Subgroups — C₂×C₂₉×#385 #16816000

Order 3712.

1232 conjugacy classes of subgroups.

The subgroup lattice has 216 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	1	yes	maximal, characteristic
4	C₂²×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#385	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₉×#95	C₂	1	2	yes	maximal, complemented
7	C₂⁵×C₂₉	C₂²	1	1	yes	characteristic
8	C₂³×C₄×C₂₉	—	2	4	no	—
9	C₂³×C₄×C₂₉	—	2	8	no	—
10	C₂³×C₄×C₂₉	C₂²	1	4	yes	—
11	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₂₉	C₂²	1	2	yes	—
14	C₂³×C₄×C₂₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₄×C₂₉	—	2	8	no	—
16	C₂×C₄⋊C₄×C₂₉	C₂²	1	8	yes	complemented
17	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
18	C₂×C₂²⋊C₄×C₂₉	C₄	1	8	yes	complemented
19	C₂×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
20	C₂×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
21	C₂₉×#95	C₂²	1	8	yes	complemented
22	C₂⁴×C₂₉	—	2	4	no	—
23	C₂⁴×C₂₉	—	2	4	no	—
24	C₂⁴×C₂₉	C₂×C₄	1	4	yes	—
25	C₂⁴×C₂₉	D₄	1	4	yes	—
26	C₂⁴×C₂₉	Q₈	1	4	yes	—
27	C₂⁴×C₂₉	C₂³	1	2	yes	—
28	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₂₉	—	2	32	no	—
30	C₂²×C₄×C₂₉	—	2	4	no	—
31	C₂²×C₄×C₂₉	—	2	8	no	—
32	C₂²×C₄×C₂₉	—	2	4	no	—
33	C₂²×C₄×C₂₉	—	2	4	no	—
34	C₂²×C₄×C₂₉	—	2	4	no	—
35	C₂²×C₄×C₂₉	—	2	16	no	—
36	C₂²×C₄×C₂₉	—	2	2	no	—
37	C₂²×C₄×C₂₉	—	2	2	no	—
38	C₂²×C₄×C₂₉	—	2	4	no	—
39	C₂²×C₄×C₂₉	—	2	4	no	—
40	C₂²×C₄×C₂₉	C₂×C₄	1	8	yes	complemented
41	C₂²×C₄×C₂₉	D₄	1	8	yes	—
42	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
43	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
44	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
45	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
46	C₄⋊C₄×C₂₉	—	2	16	no	—
47	C₂²⋊C₄×C₂₉	—	2	8	no	—
48	C₂²⋊C₄×C₂₉	C₂×C₄	1	16	yes	complemented
49	C₂³×C₂₉	—	2	16	no	—
50	C₂³×C₂₉	—	2	8	no	—
51	C₂³×C₂₉	—	2	16	no	—
52	C₂³×C₂₉	—	2	8	no	—
53	C₂³×C₂₉	—	2	4	no	—
54	C₂³×C₂₉	—	2	4	no	—
55	C₂³×C₂₉	C₄⋊C₄	1	16	yes	complemented
56	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
57	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
58	C₂³×C₂₉	C₂×D₄	1	4	yes	—
59	C₂³×C₂₉	C₂×D₄	1	2	yes	—
60	C₂³×C₂₉	C₂×D₄	1	4	yes	—
61	C₂³×C₂₉	C₂×Q₈	1	4	yes	—
62	C₂³×C₂₉	C₂×Q₈	1	2	yes	—
63	C₂³×C₂₉	#41	1	4	yes	—
64	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
65	C₂×C₄×C₂₉	—	2	32	no	—
66	C₂×C₄×C₂₉	—	2	16	no	—
67	C₂×C₄×C₂₉	—	2	16	no	—
68	C₂×C₄×C₂₉	—	2	4	no	—
69	C₂×C₄×C₂₉	—	2	4	no	—
70	C₂×C₄×C₂₉	—	2	4	no	—
71	C₂×C₄×C₂₉	—	2	4	no	—
72	C₂×C₄×C₂₉	—	2	2	no	—
73	C₂×C₄×C₂₉	—	2	2	no	—
74	C₂×C₄×C₂₉	—	2	4	no	—
75	C₂×C₄×C₂₉	—	2	4	no	—
76	C₂×C₄×C₂₉	—	4	4	no	—
77	C₂×C₄×C₂₉	—	4	4	no	—
78	C₂×C₄×C₂₉	C₂²×C₄	1	8	yes	complemented
79	C₂×C₄×C₂₉	C₂×D₄	1	8	yes	—
80	C₂×#385	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂²×C₂₉	—	2	8	no	—
82	C₂²×C₂₉	—	2	4	no	—
83	C₂²×C₂₉	—	2	8	no	—
84	C₂²×C₂₉	—	2	4	no	—
85	C₂²×C₂₉	—	2	32	no	—
86	C₂²×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
87	C₂²×C₂₉	C₂×C₄⋊C₄	1	8	yes	complemented
88	C₂²×C₂₉	C₄×D₄	1	8	yes	—
89	C₂²×C₂₉	#120	1	4	yes	—
90	C₂²×C₂₉	C₂²⋊Q₈	1	8	yes	—
91	C₂²×C₂₉	#123	1	4	yes	—
92	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
93	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
94	C₂²×C₂₉	C₂²×D₄	1	2	yes	—
95	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
96	C₂²×C₂₉	C₂×#41	1	2	yes	—
97	C₄×C₂₉	—	2	8	no	—
98	C₄×C₂₉	—	2	8	no	—
99	C₄×C₂₉	—	4	2	no	—
100	C₄×C₂₉	—	4	2	no	—
101	C₂⁴×C₄	C₂×C₂₉	1	1	yes	characteristic
102	C₂²×C₄⋊C₄	C₂×C₂₉	1	2	yes	complemented
103	C₂²×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic
104	C₂²×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic
105	#385	C₂×C₂₉	1	8	yes	direct product factor
106	C₂×#95	C₂×C₂₉	1	2	yes	complemented
107	C₂×C₂₉	—	2	8	no	—
108	C₂×C₂₉	#385	1	8	yes	direct product factor
109	C₂×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂₉	C₂×C₄×D₄	1	2	yes	—
111	C₂×C₂₉	C₂×#120	1	1	yes	characteristic
112	C₂×C₂₉	C₂×C₂²⋊Q₈	1	2	yes	—
113	C₂×C₂₉	C₂×#123	1	1	yes	characteristic
114	C₂⁵	C₂²×C₂₉	1	1	yes	characteristic
115	C₂³×C₄	—	2	4	no	—
116	C₂³×C₄	—	2	8	no	—
117	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
118	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
119	C₂³×C₄	C₂²×C₂₉	1	4	yes	—
120	C₂³×C₄	C₂²×C₂₉	1	2	yes	—
121	C₂³×C₄	C₂²×C₂₉	1	2	yes	—
122	C₂×C₄⋊C₄	—	2	8	no	—
123	C₂×C₄⋊C₄	C₂²×C₂₉	1	8	yes	complemented
124	C₂×C₂²⋊C₄	—	2	4	no	—
125	C₂×C₂²⋊C₄	C₄×C₂₉	1	8	yes	complemented
126	C₂×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
127	C₂×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
128	#95	C₂²×C₂₉	1	8	yes	complemented
129	C₂₉	C₂×#385	1	1	yes	characteristic, direct product factor, Sylow
130	C₂⁴	—	2	4	no	—
131	C₂⁴	—	2	4	no	—
132	C₂⁴	C₂×C₄×C₂₉	1	4	yes	—
133	C₂⁴	D₄×C₂₉	1	4	yes	—
134	C₂⁴	Q₈×C₂₉	1	4	yes	—
135	C₂⁴	C₂³×C₂₉	1	2	yes	—
136	C₂⁴	C₂³×C₂₉	1	1	yes	characteristic
137	C₂²×C₄	—	2	32	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	2	8	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	2	4	no	—
143	C₂²×C₄	—	2	16	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	4	no	—
147	C₂²×C₄	—	2	4	no	—
148	C₂²×C₄	C₂×C₄×C₂₉	1	8	yes	complemented
149	C₂²×C₄	D₄×C₂₉	1	8	yes	—
150	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
151	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
152	C₂²×C₄	C₂³×C₂₉	1	4	yes	—
153	C₂²×C₄	C₂³×C₂₉	1	4	yes	—
154	C₄⋊C₄	—	2	16	no	—
155	C₂²⋊C₄	—	2	8	no	—
156	C₂²⋊C₄	C₂×C₄×C₂₉	1	16	yes	complemented
157	C₂³	—	2	16	no	—
158	C₂³	—	2	8	no	—
159	C₂³	—	2	16	no	—
160	C₂³	—	2	8	no	—
161	C₂³	—	2	4	no	—
162	C₂³	—	2	4	no	—
163	C₂³	C₄⋊C₄×C₂₉	1	16	yes	complemented
164	C₂³	C₂²×C₄×C₂₉	1	4	yes	—
165	C₂³	C₂²×C₄×C₂₉	1	2	yes	—
166	C₂³	C₂×D₄×C₂₉	1	4	yes	—
167	C₂³	C₂×D₄×C₂₉	1	2	yes	—
168	C₂³	C₂×D₄×C₂₉	1	4	yes	—
169	C₂³	C₂×Q₈×C₂₉	1	4	yes	—
170	C₂³	C₂×Q₈×C₂₉	1	2	yes	—
171	C₂³	#41×C₂₉	1	4	yes	—
172	C₂³	C₂⁴×C₂₉	1	1	yes	characteristic
173	C₂×C₄	—	2	32	no	—
174	C₂×C₄	—	2	16	no	—
175	C₂×C₄	—	2	16	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	C₂²×C₄×C₂₉	1	8	yes	complemented
187	C₂×C₄	C₂×D₄×C₂₉	1	8	yes	—
188	C₂²	—	2	8	no	—
189	C₂²	—	2	4	no	—
190	C₂²	—	2	8	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	32	no	—
193	C₂²	C₂×C₄⋊C₄×C₂₉	1	4	yes	—
194	C₂²	C₂×C₄⋊C₄×C₂₉	1	8	yes	complemented
195	C₂²	C₄×D₄×C₂₉	1	8	yes	—
196	C₂²	C₂₉×#120	1	4	yes	—
197	C₂²	C₂₉×C₂²⋊Q₈	1	8	yes	—
198	C₂²	C₂₉×#123	1	4	yes	—
199	C₂²	C₂³×C₄×C₂₉	1	1	yes	characteristic
200	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
201	C₂²	C₂²×D₄×C₂₉	1	2	yes	—
202	C₂²	C₂²×Q₈×C₂₉	1	1	yes	characteristic
203	C₂²	C₂×#41×C₂₉	1	2	yes	—
204	C₄	—	2	8	no	—
205	C₄	—	2	8	no	—
206	C₄	—	4	2	no	—
207	C₄	—	4	2	no	—
208	C₂	—	2	8	no	—
209	C₂	C₂₉×#385	1	8	yes	direct product factor
210	C₂	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
211	C₂	C₂×C₄×D₄×C₂₉	1	2	yes	—
212	C₂	C₂×C₂₉×#120	1	1	yes	characteristic
213	C₂	C₂×C₂₉×C₂²⋊Q₈	1	2	yes	—
214	C₂	C₂×C₂₉×#123	1	1	yes	characteristic

	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
5. C₂₉×#385	C₂	direct (N × H)
6. C₂×C₂₉×#95	C₂	semidirect
16. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
18. C₂×C₂²⋊C₄×C₂₉	C₄	semidirect
21. C₂₉×#95	C₂²	semidirect
40. C₂²×C₄×C₂₉	C₂×C₄	semidirect
48. C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
55. C₂³×C₂₉	C₄⋊C₄	semidirect
78. C₂×C₄×C₂₉	C₂²×C₄	semidirect
80. C₂×#385	C₂₉	direct (N × H)
87. C₂²×C₂₉	C₂×C₄⋊C₄	semidirect
102. C₂²×C₄⋊C₄	C₂×C₂₉	semidirect
105. #385	C₂×C₂₉	direct (N × H)
106. C₂×#95	C₂×C₂₉	semidirect
108. C₂×C₂₉	#385	direct (N × H)
123. C₂×C₄⋊C₄	C₂²×C₂₉	semidirect
125. C₂×C₂²⋊C₄	C₄×C₂₉	semidirect
128. #95	C₂²×C₂₉	semidirect
129. C₂₉	C₂×#385	direct (N × H)
148. C₂²×C₄	C₂×C₄×C₂₉	semidirect
156. C₂²⋊C₄	C₂×C₄×C₂₉	semidirect
163. C₂³	C₄⋊C₄×C₂₉	semidirect
186. C₂×C₄	C₂²×C₄×C₂₉	semidirect
194. C₂²	C₂×C₄⋊C₄×C₂₉	semidirect
209. C₂	C₂₉×#385	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×#385	2
C₂×C₂₉×#95	2
C₂×#385	29

Subgroups — C2×C29×#385 #16816000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#385 #16816000