Subgroups — #15860980

Order 3328.

1142 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718767	C₂	1	2	yes	maximal
2	C₄×#88180	C₂	1	2	yes	maximal
3	#13114733	C₂	1	8	yes	maximal, complemented
4	#13114553	C₂	1	2	yes	maximal
5	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88180	C₂²	1	4	yes	—
10	C₂×C₁₃×#97	C₄	1	8	yes	complemented
11	C₂×C₁₃×#97	C₂²	1	4	yes	—
12	C₄×C₂²⋊Dic₁₃	—	2	4	no	—
13	#11718767	C₄	1	16	yes	complemented
14	C₂×#88058	C₂²	1	4	yes	—
15	C₂×#88057	C₂²	1	4	yes	—
16	C₄×C₄⋊Dic₁₃	C₂²	1	8	yes	—
17	#11718593	—	2	2	no	—
18	C₄²×Dic₁₃	—	2	2	no	—
19	#11718143	C₂²	1	8	yes	—
20	C₂³×C₄×C₁₃	D₄	1	2	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	—	2	4	no	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₃	D₄	1	2	yes	—
30	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
31	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
32	C₂×C₂²⋊Dic₁₃	—	2	4	no	—
33	#88180	—	2	8	no	—
34	#88180	C₂×C₄	1	16	yes	—
35	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
36	C₂×C₄×Dic₁₃	—	2	4	no	—
37	C₂×C₄×Dic₁₃	—	2	8	no	—
38	C₁₃×#97	C₂×C₄	1	16	yes	—
39	#88071	—	2	8	no	—
40	#88058	C₂×C₄	1	16	yes	complemented
41	#88057	C₂×C₄	1	16	yes	complemented
42	#20451	—	13	1	no	maximal, Sylow
43	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	—	4	4	no	—
45	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
51	C₂²×C₄×C₁₃	#41	1	4	yes	—
52	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
53	C₂²×Dic₁₃	—	2	8	no	—
54	C₂×C₈×C₁₃	—	2	8	no	—
55	C₂×C₈×C₁₃	—	2	4	no	—
56	C₂×C₈×C₁₃	C₄²	1	16	yes	complemented
57	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
58	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
60	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
61	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
62	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
63	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
64	C₂²⋊Dic₁₃	—	2	16	no	—
65	C₄⋊Dic₁₃	—	2	8	no	—
66	C₄⋊Dic₁₃	C₂²×C₄	1	16	yes	—
67	C₄×Dic₁₃	—	2	16	no	—
68	C₄×Dic₁₃	—	4	16	no	—
69	C₂×#427	—	13	2	no	—
70	C₂²×#97	D₁₃	1	1	yes	characteristic
71	C₄×#117	—	13	2	no	—
72	#1776	—	13	8	no	—
73	#1735	—	13	2	no	—
74	C₂³×C₁₃	—	2	4	no	—
75	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
76	C₂³×C₁₃	C₄×D₄	1	4	yes	—
77	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	—	2	8	no	—
79	C₂×C₄×C₁₃	—	4	8	no	—
80	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
81	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
82	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
83	C₂×C₄×C₁₃	#117	1	4	yes	—
84	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
85	C₂×C₄×C₁₃	C₄×Q₈	1	8	yes	—
86	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
90	C₂×Dic₁₃	—	2	16	no	—
91	C₂×Dic₁₃	—	4	16	no	—
92	C₈×C₁₃	—	2	4	no	—
93	C₈×C₁₃	C₂×C₄²	1	8	yes	—
94	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
95	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
96	C₂×#117	—	13	4	no	—
97	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
98	#427	—	13	16	no	—
99	C₂×#107	—	13	4	no	—
100	C₂×#106	—	13	4	no	—
101	C₂×#97	Dic₁₃	1	8	yes	complemented
102	C₂×#97	C₂×D₁₃	1	4	yes	—
103	C₄×C₄⋊C₄	—	13	8	no	—
104	C₄×C₂²⋊C₄	—	26	4	no	—
105	#376	—	26	2	no	—
106	C₄³	—	26	2	no	—
107	#340	—	13	8	no	—
108	C₂²×C₁₃	—	2	4	no	—
109	C₂²×C₁₃	—	2	8	no	—
110	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
111	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
113	C₂²×C₁₃	#575	1	4	yes	—
114	C₄×C₁₃	—	2	8	no	—
115	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
116	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
117	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
118	C₄×C₁₃	C₂×C₄×Q₈	1	2	yes	—
119	Dic₁₃	—	4	16	no	—
120	C₂³×C₄	D₅₂	1	2	yes	—
121	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
122	C₂²×C₈	—	2	4	no	—
123	C₂²×C₈	C₄×D₁₃	1	8	yes	—
124	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
125	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
126	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
127	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
128	#117	—	13	16	no	—
129	#117	—	26	8	no	—
130	C₂×C₄⋊C₄	—	13	8	no	—
131	C₂×C₂²⋊C₄	—	26	4	no	—
132	C₂×C₄²	—	26	4	no	—
133	C₂×C₄²	—	26	8	no	—
134	C₂×C₄²	Dic₂₆	1	4	yes	—
135	C₂×C₄²	D₅₂	1	2	yes	—
136	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
137	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
138	#107	—	13	16	no	—
139	#106	—	13	16	no	—
140	#97	C₂×Dic₁₃	1	16	yes	—
141	#95	—	26	8	no	—
142	C₂×C₁₃	—	2	4	no	—
143	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₁₃	#2911	1	2	yes	—
145	C₂×C₁₃	#2943	1	4	yes	—
146	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
147	C₂²×C₄	—	4	4	no	—
148	C₂²×C₄	—	26	8	no	—
149	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
150	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
151	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
152	C₂²×C₄	C₂×D₅₂	1	4	yes	—
153	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
154	C₂²×C₄	#6127	1	4	yes	—
155	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
156	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
157	C₂×C₈	—	2	8	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	C₄×Dic₁₃	1	16	yes	complemented
160	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
161	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
162	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
163	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
164	C₄⋊C₄	—	13	16	no	—
165	C₄⋊C₄	—	26	8	no	—
166	C₂²⋊C₄	—	26	16	no	—
167	C₄²	—	26	16	no	—
168	C₄²	—	52	16	no	—
169	C₄²	C₄⋊Dic₁₃	1	8	yes	—
170	C₄²	C₂×Dic₂₆	1	4	yes	—
171	C₄²	C₂²×Dic₁₃	1	4	yes	—
172	C₁₃	#20451	1	1	yes	characteristic, complemented, Sylow
173	C₂³	—	2	4	no	—
174	C₂³	C₄×D₅₂	1	4	yes	—
175	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
176	C₂³	C₂²×D₅₂	1	1	yes	characteristic
177	C₂×C₄	—	2	8	no	—
178	C₂×C₄	—	4	8	no	—
179	C₂×C₄	—	26	16	no	—
180	C₂×C₄	—	52	16	no	—
181	C₂×C₄	C₄×Dic₂₆	1	8	yes	—
182	C₂×C₄	C₄×D₅₂	1	4	yes	—
183	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
184	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
185	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
186	C₂×C₄	#88180	1	4	yes	—
187	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
188	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
189	C₂×C₄	C₂×#6127	1	2	yes	—
190	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
191	C₈	—	2	4	no	—
192	C₈	C₂×C₄×Dic₁₃	1	8	yes	—
193	C₂²	—	2	8	no	—
194	C₂²	—	2	4	no	—
195	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
196	C₂²	C₂×C₄×D₅₂	1	2	yes	—
197	C₂²	#11719453	1	4	yes	—
198	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
199	C₄	—	2	8	no	—
200	C₄	—	52	16	no	—
201	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
202	C₄	C₂×C₄×Dic₂₆	1	2	yes	—
203	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
204	C₄	C₂×#88180	1	1	yes	characteristic
205	C₂	—	2	4	no	—
206	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
207	C₂	#13123426	1	2	yes	—
208	C₂	#13123638	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	#20451
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #13114733	C₂	semidirect
10. C₂×C₁₃×#97	C₄	semidirect
13. #11718767	C₄	semidirect
40. #88058	C₂×C₄	semidirect
41. #88057	C₂×C₄	semidirect
56. C₂×C₈×C₁₃	C₄²	semidirect
101. C₂×#97	Dic₁₃	semidirect
159. C₂×C₈	C₄×Dic₁₃	semidirect
172. C₁₃	#20451	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718767	2
C₄×#88180	2
#13114733	2
#13114553	2
C₂²×C₁₃×#97	2
#20451	13