁₃₁	1	1	yes	characteristic
46	#95	C₂×C₁₃₁	1	2	yes	—
47	#95	C₂×C₁₃₁	1	2	yes	—
48	C₂²×C₄	C₂²×C₁₃₁	1	2	yes	—
49	C₂²×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
50	C₂²×C₄	C₂²×C₁₃₁	1	2	yes	—
51	C₂²×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
52	C₂²×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	2	2	no	—
55	C₂³	C₂³×C₁₃₁	1	1	yes	characteristic
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	4	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	D₄×C₁₃₁	1	2	yes	—
67	C₂×C₄	Q₈×C₁₃₁	1	2	yes	—
68	C₂²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
69	C₂²	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
70	C₂²	#41×C₁₃₁	1	1	yes	characteristic
71	C₂²	#41×C₁₃₁	1	2	yes	—
72	C₂²	#41×C₁₃₁	1	2	yes	—
73	C₄	—	2	2	no	—
74	C₄	—	2	2	no	—
75	C₄	—	4	1	no	—
76	C₄	—	4	2	no	—
77	C₄	—	4	2	no	—
78	C₂	C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
79	C₂	#123×C₁₃₁	1	1	yes	characteristic
80	C₂	#124×C₁₃₁	1	1	yes	characteristic
81	C₂	#125×C₁₃₁	1	2	yes	—
82	C₂	#126×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₁	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₁₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
41. C₁₃₁	#400	direct (N × H)
42. #400	C₁₃₁	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×C₄⋊C₄×C₁₃₁	2
#95×C₁₃₁	2
#400	131

Subgroups — #400×C131 #22552844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #400×C₁₃₁ #22552844