Subgroups — #15828669

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123469	C₂	1	2	yes	maximal
2	#13113139	C₂	1	4	yes	maximal, complemented
3	#13113136	C₂	1	8	yes	maximal, complemented
4	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#432	C₄	1	4	yes	—
7	C₁₃×#431	C₂²	1	4	yes	—
8	C₁₃×#423	C₄	1	2	yes	—
9	C₁₃×#407	C₄	1	2	yes	—
10	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
11	#11718868	C₄	1	4	yes	—
12	#11718587	C₄	1	8	yes	—
13	#11718586	C₂²	1	8	yes	—
14	#11718585	C₄	1	4	yes	—
15	C₄×#6099	C₂²	1	4	yes	—
16	#11718047	C₂²	1	4	yes	complemented
17	#11718046	C₂²	1	8	yes	complemented
18	C₈×#1055	C₂²	1	4	yes	complemented
19	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
28	C₂×#6099	C₂×C₄	1	8	yes	—
29	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
30	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
31	C₁₃×#97	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₃	C₂³	1	4	yes	—
33	C₂²⋊#1055	C₂×C₄	1	16	yes	—
34	C₄⋊#1055	C₂×C₄	1	16	yes	—
35	#88043	C₂×C₄	1	8	yes	—
36	C₄×#1055	C₂³	1	8	yes	—
37	#17339	—	13	1	no	maximal, Sylow
38	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	—	4	4	no	—
40	C₂²×C₄×C₁₃	—	4	2	no	—
41	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
43	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
44	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₁₃×M₁₆	—	4	4	no	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
51	C₄²×C₁₃	C₄²	1	4	yes	—
52	C₄²×C₁₃	C₄²	1	2	yes	—
53	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
54	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
55	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
57	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
58	#6099	—	4	8	no	—
59	C₂×#1055	C₂²×C₄	1	16	yes	—
60	#2920	—	13	2	no	—
61	#2920	D₁₃	1	1	yes	characteristic
62	#1455	—	13	4	no	—
63	#1454	—	13	8	no	—
64	C₂³×C₁₃	—	4	2	no	—
65	C₂³×C₁₃	—	4	1	no	—
66	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
67	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	4	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	8	no	—
71	C₂×C₄×C₁₃	—	2	4	no	—
72	C₂×C₄×C₁₃	—	4	4	no	—
73	C₂×C₄×C₁₃	—	4	2	no	—
74	C₂×C₄×C₁₃	—	4	2	no	—
75	C₂×C₄×C₁₃	—	4	1	no	—
76	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
80	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
81	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
82	C₈×C₁₃	—	2	8	no	—
83	#1055	—	2	16	no	—
84	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
85	#432	—	13	8	no	—
86	#432	Dic₁₃	1	4	yes	—
87	#431	—	13	8	no	—
88	#431	C₂×D₁₃	1	4	yes	—
89	#423	—	13	4	no	—
90	#423	Dic₁₃	1	2	yes	—
91	#407	—	13	4	no	—
92	#407	Dic₁₃	1	2	yes	—
93	C₄×M₁₆	—	13	4	no	—
94	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
95	#322	—	13	8	no	—
96	#322	—	13	4	no	—
97	C₈²	—	13	4	no	—
98	C₂²×C₁₃	—	2	2	no	—
99	C₂²×C₁₃	—	2	4	no	—
100	C₂²×C₁₃	—	2	1	no	—
101	C₂²×C₁₃	—	2	2	no	—
102	C₂²×C₁₃	—	4	4	no	—
103	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
104	C₄×C₁₃	—	2	2	no	—
105	C₄×C₁₃	—	2	4	no	—
106	C₄×C₁₃	—	2	1	no	—
107	C₄×C₁₃	—	2	2	no	—
108	C₄×C₁₃	#568	1	4	yes	—
109	C₄×C₁₃	#568	1	2	yes	—
110	C₂³×C₄	C₄×D₁₃	1	2	yes	—
111	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
112	C₂×M₁₆	—	13	8	no	—
113	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
114	C₂×C₄²	C₄×D₁₃	1	2	yes	—
115	C₂×C₄²	C₄×D₁₃	1	4	yes	—
116	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
117	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
118	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
119	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
120	C₄⋊C₈	—	13	16	no	—
121	C₄⋊C₈	C₂×Dic₁₃	1	8	yes	—
122	C₂²⋊C₈	—	13	16	no	—
123	C₂²⋊C₈	C₂×Dic₁₃	1	8	yes	—
124	#97	—	13	8	no	—
125	#97	C₂×Dic₁₃	1	4	yes	—
126	C₄×C₈	—	13	8	no	—
127	C₄×C₈	C₂²×D₁₃	1	4	yes	—
128	C₂×C₁₃	—	4	1	no	—
129	C₂×C₁₃	—	4	2	no	—
130	C₂×C₁₃	#2873	1	2	yes	—
131	C₂×C₁₃	#2873	1	1	yes	characteristic
132	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
133	C₂²×C₄	—	4	4	no	—
134	C₂²×C₄	—	4	2	no	—
135	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
136	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
137	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
138	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
139	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
140	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
141	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
142	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
143	M₁₆	—	4	4	no	—
144	M₁₆	—	52	8	no	—
145	C₂×C₈	—	13	16	no	—
146	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
147	C₄²	C₄×Dic₁₃	1	4	yes	—
148	C₄²	C₄×Dic₁₃	1	2	yes	—
149	C₄²	C₂×C₄×D₁₃	1	2	yes	—
150	C₄²	C₂×C₄×D₁₃	1	4	yes	—
151	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
152	C₄²	C₂²×Dic₁₃	1	2	yes	—
153	C₄²	C₂³×D₁₃	1	1	yes	characteristic
154	C₁₃	#17339	1	1	yes	characteristic, complemented, Sylow
155	C₂³	—	4	2	no	—
156	C₂³	—	4	1	no	—
157	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
158	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	4	4	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
168	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
169	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
170	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
171	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
172	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
173	C₈	—	2	8	no	—
174	C₈	—	26	16	no	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	2	1	no	—
178	C₂²	—	2	2	no	—
179	C₂²	—	4	4	no	—
180	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	2	4	no	—
183	C₄	—	2	1	no	—
184	C₄	—	2	2	no	—
185	C₄	#11719450	1	4	yes	—
186	C₄	#11719524	1	2	yes	—
187	C₂	—	4	1	no	—
188	C₂	—	4	2	no	—
189	C₂	#13123254	1	2	yes	—
190	C₂	#13123255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#2920	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17339
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. #13113139	C₂	semidirect
3. #13113136	C₂	semidirect
16. #11718047	C₂²	semidirect
17. #11718046	C₂²	semidirect
18. C₈×#1055	C₂²	semidirect
154. C₁₃	#17339	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
#13113139	2
#13113136	2
C₁₃×#2920	2
#17339	13