Subgroups — C₂₉×#7159 #20302059

Order 7424.

222 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1564	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₉×M₃₂	C₄	1	2	yes	—
5	C₂₉×#431	—	2	1	no	—
6	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
7	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₂₉×#346	—	2	1	no	—
9	C₄×C₁₆×C₂₉	—	2	1	no	—
10	C₂₉×#335	—	2	1	no	—
11	C₂₉×#335	—	2	1	no	—
12	C₂₉×#335	C₄	1	2	yes	—
13	C₂₉×#334	C₄	1	2	yes	—
14	C₂²×C₈×C₂₉	—	4	1	no	—
15	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₂₉	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
18	C₂₉×M₃₂	—	2	2	no	—
19	C₂₉×M₃₂	C₈	1	4	yes	complemented
20	C₂×C₁₆×C₂₉	—	2	2	no	—
21	C₂₉×C₄⋊C₈	—	2	2	no	—
22	C₂₉×C₄⋊C₈	—	2	2	no	—
23	C₂₉×C₄⋊C₈	—	4	1	no	—
24	C₂₉×C₂²⋊C₈	—	4	1	no	—
25	C₄×C₈×C₂₉	—	4	1	no	—
26	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
29	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
32	C₂²×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₈×C₂₉	—	2	2	no	—
34	C₂×C₈×C₂₉	—	4	2	no	—
35	C₂×C₈×C₂₉	—	4	2	no	—
36	C₂×C₈×C₂₉	—	8	2	no	—
37	C₂×C₈×C₂₉	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₂₉	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₂₉	M₁₆	1	2	yes	—
43	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₄²×C₂₉	D₈	1	1	yes	characteristic
46	C₄²×C₂₉	Q₁₆	1	1	yes	characteristic
47	C₁₆×C₂₉	—	2	4	no	—
48	#7159	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂³×C₂₉	#106	1	1	yes	characteristic
50	C₂×C₄×C₂₉	—	2	1	no	—
51	C₂×C₄×C₂₉	—	2	1	no	—
52	C₂×C₄×C₂₉	—	4	1	no	—
53	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
54	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
55	C₂×C₄×C₂₉	#102	1	1	yes	characteristic
56	C₂×C₄×C₂₉	#103	1	1	yes	characteristic
57	C₂×C₄×C₂₉	#103	1	1	yes	characteristic
58	C₂×C₄×C₂₉	C₄⋊C₈	1	2	yes	—
59	C₂×C₄×C₂₉	#107	1	1	yes	characteristic
60	C₂×C₄×C₂₉	#108	1	2	yes	—
61	C₈×C₂₉	—	2	1	no	—
62	C₈×C₂₉	—	2	1	no	—
63	C₈×C₂₉	—	8	2	no	—
64	C₈×C₂₉	—	8	2	no	—
65	C₈×C₂₉	C₄×C₈	1	1	yes	characteristic
66	C₈×C₂₉	#97	1	1	yes	characteristic
67	C₈×C₂₉	C₂²⋊C₈	1	2	yes	—
68	C₄×M₃₂	C₂×C₂₉	1	1	yes	characteristic
69	#1564	C₂×C₂₉	1	1	yes	characteristic
70	C₂×#335	C₂×C₂₉	1	1	yes	characteristic
71	C₂²×C₂₉	—	2	1	no	—
72	C₂²×C₂₉	—	2	1	no	—
73	C₂²×C₂₉	#334	1	2	yes	—
74	C₂²×C₂₉	#340	1	1	yes	characteristic
75	C₄×C₂₉	—	2	1	no	—
76	C₄×C₂₉	—	2	1	no	—
77	C₄×C₂₉	—	2	1	no	—
78	C₄×C₂₉	#335	1	2	yes	—
79	C₄×C₂₉	#336	1	1	yes	characteristic
80	C₄×C₂₉	#341	1	1	yes	characteristic
81	C₄×C₂₉	#361	1	1	yes	characteristic
82	C₄×C₂₉	#362	1	1	yes	characteristic
83	C₂×M₃₂	C₄×C₂₉	1	2	yes	—
84	#431	—	2	1	no	—
85	C₂×C₄⋊C₈	—	2	1	no	—
86	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
87	#346	—	2	1	no	—
88	C₄×C₁₆	—	2	1	no	—
89	#335	—	2	1	no	—
90	#335	—	2	1	no	—
91	#335	C₄×C₂₉	1	2	yes	—
92	#334	C₄×C₂₉	1	2	yes	—
93	C₂×C₂₉	—	2	2	no	—
94	C₂×C₂₉	#1277	1	1	yes	characteristic
95	C₂×C₂₉	#1387	1	1	yes	characteristic
96	C₂×C₂₉	#1389	1	1	yes	characteristic
97	C₂²×C₈	—	4	1	no	—
98	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
99	C₂²×C₈	Q₈×C₂₉	1	1	yes	characteristic
100	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
101	M₃₂	—	2	2	no	—
102	M₃₂	C₈×C₂₉	1	4	yes	complemented
103	C₂×C₁₆	—	2	2	no	—
104	C₄⋊C₈	—	2	2	no	—
105	C₄⋊C₈	—	2	2	no	—
106	C₄⋊C₈	—	4	1	no	—
107	C₂²⋊C₈	—	4	1	no	—
108	C₄×C₈	—	4	1	no	—
109	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
110	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
111	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
112	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
113	C₂₉	#7159	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
115	C₂²×C₄	SD₁₆×C₂₉	1	1	yes	characteristic
116	C₂²×C₄	SD₁₆×C₂₉	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	4	2	no	—
119	C₂×C₈	—	4	2	no	—
120	C₂×C₈	—	8	2	no	—
121	C₂×C₈	C₄²×C₂₉	1	1	yes	characteristic
122	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
123	C₂×C₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
124	C₂×C₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
125	C₂×C₈	C₂×C₈×C₂₉	1	2	yes	—
126	C₂×C₈	M₁₆×C₂₉	1	2	yes	—
127	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
128	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
129	C₄²	D₈×C₂₉	1	1	yes	characteristic
130	C₄²	Q₁₆×C₂₉	1	1	yes	characteristic
131	C₁₆	—	2	4	no	—
132	C₂³	C₂₉×#106	1	1	yes	characteristic
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
137	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
138	C₂×C₄	C₂₉×#102	1	1	yes	characteristic
139	C₂×C₄	C₂₉×#103	1	1	yes	characteristic
140	C₂×C₄	C₂₉×#103	1	1	yes	characteristic
141	C₂×C₄	C₂₉×C₄⋊C₈	1	2	yes	—
142	C₂×C₄	C₂₉×#107	1	1	yes	characteristic
143	C₂×C₄	C₂₉×#108	1	2	yes	—
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	8	2	no	—
147	C₈	—	8	2	no	—
148	C₈	C₄×C₈×C₂₉	1	1	yes	characteristic
149	C₈	C₂₉×#97	1	1	yes	characteristic
150	C₈	C₂₉×C₂²⋊C₈	1	2	yes	—
151	C₂²	—	2	1	no	—
152	C₂²	—	2	1	no	—
153	C₂²	C₂₉×#334	1	2	yes	—
154	C₂²	C₂₉×#340	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	C₂₉×#335	1	2	yes	—
159	C₄	C₂₉×#336	1	1	yes	characteristic
160	C₄	C₂₉×#341	1	1	yes	characteristic
161	C₄	C₂₉×#361	1	1	yes	characteristic
162	C₄	C₂₉×#362	1	1	yes	characteristic
163	C₂	—	2	2	no	—
164	C₂	C₂₉×#1277	1	1	yes	characteristic
165	C₂	C₂₉×#1387	1	1	yes	characteristic
166	C₂	C₂₉×#1389	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#102
commutator	C₈	C₄×C₈×C₂₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₂₉
socle	C₂²×C₂₉	#340
prime radical	C₂³×C₂₉	#106
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
19. C₂₉×M₃₂	C₈	semidirect
48. #7159	C₂₉	direct (N × H)
102. M₃₂	C₈×C₂₉	semidirect
113. C₂₉	#7159	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂₉×M₃₂	2
C₂₉×#1564	2
C₂×C₂₉×#335	2
#7159	29

Subgroups — C29×#7159 #20302059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7159 #20302059