Subgroups — #15780935

Order 3328.

290 conjugacy classes of subgroups.

The subgroup lattice has 186 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	1	yes	maximal, characteristic
2	#13116595	C₂	1	2	yes	maximal
3	C₂×#11718053	C₂	1	1	yes	maximal, characteristic
4	#13112925	C₂	1	2	yes	maximal
5	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#108	C₄	1	1	yes	characteristic
7	C₁₃×#427	C₄	1	1	yes	characteristic
8	C₁₃×#405	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88052	C₂²	1	2	yes	—
11	C₂²×#6090	C₂²	1	1	yes	characteristic
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₁₃×#339	C₄	1	2	yes	—
14	#11718055	—	2	2	no	—
15	C₄⋊#6090	—	2	4	no	—
16	#11718053	—	2	2	no	—
17	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×#117	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₁₃×#108	—	2	2	no	—
23	C₁₃×#107	C₈	1	2	yes	—
24	C₁₃×#106	C₈	1	2	yes	—
25	C₁₃×#97	—	2	2	no	—
26	C₄×C₈×C₁₃	—	2	2	no	—
27	C₄×C₈×C₁₃	D₄	1	2	yes	—
28	C₄×C₈×C₁₃	Q₈	1	2	yes	—
29	#88052	—	2	2	no	—
30	#88052	—	2	2	no	—
31	C₂×#6090	—	2	1	no	—
32	C₂×#6090	—	2	1	no	—
33	C₂×#6090	—	2	1	no	—
34	C₂×#6090	—	2	1	no	—
35	C₂×#6090	—	2	2	no	—
36	C₂×#6090	D₄	1	2	yes	—
37	C₂×#6090	Q₈	1	2	yes	—
38	#13162	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	—	2	1	no	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₁₃×M₁₆	—	2	2	no	—
42	C₁₃×M₁₆	—	2	2	no	—
43	C₂×C₈×C₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
53	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
54	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
55	C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	1	no	—
58	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
59	#6090	—	2	2	no	—
60	#6090	—	2	2	no	—
61	#6090	—	4	2	no	—
62	C₂×#364	—	13	1	no	—
63	#2151	—	13	2	no	—
64	C₂×#346	—	13	1	no	—
65	#1772	D₁₃	1	1	yes	characteristic
66	#1379	—	13	2	no	—
67	C₂³×C₁₃	#131	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	4	no	—
70	C₂×C₄×C₁₃	—	4	2	no	—
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
77	C₈×C₁₃	—	4	2	no	—
78	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
79	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
80	C₈×C₁₃	#121	1	1	yes	characteristic
81	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
82	C₈×C₁₃	#125	1	1	yes	characteristic
83	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
84	C₂×M₃₂	—	13	2	no	—
85	C₂²×C₁₆	—	13	1	no	—
86	C₂²×C₁₆	—	13	1	no	—
87	C₂×#108	Dic₁₃	1	1	yes	characteristic
88	#427	Dic₁₃	1	1	yes	characteristic
89	#405	C₂×D₁₃	1	2	yes	—
90	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
91	#364	—	26	2	no	—
92	C₄⋊C₁₆	—	26	4	no	—
93	#346	—	26	2	no	—
94	#339	Dic₁₃	1	2	yes	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	#424	1	1	yes	characteristic
97	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
98	C₂²×C₁₃	#446	1	1	yes	characteristic
99	C₄×C₁₃	—	4	2	no	—
100	C₄×C₁₃	—	4	4	no	—
101	C₄×C₁₃	#389	1	1	yes	characteristic
102	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
103	C₄×C₁₃	#436	1	1	yes	characteristic
104	C₄×C₁₃	C₈×Q₈	1	1	yes	characteristic
105	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
106	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
107	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
108	#117	C₂×Dic₁₃	1	2	yes	—
109	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
110	M₃₂	—	26	2	no	—
111	M₃₂	—	26	2	no	—
112	C₂×C₁₆	—	13	2	no	—
113	C₂×C₁₆	—	13	2	no	—
114	C₂×C₁₆	—	26	1	no	—
115	C₂×C₁₆	—	26	1	no	—
116	C₂×C₁₆	—	26	1	no	—
117	C₂×C₁₆	—	26	1	no	—
118	C₂×C₁₆	—	26	2	no	—
119	#108	—	2	2	no	—
120	#107	#1055	1	2	yes	—
121	#106	#1055	1	2	yes	—
122	#97	—	2	2	no	—
123	C₄×C₈	—	2	2	no	—
124	C₄×C₈	Dic₂₆	1	2	yes	—
125	C₄×C₈	D₅₂	1	2	yes	—
126	C₂×C₁₃	—	2	1	no	—
127	C₂×C₁₃	—	2	1	no	—
128	C₂×C₁₃	#1939	1	1	yes	characteristic
129	C₂×C₁₃	#2171	1	2	yes	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
132	M₁₆	—	2	2	no	—
133	M₁₆	—	2	2	no	—
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	C₂×#1055	1	1	yes	characteristic
136	C₂×C₈	C₂×#1055	1	1	yes	characteristic
137	C₂×C₈	#6099	1	2	yes	—
138	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
139	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
140	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
141	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
142	C₂×C₈	#6129	1	1	yes	characteristic
143	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
144	C₂×C₈	#6131	1	1	yes	characteristic
145	C₄⋊C₄	C₂×#1055	1	4	yes	—
146	C₂²⋊C₄	—	2	2	no	—
147	C₄²	—	2	2	no	—
148	C₄²	—	2	1	no	—
149	C₄²	C₄⋊Dic₁₃	1	2	yes	—
150	C₁₆	—	26	2	no	—
151	C₁₆	—	26	2	no	—
152	C₁₆	—	52	2	no	—
153	C₁₃	#13162	1	1	yes	characteristic, complemented, Sylow
154	C₂³	#88202	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	4	2	no	—
158	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
159	C₂×C₄	C₂×#6099	1	1	yes	characteristic
160	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
161	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
162	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
163	C₂×C₄	#88202	1	1	yes	characteristic
164	C₈	—	4	2	no	—
165	C₈	C₄⋊#1055	1	2	yes	—
166	C₈	C₄⋊#1055	1	2	yes	—
167	C₈	#88142	1	1	yes	characteristic
168	C₈	#88144	1	1	yes	characteristic
169	C₈	#88149	1	1	yes	characteristic
170	C₈	#88151	1	1	yes	characteristic
171	C₂²	—	2	2	no	—
172	C₂²	#11718660	1	1	yes	characteristic
173	C₂²	D₄×#1055	1	1	yes	characteristic
174	C₂²	#11718685	1	1	yes	characteristic
175	C₄	—	4	2	no	—
176	C₄	—	4	4	no	—
177	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
178	C₄	#11718646	1	1	yes	characteristic
179	C₄	#11718673	1	1	yes	characteristic
180	C₄	Q₈×#1055	1	1	yes	characteristic
181	C₂	—	2	1	no	—
182	C₂	—	2	1	no	—
183	C₂	#13115555	1	1	yes	characteristic
184	C₂	#13116678	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1772	C₂
socle	C₂²×C₁₃	C₈×D₄
prime radical	C₂³×C₁₃	#131
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1772	D₁₃
hypocenter	C₁₃	#13162
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
153. C₁₃	#13162	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
#13116595	2
C₂×#11718053	2
#13112925	2
C₁₃×#1772	2
#13162	13