Subgroups — C₂×C₂₉×#380 #16815992

Order 3712.

1232 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₄×C₂₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊C₄×C₂₉	C₂	1	2	yes	maximal
4	C₂₉×#380	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₂₉×#95	C₂	1	2	yes	maximal, complemented
6	C₂⁵×C₂₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₂₉	—	2	8	no	—
8	C₂³×C₄×C₂₉	C₄	1	8	yes	complemented
9	C₂³×C₄×C₂₉	C₂²	1	4	yes	—
10	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₂₉	C₂²	1	4	yes	—
12	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₂₉	—	2	8	no	—
14	C₂×C₄⋊C₄×C₂₉	C₂²	1	8	yes	complemented
15	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
16	C₂×C₂²⋊C₄×C₂₉	C₂²	1	8	yes	—
17	C₂₉×#95	C₂²	1	8	yes	complemented
18	C₂⁴×C₂₉	—	2	4	no	—
19	C₂⁴×C₂₉	—	2	4	no	—
20	C₂⁴×C₂₉	C₂×C₄	1	4	yes	—
21	C₂⁴×C₂₉	D₄	1	4	yes	—
22	C₂⁴×C₂₉	Q₈	1	4	yes	—
23	C₂⁴×C₂₉	C₂³	1	2	yes	—
24	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₂₉	—	2	4	no	—
26	C₂²×C₄×C₂₉	—	2	32	no	—
27	C₂²×C₄×C₂₉	—	2	16	no	—
28	C₂²×C₄×C₂₉	—	2	8	no	—
29	C₂²×C₄×C₂₉	—	2	8	no	—
30	C₂²×C₄×C₂₉	—	2	8	no	—
31	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₂₉	C₂×C₄	1	16	yes	complemented
34	C₂²×C₄×C₂₉	D₄	1	8	yes	—
35	C₂²×C₄×C₂₉	C₂³	1	8	yes	—
36	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
38	C₄⋊C₄×C₂₉	—	2	16	no	—
39	C₂²⋊C₄×C₂₉	—	2	16	no	—
40	C₂³×C₂₉	—	2	8	no	—
41	C₂³×C₂₉	—	2	8	no	—
42	C₂³×C₂₉	—	2	16	no	—
43	C₂³×C₂₉	—	2	16	no	—
44	C₂³×C₂₉	—	2	4	no	—
45	C₂³×C₂₉	—	2	4	no	—
46	C₂³×C₂₉	C₄⋊C₄	1	16	yes	complemented
47	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
48	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
49	C₂³×C₂₉	C₂×D₄	1	4	yes	—
50	C₂³×C₂₉	C₂×D₄	1	4	yes	—
51	C₂³×C₂₉	C₂×D₄	1	2	yes	—
52	C₂³×C₂₉	C₂×Q₈	1	4	yes	—
53	C₂³×C₂₉	C₂×Q₈	1	2	yes	—
54	C₂³×C₂₉	#41	1	4	yes	—
55	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
56	C₂×C₄×C₂₉	—	2	8	no	—
57	C₂×C₄×C₂₉	—	2	4	no	—
58	C₂×C₄×C₂₉	—	2	32	no	—
59	C₂×C₄×C₂₉	—	2	8	no	—
60	C₂×C₄×C₂₉	—	2	8	no	—
61	C₂×C₄×C₂₉	—	2	8	no	—
62	C₂×C₄×C₂₉	—	4	16	no	—
63	C₂×C₄×C₂₉	C₂²⋊C₄	1	16	yes	complemented
64	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
65	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
66	C₂×C₄×C₂₉	C₂×D₄	1	8	yes	—
67	C₂×#380	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₂₉	—	2	4	no	—
69	C₂²×C₂₉	—	2	4	no	—
70	C₂²×C₂₉	—	2	8	no	—
71	C₂²×C₂₉	—	2	8	no	—
72	C₂²×C₂₉	—	2	32	no	—
73	C₂²×C₂₉	C₂×C₂²⋊C₄	1	4	yes	—
74	C₂²×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
75	C₂²×C₂₉	C₂×C₄⋊C₄	1	8	yes	complemented
76	C₂²×C₂₉	#117	1	4	yes	—
77	C₂²×C₂₉	#121	1	8	yes	—
78	C₂²×C₂₉	C₂²⋊Q₈	1	8	yes	—
79	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
80	C₂²×C₂₉	C₂²×D₄	1	2	yes	—
81	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
82	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
83	C₂²×C₂₉	C₂×#41	1	2	yes	—
84	C₄×C₂₉	—	2	4	no	—
85	C₄×C₂₉	—	4	8	no	—
86	C₄×C₂₉	C₂×C₂²⋊C₄	1	8	yes	complemented
87	C₂⁴×C₄	C₂×C₂₉	1	1	yes	characteristic
88	C₂²×C₄⋊C₄	C₂×C₂₉	1	2	yes	complemented
89	C₂²×C₂²⋊C₄	C₂×C₂₉	1	2	yes	—
90	#380	C₂×C₂₉	1	8	yes	direct product factor
91	C₂×#95	C₂×C₂₉	1	2	yes	complemented
92	C₂×C₂₉	—	2	8	no	—
93	C₂×C₂₉	#380	1	8	yes	direct product factor
94	C₂×C₂₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
97	C₂×C₂₉	C₂×#121	1	2	yes	—
98	C₂×C₂₉	C₂×C₂²⋊Q₈	1	2	yes	—
99	C₂⁵	C₂²×C₂₉	1	1	yes	characteristic
100	C₂³×C₄	—	2	8	no	—
101	C₂³×C₄	C₄×C₂₉	1	8	yes	complemented
102	C₂³×C₄	C₂²×C₂₉	1	4	yes	—
103	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
104	C₂³×C₄	C₂²×C₂₉	1	4	yes	—
105	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
106	C₂×C₄⋊C₄	—	2	8	no	—
107	C₂×C₄⋊C₄	C₂²×C₂₉	1	8	yes	complemented
108	C₂×C₂²⋊C₄	—	2	8	no	—
109	C₂×C₂²⋊C₄	C₂²×C₂₉	1	8	yes	—
110	#95	C₂²×C₂₉	1	8	yes	complemented
111	C₂₉	C₂×#380	1	1	yes	characteristic, direct product factor, Sylow
112	C₂⁴	—	2	4	no	—
113	C₂⁴	—	2	4	no	—
114	C₂⁴	C₂×C₄×C₂₉	1	4	yes	—
115	C₂⁴	D₄×C₂₉	1	4	yes	—
116	C₂⁴	Q₈×C₂₉	1	4	yes	—
117	C₂⁴	C₂³×C₂₉	1	2	yes	—
118	C₂⁴	C₂³×C₂₉	1	1	yes	characteristic
119	C₂²×C₄	—	2	4	no	—
120	C₂²×C₄	—	2	32	no	—
121	C₂²×C₄	—	2	16	no	—
122	C₂²×C₄	—	2	8	no	—
123	C₂²×C₄	—	2	8	no	—
124	C₂²×C₄	—	2	8	no	—
125	C₂²×C₄	C₂×C₄×C₂₉	1	4	yes	—
126	C₂²×C₄	C₂×C₄×C₂₉	1	4	yes	—
127	C₂²×C₄	C₂×C₄×C₂₉	1	16	yes	complemented
128	C₂²×C₄	D₄×C₂₉	1	8	yes	—
129	C₂²×C₄	C₂³×C₂₉	1	8	yes	—
130	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
131	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
132	C₄⋊C₄	—	2	16	no	—
133	C₂²⋊C₄	—	2	16	no	—
134	C₂³	—	2	8	no	—
135	C₂³	—	2	8	no	—
136	C₂³	—	2	16	no	—
137	C₂³	—	2	16	no	—
138	C₂³	—	2	4	no	—
139	C₂³	—	2	4	no	—
140	C₂³	C₄⋊C₄×C₂₉	1	16	yes	complemented
141	C₂³	C₂²×C₄×C₂₉	1	4	yes	—
142	C₂³	C₂²×C₄×C₂₉	1	2	yes	—
143	C₂³	C₂×D₄×C₂₉	1	4	yes	—
144	C₂³	C₂×D₄×C₂₉	1	4	yes	—
145	C₂³	C₂×D₄×C₂₉	1	2	yes	—
146	C₂³	C₂×Q₈×C₂₉	1	4	yes	—
147	C₂³	C₂×Q₈×C₂₉	1	2	yes	—
148	C₂³	#41×C₂₉	1	4	yes	—
149	C₂³	C₂⁴×C₂₉	1	1	yes	characteristic
150	C₂×C₄	—	2	8	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	32	no	—
153	C₂×C₄	—	2	8	no	—
154	C₂×C₄	—	2	8	no	—
155	C₂×C₄	—	2	8	no	—
156	C₂×C₄	—	4	16	no	—
157	C₂×C₄	C₂²⋊C₄×C₂₉	1	16	yes	complemented
158	C₂×C₄	C₂²×C₄×C₂₉	1	4	yes	—
159	C₂×C₄	C₂²×C₄×C₂₉	1	4	yes	—
160	C₂×C₄	C₂×D₄×C₂₉	1	8	yes	—
161	C₂²	—	2	4	no	—
162	C₂²	—	2	4	no	—
163	C₂²	—	2	8	no	—
164	C₂²	—	2	8	no	—
165	C₂²	—	2	32	no	—
166	C₂²	C₂×C₂²⋊C₄×C₂₉	1	4	yes	—
167	C₂²	C₂×C₄⋊C₄×C₂₉	1	4	yes	—
168	C₂²	C₂×C₄⋊C₄×C₂₉	1	8	yes	complemented
169	C₂²	C₂₉×#117	1	4	yes	—
170	C₂²	C₂₉×#121	1	8	yes	—
171	C₂²	C₂₉×C₂²⋊Q₈	1	8	yes	—
172	C₂²	C₂³×C₄×C₂₉	1	1	yes	characteristic
173	C₂²	C₂²×D₄×C₂₉	1	2	yes	—
174	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
175	C₂²	C₂²×Q₈×C₂₉	1	1	yes	characteristic
176	C₂²	C₂×#41×C₂₉	1	2	yes	—
177	C₄	—	2	4	no	—
178	C₄	—	4	8	no	—
179	C₄	C₂×C₂²⋊C₄×C₂₉	1	8	yes	complemented
180	C₂	—	2	8	no	—
181	C₂	C₂₉×#380	1	8	yes	direct product factor
182	C₂	C₂²×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
183	C₂	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
184	C₂	C₂×C₂₉×#117	1	1	yes	characteristic
185	C₂	C₂×C₂₉×#121	1	2	yes	—
186	C₂	C₂×C₂₉×C₂²⋊Q₈	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂³
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₄×C₂₉	C₂	semidirect
4. C₂₉×#380	C₂	direct (N × H)
5. C₂×C₂₉×#95	C₂	semidirect
8. C₂³×C₄×C₂₉	C₄	semidirect
14. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
17. C₂₉×#95	C₂²	semidirect
33. C₂²×C₄×C₂₉	C₂×C₄	semidirect
46. C₂³×C₂₉	C₄⋊C₄	semidirect
63. C₂×C₄×C₂₉	C₂²⋊C₄	semidirect
67. C₂×#380	C₂₉	direct (N × H)
75. C₂²×C₂₉	C₂×C₄⋊C₄	semidirect
86. C₄×C₂₉	C₂×C₂²⋊C₄	semidirect
88. C₂²×C₄⋊C₄	C₂×C₂₉	semidirect
90. #380	C₂×C₂₉	direct (N × H)
91. C₂×#95	C₂×C₂₉	semidirect
93. C₂×C₂₉	#380	direct (N × H)
101. C₂³×C₄	C₄×C₂₉	semidirect
107. C₂×C₄⋊C₄	C₂²×C₂₉	semidirect
110. #95	C₂²×C₂₉	semidirect
111. C₂₉	C₂×#380	direct (N × H)
127. C₂²×C₄	C₂×C₄×C₂₉	semidirect
140. C₂³	C₄⋊C₄×C₂₉	semidirect
157. C₂×C₄	C₂²⋊C₄×C₂₉	semidirect
168. C₂²	C₂×C₄⋊C₄×C₂₉	semidirect
179. C₄	C₂×C₂²⋊C₄×C₂₉	semidirect
181. C₂	C₂₉×#380	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×C₂₉	2
C₂²×C₄⋊C₄×C₂₉	2
C₂²×C₂²⋊C₄×C₂₉	2
C₂₉×#380	2
C₂×C₂₉×#95	2
C₂×#380	29

Subgroups — C2×C29×#380 #16815992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#380 #16815992