Subgroups — C₂₉×#2955 #16816669

Order 3712.

456 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#131	C₂	1	2	yes	maximal, complemented
3	C₂₉×#444	C₂	1	4	yes	maximal, complemented
4	C₂₉×#443	C₂	1	4	yes	maximal, complemented
5	C₂₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#421	C₂	1	2	yes	maximal, complemented
7	C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#41×C₂₉	C₂²	1	2	yes	—
9	C₂₉×#137	C₄	1	4	yes	complemented
10	C₂₉×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
11	C₂₉×#135	C₂²	1	4	yes	—
12	C₂₉×#131	—	2	2	no	—
13	C₂₉×#131	—	2	2	no	—
14	C₂₉×#131	C₂²	1	4	yes	complemented
15	C₂₉×#131	C₂²	1	4	yes	complemented
16	C₂×M₁₆×C₂₉	—	2	2	no	—
17	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
18	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₂₉	—	2	2	no	—
20	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×#117	C₂²	1	1	yes	characteristic
22	C₂₉×#108	C₂²	1	4	yes	complemented
23	C₂₉×#104	C₂²	1	8	yes	complemented
24	C₂₉×#97	C₂²	1	2	yes	complemented
25	C₄×C₈×C₂₉	C₂²	1	2	yes	complemented
26	#41×C₂₉	—	2	2	no	—
27	#41×C₂₉	—	2	2	no	—
28	#41×C₂₉	C₂×C₄	1	4	yes	—
29	#41×C₂₉	C₂³	1	4	yes	—
30	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
31	C₂×D₄×C₂₉	—	2	2	no	—
32	C₂×D₄×C₂₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₂₉	—	2	2	no	—
34	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
35	Q₁₆×C₂₉	C₂×C₄	1	4	yes	—
36	SD₁₆×C₂₉	C₂×C₄	1	8	yes	—
37	D₈×C₂₉	C₂×C₄	1	4	yes	—
38	M₁₆×C₂₉	—	2	2	no	—
39	M₁₆×C₂₉	—	2	4	no	—
40	M₁₆×C₂₉	—	2	4	no	—
41	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
42	M₁₆×C₂₉	C₂³	1	4	yes	—
43	C₂×C₈×C₂₉	—	2	2	no	—
44	C₂×C₈×C₂₉	—	2	4	no	—
45	C₂×C₈×C₂₉	—	2	4	no	—
46	C₂×C₈×C₂₉	D₄	1	2	yes	—
47	C₂×C₈×C₂₉	D₄	1	2	yes	—
48	C₂×C₈×C₂₉	C₂³	1	2	yes	—
49	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
51	C₄⋊C₄×C₂₉	—	2	1	no	—
52	C₂²⋊C₄×C₂₉	—	2	1	no	—
53	C₄²×C₂₉	C₂³	1	2	yes	—
54	C₂³×C₂₉	—	2	2	no	—
55	C₂³×C₂₉	#41	1	1	yes	characteristic
56	Q₈×C₂₉	—	2	2	no	—
57	Q₈×C₂₉	C₂²×C₄	1	4	yes	—
58	D₄×C₂₉	—	2	4	no	—
59	D₄×C₂₉	—	2	4	no	—
60	D₄×C₂₉	—	2	2	no	—
61	D₄×C₂₉	C₂²×C₄	1	4	yes	—
62	C₂×C₄×C₂₉	—	2	2	no	—
63	C₂×C₄×C₂₉	—	2	4	no	—
64	C₂×C₄×C₂₉	—	2	4	no	—
65	C₂×C₄×C₂₉	—	2	2	no	—
66	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
67	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
69	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
70	C₈×C₂₉	—	2	4	no	—
71	C₈×C₂₉	C₂²×C₄	1	4	yes	—
72	C₈×C₂₉	C₂×D₄	1	2	yes	—
73	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
74	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
75	#2955	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂²×C₂₉	—	2	4	no	—
77	C₂²×C₂₉	—	4	1	no	—
78	C₂²×C₂₉	—	4	4	no	—
79	C₂²×C₂₉	C₄×D₄	1	2	yes	—
80	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
81	C₄×C₂₉	—	2	4	no	—
82	C₄×C₂₉	—	4	2	no	—
83	C₄×C₂₉	C₄×D₄	1	2	yes	—
84	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
85	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
86	#575	C₂×C₂₉	1	1	yes	characteristic
87	C₂×#131	C₂×C₂₉	1	2	yes	complemented
88	#444	C₂×C₂₉	1	4	yes	complemented
89	#443	C₂×C₂₉	1	4	yes	complemented
90	#430	C₂×C₂₉	1	1	yes	characteristic, complemented
91	#421	C₂×C₂₉	1	2	yes	complemented
92	#405	C₂×C₂₉	1	1	yes	characteristic, complemented
93	C₂×C₂₉	—	2	1	no	—
94	C₂×C₂₉	—	2	2	no	—
95	C₂×C₂₉	—	4	4	no	—
96	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
97	C₂×#41	C₂²×C₂₉	1	2	yes	—
98	#137	C₄×C₂₉	1	4	yes	complemented
99	AGL(1,ℤ/8)	C₄×C₂₉	1	4	yes	complemented
100	#135	C₂²×C₂₉	1	4	yes	—
101	#131	—	2	2	no	—
102	#131	—	2	2	no	—
103	#131	C₂²×C₂₉	1	4	yes	complemented
104	#131	C₂²×C₂₉	1	4	yes	complemented
105	C₂×M₁₆	—	2	2	no	—
106	C₂×M₁₆	C₂²×C₂₉	1	2	yes	—
107	C₂×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
108	C₂²×C₈	—	2	2	no	—
109	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic
110	#117	C₂²×C₂₉	1	1	yes	characteristic
111	#108	C₂²×C₂₉	1	4	yes	complemented
112	#104	C₂²×C₂₉	1	8	yes	complemented
113	#97	C₂²×C₂₉	1	2	yes	complemented
114	C₄×C₈	C₂²×C₂₉	1	2	yes	complemented
115	C₂₉	#2955	1	1	yes	characteristic, direct product factor, Sylow
116	#41	—	2	2	no	—
117	#41	—	2	2	no	—
118	#41	C₂×C₄×C₂₉	1	4	yes	—
119	#41	C₂³×C₂₉	1	4	yes	—
120	C₂×Q₈	C₂×C₄×C₂₉	1	2	yes	—
121	C₂×D₄	—	2	2	no	—
122	C₂×D₄	C₂×C₄×C₂₉	1	2	yes	—
123	C₂²×C₄	—	2	2	no	—
124	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
125	Q₁₆	C₂×C₄×C₂₉	1	4	yes	—
126	SD₁₆	C₂×C₄×C₂₉	1	8	yes	—
127	D₈	C₂×C₄×C₂₉	1	4	yes	—
128	M₁₆	—	2	2	no	—
129	M₁₆	—	2	4	no	—
130	M₁₆	—	2	4	no	—
131	M₁₆	C₂×C₄×C₂₉	1	4	yes	—
132	M₁₆	C₂³×C₂₉	1	4	yes	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	D₄×C₂₉	1	2	yes	—
137	C₂×C₈	D₄×C₂₉	1	2	yes	—
138	C₂×C₈	C₂³×C₂₉	1	2	yes	—
139	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
140	C₂×C₈	C₂³×C₂₉	1	1	yes	characteristic
141	C₄⋊C₄	—	2	1	no	—
142	C₂²⋊C₄	—	2	1	no	—
143	C₄²	C₂³×C₂₉	1	2	yes	—
144	C₂³	—	2	2	no	—
145	C₂³	#41×C₂₉	1	1	yes	characteristic
146	Q₈	—	2	2	no	—
147	Q₈	C₂²×C₄×C₂₉	1	4	yes	—
148	D₄	—	2	4	no	—
149	D₄	—	2	4	no	—
150	D₄	—	2	2	no	—
151	D₄	C₂²×C₄×C₂₉	1	4	yes	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
157	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
158	C₂×C₄	#41×C₂₉	1	1	yes	characteristic
159	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
160	C₈	—	2	4	no	—
161	C₈	C₂²×C₄×C₂₉	1	4	yes	—
162	C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
163	C₈	C₂×D₄×C₂₉	1	2	yes	—
164	C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
165	C₂²	—	2	4	no	—
166	C₂²	—	4	1	no	—
167	C₂²	—	4	4	no	—
168	C₂²	C₄×D₄×C₂₉	1	2	yes	—
169	C₂²	C₂×#41×C₂₉	1	1	yes	characteristic
170	C₄	—	2	4	no	—
171	C₄	—	4	2	no	—
172	C₄	C₄×D₄×C₂₉	1	2	yes	—
173	C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
174	C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
175	C₂	—	2	1	no	—
176	C₂	—	2	2	no	—
177	C₂	—	4	4	no	—
178	C₂	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂×C₂₉	C₂×C₄×D₄
prime radical	C₂₉×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#131	C₂	semidirect
3. C₂₉×#444	C₂	semidirect
4. C₂₉×#443	C₂	semidirect
5. C₂₉×#430	C₂	semidirect
6. C₂₉×#421	C₂	semidirect
7. C₂₉×#405	C₂	semidirect
9. C₂₉×#137	C₄	semidirect
10. C₂₉×AGL(1,ℤ/8)	C₄	semidirect
14. C₂₉×#131	C₂²	semidirect
15. C₂₉×#131	C₂²	semidirect
22. C₂₉×#108	C₂²	semidirect
23. C₂₉×#104	C₂²	semidirect
24. C₂₉×#97	C₂²	semidirect
25. C₄×C₈×C₂₉	C₂²	semidirect
75. #2955	C₂₉	direct (N × H)
87. C₂×#131	C₂×C₂₉	semidirect
88. #444	C₂×C₂₉	semidirect
89. #443	C₂×C₂₉	semidirect
90. #430	C₂×C₂₉	semidirect
91. #421	C₂×C₂₉	semidirect
92. #405	C₂×C₂₉	semidirect
98. #137	C₄×C₂₉	semidirect
99. AGL(1,ℤ/8)	C₄×C₂₉	semidirect
103. #131	C₂²×C₂₉	semidirect
104. #131	C₂²×C₂₉	semidirect
111. #108	C₂²×C₂₉	semidirect
112. #104	C₂²×C₂₉	semidirect
113. #97	C₂²×C₂₉	semidirect
114. C₄×C₈	C₂²×C₂₉	semidirect
115. C₂₉	#2955	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#575	2
C₂×C₂₉×#131	2
C₂₉×#444	2
C₂₉×#443	2
C₂₉×#430	2
C₂₉×#421	2
C₂₉×#405	2
#2955	29

Subgroups — C29×#2955 #16816669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2955 #16816669