Subgroups — C₂×#11716794 #13104251

Order 1600.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87775	C₂	1	2	yes	maximal
2	C₂×#87765	C₂	1	1	yes	maximal, characteristic
3	#11716794	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×Dic₁₀	—	2	2	no	—
5	C₂×#6029	C₂²	1	1	yes	characteristic
6	#87775	—	2	2	no	—
7	#87775	C₂²	1	4	yes	—
8	#87765	C₂²	1	2	yes	—
9	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
10	C₂×C₅×Dic₅	—	4	2	no	—
11	C₅×Dic₁₀	—	2	4	no	—
12	C₅×Dic₁₀	—	4	2	no	—
13	#6029	D₄	1	1	yes	characteristic
14	#6029	C₂³	1	1	yes	characteristic
15	C₂×#689	—	10	2	no	—
16	C₂×#674	—	10	1	no	—
17	C₂²×C₅²	D₈	1	1	yes	characteristic
18	C₄×C₅²	D₈	1	1	yes	characteristic
19	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
20	C₅×Dic₅	—	4	4	no	—
21	C₂×C₅×Q₈	—	10	2	no	—
22	C₂×Dic₁₀	—	2	2	no	—
23	#689	—	10	4	no	—
24	#689	—	10	4	no	—
25	C₂×#168	—	10	1	no	—
26	C₂×#168	—	10	2	no	—
27	#674	—	10	2	no	—
28	C₂×Q₃₂	—	25	1	no	maximal, Sylow
29	C₂×C₅²	Q₃₂	1	2	yes	complemented
30	C₂×C₅²	C₂×D₈	1	1	yes	characteristic
31	C₅×Q₈	—	10	4	no	—
32	C₅×Q₈	—	20	2	no	—
33	C₂×C₄×C₅	—	2	1	no	—
34	C₂×C₄×C₅	—	2	2	no	—
35	C₂×C₄×C₅	—	20	2	no	—
36	C₂×Dic₅	—	4	2	no	—
37	Dic₁₀	—	2	4	no	—
38	Dic₁₀	—	4	2	no	—
39	#168	—	10	1	no	—
40	#168	—	10	2	no	—
41	#168	—	10	1	no	—
42	#168	—	10	2	no	—
43	C₂×Q₁₆	—	25	2	no	—
44	Q₃₂	—	25	4	no	—
45	C₂×C₁₆	—	25	1	no	—
46	C₅²	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₅	—	2	2	no	—
48	C₂²×C₅	—	2	1	no	—
49	C₄×C₅	—	2	2	no	—
50	C₄×C₅	—	2	1	no	—
51	C₄×C₅	—	2	2	no	—
52	C₄×C₅	—	2	1	no	—
53	C₄×C₅	—	20	4	no	—
54	Dic₅	—	4	4	no	—
55	C₂×Q₈	—	10	2	no	—
56	Q₁₆	—	25	4	no	—
57	Q₁₆	—	50	2	no	—
58	C₂×C₈	—	25	1	no	—
59	C₁₆	—	25	2	no	—
60	C₂×C₅	—	2	2	no	—
61	C₂×C₅	—	2	1	no	—
62	C₂×C₅	—	2	4	no	—
63	C₂×C₅	—	2	2	no	—
64	Q₈	—	10	4	no	—
65	Q₈	—	20	2	no	—
66	C₂×C₄	—	20	2	no	—
67	C₂×C₄	D₅²⋊C₂	1	1	yes	characteristic
68	C₈	—	25	1	no	—
69	C₈	—	25	1	no	—
70	C₅	—	2	2	no	—
71	C₅	—	2	1	no	—
72	C₂²	#87837	1	1	yes	characteristic
73	C₄	—	20	4	no	—
74	C₄	#87837	1	1	yes	characteristic
75	C₄	C₂×D₅²⋊C₂	1	1	yes	characteristic
76	C₂	#11716794	1	2	yes	direct product factor
77	C₂	C₂×#87837	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#87837
commutator, cosocle	#6029	C₂³
Frattini	C₄	C₂×D₅²⋊C₂
Fitting	C₂×C₄×C₅²	D₄
socle, prime radical	C₂²×C₅²	D₈
hypercenter	C₂×C₄	D₅²⋊C₂
hypocenter	C₅²	C₂×Q₃₂
LCS	G ▷ #6029 ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. #11716794	C₂	direct (N × H)
29. C₂×C₅²	Q₃₂	semidirect
46. C₅²	C₂×Q₃₂	semidirect
76. C₂	#11716794	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×#87775	2
C₂×#87765	2
#11716794	2
C₂×Q₃₂	25

Subgroups — C2×#11716794 #13104251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716794 #13104251