Subgroups — C₁₃×#13173 #15699512

Order 3328.

262 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1953	C₂	1	2	yes	maximal
5	C₁₃×#1388	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×#430	—	2	2	no	—
9	C₂×C₁₃×#108	C₂²	1	2	yes	—
10	C₂×C₁₃×#108	C₂²	1	2	yes	—
11	C₁₃×#405	C₂²	1	1	yes	characteristic
12	C₁₃×#368	—	2	1	no	—
13	C₁₃×#368	—	2	1	no	—
14	C₁₃×#368	C₄	1	4	yes	complemented
15	C₁₃×#346	—	2	1	no	—
16	C₄×C₁₃×C₁₆	—	2	1	no	—
17	C₁₃×#344	—	2	2	no	—
18	C₂×C₁₃×M₁₆	—	2	2	no	—
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₁₃×#117	D₄	1	1	yes	characteristic
23	C₁₃×M₃₂	—	2	1	no	—
24	C₁₃×M₃₂	Q₈	1	2	yes	—
25	C₂×C₁₃×C₁₆	—	2	1	no	—
26	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
28	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
30	C₁₃×#108	—	2	2	no	—
31	C₁₃×#108	—	2	2	no	—
32	C₁₃×#108	—	2	2	no	—
33	C₁₃×#108	—	4	4	no	—
34	C₁₃×#108	C₂×C₄	1	4	yes	—
35	C₁₃×#97	—	2	1	no	—
36	C₄×C₈×C₁₃	—	2	1	no	—
37	#13173	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₁₃×M₁₆	—	2	1	no	—
40	C₁₃×M₁₆	—	2	4	no	—
41	C₁₃×M₁₆	—	4	2	no	—
42	C₁₃×M₁₆	—	4	2	no	—
43	C₁₃×M₁₆	—	4	2	no	—
44	C₁₃×M₁₆	D₈	1	2	yes	—
45	C₂×C₈×C₁₃	—	2	1	no	—
46	C₂×C₈×C₁₃	—	4	2	no	—
47	C₂×C₈×C₁₃	—	4	2	no	—
48	C₂×C₈×C₁₃	C₂²×C₄	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	—	2	1	no	—
55	C₁₃×C₂²⋊C₄	Q₁₆	1	2	yes	—
56	C₄²×C₁₃	—	2	1	no	—
57	C₁₃×C₁₆	—	2	2	no	—
58	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
59	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
60	C₂×#368	C₂×C₁₃	1	1	yes	characteristic
61	C₂×#368	C₂×C₁₃	1	1	yes	characteristic
62	#2108	C₂×C₁₃	1	1	yes	characteristic
63	#1953	C₂×C₁₃	1	2	yes	—
64	#1388	C₂×C₁₃	1	2	yes	—
65	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
72	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
73	C₈×C₁₃	—	2	2	no	—
74	C₈×C₁₃	—	4	4	no	—
75	C₈×C₁₃	—	8	2	no	—
76	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
78	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
79	C₈×C₁₃	#125	1	1	yes	characteristic
80	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
81	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
82	#430	—	2	2	no	—
83	C₂×#108	C₂²×C₁₃	1	2	yes	—
84	C₂×#108	C₂²×C₁₃	1	2	yes	—
85	#405	C₂²×C₁₃	1	1	yes	characteristic
86	#368	—	2	1	no	—
87	#368	—	2	1	no	—
88	#368	C₄×C₁₃	1	4	yes	complemented
89	#346	—	2	1	no	—
90	C₄×C₁₆	—	2	1	no	—
91	#344	—	2	2	no	—
92	C₂²×C₁₃	—	4	1	no	—
93	C₂²×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
94	C₂²×C₁₃	#467	1	1	yes	characteristic
95	C₂²×C₁₃	#500	1	1	yes	characteristic
96	C₄×C₁₃	—	4	2	no	—
97	C₄×C₁₃	#389	1	1	yes	characteristic
98	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
99	C₄×C₁₃	#466	1	1	yes	characteristic
100	C₄×C₁₃	#499	1	1	yes	characteristic
101	C₂×M₁₆	—	2	2	no	—
102	C₂×M₁₆	—	2	2	no	—
103	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
104	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
105	#117	D₄×C₁₃	1	1	yes	characteristic
106	M₃₂	—	2	1	no	—
107	M₃₂	Q₈×C₁₃	1	2	yes	—
108	C₂×C₁₆	—	2	1	no	—
109	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
110	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
111	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
112	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
113	#108	—	2	2	no	—
114	#108	—	2	2	no	—
115	#108	—	2	2	no	—
116	#108	—	4	4	no	—
117	#108	C₂×C₄×C₁₃	1	4	yes	—
118	#97	—	2	1	no	—
119	C₄×C₈	—	2	1	no	—
120	C₂×C₁₃	—	2	1	no	—
121	C₂×C₁₃	—	2	1	no	—
122	C₂×C₁₃	—	2	1	no	—
123	C₂×C₁₃	#1942	1	1	yes	characteristic
124	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
125	M₁₆	—	2	1	no	—
126	M₁₆	—	2	4	no	—
127	M₁₆	—	4	2	no	—
128	M₁₆	—	4	2	no	—
129	M₁₆	—	4	2	no	—
130	M₁₆	C₁₃×D₈	1	2	yes	—
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
135	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
136	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
137	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
138	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
139	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
140	C₄⋊C₄	—	2	1	no	—
141	C₂²⋊C₄	C₁₃×Q₁₆	1	2	yes	—
142	C₄²	—	2	1	no	—
143	C₁₆	—	2	2	no	—
144	C₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
145	C₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
146	C₁₃	#13173	1	1	yes	characteristic, direct product factor, Sylow
147	C₂³	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
150	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
151	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
152	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
153	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
154	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
155	C₈	—	2	2	no	—
156	C₈	—	4	4	no	—
157	C₈	—	8	2	no	—
158	C₈	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
159	C₈	C₄×Q₈×C₁₃	1	1	yes	characteristic
160	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
161	C₈	C₁₃×#125	1	1	yes	characteristic
162	C₂²	—	4	1	no	—
163	C₂²	C₄×C₁₃×Q₁₆	1	1	yes	characteristic
164	C₂²	C₁₃×#467	1	1	yes	characteristic
165	C₂²	C₁₃×#500	1	1	yes	characteristic
166	C₄	—	4	2	no	—
167	C₄	C₁₃×#389	1	1	yes	characteristic
168	C₄	C₄×C₁₃×D₈	1	1	yes	characteristic
169	C₄	C₁₃×#466	1	1	yes	characteristic
170	C₄	C₁₃×#499	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	C₁₃×#1942	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#466
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1942
prime radical	C₂³×C₁₃	C₂×Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
14. C₁₃×#368	C₄	semidirect
37. #13173	C₁₃	direct (N × H)
88. #368	C₄×C₁₃	semidirect
146. C₁₃	#13173	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#368	2
C₁₃×#2108	2
C₁₃×#1953	2
C₁₃×#1388	2
#13173	13

Subgroups — C13×#13173 #15699512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13173 #15699512