Subgroups — C₅×#7197 #11929917

Order 1280.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2163	C₂	1	2	yes	maximal
2	C₅×#1452	C₂	1	1	yes	maximal, characteristic
3	C₅×#431	C₄	1	2	yes	—
4	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₅×C₄⋊C₁₆	—	2	2	no	—
6	C₅×C₂²⋊C₁₆	C₄	1	4	yes	—
7	C₅×#346	—	2	2	no	—
8	C₅×#322	—	2	2	no	—
9	#7197	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₅×C₁₆	—	2	4	no	—
13	C₅×C₄⋊C₈	—	2	2	no	—
14	C₅×C₂²⋊C₈	C₈	1	4	yes	—
15	C₄×C₅×C₈	—	2	2	no	—
16	C₄×C₅×C₈	D₄	1	2	yes	—
17	C₄×C₅×C₈	D₄	1	1	yes	characteristic
18	C₄×C₅×C₈	Q₈	1	1	yes	characteristic
19	#2163	C₂×C₅	1	2	yes	—
20	#1452	C₂×C₅	1	1	yes	characteristic
21	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
23	C₂×C₅×C₈	—	2	4	no	—
24	C₂×C₅×C₈	—	4	2	no	—
25	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
26	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
27	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
28	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
29	C₄²×C₅	M₁₆	1	2	yes	—
30	C₅×C₁₆	—	4	4	no	—
31	#431	C₄×C₅	1	2	yes	—
32	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
33	C₄⋊C₁₆	—	2	2	no	—
34	C₂²⋊C₁₆	C₄×C₅	1	4	yes	—
35	#346	—	2	2	no	—
36	#322	—	2	2	no	—
37	C₂³×C₅	C₄×C₈	1	1	yes	characteristic
38	C₂×C₄×C₅	—	2	2	no	—
39	C₂×C₄×C₅	—	4	2	no	—
40	C₂×C₄×C₅	#95	1	1	yes	characteristic
41	C₂×C₄×C₅	#97	1	1	yes	characteristic
42	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
43	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
44	C₅×C₈	—	2	2	no	—
45	C₅×C₈	—	2	2	no	—
46	C₅×C₈	—	4	4	no	—
47	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
48	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
49	C₂×C₁₆	—	2	4	no	—
50	C₄⋊C₈	—	2	2	no	—
51	C₂²⋊C₈	C₅×C₈	1	4	yes	—
52	C₄×C₈	—	2	2	no	—
53	C₄×C₈	C₅×D₄	1	2	yes	—
54	C₄×C₈	C₅×D₄	1	1	yes	characteristic
55	C₄×C₈	C₅×Q₈	1	1	yes	characteristic
56	C₂²×C₅	—	2	1	no	—
57	C₂²×C₅	—	2	2	no	—
58	C₂²×C₅	#336	1	1	yes	characteristic
59	C₄×C₅	—	2	1	no	—
60	C₄×C₅	—	2	2	no	—
61	C₄×C₅	—	2	2	no	—
62	C₄×C₅	#344	1	2	yes	—
63	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
64	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
65	C₂×C₈	—	2	4	no	—
66	C₂×C₈	—	4	2	no	—
67	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
68	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
69	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
70	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
71	C₄²	C₅×M₁₆	1	2	yes	—
72	C₁₆	—	4	4	no	—
73	C₂×C₅	—	4	1	no	—
74	C₂×C₅	#1281	1	1	yes	characteristic
75	C₂×C₅	#1378	1	2	yes	—
76	C₂³	C₄×C₅×C₈	1	1	yes	characteristic
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	C₅×#95	1	1	yes	characteristic
80	C₂×C₄	C₅×#97	1	1	yes	characteristic
81	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
82	C₂×C₄	C₅×C₄⋊C₈	1	2	yes	—
83	C₈	—	2	2	no	—
84	C₈	—	2	2	no	—
85	C₈	—	4	4	no	—
86	C₅	#7197	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²	—	2	2	no	—
88	C₂²	—	2	1	no	—
89	C₂²	C₅×#336	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	2	2	no	—
92	C₄	—	2	1	no	—
93	C₄	C₅×#344	1	2	yes	—
94	C₂	—	4	1	no	—
95	C₂	C₅×#1281	1	1	yes	characteristic
96	C₂	C₅×#1378	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	#95
commutator	C₂³	C₄×C₅×C₈
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₅
socle	C₂²×C₅	#336
prime radical	C₂³×C₅	C₄×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
9. #7197	C₅	direct (N × H)
86. C₅	#7197	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×#2163	2
C₅×#1452	2
#7197	5

Subgroups — C5×#7197 #11929917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7197 #11929917