Subgroups — C₅×#7317 #11930037

Order 1280.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1784	C₂	1	3	yes	maximal
2	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
3	C₂×C₅×#101	—	2	6	no	—
4	C₅×#407	C₄	1	6	yes	—
5	#7317	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂²×C₅×Q₈	—	4	6	no	—
7	C₂²×C₅×Q₈	D₄	1	3	yes	—
8	C₂²×C₅×Q₈	Q₈	1	1	yes	characteristic
9	C₂³×C₄×C₅	C₂×C₄	1	3	yes	—
10	C₂×C₅×M₁₆	—	2	6	no	—
11	C₅×#101	—	4	12	no	—
12	C₅×C₂²⋊C₈	—	4	6	no	—
13	#1784	C₂×C₅	1	3	yes	—
14	C₂⁴×C₅	C₄²	1	1	yes	characteristic
15	C₂×C₅×Q₈	—	2	12	no	—
16	C₂×C₅×Q₈	—	4	3	no	—
17	C₂×C₅×Q₈	—	4	3	no	—
18	C₂×C₅×Q₈	—	4	16	no	—
19	C₂²×C₄×C₅	—	2	6	no	—
20	C₂²×C₄×C₅	—	4	6	no	—
21	C₂²×C₄×C₅	C₂²⋊C₄	1	3	yes	—
22	C₂²×C₄×C₅	C₄⋊C₄	1	3	yes	—
23	C₅×M₁₆	—	4	12	no	—
24	C₂×C₅×C₈	—	4	6	no	—
25	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
26	C₂×#101	—	2	6	no	—
27	#407	C₄×C₅	1	6	yes	—
28	C₂³×C₅	—	2	3	no	—
29	C₂³×C₅	—	4	2	no	—
30	C₂³×C₅	#95	1	1	yes	characteristic
31	C₅×Q₈	—	4	12	no	—
32	C₅×Q₈	—	4	4	no	—
33	C₂×C₄×C₅	—	2	6	no	—
34	C₂×C₄×C₅	—	2	3	no	—
35	C₂×C₄×C₅	—	2	6	no	—
36	C₂×C₄×C₅	—	4	12	no	—
37	C₂×C₄×C₅	#99	1	6	yes	—
38	C₅×C₈	—	8	6	no	—
39	C₂²×Q₈	—	4	6	no	—
40	C₂²×Q₈	C₅×D₄	1	3	yes	—
41	C₂²×Q₈	C₅×Q₈	1	1	yes	characteristic
42	C₂³×C₄	C₂×C₄×C₅	1	3	yes	—
43	C₂×M₁₆	—	2	6	no	—
44	#101	—	4	12	no	—
45	C₂²⋊C₈	—	4	6	no	—
46	C₂²×C₅	—	2	6	no	—
47	C₂²×C₅	—	4	1	no	—
48	C₂²×C₅	—	4	3	no	—
49	C₂²×C₅	—	4	1	no	—
50	C₂²×C₅	#342	1	3	yes	—
51	C₄×C₅	—	2	6	no	—
52	C₄×C₅	—	4	3	no	—
53	C₂⁴	C₄²×C₅	1	1	yes	characteristic
54	C₂×Q₈	—	2	12	no	—
55	C₂×Q₈	—	4	3	no	—
56	C₂×Q₈	—	4	3	no	—
57	C₂×Q₈	—	4	16	no	—
58	C₂²×C₄	—	2	6	no	—
59	C₂²×C₄	—	4	6	no	—
60	C₂²×C₄	C₅×C₂²⋊C₄	1	3	yes	—
61	C₂²×C₄	C₅×C₄⋊C₄	1	3	yes	—
62	M₁₆	—	4	12	no	—
63	C₂×C₈	—	4	6	no	—
64	C₂×C₅	—	2	3	no	—
65	C₂×C₅	—	4	2	no	—
66	C₂×C₅	#1304	1	1	yes	characteristic
67	C₂³	—	2	3	no	—
68	C₂³	—	4	2	no	—
69	C₂³	C₅×#95	1	1	yes	characteristic
70	Q₈	—	4	12	no	—
71	Q₈	—	4	4	no	—
72	C₂×C₄	—	2	6	no	—
73	C₂×C₄	—	2	3	no	—
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	4	12	no	—
76	C₂×C₄	C₅×#99	1	6	yes	—
77	C₈	—	8	6	no	—
78	C₅	#7317	1	1	yes	characteristic, direct product factor, Sylow
79	C₂²	—	2	6	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	4	3	no	—
82	C₂²	—	4	1	no	—
83	C₂²	C₅×#342	1	3	yes	—
84	C₄	—	2	6	no	—
85	C₄	—	4	3	no	—
86	C₂	—	2	3	no	—
87	C₂	—	4	2	no	—
88	C₂	C₅×#1304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#1304
commutator	C₂⁴	C₄²×C₅
Frattini, cosocle	C₂³×Q₈	C₂²×C₅
prime radical	C₂⁴×C₅	C₄²
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂³×C₅ ◁ C₂³×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
5. #7317	C₅	direct (N × H)
78. C₅	#7317	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1784	2
#7317	5

Subgroups — C5×#7317 #11930037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7317 #11930037