Subgroups — C₂₅×#395 #13098544

Order 1600.

273 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₅	C₂	1	3	yes	maximal
3	C₂₅×#95	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₅	—	2	6	no	—
5	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
7	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
8	C₄⋊C₄×C₂₅	—	2	6	no	—
9	C₅×#395	C₅	1	1	yes	maximal, characteristic
10	C₂³×C₂₅	C₂³	1	1	yes	characteristic
11	Q₈×C₂₅	—	2	8	no	—
12	C₂×C₄×C₂₅	—	2	3	no	—
13	C₂×C₄×C₂₅	—	2	6	no	—
14	C₂×C₄×C₂₅	—	2	3	no	—
15	C₂×C₄×C₂₅	—	2	3	no	—
16	C₂×C₄×C₂₅	D₄	1	6	yes	—
17	C₂×C₄×C₂₅	Q₈	1	6	yes	complemented
18	C₂²×C₅×Q₈	C₂×C₅	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₄	C₂×C₅	1	3	yes	—
20	C₅×#95	C₂×C₅	1	3	yes	—
21	C₂²×C₂₅	C₂×D₄	1	3	yes	—
22	C₂²×C₂₅	C₂×Q₈	1	3	yes	—
23	C₂²×C₂₅	#41	1	1	yes	characteristic
24	C₄×C₂₅	—	2	6	no	—
25	C₄×C₂₅	—	2	6	no	—
26	C₄×C₂₅	—	4	1	no	—
27	C₂×C₅×Q₈	—	2	6	no	—
28	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
29	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
30	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
31	C₅×C₄⋊C₄	—	2	6	no	—
32	#395	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₂₅	#120	1	1	yes	characteristic
34	C₂×C₂₅	C₂²⋊Q₈	1	3	yes	—
35	C₂×C₂₅	C₄⋊Q₈	1	3	yes	—
36	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
37	C₅×Q₈	—	2	8	no	—
38	C₂×C₄×C₅	—	2	3	no	—
39	C₂×C₄×C₅	—	2	6	no	—
40	C₂×C₄×C₅	—	2	3	no	—
41	C₂×C₄×C₅	—	2	3	no	—
42	C₂×C₄×C₅	C₅×D₄	1	6	yes	—
43	C₂×C₄×C₅	C₅×Q₈	1	6	yes	—
44	C₂²×Q₈	C₂×C₂₅	1	1	yes	characteristic
45	C₂×C₄⋊C₄	C₂×C₂₅	1	3	yes	—
46	#95	C₂×C₂₅	1	3	yes	—
47	C₂₅	#395	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₅	C₂×C₅×D₄	1	3	yes	—
49	C₂²×C₅	C₂×C₅×Q₈	1	3	yes	—
50	C₂²×C₅	C₅×#41	1	1	yes	characteristic
51	C₄×C₅	—	2	6	no	—
52	C₄×C₅	—	2	6	no	—
53	C₄×C₅	—	4	1	no	—
54	C₂×Q₈	—	2	6	no	—
55	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
56	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
57	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
58	C₄⋊C₄	—	2	6	no	—
59	C₂×C₅	C₅×#120	1	1	yes	characteristic
60	C₂×C₅	C₅×C₂²⋊Q₈	1	3	yes	—
61	C₂×C₅	C₅×C₄⋊Q₈	1	3	yes	—
62	C₂³	C₂³×C₂₅	1	1	yes	characteristic
63	Q₈	—	2	8	no	—
64	C₂×C₄	—	2	3	no	—
65	C₂×C₄	—	2	6	no	—
66	C₂×C₄	—	2	3	no	—
67	C₂×C₄	—	2	3	no	—
68	C₂×C₄	D₄×C₂₅	1	6	yes	—
69	C₂×C₄	Q₈×C₂₅	1	6	yes	complemented
70	C₅	C₅×#395	1	1	yes	characteristic
71	C₂²	C₂×D₄×C₂₅	1	3	yes	—
72	C₂²	C₂×Q₈×C₂₅	1	3	yes	—
73	C₂²	#41×C₂₅	1	1	yes	characteristic
74	C₄	—	2	6	no	—
75	C₄	—	2	6	no	—
76	C₄	—	4	1	no	—
77	C₂	C₂₅×#120	1	1	yes	characteristic
78	C₂	C₂₅×C₂²⋊Q₈	1	3	yes	—
79	C₂	C₂₅×C₄⋊Q₈	1	3	yes	—

	subgroup	G/H
center	C₂³×C₂₅	C₂³
commutator	C₂³	C₂³×C₂₅
Frattini, socle, prime radical, cosocle	C₂³×C₅	C₂³×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₂×C₄×C₂₅	Q₈	semidirect
32. #395	C₂₅	direct (N × H)
47. C₂₅	#395	direct (N × H)
69. C₂×C₄	Q₈×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₂₅	2
C₂×C₄⋊C₄×C₂₅	2
C₂₅×#95	2
C₅×#395	5

Subgroups — C25×#395 #13098544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#395 #13098544