Subgroups — #44500692

Order 30656.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₉₁₆	C₂	1	1	yes	maximal, characteristic
2	#29506315	C₂	1	1	yes	maximal, characteristic, complemented
3	#29506313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊(C₄₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#29506302	C₂	1	1	yes	maximal, characteristic
6	#29506302	C₂	1	1	yes	maximal, characteristic
7	#125×C₄₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₉₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄₇₉	—	2	1	no	—
10	C₂×C₄₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄₇₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₇₉	C₂²	1	1	yes	characteristic
13	(C₂×D₄₇₉)⋊C₄	—	2	1	no	—
14	C₄⋊C₄×C₄₇₉	—	2	1	no	—
15	C₄⋊C₄×C₄₇₉	—	2	1	no	—
16	C₄⋊C₄×C₄₇₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₄₇₉	C₂²	1	1	yes	characteristic
18	C₄²×C₄₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄₇₉	—	2	1	no	—
20	D₁₉₁₆	—	2	1	no	—
21	D₁₉₁₆	Q₈	1	2	yes	—
22	C₂×Dic₄₇₉	—	2	1	no	—
23	C₄×D₄₇₉	—	4	2	no	—
24	C₄₇₉⋊C₈	—	2	1	no	—
25	C₄₇₉⋊C₈	—	2	1	no	—
26	C₂×C₄×C₄₇₉	—	2	1	no	—
27	C₂×C₄×C₄₇₉	—	2	1	no	—
28	C₂×C₄×C₄₇₉	D₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇₉	D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×D₄₇₉	—	2	2	no	—
33	C₂×D₄₇₉	—	4	1	no	—
34	C₂×D₄₇₉	—	4	1	no	—
35	C₄×C₄₇₉	—	2	1	no	—
36	C₄×C₄₇₉	—	2	1	no	—
37	C₄×C₄₇₉	—	4	1	no	—
38	C₄×C₄₇₉	—	4	1	no	—
39	C₄×C₄₇₉	C₂×Q₈	1	1	yes	characteristic
40	C₄×C₄₇₉	#41	1	1	yes	characteristic
41	Dic₄₇₉	—	4	1	no	—
42	C₂×C₄₇₉	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₄₇₉	#135	1	1	yes	characteristic
44	C₂×C₄₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₄₇₉	—	4	2	no	—
46	C₄₇₉	#478	1	1	yes	characteristic, complemented, Sylow
47	#478	—	479	1	no	maximal, Sylow
48	#125	D₄₇₉	1	1	yes	characteristic, complemented
49	C₄×D₄	—	479	1	no	—
50	#107	—	479	1	no	—
51	#106	—	479	1	no	—
52	C₄⋊C₈	—	479	1	no	—
53	#102	—	479	1	no	—
54	#102	—	479	1	no	—
55	C₂×D₄	—	479	1	no	—
56	C₂²×C₄	—	958	1	no	—
57	C₂×C₈	—	479	1	no	—
58	C₂×C₈	—	479	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	479	1	no	—
62	C₄⋊C₄	C₂×D₄₇₉	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₄₇₉	1	1	yes	characteristic
64	C₂²⋊C₄	—	958	1	no	—
65	C₄²	C₂×D₄₇₉	1	1	yes	characteristic
66	C₂³	—	958	1	no	—
67	D₄	—	958	1	no	—
68	D₄	—	479	2	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	1916	2	no	—
72	C₂×C₄	—	958	1	no	—
73	C₂×C₄	C₂²⋊D₄₇₉	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊D₄₇₉	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₄₇₉	1	1	yes	characteristic
76	C₈	—	958	1	no	—
77	C₈	—	958	1	no	—
78	C₂²	—	1916	1	no	—
79	C₂²	—	1916	1	no	—
80	C₂²	—	958	2	no	—
81	C₂²	C₂×C₂²⋊D₄₇₉	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	1916	1	no	—
87	C₄	Q₈×D₄₇₉	1	1	yes	characteristic
88	C₄	#21440163	1	1	yes	characteristic
89	C₂	—	1916	2	no	—
90	C₂	#29506358	1	1	yes	characteristic
91	C₂	#29506402	1	1	yes	characteristic
92	C₂	#29506407	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇₉
commutator, cosocle	C₂×C₄×C₄₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₄₇₉
Fitting	#125×C₄₇₉	C₂
socle	C₂²×C₄₇₉	C₂×D₄
prime radical	C₂×D₁₉₁₆	C₂²
hypercenter	#125	D₄₇₉
hypocenter	C₄₇₉	#478
LCS	G ▷ C₂×C₄×C₄₇₉ ▷ C₂×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #29506315	C₂	semidirect
3. #29506313	C₂	semidirect
4. C₄⋊(C₄₇₉⋊C₈)	C₂	semidirect
7. #125×C₄₇₉	C₂	semidirect
46. C₄₇₉	#478	semidirect
48. #125	D₄₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₉₁₆	2
#29506315	2
#29506313	2
C₄⋊(C₄₇₉⋊C₈)	2
#29506302	2
#125×C₄₇₉	2
#478	479