Subgroups — #15779273

Order 3328.

298 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	2	yes	maximal
2	#13112920	C₂	1	2	yes	maximal
3	#13112916	C₂	1	2	yes	maximal
4	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
6	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#376	C₄	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	4	yes	—
13	#11718055	—	2	4	no	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₁₃×#97	—	2	2	no	—
22	C₁₃×#97	—	2	2	no	—
23	C₁₃×#97	—	2	2	no	—
24	C₄×C₈×C₁₃	—	2	2	no	—
25	C₄×C₈×C₁₃	C₈	1	4	yes	—
26	C₄×C₈×C₁₃	D₄	1	2	yes	—
27	C₄×C₈×C₁₃	Q₈	1	2	yes	—
28	C₁₃×#95	—	2	2	no	—
29	#88052	—	2	4	no	—
30	#88052	—	2	4	no	—
31	C₂×#6090	—	2	4	no	—
32	#12881	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	—	2	1	no	—
34	C₂²×C₄×C₁₃	—	2	1	no	—
35	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	—	2	1	no	—
38	C₂×C₈×C₁₃	—	2	1	no	—
39	C₂×C₈×C₁₃	—	2	1	no	—
40	C₂×C₈×C₁₃	—	2	1	no	—
41	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
42	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
45	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
46	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₃	#41	1	2	yes	—
49	C₂×C₈×C₁₃	#41	1	2	yes	—
50	C₄²×C₁₃	—	2	1	no	—
51	C₄²×C₁₃	—	2	1	no	—
52	C₄²×C₁₃	—	2	1	no	—
53	C₄²×C₁₃	—	2	1	no	—
54	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
55	C₄²×C₁₃	C₂×C₈	1	2	yes	—
56	#6090	—	4	4	no	—
57	C₂×#364	—	13	2	no	—
58	#1726	D₁₃	1	1	yes	characteristic
59	#1377	—	13	2	no	—
60	#1375	—	13	2	no	—
61	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	4	2	no	—
66	C₂×C₄×C₁₃	—	4	2	no	—
67	C₂×C₄×C₁₃	—	4	2	no	—
68	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
70	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
74	C₈×C₁₃	—	2	2	no	—
75	C₈×C₁₃	—	2	2	no	—
76	C₈×C₁₃	C₄⋊C₈	1	4	yes	—
77	C₈×C₁₃	#124	1	2	yes	—
78	C₈×C₁₃	#125	1	2	yes	—
79	C₂×M₃₂	—	13	4	no	—
80	C₂×#97	Dic₁₃	1	1	yes	characteristic
81	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
82	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
83	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
84	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
86	#376	Dic₁₃	1	1	yes	characteristic
87	#364	—	26	4	no	—
88	C₂²×C₁₃	—	2	2	no	—
89	C₂²×C₁₃	#423	1	1	yes	characteristic
90	C₂²×C₁₃	#431	1	1	yes	characteristic
91	C₂²×C₁₃	#432	1	1	yes	characteristic
92	C₄×C₁₃	—	4	2	no	—
93	C₄×C₁₃	—	4	2	no	—
94	C₄×C₁₃	—	4	2	no	—
95	C₄×C₁₃	#382	1	1	yes	characteristic
96	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
97	C₄×C₁₃	#431	1	1	yes	characteristic
98	C₄×C₁₃	#432	1	1	yes	characteristic
99	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
100	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
101	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
102	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
103	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
104	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
105	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
106	M₃₂	—	26	4	no	—
107	M₃₂	—	26	4	no	—
108	C₂×C₁₆	—	26	4	no	—
109	#97	—	2	2	no	—
110	#97	—	2	2	no	—
111	#97	—	2	2	no	—
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	#1055	1	4	yes	—
114	C₄×C₈	Dic₂₆	1	2	yes	—
115	C₄×C₈	D₅₂	1	2	yes	—
116	#95	—	2	2	no	—
117	C₂×C₁₃	—	2	1	no	—
118	C₂×C₁₃	—	2	1	no	—
119	C₂×C₁₃	#1831	1	1	yes	characteristic
120	C₂×C₁₃	#2166	1	2	yes	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	2	1	no	—
123	C₂²×C₄	#6099	1	2	yes	—
124	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	C₂×#1055	1	2	yes	—
130	C₂×C₈	C₂×#1055	1	2	yes	—
131	C₂×C₈	#6099	1	2	yes	—
132	C₂×C₈	#6099	1	2	yes	—
133	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
134	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
135	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
136	C₂×C₈	#6127	1	2	yes	—
137	C₂×C₈	#6127	1	2	yes	—
138	C₄²	—	2	1	no	—
139	C₄²	—	2	1	no	—
140	C₄²	—	2	1	no	—
141	C₄²	—	2	1	no	—
142	C₄²	C₂×#1055	1	2	yes	—
143	C₄²	C₄⋊Dic₁₃	1	2	yes	—
144	C₁₆	—	52	4	no	—
145	C₁₃	#12881	1	1	yes	characteristic, complemented, Sylow
146	C₂³	C₂×#6099	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	4	2	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
154	C₂×C₄	C₂×#6099	1	1	yes	characteristic
155	C₂×C₄	C₂×#6099	1	1	yes	characteristic
156	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
157	C₂×C₄	#88180	1	1	yes	characteristic
158	C₂×C₄	#88180	1	1	yes	characteristic
159	C₈	—	2	2	no	—
160	C₈	—	2	2	no	—
161	C₈	C₄⋊#1055	1	4	yes	—
162	C₈	#88124	1	2	yes	—
163	C₈	#88129	1	2	yes	—
164	C₂²	—	2	2	no	—
165	C₂²	#11718585	1	1	yes	characteristic
166	C₂²	#11718586	1	1	yes	characteristic
167	C₂²	#11718587	1	1	yes	characteristic
168	C₄	—	4	2	no	—
169	C₄	—	4	2	no	—
170	C₄	—	4	2	no	—
171	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
172	C₄	#11718586	1	1	yes	characteristic
173	C₄	#11718587	1	1	yes	characteristic
174	C₄	#11718597	1	1	yes	characteristic
175	C₂	—	2	1	no	—
176	C₂	—	2	1	no	—
177	C₂	#13114953	1	1	yes	characteristic
178	C₂	#13116652	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#88180
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1726	C₂
socle	C₂²×C₁₃	#432
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1726	D₁₃
hypocenter	C₁₃	#12881
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1726

Complements

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

N	H ≅ G/N	type
145. C₁₃	#12881	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718055	2
#13112920	2
#13112916	2
C₁₃×#1726	2
#12881	13