Subgroups — #13098353

Order 1600.

183 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#87723	C₂	1	4	yes	maximal
3	#11716431	C₂	1	1	yes	maximal, characteristic
4	C₄×#6014	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₅	C₂²	1	2	yes	—
6	C₂×Dic₅₀	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₅	—	2	2	no	—
8	C₄²×C₂₅	C₂²	1	1	yes	characteristic
9	#87723	—	2	8	no	—
10	C₄⋊Dic₂₅	—	2	2	no	—
11	C₂×#6014	C₂²	1	2	yes	—
12	#65381	—	5	1	no	maximal
13	Q₈×C₂₅	—	2	4	no	—
14	C₂×C₄×C₂₅	—	2	2	no	—
15	C₂×C₄×C₂₅	D₄	1	2	yes	—
16	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₅	—	2	2	no	—
18	Dic₅₀	—	2	4	no	—
19	#6014	D₄	1	4	yes	—
20	C₅×C₄⋊Q₈	D₅	1	1	yes	characteristic
21	C₂×#689	—	5	4	no	—
22	#4015	—	5	1	no	—
23	C₄×#168	—	5	1	no	—
24	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
25	C₄×C₂₅	—	4	2	no	—
26	C₄×C₂₅	Q₁₆	1	4	yes	complemented
27	C₄×C₂₅	C₂×D₄	1	2	yes	—
28	Dic₂₅	—	4	2	no	—
29	C₂×C₅×Q₈	C₂×D₅	1	2	yes	—
30	C₂×Dic₁₀	—	5	2	no	—
31	C₅×C₄⋊C₄	—	2	2	no	—
32	C₄²×C₅	C₂×D₅	1	1	yes	characteristic
33	#689	—	10	8	no	—
34	C₄⋊Dic₅	—	10	2	no	—
35	C₂×#168	—	5	2	no	—
36	#494	—	25	1	no	Sylow
37	C₂×C₂₅	#127	1	1	yes	characteristic
38	C₂×C₂₅	C₂×Q₁₆	1	2	yes	—
39	C₅×Q₈	—	2	4	no	—
40	C₂×C₄×C₅	—	2	2	no	—
41	C₂×C₄×C₅	C₂²⋊D₅	1	2	yes	—
42	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
43	C₂×Dic₅	—	10	2	no	—
44	Dic₁₀	—	10	4	no	—
45	#168	—	5	4	no	—
46	C₂×Q₁₆	—	25	4	no	—
47	C₄⋊Q₈	—	25	1	no	—
48	C₄⋊Q₈	D₂₅	1	1	yes	characteristic
49	C₄×C₈	—	25	1	no	—
50	C₂₅	#494	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
52	C₄×C₅	—	4	2	no	—
53	C₄×C₅	#689	1	4	yes	—
54	C₄×C₅	D₄×D₅	1	2	yes	—
55	Dic₅	—	20	2	no	—
56	C₂×Q₈	—	25	2	no	—
57	C₂×Q₈	C₂×D₂₅	1	2	yes	—
58	Q₁₆	—	50	8	no	—
59	C₂×C₈	—	25	2	no	—
60	C₄⋊C₄	—	2	2	no	—
61	C₄⋊C₄	—	50	2	no	—
62	C₄²	C₂×D₂₅	1	1	yes	characteristic
63	C₂×C₅	#4086	1	1	yes	characteristic
64	C₂×C₅	C₂×#689	1	2	yes	—
65	Q₈	—	2	4	no	—
66	Q₈	—	50	4	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	50	2	no	—
69	C₂×C₄	C₂²⋊D₂₅	1	2	yes	—
70	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
71	C₈	—	25	4	no	—
72	C₅	#65381	1	1	yes	characteristic
73	C₂²	C₂×C₂²⋊D₂₅	1	1	yes	characteristic
74	C₄	—	4	2	no	—
75	C₄	—	100	2	no	—
76	C₄	#87723	1	4	yes	complemented
77	C₄	D₄×D₂₅	1	2	yes	—
78	C₂	#11716502	1	1	yes	characteristic
79	C₂	C₂×#87723	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₅
commutator, cosocle	C₂×C₄×C₂₅	C₂³
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂₅×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₅	C₂×C₂²⋊D₅
hypercenter	C₄⋊Q₈	D₂₅
hypocenter	C₂₅	#494
LCS	G ▷ C₂×C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
26. C₄×C₂₅	Q₁₆	semidirect
50. C₂₅	#494	semidirect
76. C₄	#87723	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×C₄⋊Q₈	2
C₂×#87723	2
#11716431	2
C₄×#6014	2
#65381	5