Subgroups — #15871263

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115560	C₂	1	2	yes	maximal
2	#13115402	C₂	1	4	yes	maximal
3	#13114956	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×#1055	C₂	1	4	yes	maximal
5	C₄⋊C₄×#1055	C₂	1	2	yes	maximal
6	#13114523	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2402	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#400	C₄	1	4	yes	—
9	C₁₃×#398	C₄	1	4	yes	—
10	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
11	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₁₃×#376	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#1055	C₂²	1	4	yes	—
14	C₂×C₄⋊#1055	C₂²	1	2	yes	—
15	C₂×#88043	C₂²	1	2	yes	—
16	C₂×#88043	C₂²	1	1	yes	characteristic
17	C₂×C₄×#1055	C₂²	1	4	yes	—
18	C₂×C₄×#1055	C₂²	1	2	yes	—
19	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
20	#11718116	C₂²	1	4	yes	—
21	#11718116	C₂²	1	4	yes	—
22	#11718116	C₂²	1	4	yes	—
23	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
24	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
29	C₂²×#1055	C₂³	1	4	yes	—
30	C₂²×#1055	C₂³	1	1	yes	characteristic
31	C₂²×#1055	C₂³	1	2	yes	—
32	C₂²×#1055	C₂³	1	1	yes	characteristic
33	C₁₃×#95	C₂×C₄	1	2	yes	—
34	C₁₃×#95	C₂×C₄	1	4	yes	—
35	C₁₃×#95	C₂×C₄	1	4	yes	—
36	C₁₃×#95	C₂×C₄	1	2	yes	—
37	C₁₃×#95	C₂×C₄	1	4	yes	—
38	C₄⋊#1055	—	2	4	no	—
39	C₄⋊#1055	—	2	8	no	—
40	#88043	—	2	2	no	—
41	#88043	—	2	4	no	—
42	C₄×#1055	—	2	4	no	—
43	C₄×#1055	—	2	8	no	—
44	C₄×#1055	Q₈	1	4	yes	—
45	#21676	—	13	1	no	maximal, Sylow
46	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
51	C₁₃×C₄⋊C₄	—	2	8	no	—
52	C₁₃×C₄⋊C₄	—	2	8	no	—
53	C₁₃×C₄⋊C₄	—	2	8	no	—
54	C₄²×C₁₃	—	2	4	no	—
55	C₄²×C₁₃	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	4	no	—
58	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
59	C₄²×C₁₃	#41	1	2	yes	—
60	C₂×#1055	—	2	2	no	—
61	C₂×#1055	—	2	2	no	—
62	C₂×#1055	—	2	2	no	—
63	C₂×#1055	—	2	4	no	—
64	C₂×#1055	—	2	4	no	—
65	C₂×#1055	—	2	4	no	—
66	C₂×#1055	C₂×Q₈	1	2	yes	—
67	C₂×#1055	C₂×Q₈	1	2	yes	—
68	C₂×#1055	#41	1	4	yes	—
69	C₂×#1055	#41	1	4	yes	—
70	#2402	D₁₃	1	1	yes	characteristic
71	#1940	—	13	2	no	—
72	#1917	—	13	4	no	—
73	#1832	—	13	1	no	—
74	C₈×C₄⋊C₄	—	13	4	no	—
75	C₈×C₄⋊C₄	—	13	2	no	—
76	#1726	—	13	1	no	—
77	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	2	4	no	—
80	C₂×C₄×C₁₃	—	2	4	no	—
81	C₂×C₄×C₁₃	—	2	4	no	—
82	C₂×C₄×C₁₃	—	2	4	no	—
83	C₂×C₄×C₁₃	—	2	4	no	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
88	C₂×C₄×C₁₃	#131	1	8	yes	—
89	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
93	#1055	—	2	4	no	—
94	#1055	—	2	2	no	—
95	#1055	—	4	4	no	—
96	#1055	#125	1	4	yes	—
97	C₂×C₄⋊C₈	—	13	2	no	—
98	C₂×C₄⋊C₈	—	13	4	no	—
99	C₂×#97	—	13	2	no	—
100	C₂×#97	—	13	1	no	—
101	C₂×C₄×C₈	—	13	1	no	—
102	C₂×C₄×C₈	—	13	2	no	—
103	C₂×C₄×C₈	—	13	4	no	—
104	#400	Dic₁₃	1	4	yes	—
105	#398	Dic₁₃	1	4	yes	—
106	C₄×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
107	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
108	#376	C₂×D₁₃	1	1	yes	characteristic
109	#336	—	13	4	no	—
110	#336	—	13	4	no	—
111	#336	—	13	4	no	—
112	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
113	C₂²×C₁₃	C₄×#41	1	2	yes	—
114	C₂²×C₁₃	C₂×#131	1	4	yes	—
115	C₄×C₁₃	—	2	4	no	—
116	C₄×C₁₃	—	2	8	no	—
117	C₄×C₁₃	—	4	4	no	—
118	C₄×C₁₃	—	4	4	no	—
119	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
120	C₄×C₁₃	#529	1	2	yes	—
121	C₄×C₁₃	#533	1	1	yes	characteristic
122	C₂²×C₈	—	13	1	no	—
123	C₂²×C₈	—	13	1	no	—
124	C₂²×C₈	—	13	2	no	—
125	C₂²×C₈	—	13	4	no	—
126	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
127	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
128	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
129	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
130	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
131	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
132	C₄⋊C₈	—	26	8	no	—
133	C₄⋊C₈	—	26	4	no	—
134	#97	—	26	4	no	—
135	#97	—	26	2	no	—
136	C₄×C₈	—	13	4	no	—
137	C₄×C₈	—	26	4	no	—
138	C₄×C₈	—	26	8	no	—
139	#95	C₂×Dic₁₃	1	4	yes	—
140	#95	C₂×Dic₁₃	1	2	yes	—
141	#95	C₂×Dic₁₃	1	4	yes	—
142	#95	C₂×Dic₁₃	1	4	yes	—
143	#95	C₂×Dic₁₃	1	2	yes	—
144	C₂×C₁₃	C₄×#125	1	1	yes	characteristic
145	C₂×C₁₃	#2960	1	2	yes	—
146	C₂×C₁₃	#2966	1	4	yes	—
147	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
148	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
149	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
150	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
151	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
152	C₂×C₈	—	13	2	no	—
153	C₂×C₈	—	13	4	no	—
154	C₂×C₈	—	13	2	no	—
155	C₂×C₈	—	13	4	no	—
156	C₂×C₈	—	26	2	no	—
157	C₂×C₈	—	26	2	no	—
158	C₂×C₈	—	26	2	no	—
159	C₂×C₈	—	26	4	no	—
160	C₂×C₈	—	26	4	no	—
161	C₂×C₈	—	26	4	no	—
162	C₄⋊C₄	—	2	8	no	—
163	C₄⋊C₄	—	2	8	no	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	2	no	—
167	C₄²	—	2	2	no	—
168	C₄²	—	2	4	no	—
169	C₄²	Q₈×D₁₃	1	2	yes	—
170	C₄²	#6131	1	2	yes	—
171	C₁₃	#21676	1	1	yes	characteristic, complemented, Sylow
172	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	Q₈×Dic₁₃	1	4	yes	—
183	C₂×C₄	#88202	1	8	yes	—
184	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
185	C₂×C₄	C₂×#6131	1	1	yes	characteristic
186	C₂×C₄	#41×D₁₃	1	2	yes	—
187	C₂×C₄	#41×D₁₃	1	2	yes	—
188	C₈	—	13	4	no	—
189	C₈	—	26	2	no	—
190	C₈	—	26	4	no	—
191	C₈	—	52	4	no	—
192	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
193	C₂²	C₂×#88202	1	4	yes	—
194	C₂²	#41×Dic₁₃	1	2	yes	—
195	C₄	—	2	4	no	—
196	C₄	—	2	8	no	—
197	C₄	—	4	4	no	—
198	C₄	—	4	4	no	—
199	C₄	D₁₃×#125	1	1	yes	characteristic
200	C₄	#11719393	1	1	yes	characteristic
201	C₄	#11719396	1	2	yes	—
202	C₂	#125×Dic₁₃	1	1	yes	characteristic
203	C₂	#13123771	1	2	yes	—
204	C₂	#13123812	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2402	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2402	D₁₃
hypocenter	C₁₃	#21676
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2402

Complements

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

N	H ≅ G/N	type
171. C₁₃	#21676	semidirect

Maximal subgroups

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

subgroup	index
#13115560	2
#13115402	2
#13114956	2
C₄⋊C₄×#1055	2
#13114523	2
C₁₃×#2402	2
#21676	13