Subgroups — C₁₃×#23836 #15710175

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#125	C₂	1	2	yes	maximal
2	C₁₃×#2085	C₂	1	4	yes	maximal
3	C₁₃×#2059	C₂	1	4	yes	maximal
4	C₄×C₁₃×#107	C₂	1	2	yes	maximal
5	C₄×C₁₃×#106	C₂	1	2	yes	maximal
6	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#125	C₂²	1	2	yes	—
8	C₂×C₁₃×#107	C₂²	1	4	yes	—
9	C₂×C₁₃×#106	C₂²	1	4	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#389	C₂²	1	4	yes	—
13	C₁₃×#387	—	2	4	no	—
14	C₁₃×#382	C₂²	1	2	yes	—
15	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
16	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
17	C₄³×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#340	C₂²	1	2	yes	—
19	C₁₃×#340	C₂²	1	2	yes	—
20	C₁₃×#340	C₂²	1	2	yes	—
21	C₁₃×#340	C₂²	1	2	yes	—
22	C₁₃×#336	C₂²	1	4	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
25	C₁₃×#125	—	2	8	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
30	C₂×C₄²×C₁₃	—	2	4	no	—
31	C₂×C₄²×C₁₃	D₄	1	2	yes	—
32	C₂×C₄²×C₁₃	D₄	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×#107	—	2	8	no	—
36	C₁₃×#106	—	2	8	no	—
37	C₄×C₈×C₁₃	Q₈	1	4	yes	—
38	C₄×C₈×C₁₃	Q₈	1	4	yes	—
39	C₁₃×#95	—	2	4	no	—
40	C₁₃×#95	—	2	4	no	—
41	C₁₃×#95	—	2	4	no	—
42	#23836	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₄×C₁₃	—	2	4	no	—
44	C₂²×C₄×C₁₃	—	2	4	no	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
49	C₂×C₈×C₁₃	—	2	4	no	—
50	C₂×C₈×C₁₃	—	2	4	no	—
51	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
52	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
53	C₁₃×C₄⋊C₄	—	2	16	no	—
54	C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₁₃×C₄⋊C₄	—	4	8	no	—
58	C₁₃×C₄⋊C₄	#41	1	8	yes	—
59	C₄²×C₁₃	—	2	4	no	—
60	C₄²×C₁₃	—	2	4	no	—
61	C₄²×C₁₃	—	4	2	no	—
62	C₄²×C₁₃	—	4	8	no	—
63	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
64	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
65	C₄×#125	C₂×C₁₃	1	2	yes	—
66	#2085	C₂×C₁₃	1	4	yes	—
67	#2059	C₂×C₁₃	1	4	yes	—
68	C₄×#107	C₂×C₁₃	1	2	yes	—
69	C₄×#106	C₂×C₁₃	1	2	yes	—
70	#1744	C₂×C₁₃	1	1	yes	characteristic
71	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	4	no	—
74	C₂×C₄×C₁₃	—	2	8	no	—
75	C₂×C₄×C₁₃	—	2	4	no	—
76	C₂×C₄×C₁₃	—	2	4	no	—
77	C₂×C₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	4	4	no	—
79	C₂×C₄×C₁₃	—	4	4	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	—	4	4	no	—
82	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
83	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
84	C₂×C₄×C₁₃	#135	1	4	yes	—
85	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
88	C₈×C₁₃	—	2	4	no	—
89	C₈×C₁₃	—	2	4	no	—
90	C₂×#125	C₂²×C₁₃	1	2	yes	—
91	C₂×#107	C₂²×C₁₃	1	4	yes	—
92	C₂×#106	C₂²×C₁₃	1	4	yes	—
93	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
94	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
95	#389	C₂²×C₁₃	1	4	yes	—
96	#387	—	2	4	no	—
97	#382	C₂²×C₁₃	1	2	yes	—
98	C₄×C₄⋊C₄	—	2	4	no	—
99	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
100	C₄³	C₂²×C₁₃	1	1	yes	characteristic
101	#340	C₂²×C₁₃	1	2	yes	—
102	#340	C₂²×C₁₃	1	2	yes	—
103	#340	C₂²×C₁₃	1	2	yes	—
104	#340	C₂²×C₁₃	1	2	yes	—
105	#336	C₂²×C₁₃	1	4	yes	—
106	C₂²×C₁₃	#525	1	2	yes	—
107	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
108	C₂²×C₁₃	C₂×#135	1	2	yes	—
109	C₂²×C₁₃	#575	1	2	yes	—
110	C₄×C₁₃	—	2	2	no	—
111	C₄×C₁₃	—	4	4	no	—
112	C₄×C₁₃	—	4	8	no	—
113	C₄×C₁₃	—	8	4	no	—
114	C₄×C₁₃	#499	1	4	yes	—
115	C₄×C₁₃	#533	1	2	yes	—
116	C₄×C₁₃	#533	1	2	yes	—
117	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
118	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
119	#125	—	2	8	no	—
120	C₂×C₄⋊C₄	—	2	4	no	—
121	C₂×C₄⋊C₄	—	2	4	no	—
122	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
123	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
124	C₂×C₄²	—	2	4	no	—
125	C₂×C₄²	D₄×C₁₃	1	2	yes	—
126	C₂×C₄²	D₄×C₁₃	1	2	yes	—
127	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
128	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
129	#107	—	2	8	no	—
130	#106	—	2	8	no	—
131	C₄×C₈	Q₈×C₁₃	1	4	yes	—
132	C₄×C₈	Q₈×C₁₃	1	4	yes	—
133	#95	—	2	4	no	—
134	#95	—	2	4	no	—
135	#95	—	2	4	no	—
136	C₂×C₁₃	#2399	1	1	yes	characteristic
137	C₂×C₁₃	#3102	1	4	yes	—
138	C₂×C₁₃	C₂×#499	1	1	yes	characteristic
139	C₂×C₁₃	#3162	1	1	yes	characteristic
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
143	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
145	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	—	2	4	no	—
148	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
149	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
150	C₄⋊C₄	—	2	16	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	4	8	no	—
155	C₄⋊C₄	C₁₃×#41	1	8	yes	—
156	C₄²	—	2	4	no	—
157	C₄²	—	2	4	no	—
158	C₄²	—	4	2	no	—
159	C₄²	—	4	8	no	—
160	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
161	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
162	C₁₃	#23836	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	8	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
175	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
176	C₂×C₄	C₁₃×#135	1	4	yes	—
177	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
178	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
179	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
180	C₈	—	2	4	no	—
181	C₈	—	2	4	no	—
182	C₂²	C₁₃×#525	1	2	yes	—
183	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
184	C₂²	C₂×C₁₃×#135	1	2	yes	—
185	C₂²	C₁₃×#575	1	2	yes	—
186	C₄	—	2	2	no	—
187	C₄	—	4	4	no	—
188	C₄	—	4	8	no	—
189	C₄	—	8	4	no	—
190	C₄	C₁₃×#499	1	4	yes	—
191	C₄	C₁₃×#533	1	2	yes	—
192	C₄	C₁₃×#533	1	2	yes	—
193	C₂	C₁₃×#2399	1	1	yes	characteristic
194	C₂	C₁₃×#3102	1	4	yes	—
195	C₂	C₂×C₁₃×#499	1	1	yes	characteristic
196	C₂	C₁₃×#3162	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
42. #23836	C₁₃	direct (N × H)
162. C₁₃	#23836	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#125	2
C₁₃×#2085	2
C₁₃×#2059	2
C₄×C₁₃×#107	2
C₄×C₁₃×#106	2
C₁₃×#1744	2
#23836	13

Subgroups — C13×#23836 #15710175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23836 #15710175