Subgroups — #14271767

Order 1856.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745301	C₂	1	4	yes	maximal, complemented
3	#11745300	C₂	1	2	yes	maximal, complemented
4	#11745297	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₂₉	C₂	1	2	yes	maximal, complemented
6	#11745234	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₂₉	C₂²	1	2	yes	—
9	C₂×D₄×C₂₉	C₂²	1	4	yes	—
10	C₂×C₂²⋊D₂₉	C₂²	1	4	yes	—
11	C₂²×Dic₂₉	C₂²	1	4	yes	—
12	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
13	C₄²×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²⋊Dic₂₉	C₂²	1	4	yes	—
15	C₂²⋊Dic₂₉	C₂²	1	4	yes	—
16	#90781	C₂²	1	2	yes	—
17	C₄⋊Dic₂₉	C₂²	1	2	yes	—
18	#90779	C₂²	1	2	yes	—
19	#90779	C₂²	1	4	yes	—
20	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
21	C₂³×C₂₉	C₂³	1	4	yes	—
22	C₂²×D₂₉	C₂³	1	1	yes	characteristic
23	D₄×C₂₉	—	2	4	no	—
24	D₄×C₂₉	—	4	4	no	—
25	C₂×C₄×C₂₉	C₂³	1	2	yes	—
26	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
27	C₂²⋊D₂₉	—	4	4	no	—
28	C₂×Dic₂₉	—	4	4	no	—
29	C₂×Dic₂₉	C₂³	1	2	yes	—
30	C₂×Dic₂₉	C₂³	1	4	yes	—
31	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
32	C₄×D₂₉	—	2	2	no	—
33	C₂²×C₂₉	—	2	4	no	—
34	C₂²×C₂₉	—	2	4	no	—
35	C₂²×C₂₉	—	2	4	no	—
36	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
37	C₂×D₂₉	—	2	1	no	—
38	C₂×D₂₉	—	2	2	no	—
39	C₄×C₂₉	—	2	2	no	—
40	C₄×C₂₉	#41	1	2	yes	—
41	Dic₂₉	—	2	1	no	—
42	Dic₂₉	—	2	2	no	—
43	Dic₂₉	—	2	4	no	—
44	#540	—	29	1	no	maximal, Sylow
45	C₂×C₂₉	—	4	4	no	—
46	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
47	C₂×C₂₉	H(5,𝔽₂)	1	2	yes	—
48	D₂₉	—	4	1	no	—
49	#127	D₂₉	1	1	yes	characteristic, complemented
50	#125	—	29	1	no	—
51	#123	—	29	4	no	—
52	#121	—	29	2	no	—
53	#121	—	29	4	no	—
54	C₄×D₄	—	29	2	no	—
55	#117	—	29	1	no	—
56	C₂₉	#540	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	29	4	no	—
58	C₂×D₄	C₂×D₂₉	1	2	yes	—
59	C₂×D₄	C₂×D₂₉	1	4	yes	—
60	C₂²×C₄	—	29	4	no	—
61	C₂²×C₄	—	29	1	no	—
62	C₄⋊C₄	—	29	2	no	—
63	C₄⋊C₄	—	29	2	no	—
64	C₄⋊C₄	—	29	4	no	—
65	C₂²⋊C₄	—	29	4	no	—
66	C₂²⋊C₄	—	29	4	no	—
67	C₂²⋊C₄	—	29	2	no	—
68	C₄²	—	29	1	no	—
69	C₄²	C₂×D₂₉	1	1	yes	characteristic
70	C₂³	—	29	1	no	—
71	C₂³	C₂²×D₂₉	1	4	yes	—
72	D₄	—	2	4	no	—
73	D₄	—	4	4	no	—
74	D₄	—	116	4	no	—
75	C₂×C₄	—	29	2	no	—
76	C₂×C₄	—	29	1	no	—
77	C₂×C₄	—	29	4	no	—
78	C₂×C₄	—	58	2	no	—
79	C₂×C₄	—	116	4	no	—
80	C₂×C₄	C₂²×D₂₉	1	2	yes	—
81	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
82	C₂²	—	2	4	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	4	no	—
85	C₂²	—	58	1	no	—
86	C₂²	—	58	2	no	—
87	C₂²	C₂³×D₂₉	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	58	1	no	—
90	C₄	—	58	2	no	—
91	C₄	—	58	4	no	—
92	C₄	#90807	1	2	yes	—
93	C₂	—	4	4	no	—
94	C₂	—	116	1	no	—
95	C₂	C₂×#90807	1	1	yes	characteristic
96	C₂	#11745359	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#127	C₂
hypercenter	#127	D₂₉
hypocenter	C₂₉	#540
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂₉×#127	C₂	semidirect
2. #11745301	C₂	semidirect
3. #11745300	C₂	semidirect
4. #11745297	C₂	semidirect
5. D₄×Dic₂₉	C₂	semidirect
6. #11745234	C₂	semidirect
7. #11745232	C₂	semidirect
49. #127	D₂₉	semidirect
56. C₂₉	#540	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#127	2
#11745301	2
#11745300	2
#11745297	2
D₄×Dic₂₉	2
#11745234	2
#11745232	2
#540	29