Subgroups — C₂₅×#399 #13098548

Order 1600.

279 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₅	C₂	1	3	yes	maximal, complemented
2	C₂×C₂²⋊C₄×C₂₅	C₂	1	3	yes	maximal
3	C₂₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₂₅	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
6	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
7	C₄⋊C₄×C₂₅	—	2	6	no	—
8	C₂²⋊C₄×C₂₅	—	2	6	no	—
9	C₅×#399	C₅	1	1	yes	maximal, characteristic
10	C₂³×C₂₅	—	2	3	no	—
11	C₂³×C₂₅	—	2	3	no	—
12	C₂³×C₂₅	Q₈	1	2	yes	—
13	C₂³×C₂₅	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₂₅	—	2	6	no	—
15	C₂×C₄×C₂₅	—	2	3	no	—
16	C₂×C₄×C₂₅	—	2	6	no	—
17	C₂×C₄×C₂₅	D₄	1	6	yes	—
18	C₂×C₅×C₄⋊C₄	C₂×C₅	1	3	yes	—
19	C₂×C₅×C₂²⋊C₄	C₂×C₅	1	3	yes	—
20	C₅×#95	C₂×C₅	1	1	yes	characteristic
21	C₂²×C₂₅	—	2	6	no	—
22	C₂²×C₂₅	—	4	3	no	—
23	C₂²×C₂₅	—	4	1	no	—
24	C₂²×C₂₅	C₂×D₄	1	3	yes	—
25	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
26	C₂²×C₂₅	#41	1	3	yes	—
27	C₄×C₂₅	—	2	6	no	—
28	C₄×C₂₅	—	4	3	no	—
29	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
30	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
31	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
32	C₅×C₄⋊C₄	—	2	6	no	—
33	C₅×C₂²⋊C₄	—	2	6	no	—
34	#399	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₂₅	—	4	2	no	—
36	C₂×C₂₅	C₂²⋊Q₈	1	3	yes	—
37	C₂×C₂₅	#123	1	3	yes	—
38	C₂×C₂₅	#127	1	1	yes	characteristic
39	C₂³×C₅	—	2	3	no	—
40	C₂³×C₅	—	2	3	no	—
41	C₂³×C₅	C₅×Q₈	1	2	yes	—
42	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
43	C₂×C₄×C₅	—	2	6	no	—
44	C₂×C₄×C₅	—	2	3	no	—
45	C₂×C₄×C₅	—	2	6	no	—
46	C₂×C₄×C₅	C₅×D₄	1	6	yes	—
47	C₂×C₄⋊C₄	C₂×C₂₅	1	3	yes	complemented
48	C₂×C₂²⋊C₄	C₂×C₂₅	1	3	yes	—
49	#95	C₂×C₂₅	1	1	yes	characteristic, complemented
50	C₂₅	#399	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₅	—	2	6	no	—
52	C₂²×C₅	—	4	3	no	—
53	C₂²×C₅	—	4	1	no	—
54	C₂²×C₅	C₂×C₅×D₄	1	3	yes	—
55	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
56	C₂²×C₅	C₅×#41	1	3	yes	—
57	C₄×C₅	—	2	6	no	—
58	C₄×C₅	—	4	3	no	—
59	C₂⁴	C₂²×C₂₅	1	1	yes	characteristic
60	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
61	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
62	C₄⋊C₄	—	2	6	no	—
63	C₂²⋊C₄	—	2	6	no	—
64	C₂×C₅	—	4	2	no	—
65	C₂×C₅	C₅×C₂²⋊Q₈	1	3	yes	—
66	C₂×C₅	C₅×#123	1	3	yes	—
67	C₂×C₅	C₅×#127	1	1	yes	characteristic
68	C₂³	—	2	3	no	—
69	C₂³	—	2	3	no	—
70	C₂³	Q₈×C₂₅	1	2	yes	—
71	C₂³	C₂³×C₂₅	1	1	yes	characteristic
72	C₂×C₄	—	2	6	no	—
73	C₂×C₄	—	2	3	no	—
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	D₄×C₂₅	1	6	yes	—
76	C₅	C₅×#399	1	1	yes	characteristic
77	C₂²	—	2	6	no	—
78	C₂²	—	4	3	no	—
79	C₂²	—	4	1	no	—
80	C₂²	C₂×D₄×C₂₅	1	3	yes	—
81	C₂²	C₂×Q₈×C₂₅	1	1	yes	characteristic
82	C₂²	#41×C₂₅	1	3	yes	—
83	C₄	—	2	6	no	—
84	C₄	—	4	3	no	—
85	C₂	—	4	2	no	—
86	C₂	C₂₅×C₂²⋊Q₈	1	3	yes	—
87	C₂	C₂₅×#123	1	3	yes	—
88	C₂	C₂₅×#127	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₂₅	C₂³
commutator	C₂³	C₂³×C₂₅
Frattini, socle, cosocle	C₂³×C₅	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²×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
1. C₂×C₄⋊C₄×C₂₅	C₂	semidirect
3. C₂₅×#95	C₂	semidirect
34. #399	C₂₅	direct (N × H)
47. C₂×C₄⋊C₄	C₂×C₂₅	semidirect
49. #95	C₂×C₂₅	semidirect
50. C₂₅	#399	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×C₂₅	2
C₂×C₂²⋊C₄×C₂₅	2
C₂₅×#95	2
C₅×#399	5

Subgroups — C25×#399 #13098548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#399 #13098548