Subgroups — C₂×#29506373 #44500916

Order 30656.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29506373	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊Dic₄₇₉	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₄₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₇₉⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₄₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₄₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₄₇₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₄₇₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇₉	C₂²	1	2	yes	—
10	C₄⋊Dic₄₇₉	C₂²	1	8	yes	—
11	C₄⋊Dic₄₇₉	C₂²	1	4	yes	—
12	Dic₄₇₉⋊C₄	C₂²	1	8	yes	—
13	C₄×Dic₄₇₉	C₂²	1	4	yes	—
14	C₂²×C₄×C₄₇₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₇₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₄₇₉	C₂²	1	4	yes	—
17	C₂×Dic₄₇₉	—	2	2	no	—
18	C₂×Dic₄₇₉	—	2	2	no	—
19	C₂×Dic₄₇₉	—	2	4	no	—
20	C₂×Dic₄₇₉	C₂³	1	2	yes	—
21	C₂×Dic₄₇₉	C₂³	1	2	yes	—
22	C₂×Dic₄₇₉	C₂³	1	4	yes	—
23	C₂³×C₄₇₉	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₄₇₉	—	2	4	no	—
25	C₂×C₄×C₄₇₉	Q₈	1	4	yes	—
26	C₂×C₄×C₄₇₉	C₂³	1	4	yes	—
27	C₂×C₄×C₄₇₉	C₂³	1	2	yes	—
28	C₂²×C₄₇₉	C₂×Q₈	1	2	yes	—
29	C₂²×C₄₇₉	#41	1	2	yes	—
30	C₂²×C₄₇₉	#41	1	2	yes	—
31	C₂²×C₄₇₉	C₂⁴	1	1	yes	characteristic
32	C₄×C₄₇₉	—	2	4	no	—
33	C₄×C₄₇₉	C₂×Q₈	1	4	yes	—
34	Dic₄₇₉	—	2	2	no	—
35	Dic₄₇₉	—	2	2	no	—
36	Dic₄₇₉	—	2	4	no	—
37	C₂×C₄₇₉	#125	1	4	yes	complemented
38	C₂×C₄₇₉	C₂²×Q₈	1	1	yes	characteristic
39	C₂×C₄₇₉	C₂×#41	1	1	yes	characteristic
40	C₂×C₄₇₉	C₂×#41	1	1	yes	characteristic
41	C₄₇₉	C₂×#125	1	1	yes	characteristic, complemented, Sylow
42	C₂×#125	—	479	1	no	maximal, Sylow
43	#125	—	479	8	no	—
44	C₂×C₄⋊C₄	—	479	2	no	—
45	C₂×C₄⋊C₄	—	479	2	no	—
46	C₂×C₄⋊C₄	—	479	1	no	—
47	C₂×C₄⋊C₄	D₄₇₉	1	1	yes	characteristic
48	C₂×C₄²	—	479	1	no	—
49	C₂²×C₄	—	479	1	no	—
50	C₂²×C₄	—	479	1	no	—
51	C₂²×C₄	—	479	2	no	—
52	C₂²×C₄	C₂×D₄₇₉	1	2	yes	—
53	C₂²×C₄	C₂×D₄₇₉	1	1	yes	characteristic
54	C₄⋊C₄	—	479	8	no	—
55	C₄⋊C₄	—	479	8	no	—
56	C₄⋊C₄	—	479	4	no	—
57	C₄⋊C₄	C₂×D₄₇₉	1	4	yes	—
58	C₄²	—	479	4	no	—
59	C₂³	C₂²×D₄₇₉	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	958	2	no	—
62	C₂×C₄	—	958	2	no	—
63	C₂×C₄	—	958	4	no	—
64	C₂×C₄	—	479	2	no	—
65	C₂×C₄	—	479	2	no	—
66	C₂×C₄	—	479	4	no	—
67	C₂×C₄	Dic₉₅₈	1	4	yes	—
68	C₂×C₄	C₂²×D₄₇₉	1	4	yes	—
69	C₂×C₄	C₂²×D₄₇₉	1	2	yes	—
70	C₂²	C₂×Dic₉₅₈	1	2	yes	—
71	C₂²	#21440161	1	2	yes	—
72	C₂²	#21440163	1	2	yes	—
73	C₂²	C₂³×D₄₇₉	1	1	yes	characteristic
74	C₄	—	2	4	no	—
75	C₄	—	958	2	no	—
76	C₄	—	958	2	no	—
77	C₄	—	958	4	no	—
78	C₄	C₂×Dic₉₅₈	1	4	yes	—
79	C₂	#29506373	1	4	yes	direct product factor
80	C₂	C₂²×Dic₉₅₈	1	1	yes	characteristic
81	C₂	C₂×#21440161	1	1	yes	characteristic
82	C₂	C₂×#21440163	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₄₇₉
commutator, cosocle	C₂²×C₄₇₉	C₂⁴
Frattini	C₂²	C₂³×D₄₇₉
Fitting	C₂×C₄⋊C₄×C₄₇₉	C₂
socle, prime radical	C₂³×C₄₇₉	C₂³
hypercenter	C₂×C₄⋊C₄	D₄₇₉
hypocenter	C₄₇₉	C₂×#125
LCS	G ▷ C₂²×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #29506373	C₂	direct (N × H)
37. C₂×C₄₇₉	#125	semidirect
41. C₄₇₉	C₂×#125	semidirect
79. C₂	#29506373	direct (N × H)

Maximal subgroups

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

subgroup	index
#29506373	2
C₂×C₄⋊Dic₄₇₉	2
C₂×Dic₄₇₉⋊C₄	2
C₂×C₄×Dic₄₇₉	2
C₂×C₄⋊C₄×C₄₇₉	2
C₂×#125	479

Subgroups — C2×#29506373 #44500916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#29506373 #44500916