Subgroups — C₂²⋊#87764 #13100293

Order 1600.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6029	C₂	1	1	yes	maximal, characteristic
2	C₂×#87764	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₅²	C₄	1	1	yes	characteristic
4	C₂×#6029	—	2	2	no	—
5	C₂×#6029	C₄	1	1	yes	characteristic
6	C₂×#6029	C₂²	1	1	yes	characteristic
7	#87764	—	2	2	no	—
8	C₂²⋊#674	—	5	6	no	maximal
9	C₂³×C₅²	C₈	1	1	yes	characteristic
10	C₂×C₄×C₅²	—	2	1	no	—
11	C₂×C₄×C₅²	—	2	1	no	—
12	C₂×C₄×C₅²	C₈	1	1	yes	characteristic
13	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
14	#6029	—	2	1	no	—
15	#6029	D₄	1	2	yes	—
16	C₂²×#168	—	5	6	no	—
17	C₂×#674	—	5	12	no	—
18	C₂²×C₅²	—	2	1	no	—
19	C₂²×C₅²	—	2	1	no	—
20	C₂²×C₅²	C₁₆	1	2	yes	complemented
21	C₂²×C₅²	C₂×C₈	1	1	yes	characteristic
22	C₄×C₅²	—	2	1	no	—
23	C₄×C₅²	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₅²	M₁₆	1	1	yes	characteristic
25	C₂²×C₄×C₅	AGL(1,𝔽₅)	1	6	yes	—
26	C₂×#168	—	5	6	no	—
27	C₂×#168	—	5	6	no	—
28	C₂×#168	—	10	12	no	—
29	#674	—	10	12	no	—
30	C₂²⋊C₁₆	—	25	1	no	Sylow
31	C₂×C₅²	—	2	2	no	—
32	C₂×C₅²	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₅²	C₂×C₁₆	1	1	yes	characteristic
34	C₂×C₅²	M₃₂	1	1	yes	characteristic
35	C₂³×C₅	#170	1	6	yes	—
36	C₂×C₄×C₅	—	2	6	no	—
37	C₂×C₄×C₅	—	2	6	no	—
38	C₂×C₄×C₅	#170	1	6	yes	—
39	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	—
40	#168	—	5	12	no	—
41	#168	—	10	6	no	—
42	C₂²×C₈	—	25	1	no	—
43	C₂×C₁₆	—	25	2	no	—
44	C₅²	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₅	—	2	6	no	—
46	C₂²×C₅	—	2	6	no	—
47	C₂²×C₅	#674	1	12	yes	complemented
48	C₂²×C₅	C₂×#170	1	6	yes	—
49	C₄×C₅	—	2	6	no	—
50	C₄×C₅	#704	1	6	yes	—
51	C₄×C₅	C₂²⋊AGL(1,𝔽₅)	1	6	yes	—
52	C₂²×C₄	#1043	1	1	yes	characteristic
53	C₂×C₈	—	25	1	no	—
54	C₂×C₈	—	25	1	no	—
55	C₂×C₈	—	50	2	no	—
56	C₁₆	—	50	2	no	—
57	C₂×C₅	—	2	12	no	—
58	C₂×C₅	C₂×#674	1	6	yes	—
59	C₂×C₅	#3998	1	6	yes	—
60	C₂×C₅	C₂²⋊#170	1	6	yes	—
61	C₂³	#6033	1	1	yes	characteristic
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	#6033	1	1	yes	characteristic
65	C₂×C₄	C₂×#1043	1	1	yes	characteristic
66	C₈	—	25	2	no	—
67	C₈	—	50	1	no	—
68	C₅	C₂²⋊#674	1	6	yes	complemented
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	#87764	1	2	yes	complemented
72	C₂²	C₂×#6033	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	#87860	1	1	yes	characteristic
75	C₄	C₂²⋊#1043	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×#87764	1	1	yes	characteristic
78	C₂	#11716866	1	1	yes	characteristic
79	C₂	C₂²⋊#6033	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#1043
commutator	C₂×C₅²	C₂×C₁₆
Fitting	C₂²×C₄×C₅²	C₄
socle	C₂²×C₅²	C₂×C₈
prime radical	C₂³×C₅²	C₈
cosocle	C₂×#6029	C₂²
hypercenter	C₂²×C₄	#1043
hypocenter	C₅²	C₂²⋊C₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#87764	C₂	semidirect
20. C₂²×C₅²	C₁₆	semidirect
44. C₅²	C₂²⋊C₁₆	semidirect
47. C₂²×C₅	#674	semidirect
68. C₅	C₂²⋊#674	semidirect
71. C₂²	#87764	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6029	2
C₂×#87764	2
C₂²⋊#674	5

Subgroups — C22⋊#87764 #13100293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#87764 #13100293