Subgroups — #15863070

Order 3328.

1158 conjugacy classes of subgroups.

The subgroup lattice has 194 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	#13114953	C₂	1	8	yes	maximal, complemented
3	#13114530	C₂	1	4	yes	maximal
4	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₄	1	4	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#6099	C₂²	1	4	yes	—
9	C₄³×C₁₃	C₄	1	2	yes	—
10	C₄³×C₁₃	C₄	1	2	yes	—
11	C₄³×C₁₃	C₂²	1	4	yes	—
12	#11718585	—	2	8	no	—
13	C₂×C₄⋊#1055	C₂²	1	8	yes	—
14	#11718116	C₂²	1	16	yes	—
15	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
16	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	—	2	8	no	—
19	C₂×C₄²×C₁₃	—	2	16	no	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₁₃	D₄	1	4	yes	—
27	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
28	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
30	C₂×#6099	—	2	8	no	—
31	C₂×#6099	—	2	16	no	—
32	C₂²×#1055	C₂³	1	8	yes	—
33	C₄⋊#1055	—	2	16	no	—
34	#20752	—	13	1	no	maximal, Sylow
35	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	—	2	8	no	—
37	C₂²×C₄×C₁₃	—	2	16	no	—
38	C₂²×C₄×C₁₃	—	2	8	no	—
39	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
42	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
46	C₂²×C₄×C₁₃	#41	1	8	yes	—
47	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
48	C₄²×C₁₃	—	2	8	no	—
49	C₄²×C₁₃	—	2	16	no	—
50	C₄²×C₁₃	—	2	8	no	—
51	C₄²×C₁₃	—	2	8	no	—
52	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
53	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
54	C₄²×C₁₃	M₁₆	1	16	yes	complemented
55	C₄²×C₁₃	C₂×D₄	1	4	yes	—
56	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
57	#6099	—	4	16	no	—
58	C₂×#1055	—	2	8	no	—
59	C₂×#1055	—	2	16	no	—
60	C₂×#423	—	13	2	no	—
61	C₂×C₄³	D₁₃	1	1	yes	characteristic
62	#1831	—	13	8	no	—
63	#1728	—	13	4	no	—
64	C₂³×C₁₃	—	2	4	no	—
65	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
66	C₂³×C₁₃	#117	1	4	yes	—
67	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	32	no	—
69	C₂×C₄×C₁₃	—	2	8	no	—
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	—	2	8	no	—
72	C₂×C₄×C₁₃	—	2	16	no	—
73	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
74	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
75	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
76	C₂×C₄×C₁₃	#117	1	4	yes	—
77	C₂×C₄×C₁₃	#124	1	8	yes	—
78	C₂×C₄×C₁₃	#125	1	8	yes	—
79	C₂×C₄×C₁₃	C₂×M₁₆	1	16	yes	—
80	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
81	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
84	#1055	—	4	8	no	—
85	C₂²×M₁₆	—	13	4	no	—
86	C₂²×C₄²	Dic₁₃	1	4	yes	—
87	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
88	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
89	#423	—	26	8	no	—
90	C₂×C₄⋊C₈	—	13	8	no	—
91	C₄³	Dic₁₃	1	2	yes	—
92	C₄³	Dic₁₃	1	2	yes	—
93	C₄³	C₂×D₁₃	1	4	yes	—
94	#336	—	13	16	no	—
95	C₂²×C₁₃	—	2	4	no	—
96	C₂²×C₁₃	—	2	8	no	—
97	C₂²×C₁₃	#382	1	4	yes	—
98	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₁₃	C₂×#117	1	2	yes	—
100	C₂²×C₁₃	C₂²×M₁₆	1	4	yes	—
101	C₄×C₁₃	—	2	4	no	—
102	C₄×C₁₃	—	2	16	no	—
103	C₄×C₁₃	#382	1	4	yes	—
104	C₄×C₁₃	#423	1	8	yes	—
105	C₄×C₁₃	C₂×#124	1	2	yes	—
106	C₄×C₁₃	C₂×#125	1	2	yes	—
107	C₂³×C₄	C₂×Dic₁₃	1	4	yes	—
108	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
109	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
110	C₂×M₁₆	—	26	8	no	—
111	C₂×M₁₆	—	26	16	no	—
112	C₂²×C₈	—	13	8	no	—
113	C₂×C₄²	—	2	8	no	—
114	C₂×C₄²	—	2	16	no	—
115	C₂×C₄²	Dic₂₆	1	4	yes	—
116	C₂×C₄²	D₅₂	1	4	yes	—
117	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
118	C₂×C₄²	C₂×Dic₁₃	1	8	yes	—
119	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
120	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
121	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
122	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
123	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
124	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
125	C₄⋊C₈	—	26	16	no	—
126	C₂×C₁₃	—	2	4	no	—
127	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
128	C₂×C₁₃	C₂×#423	1	2	yes	—
129	C₂×C₁₃	#2920	1	4	yes	—
130	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
131	C₂²×C₄	—	2	8	no	—
132	C₂²×C₄	—	2	16	no	—
133	C₂²×C₄	—	2	8	no	—
134	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
135	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
136	C₂²×C₄	C₂×D₅₂	1	2	yes	—
137	C₂²×C₄	#6127	1	8	yes	—
138	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
139	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
140	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
141	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
142	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
143	M₁₆	—	52	16	no	—
144	C₂×C₈	—	26	8	no	—
145	C₂×C₈	—	26	16	no	—
146	C₄²	—	2	16	no	—
147	C₄²	—	2	8	no	—
148	C₄²	—	2	8	no	—
149	C₄²	—	2	8	no	—
150	C₄²	#6099	1	16	yes	complemented
151	C₄²	C₄⋊Dic₁₃	1	4	yes	—
152	C₄²	C₄⋊Dic₁₃	1	4	yes	—
153	C₄²	C₂×Dic₂₆	1	4	yes	—
154	C₄²	C₂×D₅₂	1	4	yes	—
155	C₁₃	#20752	1	1	yes	characteristic, complemented, Sylow
156	C₂³	—	2	4	no	—
157	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
158	C₂³	#88180	1	4	yes	—
159	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
160	C₂×C₄	—	2	32	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	2	8	no	—
163	C₂×C₄	—	2	8	no	—
164	C₂×C₄	—	2	16	no	—
165	C₂×C₄	#88124	1	8	yes	—
166	C₂×C₄	#88129	1	8	yes	—
167	C₂×C₄	C₂×#6099	1	16	yes	—
168	C₂×C₄	C₂×#6099	1	8	yes	—
169	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
170	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
171	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
172	C₂×C₄	#88180	1	4	yes	—
173	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
174	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
175	C₂×C₄	C₂×#6127	1	4	yes	—
176	C₈	—	52	8	no	—
177	C₂²	—	2	4	no	—
178	C₂²	—	2	8	no	—
179	C₂²	#11718597	1	4	yes	—
180	C₂²	C₂²×#6099	1	4	yes	—
181	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
182	C₂²	C₂×#88180	1	2	yes	—
183	C₄	—	2	4	no	—
184	C₄	—	2	16	no	—
185	C₄	#11718585	1	8	yes	—
186	C₄	#11718597	1	4	yes	—
187	C₄	C₂×#88124	1	2	yes	—
188	C₄	C₂×#88129	1	2	yes	—
189	C₂	—	2	4	no	—
190	C₂	C₂×#11718597	1	1	yes	characteristic
191	C₂	C₂×#11718585	1	2	yes	—
192	C₂	#13123469	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₄³×C₁₃	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	#20752
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
2. #13114953	C₂	semidirect
54. C₄²×C₁₃	M₁₆	semidirect
150. C₄²	#6099	semidirect
155. C₁₃	#20752	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
#13114953	2
#13114530	2
C₂×C₄³×C₁₃	2
#20752	13