Subgroups — C₂₅×#393 #13098542

Order 1600.

303 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, complemented
2	C₂×C₂²⋊C₄×C₂₅	C₂	1	3	yes	maximal
3	C₂₅×#95	C₂	1	3	yes	maximal, complemented
4	C₂⁴×C₂₅	C₂²	1	1	yes	characteristic
5	C₂×Q₈×C₂₅	—	2	6	no	—
6	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
7	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
8	C₂²⋊C₄×C₂₅	—	2	6	no	—
9	C₅×#393	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	complemented
13	C₂³×C₂₅	C₂³	1	1	yes	characteristic
14	Q₈×C₂₅	—	2	8	no	—
15	C₂×C₄×C₂₅	—	2	6	no	—
16	C₂×C₄×C₂₅	—	2	3	no	—
17	C₂×C₄×C₂₅	—	2	6	no	—
18	C₂×C₄×C₂₅	D₄	1	6	yes	—
19	C₂²×C₅×Q₈	C₂×C₅	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊C₄	C₂×C₅	1	3	yes	—
21	C₅×#95	C₂×C₅	1	3	yes	—
22	C₂²×C₂₅	—	2	6	no	—
23	C₂²×C₂₅	—	4	1	no	—
24	C₂²×C₂₅	—	4	3	no	—
25	C₂²×C₂₅	C₂×D₄	1	3	yes	—
26	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
27	C₂²×C₂₅	#41	1	3	yes	—
28	C₄×C₂₅	—	2	6	no	—
29	C₄×C₂₅	—	4	3	no	—
30	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
31	C₂×C₅×Q₈	—	2	6	no	—
32	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
33	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
34	C₅×C₂²⋊C₄	—	2	6	no	—
35	#393	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₂₅	—	4	2	no	—
37	C₂×C₂₅	#120	1	1	yes	characteristic
38	C₂×C₂₅	C₂²⋊Q₈	1	3	yes	—
39	C₂×C₂₅	#124	1	3	yes	—
40	C₂³×C₅	—	2	3	no	—
41	C₂³×C₅	—	2	3	no	—
42	C₂³×C₅	C₅×Q₈	1	2	yes	—
43	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
44	C₅×Q₈	—	2	8	no	—
45	C₂×C₄×C₅	—	2	6	no	—
46	C₂×C₄×C₅	—	2	3	no	—
47	C₂×C₄×C₅	—	2	6	no	—
48	C₂×C₄×C₅	C₅×D₄	1	6	yes	—
49	C₂²×Q₈	C₂×C₂₅	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊C₄	C₂×C₂₅	1	3	yes	—
51	#95	C₂×C₂₅	1	3	yes	complemented
52	C₂₅	#393	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²×C₅	—	2	6	no	—
54	C₂²×C₅	—	4	1	no	—
55	C₂²×C₅	—	4	3	no	—
56	C₂²×C₅	C₂×C₅×D₄	1	3	yes	—
57	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
58	C₂²×C₅	C₅×#41	1	3	yes	—
59	C₄×C₅	—	2	6	no	—
60	C₄×C₅	—	4	3	no	—
61	C₂⁴	C₂²×C₂₅	1	1	yes	characteristic
62	C₂×Q₈	—	2	6	no	—
63	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
64	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
65	C₂²⋊C₄	—	2	6	no	—
66	C₂×C₅	—	4	2	no	—
67	C₂×C₅	C₅×#120	1	1	yes	characteristic
68	C₂×C₅	C₅×C₂²⋊Q₈	1	3	yes	—
69	C₂×C₅	C₅×#124	1	3	yes	—
70	C₂³	—	2	3	no	—
71	C₂³	—	2	3	no	—
72	C₂³	Q₈×C₂₅	1	2	yes	complemented
73	C₂³	C₂³×C₂₅	1	1	yes	characteristic
74	Q₈	—	2	8	no	—
75	C₂×C₄	—	2	6	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	D₄×C₂₅	1	6	yes	—
79	C₅	C₅×#393	1	1	yes	characteristic
80	C₂²	—	2	6	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	3	no	—
83	C₂²	C₂×D₄×C₂₅	1	3	yes	—
84	C₂²	C₂×Q₈×C₂₅	1	1	yes	characteristic
85	C₂²	#41×C₂₅	1	3	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	3	no	—
88	C₂	—	4	2	no	—
89	C₂	C₂₅×#120	1	1	yes	characteristic
90	C₂	C₂₅×C₂²⋊Q₈	1	3	yes	—
91	C₂	C₂₅×#124	1	3	yes	—

	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. C₂²×Q₈×C₂₅	C₂	semidirect
3. C₂₅×#95	C₂	semidirect
12. C₂³×C₂₅	Q₈	semidirect
35. #393	C₂₅	direct (N × H)
49. C₂²×Q₈	C₂×C₂₅	semidirect
51. #95	C₂×C₂₅	semidirect
52. C₂₅	#393	direct (N × H)
72. C₂³	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×C₂²⋊C₄×C₂₅	2
C₂₅×#95	2
C₅×#393	5

Subgroups — C25×#393 #13098542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#393 #13098542