Subgroups — C₁₃×#12658 #15698997

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2150	C₂	1	2	yes	maximal
2	C₂×C₁₃×#347	C₂	1	2	yes	maximal
3	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1375	C₂	1	2	yes	maximal
5	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
8	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄³×C₁₃	C₄	1	1	yes	characteristic
13	C₁₃×C₄⋊C₁₆	C₄	1	8	yes	complemented
14	C₁₃×#347	—	2	4	no	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	—	2	2	no	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₁₃×M₃₂	—	2	4	no	—
24	C₁₃×M₃₂	—	2	4	no	—
25	C₂×C₁₃×C₁₆	C₂×C₄	1	8	yes	—
26	C₁₃×#97	—	2	2	no	—
27	C₁₃×#97	—	2	2	no	—
28	C₁₃×#97	—	2	2	no	—
29	C₁₃×#97	D₄	1	2	yes	—
30	C₁₃×#97	Q₈	1	2	yes	—
31	C₄×C₈×C₁₃	—	2	1	no	—
32	C₄×C₈×C₁₃	—	2	1	no	—
33	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
34	#12658	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄×C₁₃	—	2	1	no	—
36	C₂²×C₄×C₁₃	—	2	1	no	—
37	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	—	2	1	no	—
40	C₂×C₈×C₁₃	—	2	1	no	—
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	—	2	1	no	—
43	C₂×C₈×C₁₃	—	2	1	no	—
44	C₂×C₈×C₁₃	—	2	1	no	—
45	C₂×C₈×C₁₃	C₄²	1	2	yes	—
46	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
47	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₃	#41	1	2	yes	—
52	C₄²×C₁₃	—	2	1	no	—
53	C₄²×C₁₃	—	2	1	no	—
54	C₄²×C₁₃	—	4	4	no	—
55	C₄²×C₁₃	C₄²	1	2	yes	—
56	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
57	C₄²×C₁₃	M₁₆	1	2	yes	—
58	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
59	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
60	C₁₃×C₁₆	—	2	8	no	—
61	#2150	C₂×C₁₃	1	2	yes	—
62	C₂×#347	C₂×C₁₃	1	2	yes	—
63	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
64	#1375	C₂×C₁₃	1	2	yes	—
65	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
66	C₂×C₄×C₁₃	—	2	4	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	4	2	no	—
70	C₂×C₄×C₁₃	—	4	2	no	—
71	C₂×C₄×C₁₃	#97	1	2	yes	—
72	C₂×C₄×C₁₃	#97	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
79	C₈×C₁₃	—	2	2	no	—
80	C₈×C₁₃	—	2	2	no	—
81	C₈×C₁₃	—	2	2	no	—
82	C₈×C₁₃	C₄×D₄	1	2	yes	—
83	C₈×C₁₃	C₄×Q₈	1	2	yes	—
84	C₂×M₃₂	C₂²×C₁₃	1	4	yes	—
85	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
86	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
87	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
88	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
89	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
91	C₄³	C₄×C₁₃	1	1	yes	characteristic
92	C₄⋊C₁₆	C₄×C₁₃	1	8	yes	complemented
93	#347	—	2	4	no	—
94	C₂²×C₁₃	—	2	2	no	—
95	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
96	C₂²×C₁₃	#423	1	1	yes	characteristic
97	C₂²×C₁₃	#432	1	1	yes	characteristic
98	C₄×C₁₃	—	2	2	no	—
99	C₄×C₁₃	—	4	2	no	—
100	C₄×C₁₃	—	4	2	no	—
101	C₄×C₁₃	#347	1	4	yes	complemented
102	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
103	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
104	C₄×C₁₃	#423	1	1	yes	characteristic
105	C₄×C₁₃	#432	1	1	yes	characteristic
106	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
107	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
108	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
109	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
110	C₂×C₄²	—	2	2	no	—
111	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
112	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
113	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
114	M₃₂	—	2	4	no	—
115	M₃₂	—	2	4	no	—
116	C₂×C₁₆	C₂×C₄×C₁₃	1	8	yes	—
117	#97	—	2	2	no	—
118	#97	—	2	2	no	—
119	#97	—	2	2	no	—
120	#97	D₄×C₁₃	1	2	yes	—
121	#97	Q₈×C₁₃	1	2	yes	—
122	C₄×C₈	—	2	1	no	—
123	C₄×C₈	—	2	1	no	—
124	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
125	C₂×C₁₃	—	2	1	no	—
126	C₂×C₁₃	—	2	1	no	—
127	C₂×C₁₃	#1767	1	1	yes	characteristic
128	C₂×C₁₃	C₂×#347	1	2	yes	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
132	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
133	C₂×C₈	—	2	1	no	—
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	2	1	no	—
139	C₂×C₈	C₄²×C₁₃	1	2	yes	—
140	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
141	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
142	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
143	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
144	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
145	C₂×C₈	C₁₃×#41	1	2	yes	—
146	C₄²	—	2	1	no	—
147	C₄²	—	2	1	no	—
148	C₄²	—	4	4	no	—
149	C₄²	C₄²×C₁₃	1	2	yes	—
150	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
151	C₄²	C₁₃×M₁₆	1	2	yes	—
152	C₄²	C₁₃×M₁₆	1	1	yes	characteristic
153	C₄²	C₁₃×M₁₆	1	1	yes	characteristic
154	C₁₆	—	2	8	no	—
155	C₁₃	#12658	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	C₁₃×#97	1	2	yes	—
163	C₂×C₄	C₁₃×#97	1	2	yes	—
164	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
165	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
167	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
168	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
169	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
170	C₈	—	2	2	no	—
171	C₈	—	2	2	no	—
172	C₈	—	2	2	no	—
173	C₈	C₄×D₄×C₁₃	1	2	yes	—
174	C₈	C₄×Q₈×C₁₃	1	2	yes	—
175	C₂²	—	2	2	no	—
176	C₂²	C₂×C₁₃×#97	1	1	yes	characteristic
177	C₂²	C₁₃×#423	1	1	yes	characteristic
178	C₂²	C₁₃×#432	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	4	2	no	—
181	C₄	—	4	2	no	—
182	C₄	C₁₃×#347	1	4	yes	complemented
183	C₄	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
184	C₄	C₄×C₁₃×M₁₆	1	1	yes	characteristic
185	C₄	C₁₃×#423	1	1	yes	characteristic
186	C₄	C₁₃×#432	1	1	yes	characteristic
187	C₂	—	2	1	no	—
188	C₂	—	2	1	no	—
189	C₂	C₁₃×#1767	1	1	yes	characteristic
190	C₂	C₂×C₁₃×#347	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×C₄⋊C₁₆	C₄	semidirect
34. #12658	C₁₃	direct (N × H)
92. C₄⋊C₁₆	C₄×C₁₃	semidirect
101. C₄×C₁₃	#347	semidirect
155. C₁₃	#12658	direct (N × H)
182. C₄	C₁₃×#347	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#2150	2
C₂×C₁₃×#347	2
C₄×C₁₃×#97	2
C₁₃×#1375	2
#12658	13

Subgroups — C13×#12658 #15698997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12658 #15698997