Subgroups — C₁₃×#12903 #15699242

Order 3328.

334 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×#365	C₂	1	4	yes	maximal
2	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
6	C₂×C₁₃×#108	—	2	1	no	—
7	C₂×C₁₃×#108	C₂²	1	2	yes	—
8	C₂×C₁₃×#106	—	2	1	no	—
9	C₂×C₁₃×#106	C₂²	1	2	yes	—
10	C₁₃×#423	—	2	1	no	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#384	—	2	1	no	—
13	C₁₃×#365	—	2	8	no	—
14	C₁₃×#346	C₄	1	2	yes	complemented
15	C₄×C₁₃×C₁₆	C₄	1	2	yes	complemented
16	C₂×C₁₃×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
21	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₁₃×M₃₂	D₄	1	4	yes	—
23	C₁₃×M₃₂	Q₈	1	4	yes	—
24	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
25	C₁₃×#108	—	2	4	no	—
26	C₁₃×#108	—	4	2	no	—
27	C₁₃×#106	—	2	4	no	—
28	C₁₃×#106	—	4	2	no	—
29	C₁₃×C₄⋊C₈	—	4	2	no	—
30	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
33	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
34	#12903	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄×C₁₃	—	4	2	no	—
36	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₁₃×M₁₆	—	4	2	no	—
39	C₁₃×M₁₆	—	4	2	no	—
40	C₂×C₈×C₁₃	—	4	2	no	—
41	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
47	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
48	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₁₃×C₄⋊C₄	—	4	2	no	—
50	C₁₃×C₄⋊C₄	—	4	2	no	—
51	C₁₃×C₄⋊C₄	—	8	4	no	—
52	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
54	C₄²×C₁₃	SD₁₆	1	2	yes	—
55	C₁₃×C₁₆	C₄⋊C₄	1	8	yes	complemented
56	C₂×#365	C₂×C₁₃	1	4	yes	—
57	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
58	#1848	C₂×C₁₃	1	1	yes	characteristic
59	#1844	C₂×C₁₃	1	1	yes	characteristic
60	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	4	no	—
62	C₂×C₄×C₁₃	—	8	4	no	—
63	C₂×C₄×C₁₃	—	8	2	no	—
64	C₂×C₄×C₁₃	#106	1	2	yes	—
65	C₂×C₄×C₁₃	#106	1	2	yes	—
66	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
72	C₈×C₁₃	—	8	2	no	—
73	C₈×C₁₃	#106	1	2	yes	—
74	C₈×C₁₃	#106	1	2	yes	—
75	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
76	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
77	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
78	C₂×#108	—	2	1	no	—
79	C₂×#108	C₂²×C₁₃	1	2	yes	—
80	C₂×#106	—	2	1	no	—
81	C₂×#106	C₂²×C₁₃	1	2	yes	—
82	#423	—	2	1	no	—
83	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
84	#384	—	2	1	no	—
85	#365	—	2	8	no	—
86	#346	C₄×C₁₃	1	2	yes	complemented
87	C₄×C₁₆	C₄×C₁₃	1	2	yes	complemented
88	C₂²×C₁₃	—	2	2	no	—
89	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
90	C₂²×C₁₃	#492	1	1	yes	characteristic
91	C₂²×C₁₃	#498	1	1	yes	characteristic
92	C₄×C₁₃	—	2	2	no	—
93	C₄×C₁₃	—	16	2	no	—
94	C₄×C₁₃	#365	1	4	yes	complemented
95	C₄×C₁₃	#384	1	1	yes	characteristic
96	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
97	C₄×C₁₃	#492	1	1	yes	characteristic
98	C₄×C₁₃	#498	1	1	yes	characteristic
99	C₂×M₁₆	—	2	2	no	—
100	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
101	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
102	C₂×C₄⋊C₄	—	2	2	no	—
103	C₂×C₄⋊C₄	—	4	2	no	—
104	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
105	M₃₂	D₄×C₁₃	1	4	yes	—
106	M₃₂	Q₈×C₁₃	1	4	yes	—
107	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
108	#108	—	2	4	no	—
109	#108	—	4	2	no	—
110	#106	—	2	4	no	—
111	#106	—	4	2	no	—
112	C₄⋊C₈	—	4	2	no	—
113	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
114	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
115	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
116	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
117	C₂×C₁₃	—	2	1	no	—
118	C₂×C₁₃	—	2	1	no	—
119	C₂×C₁₃	#1844	1	1	yes	characteristic
120	C₂×C₁₃	C₂×#365	1	2	yes	—
121	C₂²×C₄	—	4	2	no	—
122	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
123	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
124	M₁₆	—	4	2	no	—
125	M₁₆	—	4	2	no	—
126	C₂×C₈	—	4	2	no	—
127	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
130	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
131	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
132	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
133	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
134	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
135	C₄⋊C₄	—	4	2	no	—
136	C₄⋊C₄	—	4	2	no	—
137	C₄⋊C₄	—	8	4	no	—
138	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
139	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
140	C₄²	C₁₃×SD₁₆	1	2	yes	—
141	C₁₆	C₁₃×C₄⋊C₄	1	8	yes	complemented
142	C₁₃	#12903	1	1	yes	characteristic, direct product factor, Sylow
143	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	8	4	no	—
146	C₂×C₄	—	8	2	no	—
147	C₂×C₄	C₁₃×#106	1	2	yes	—
148	C₂×C₄	C₁₃×#106	1	2	yes	—
149	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
151	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
152	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
153	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
154	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
155	C₈	—	8	2	no	—
156	C₈	C₁₃×#106	1	2	yes	—
157	C₈	C₁₃×#106	1	2	yes	—
158	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
159	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
160	C₂²	—	2	2	no	—
161	C₂²	C₂×C₁₃×#106	1	1	yes	characteristic
162	C₂²	C₁₃×#492	1	1	yes	characteristic
163	C₂²	C₁₃×#498	1	1	yes	characteristic
164	C₄	—	2	2	no	—
165	C₄	—	16	2	no	—
166	C₄	C₁₃×#365	1	4	yes	complemented
167	C₄	C₁₃×#384	1	1	yes	characteristic
168	C₄	C₂×C₁₃×#106	1	1	yes	characteristic
169	C₄	C₁₃×#492	1	1	yes	characteristic
170	C₄	C₁₃×#498	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	C₁₃×#1844	1	1	yes	characteristic
174	C₂	C₂×C₁₃×#365	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₁₃×#346	C₄	semidirect
15. C₄×C₁₃×C₁₆	C₄	semidirect
34. #12903	C₁₃	direct (N × H)
55. C₁₃×C₁₆	C₄⋊C₄	semidirect
86. #346	C₄×C₁₃	semidirect
87. C₄×C₁₆	C₄×C₁₃	semidirect
94. C₄×C₁₃	#365	semidirect
141. C₁₆	C₁₃×C₄⋊C₄	semidirect
142. C₁₃	#12903	direct (N × H)
166. C₄	C₁₃×#365	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#365	2
C₄×C₁₃×M₃₂	2
C₁₃×#1848	2
C₁₃×#1844	2
#12903	13

Subgroups — C13×#12903 #15699242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12903 #15699242