Subgroups — C₂×#14270925 #16819205

Order 3712.

512 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6597	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	#14270925	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₂₉	—	2	1	no	—
6	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₂₉	—	2	1	no	—
8	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
10	C₂×C₄⋊C₄×C₂₉	C₄	1	4	yes	complemented
11	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₂₉	—	2	2	no	—
13	C₂×C₄⋊Dic₂₉	—	2	1	no	—
14	C₂×C₄⋊Dic₂₉	C₄	1	4	yes	complemented
15	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
16	C₂²×#6597	—	2	2	no	—
17	C₂²×#6597	—	2	2	no	—
18	C₂²×#6597	C₄	1	4	yes	complemented
19	C₂²×#6597	C₂²	1	2	yes	—
20	C₂⁴×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	—	2	4	no	—
22	C₂²×C₄×C₂₉	—	2	2	no	—
23	C₂²×C₄×C₂₉	—	4	2	no	—
24	C₂²×C₄×C₂₉	—	4	2	no	—
25	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₂₉	D₄	1	2	yes	—
29	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₂₉	D₄	1	2	yes	—
31	C₂²×C₄×C₂₉	Q₈	1	2	yes	—
32	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₂₉	—	2	4	no	—
34	C₂²×Dic₂₉	—	2	2	no	—
35	C₂²×Dic₂₉	—	4	2	no	—
36	C₂²×Dic₂₉	—	4	2	no	—
37	C₄⋊C₄×C₂₉	—	2	4	no	—
38	C₄⋊C₄×C₂₉	—	2	2	no	—
39	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	complemented
40	C₄⋊Dic₂₉	—	2	4	no	—
41	C₄⋊Dic₂₉	—	2	2	no	—
42	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	complemented
43	C₂×#6597	—	2	8	no	—
44	C₂×#6597	—	2	2	no	—
45	C₂×#6597	—	2	2	no	—
46	C₂×#6597	C₂×C₄	1	4	yes	complemented
47	C₂³×C₂₉	C₂²⋊C₄	1	2	yes	—
48	C₂³×C₂₉	C₂²⋊C₄	1	2	yes	—
49	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
50	C₂³×C₂₉	D₈	1	2	yes	—
51	C₂³×C₂₉	SD₁₆	1	2	yes	—
52	C₂³×C₂₉	SD₁₆	1	2	yes	—
53	C₂³×C₂₉	Q₁₆	1	2	yes	—
54	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₂₉	—	2	4	no	—
56	C₂×C₄×C₂₉	—	4	8	no	—
57	C₂×C₄×C₂₉	—	4	2	no	—
58	C₂×C₄×C₂₉	—	4	2	no	—
59	C₂×C₄×C₂₉	C₄²	1	4	yes	—
60	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
62	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
64	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
65	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
66	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
72	C₂×Dic₂₉	—	2	4	no	—
73	C₂×Dic₂₉	—	4	8	no	—
74	C₂×Dic₂₉	—	4	2	no	—
75	C₂×Dic₂₉	—	4	2	no	—
76	#6597	—	2	4	no	—
77	C₂×#340	—	29	1	no	maximal, Sylow
78	C₂²×C₂₉	#95	1	4	yes	—
79	C₂²×C₂₉	#102	1	4	yes	—
80	C₂²×C₂₉	#102	1	4	yes	—
81	C₂²×C₂₉	#103	1	4	yes	—
82	C₂²×C₂₉	#103	1	4	yes	—
83	C₂²×C₂₉	#106	1	4	yes	—
84	C₂²×C₂₉	#107	1	4	yes	—
85	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
89	C₂²×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₂²×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂²×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
92	C₄×C₂₉	—	4	4	no	—
93	C₄×C₂₉	#95	1	4	yes	—
94	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
95	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
98	Dic₂₉	—	4	4	no	—
99	C₂³×C₈	—	29	1	no	—
100	C₂²×C₄⋊C₄	—	29	1	no	—
101	C₂²×C₄⋊C₄	D₂₉	1	1	yes	characteristic
102	#340	—	29	4	no	—
103	C₂×C₂₉	#340	1	8	yes	complemented
104	C₂×C₂₉	C₂×#95	1	1	yes	characteristic
105	C₂×C₂₉	C₂×#102	1	1	yes	characteristic
106	C₂×C₂₉	C₂×#102	1	1	yes	characteristic
107	C₂×C₂₉	C₂×#103	1	1	yes	characteristic
108	C₂×C₂₉	C₂×#103	1	1	yes	characteristic
109	C₂×C₂₉	C₂×#106	1	1	yes	characteristic
110	C₂×C₂₉	C₂×#107	1	1	yes	characteristic
111	C₂³×C₄	—	2	1	no	—
112	C₂³×C₄	—	58	1	no	—
113	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
114	C₂²×C₈	—	29	4	no	—
115	C₂²×C₈	—	29	2	no	—
116	C₂²×C₈	—	58	2	no	—
117	C₂²×C₈	—	58	2	no	—
118	C₂×C₄⋊C₄	—	2	1	no	—
119	C₂×C₄⋊C₄	—	2	2	no	—
120	C₂×C₄⋊C₄	—	29	4	no	—
121	C₂×C₄⋊C₄	—	29	2	no	—
122	C₂×C₄⋊C₄	—	58	2	no	—
123	C₂×C₄⋊C₄	—	58	1	no	—
124	C₂×C₄⋊C₄	Dic₂₉	1	4	yes	complemented
125	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
126	C₂₉	C₂×#340	1	1	yes	characteristic, complemented, Sylow
127	C₂⁴	C₂²⋊D₂₉	1	1	yes	characteristic
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	—	2	2	no	—
130	C₂²×C₄	—	4	2	no	—
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	—	58	4	no	—
133	C₂²×C₄	—	58	2	no	—
134	C₂²×C₄	—	116	2	no	—
135	C₂²×C₄	—	116	2	no	—
136	C₂²×C₄	Dic₅₈	1	2	yes	—
137	C₂²×C₄	C₄×D₂₉	1	2	yes	—
138	C₂²×C₄	C₄×D₂₉	1	2	yes	—
139	C₂²×C₄	D₁₁₆	1	2	yes	—
140	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
141	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
142	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
143	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
144	C₂×C₈	—	29	4	no	—
145	C₂×C₈	—	58	8	no	—
146	C₂×C₈	—	58	2	no	—
147	C₂×C₈	—	58	2	no	—
148	C₄⋊C₄	—	2	4	no	—
149	C₄⋊C₄	—	2	2	no	—
150	C₄⋊C₄	—	29	4	no	—
151	C₄⋊C₄	—	58	4	no	—
152	C₄⋊C₄	—	58	2	no	—
153	C₄⋊C₄	C₂×Dic₂₉	1	4	yes	complemented
154	C₂³	#90779	1	2	yes	—
155	C₂³	#90781	1	2	yes	—
156	C₂³	#90782	1	2	yes	—
157	C₂³	#90783	1	2	yes	—
158	C₂³	#90784	1	2	yes	—
159	C₂³	#90785	1	2	yes	—
160	C₂³	C₂²⋊Dic₂₉	1	2	yes	—
161	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	4	2	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	4	8	no	—
166	C₂×C₄	—	58	4	no	—
167	C₂×C₄	—	116	2	no	—
168	C₂×C₄	—	116	2	no	—
169	C₂×C₄	—	116	8	no	—
170	C₂×C₄	C₄×Dic₂₉	1	4	yes	—
171	C₂×C₄	#90779	1	4	yes	—
172	C₂×C₄	#90779	1	2	yes	—
173	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
174	C₂×C₄	#90781	1	4	yes	—
175	C₂×C₄	#90781	1	2	yes	—
176	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
177	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
178	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
179	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
180	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
181	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
182	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
183	C₈	—	58	4	no	—
184	C₂²	#11745155	1	4	yes	—
185	C₂²	#11745156	1	4	yes	—
186	C₂²	#11745157	1	4	yes	—
187	C₂²	#11745158	1	4	yes	—
188	C₂²	#11745179	1	4	yes	—
189	C₂²	#11745180	1	4	yes	—
190	C₂²	#11745183	1	4	yes	—
191	C₂²	C₂×#90779	1	1	yes	characteristic
192	C₂²	C₂×#90781	1	1	yes	characteristic
193	C₂²	C₂×#90782	1	1	yes	characteristic
194	C₂²	C₂×#90783	1	1	yes	characteristic
195	C₂²	C₂×#90784	1	1	yes	characteristic
196	C₂²	C₂×#90785	1	1	yes	characteristic
197	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
198	C₄	—	4	4	no	—
199	C₄	—	116	4	no	—
200	C₄	#11745179	1	4	yes	—
201	C₄	C₂×C₄×Dic₂₉	1	1	yes	characteristic
202	C₄	C₂×#90779	1	1	yes	characteristic
203	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
204	C₄	C₂×#90781	1	1	yes	characteristic
205	C₂	#14270925	1	8	yes	direct product factor
206	C₂	C₂×#11745179	1	1	yes	characteristic
207	C₂	C₂×#11745157	1	1	yes	characteristic
208	C₂	C₂×#11745180	1	1	yes	characteristic
209	C₂	C₂×#11745158	1	1	yes	characteristic
210	C₂	C₂×#11745183	1	1	yes	characteristic
211	C₂	C₂×#11745156	1	1	yes	characteristic
212	C₂	C₂×#11745155	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂²×C₄⋊C₄×C₂₉	C₂
socle, prime radical	C₂⁴×C₂₉	D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂²×C₄⋊C₄	D₂₉
hypocenter	C₂₉	C₂×#340
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #14270925	C₂	direct (N × H)
10. C₂×C₄⋊C₄×C₂₉	C₄	semidirect
14. C₂×C₄⋊Dic₂₉	C₄	semidirect
18. C₂²×#6597	C₄	semidirect
39. C₄⋊C₄×C₂₉	C₂×C₄	semidirect
42. C₄⋊Dic₂₉	C₂×C₄	semidirect
46. C₂×#6597	C₂×C₄	semidirect
103. C₂×C₂₉	#340	semidirect
124. C₂×C₄⋊C₄	Dic₂₉	semidirect
126. C₂₉	C₂×#340	semidirect
153. C₄⋊C₄	C₂×Dic₂₉	semidirect
205. C₂	#14270925	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6597	2
C₂²×C₄⋊Dic₂₉	2
#14270925	2
C₂²×C₄⋊C₄×C₂₉	2
C₂×#340	29

Subgroups — C2×#14270925 #16819205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270925 #16819205