Subgroups — C₁₃×#34638 #15720977

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2647	C₂	1	8	yes	maximal, complemented
2	C₁₃×#2646	C₂	1	8	yes	maximal
3	C₁₃×#2402	C₂	1	8	yes	maximal, complemented
4	C₁₃×#2296	C₂	1	4	yes	maximal
5	C₁₃×#2285	C₂	1	2	yes	maximal
6	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#117	C₂²	1	4	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#400	C₂²	1	32	yes	—
11	C₁₃×#398	C₂²	1	32	yes	—
12	C₁₃×#389	C₂²	1	16	yes	—
13	C₁₃×#385	C₂²	1	16	yes	—
14	C₁₃×#384	C₂²	1	4	yes	—
15	C₁₃×#382	C₂²	1	4	yes	—
16	C₁₃×#380	C₂²	1	8	yes	—
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	16	yes	—
19	C₁₃×#376	C₂²	1	4	yes	—
20	C₁₃×#376	C₂²	1	4	yes	—
21	C₂×C₁₃×#95	C₂²	1	4	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×#117	—	2	16	no	—
26	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
27	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
29	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
30	C₂×C₄²×C₁₃	—	2	8	no	—
31	C₂×C₄²×C₁₃	Q₈	1	8	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
37	C₁₃×#95	C₂³	1	16	yes	—
38	C₁₃×#95	C₂³	1	32	yes	—
39	C₁₃×#95	C₂³	1	16	yes	—
40	#34638	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	—	2	8	no	—
43	C₂²×C₄×C₁₃	—	4	4	no	—
44	C₂²×C₄×C₁₃	—	4	8	no	—
45	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
46	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
47	C₂²×C₄×C₁₃	#41	1	8	yes	—
48	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
49	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
51	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
53	C₁₃×C₄⋊C₄	—	2	16	no	—
54	C₁₃×C₄⋊C₄	—	4	16	no	—
55	C₁₃×C₄⋊C₄	—	4	32	no	—
56	C₁₃×C₂²⋊C₄	—	2	16	no	—
57	C₄²×C₁₃	—	2	8	no	—
58	C₄²×C₁₃	—	2	8	no	—
59	C₄²×C₁₃	—	2	16	no	—
60	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
61	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
62	#2647	C₂×C₁₃	1	8	yes	complemented
63	#2646	C₂×C₁₃	1	8	yes	—
64	#2402	C₂×C₁₃	1	8	yes	complemented
65	#2296	C₂×C₁₃	1	4	yes	—
66	#2285	C₂×C₁₃	1	2	yes	—
67	C₂×#376	C₂×C₁₃	1	1	yes	characteristic
68	C₂³×C₁₃	—	2	4	no	—
69	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
70	C₂³×C₁₃	C₂×#41	1	4	yes	—
71	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
72	C₂×C₄×C₁₃	—	2	8	no	—
73	C₂×C₄×C₁₃	—	2	8	no	—
74	C₂×C₄×C₁₃	—	2	16	no	—
75	C₂×C₄×C₁₃	—	2	32	no	—
76	C₂×C₄×C₁₃	—	2	16	no	—
77	C₂×C₄×C₁₃	—	4	8	no	—
78	C₂×C₄×C₁₃	—	4	16	no	—
79	C₂×C₄×C₁₃	#125	1	16	yes	—
80	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
81	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
82	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
83	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
84	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
85	C₂×#117	C₂²×C₁₃	1	4	yes	—
86	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
87	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
88	#400	C₂²×C₁₃	1	32	yes	—
89	#398	C₂²×C₁₃	1	32	yes	—
90	#389	C₂²×C₁₃	1	16	yes	—
91	#385	C₂²×C₁₃	1	16	yes	—
92	#384	C₂²×C₁₃	1	4	yes	—
93	#382	C₂²×C₁₃	1	4	yes	—
94	#380	C₂²×C₁₃	1	8	yes	—
95	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
96	C₄×C₄⋊C₄	C₂²×C₁₃	1	16	yes	—
97	#376	C₂²×C₁₃	1	4	yes	—
98	#376	C₂²×C₁₃	1	4	yes	—
99	C₂×#95	C₂²×C₁₃	1	4	yes	—
100	C₂²×C₁₃	—	2	8	no	—
101	C₂²×C₁₃	—	2	4	no	—
102	C₂²×C₁₃	C₂×#125	1	4	yes	—
103	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
104	C₂²×C₁₃	C₂²×#41	1	2	yes	—
105	C₂²×C₁₃	#585	1	4	yes	—
106	C₄×C₁₃	—	2	8	no	—
107	C₄×C₁₃	—	4	16	no	—
108	C₄×C₁₃	—	4	8	no	—
109	C₄×C₁₃	C₂×#125	1	4	yes	—
110	C₄×C₁₃	C₂×#125	1	4	yes	—
111	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
112	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
113	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
114	#117	—	2	16	no	—
115	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
116	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
117	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
118	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
119	C₂×C₄²	—	2	8	no	—
120	C₂×C₄²	Q₈×C₁₃	1	8	yes	—
121	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
122	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
123	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
124	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
125	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
126	#95	C₂³×C₁₃	1	16	yes	—
127	#95	C₂³×C₁₃	1	16	yes	—
128	#95	C₂³×C₁₃	1	32	yes	—
129	C₂×C₁₃	—	2	4	no	—
130	C₂×C₁₃	C₂²×#125	1	1	yes	characteristic
131	C₂×C₁₃	#3455	1	4	yes	—
132	C₂×C₁₃	#3458	1	2	yes	—
133	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
134	C₂²×C₄	—	2	8	no	—
135	C₂²×C₄	—	4	4	no	—
136	C₂²×C₄	—	4	8	no	—
137	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
138	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
139	C₂²×C₄	C₁₃×#41	1	8	yes	—
140	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
141	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
142	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
143	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
145	C₄⋊C₄	—	2	16	no	—
146	C₄⋊C₄	—	4	16	no	—
147	C₄⋊C₄	—	4	32	no	—
148	C₂²⋊C₄	—	2	16	no	—
149	C₄²	—	2	8	no	—
150	C₄²	—	2	8	no	—
151	C₄²	—	2	16	no	—
152	C₄²	C₂×Q₈×C₁₃	1	8	yes	—
153	C₄²	C₂×Q₈×C₁₃	1	8	yes	—
154	C₁₃	#34638	1	1	yes	characteristic, direct product factor, Sylow
155	C₂³	—	2	4	no	—
156	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
157	C₂³	C₂×C₁₃×#41	1	4	yes	—
158	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	8	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	2	16	no	—
162	C₂×C₄	—	2	32	no	—
163	C₂×C₄	—	2	16	no	—
164	C₂×C₄	—	4	8	no	—
165	C₂×C₄	—	4	16	no	—
166	C₂×C₄	C₁₃×#125	1	16	yes	—
167	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
168	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
169	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
170	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
171	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
172	C₂²	—	2	8	no	—
173	C₂²	—	2	4	no	—
174	C₂²	C₂×C₁₃×#125	1	4	yes	—
175	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
176	C₂²	C₂²×C₁₃×#41	1	2	yes	—
177	C₂²	C₁₃×#585	1	4	yes	—
178	C₄	—	2	8	no	—
179	C₄	—	4	16	no	—
180	C₄	—	4	8	no	—
181	C₄	C₂×C₁₃×#125	1	4	yes	—
182	C₄	C₂×C₁₃×#125	1	4	yes	—
183	C₂	—	2	4	no	—
184	C₂	C₂²×C₁₃×#125	1	1	yes	characteristic
185	C₂	C₁₃×#3455	1	4	yes	—
186	C₂	C₁₃×#3458	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2647	C₂	semidirect
3. C₁₃×#2402	C₂	semidirect
40. #34638	C₁₃	direct (N × H)
62. #2647	C₂×C₁₃	semidirect
64. #2402	C₂×C₁₃	semidirect
154. C₁₃	#34638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2647	2
C₁₃×#2646	2
C₁₃×#2402	2
C₁₃×#2296	2
C₁₃×#2285	2
C₂×C₁₃×#376	2
#34638	13

Subgroups — C13×#34638 #15720977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34638 #15720977