Subgroups — #44500999

Order 30656.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29506374	C₂	1	1	yes	maximal, characteristic, complemented
2	#29506363	C₂	1	4	yes	maximal, complemented
3	#29506354	C₂	1	4	yes	maximal, complemented
4	#29506353	C₂	1	2	yes	maximal, complemented
5	D₄×Dic₄₇₉	C₂	1	2	yes	maximal, complemented
6	#29506339	C₂	1	1	yes	maximal, characteristic, complemented
7	#127×C₄₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂²⋊D₄₇₉	C₂²	1	4	yes	—
9	C₂²×Dic₄₇₉	C₂²	1	4	yes	—
10	C₂×C₄×D₄₇₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₇₉	C₂²	1	2	yes	—
12	Dic₄₇₉⋊C₄	C₂²	1	2	yes	—
13	Dic₄₇₉⋊C₄	C₂²	1	4	yes	—
14	C₂²⋊Dic₄₇₉	C₂²	1	4	yes	—
15	C₂²⋊Dic₄₇₉	C₂²	1	4	yes	—
16	(C₂×D₄₇₉)⋊C₄	C₂²	1	2	yes	—
17	C₄×Dic₄₇₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₄₇₉	C₂²	1	2	yes	—
19	C₂×D₄×C₄₇₉	C₂²	1	4	yes	—
20	C₄²×C₄₇₉	C₂²	1	1	yes	characteristic
21	C₂²×D₄₇₉	C₂³	1	1	yes	characteristic
22	C₂²⋊D₄₇₉	—	4	4	no	—
23	C₂×Dic₄₇₉	—	4	4	no	—
24	C₂×Dic₄₇₉	C₂³	1	2	yes	—
25	C₂×Dic₄₇₉	C₂³	1	1	yes	characteristic
26	C₂×Dic₄₇₉	C₂³	1	4	yes	—
27	C₄×D₄₇₉	—	2	2	no	—
28	C₂³×C₄₇₉	C₂³	1	4	yes	—
29	D₄×C₄₇₉	—	2	4	no	—
30	D₄×C₄₇₉	—	4	4	no	—
31	C₂×C₄×C₄₇₉	C₂³	1	2	yes	—
32	C₂×C₄×C₄₇₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄₇₉	—	2	4	no	—
34	C₂²×C₄₇₉	—	2	4	no	—
35	C₂²×C₄₇₉	—	2	4	no	—
36	C₂²×C₄₇₉	C₂⁴	1	1	yes	characteristic
37	C₂×D₄₇₉	—	2	1	no	—
38	C₂×D₄₇₉	—	2	2	no	—
39	C₄×C₄₇₉	—	2	2	no	—
40	C₄×C₄₇₉	#41	1	2	yes	—
41	Dic₄₇₉	—	2	1	no	—
42	Dic₄₇₉	—	2	2	no	—
43	Dic₄₇₉	—	2	4	no	—
44	C₂×C₄₇₉	—	4	4	no	—
45	C₂×C₄₇₉	C₂×#41	1	1	yes	characteristic
46	C₂×C₄₇₉	H(5,𝔽₂)	1	2	yes	—
47	D₄₇₉	—	4	1	no	—
48	C₄₇₉	#540	1	1	yes	characteristic, complemented, Sylow
49	#540	—	479	1	no	maximal, Sylow
50	#127	D₄₇₉	1	1	yes	characteristic, complemented
51	#125	—	479	1	no	—
52	#123	—	479	4	no	—
53	#121	—	479	2	no	—
54	#121	—	479	4	no	—
55	C₄×D₄	—	479	2	no	—
56	#117	—	479	1	no	—
57	C₂×D₄	—	479	4	no	—
58	C₂×D₄	C₂×D₄₇₉	1	2	yes	—
59	C₂×D₄	C₂×D₄₇₉	1	4	yes	—
60	C₂²×C₄	—	479	4	no	—
61	C₂²×C₄	—	479	1	no	—
62	C₄⋊C₄	—	479	2	no	—
63	C₄⋊C₄	—	479	2	no	—
64	C₄⋊C₄	—	479	4	no	—
65	C₂²⋊C₄	—	479	4	no	—
66	C₂²⋊C₄	—	479	4	no	—
67	C₂²⋊C₄	—	479	2	no	—
68	C₄²	—	479	1	no	—
69	C₄²	C₂×D₄₇₉	1	1	yes	characteristic
70	C₂³	—	479	1	no	—
71	C₂³	C₂²×D₄₇₉	1	4	yes	—
72	D₄	—	2	4	no	—
73	D₄	—	4	4	no	—
74	D₄	—	1916	4	no	—
75	C₂×C₄	—	1916	4	no	—
76	C₂×C₄	—	958	2	no	—
77	C₂×C₄	—	479	2	no	—
78	C₂×C₄	—	479	1	no	—
79	C₂×C₄	—	479	4	no	—
80	C₂×C₄	C₂²×D₄₇₉	1	2	yes	—
81	C₂×C₄	C₂²×D₄₇₉	1	1	yes	characteristic
82	C₂²	—	2	4	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	4	no	—
85	C₂²	—	958	1	no	—
86	C₂²	—	958	2	no	—
87	C₂²	C₂³×D₄₇₉	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	958	1	no	—
90	C₄	—	958	2	no	—
91	C₄	—	958	4	no	—
92	C₄	#21440161	1	2	yes	—
93	C₂	—	4	4	no	—
94	C₂	—	1916	1	no	—
95	C₂	C₂×#21440161	1	1	yes	characteristic
96	C₂	#29506427	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₇₉
commutator, socle, cosocle	C₂²×C₄₇₉	C₂⁴
Fitting	#127×C₄₇₉	C₂
hypercenter	#127	D₄₇₉
hypocenter	C₄₇₉	#540
LCS	G ▷ C₂²×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #29506374	C₂	semidirect
2. #29506363	C₂	semidirect
3. #29506354	C₂	semidirect
4. #29506353	C₂	semidirect
5. D₄×Dic₄₇₉	C₂	semidirect
6. #29506339	C₂	semidirect
7. #127×C₄₇₉	C₂	semidirect
48. C₄₇₉	#540	semidirect
50. #127	D₄₇₉	semidirect

Maximal subgroups

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

subgroup	index
#29506374	2
#29506363	2
#29506354	2
#29506353	2
D₄×Dic₄₇₉	2
#29506339	2
#127×C₄₇₉	2
#540	479