Subgroups — #15863074

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	2	yes	maximal
2	#13114956	C₂	1	8	yes	maximal, complemented
3	#13114530	C₂	1	4	yes	maximal
4	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6099	C₂²	1	4	yes	—
8	C₁₃×#376	C₄	1	4	yes	—
9	C₁₃×#376	C₂²	1	4	yes	—
10	C₂×C₁₃×#95	C₄	1	4	yes	—
11	#11718585	—	2	8	no	—
12	C₂×C₄⋊#1055	C₂²	1	8	yes	—
13	#11718116	C₂²	1	16	yes	—
14	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
15	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	—	2	8	no	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₃	D₄	1	4	yes	—
21	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
22	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
24	C₂×#6099	—	2	8	no	—
25	C₂×#6099	—	2	16	no	—
26	C₂²×#1055	C₂³	1	8	yes	—
27	C₁₃×#95	C₂×C₄	1	16	yes	—
28	C₄⋊#1055	—	2	16	no	—
29	#20753	—	13	1	no	maximal, Sylow
30	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	—	2	8	no	—
32	C₂²×C₄×C₁₃	—	4	4	no	—
33	C₂²×C₄×C₁₃	—	4	8	no	—
34	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
37	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
40	C₂²×C₄×C₁₃	#41	1	8	yes	—
41	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
42	C₄²×C₁₃	—	2	8	no	—
43	C₄²×C₁₃	—	2	8	no	—
44	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
45	C₄²×C₁₃	C₂×D₄	1	4	yes	—
46	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
47	#6099	—	4	16	no	—
48	C₂×#1055	—	2	8	no	—
49	C₂×#1055	—	2	16	no	—
50	C₂×#423	—	13	2	no	—
51	C₂×#376	D₁₃	1	1	yes	characteristic
52	#1832	—	13	8	no	—
53	#1728	—	13	4	no	—
54	C₂³×C₁₃	—	2	4	no	—
55	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
56	C₂³×C₁₃	#117	1	4	yes	—
57	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	—	2	8	no	—
59	C₂×C₄×C₁₃	—	2	8	no	—
60	C₂×C₄×C₁₃	—	2	16	no	—
61	C₂×C₄×C₁₃	—	4	8	no	—
62	C₂×C₄×C₁₃	—	4	16	no	—
63	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
64	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
65	C₂×C₄×C₁₃	#117	1	4	yes	—
66	C₂×C₄×C₁₃	#124	1	8	yes	—
67	C₂×C₄×C₁₃	#125	1	8	yes	—
68	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
71	#1055	—	4	8	no	—
72	C₂²×M₁₆	—	13	4	no	—
73	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
74	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
75	#423	—	26	8	no	—
76	C₂×C₄⋊C₈	—	13	8	no	—
77	#376	Dic₁₃	1	4	yes	—
78	#376	C₂×D₁₃	1	4	yes	—
79	C₂×#95	Dic₁₃	1	4	yes	—
80	#336	—	13	16	no	—
81	C₂²×C₁₃	—	2	4	no	—
82	C₂²×C₁₃	—	2	8	no	—
83	C₂²×C₁₃	#382	1	4	yes	—
84	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₁₃	C₂×#117	1	2	yes	—
86	C₂²×C₁₃	#568	1	4	yes	—
87	C₄×C₁₃	—	2	8	no	—
88	C₄×C₁₃	—	4	8	no	—
89	C₄×C₁₃	#382	1	4	yes	—
90	C₄×C₁₃	C₂×#124	1	2	yes	—
91	C₄×C₁₃	C₂×#125	1	2	yes	—
92	C₂³×C₄	C₂×Dic₁₃	1	4	yes	—
93	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
94	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
95	C₂×M₁₆	—	26	8	no	—
96	C₂×M₁₆	—	26	16	no	—
97	C₂²×C₈	—	13	8	no	—
98	C₂×C₄²	—	2	8	no	—
99	C₂×C₄²	Dic₂₆	1	4	yes	—
100	C₂×C₄²	D₅₂	1	4	yes	—
101	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
102	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
103	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
104	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
105	C₄⋊C₈	—	26	16	no	—
106	#95	C₂×Dic₁₃	1	16	yes	—
107	C₂×C₁₃	—	2	4	no	—
108	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
109	C₂×C₁₃	#2905	1	2	yes	—
110	C₂×C₁₃	#2921	1	4	yes	—
111	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
112	C₂²×C₄	—	2	8	no	—
113	C₂²×C₄	—	4	4	no	—
114	C₂²×C₄	—	4	8	no	—
115	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
116	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
117	C₂²×C₄	C₂×D₅₂	1	2	yes	—
118	C₂²×C₄	#6127	1	8	yes	—
119	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
120	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
121	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
122	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
123	M₁₆	—	52	16	no	—
124	C₂×C₈	—	26	8	no	—
125	C₂×C₈	—	26	16	no	—
126	C₄²	—	2	8	no	—
127	C₄²	—	2	8	no	—
128	C₄²	C₄⋊Dic₁₃	1	8	yes	—
129	C₄²	C₂×Dic₂₆	1	4	yes	—
130	C₄²	C₂×D₅₂	1	4	yes	—
131	C₁₃	#20753	1	1	yes	characteristic, complemented, Sylow
132	C₂³	—	2	4	no	—
133	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
134	C₂³	#88180	1	4	yes	—
135	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	8	no	—
138	C₂×C₄	—	2	16	no	—
139	C₂×C₄	—	4	8	no	—
140	C₂×C₄	—	4	16	no	—
141	C₂×C₄	#88124	1	8	yes	—
142	C₂×C₄	#88129	1	8	yes	—
143	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
144	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
145	C₂×C₄	#88180	1	4	yes	—
146	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
147	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
148	C₂×C₄	C₂×#6127	1	4	yes	—
149	C₈	—	52	8	no	—
150	C₂²	—	2	4	no	—
151	C₂²	—	2	8	no	—
152	C₂²	#11718597	1	4	yes	—
153	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
154	C₂²	C₂×#88180	1	2	yes	—
155	C₂²	#11719524	1	4	yes	—
156	C₄	—	2	8	no	—
157	C₄	—	4	8	no	—
158	C₄	#11718597	1	4	yes	—
159	C₄	C₂×#88124	1	2	yes	—
160	C₄	C₂×#88129	1	2	yes	—
161	C₂	—	2	4	no	—
162	C₂	C₂×#11718597	1	1	yes	characteristic
163	C₂	#13123400	1	2	yes	—
164	C₂	#13123474	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₁₃×#376	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#376	D₁₃
hypocenter	C₁₃	#20753
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
2. #13114956	C₂	semidirect
131. C₁₃	#20753	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
#13114956	2
#13114530	2
C₂×C₁₃×#376	2
#20753	13