Subgroups — C₁₃×#9618 #15695957

Order 3328.

370 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1948	C₂	1	2	yes	maximal
2	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1296	C₂	1	2	yes	maximal
6	C₂×C₁₃×#106	—	2	1	no	—
7	C₂×C₁₃×#106	—	2	1	no	—
8	C₂×C₁₃×#106	—	2	2	no	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#97	—	2	1	no	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#384	C₂²	1	2	yes	—
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₁₃×#340	—	2	2	no	—
16	C₁₃×#336	—	2	1	no	—
17	C₁₃×#335	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₃	—	2	1	no	—
19	C₂²×C₈×C₁₃	—	2	2	no	—
20	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
26	C₂×C₄²×C₁₃	—	2	1	no	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×#106	—	4	4	no	—
29	C₁₃×#106	—	4	2	no	—
30	C₁₃×#106	—	4	2	no	—
31	C₁₃×C₄⋊C₈	—	2	2	no	—
32	C₁₃×C₄⋊C₈	—	2	1	no	—
33	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
34	C₁₃×C₄⋊C₈	Q₈	1	2	yes	—
35	C₁₃×#97	—	4	2	no	—
36	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₃	Q₈	1	2	yes	—
38	C₁₃×#95	—	2	1	no	—
39	#9618	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₄×C₁₃	—	2	2	no	—
41	C₂²×C₄×C₁₃	—	4	2	no	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
45	C₂×C₈×C₁₃	—	2	1	no	—
46	C₂×C₈×C₁₃	—	2	1	no	—
47	C₂×C₈×C₁₃	—	2	4	no	—
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	4	1	no	—
50	C₂×C₈×C₁₃	—	4	2	no	—
51	C₂×C₈×C₁₃	—	4	2	no	—
52	C₂×C₈×C₁₃	—	4	1	no	—
53	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
56	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
57	C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₁₃×C₄⋊C₄	—	4	2	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	8	2	no	—
64	C₄²×C₁₃	—	4	1	no	—
65	C₄²×C₁₃	—	4	1	no	—
66	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
69	C₄²×C₁₃	#41	1	1	yes	characteristic
70	#1948	C₂×C₁₃	1	2	yes	—
71	#1844	C₂×C₁₃	1	1	yes	characteristic
72	#1770	C₂×C₁₃	1	1	yes	characteristic
73	C₂×#335	C₂×C₁₃	1	1	yes	characteristic
74	#1296	C₂×C₁₃	1	2	yes	—
75	C₂³×C₁₃	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	4	2	no	—
78	C₂×C₄×C₁₃	—	4	2	no	—
79	C₂×C₄×C₁₃	—	4	2	no	—
80	C₂×C₄×C₁₃	—	8	2	no	—
81	C₂×C₄×C₁₃	—	8	2	no	—
82	C₂×C₄×C₁₃	—	8	2	no	—
83	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#137	1	2	yes	—
95	C₈×C₁₃	—	2	2	no	—
96	C₈×C₁₃	—	4	4	no	—
97	C₈×C₁₃	—	4	2	no	—
98	C₈×C₁₃	#106	1	4	yes	complemented
99	C₂×#106	—	2	1	no	—
100	C₂×#106	—	2	1	no	—
101	C₂×#106	—	2	2	no	—
102	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
103	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
104	C₂×#97	—	2	1	no	—
105	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
106	#384	C₂²×C₁₃	1	2	yes	—
107	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
108	#340	—	2	2	no	—
109	#336	—	2	1	no	—
110	#335	C₄×C₁₃	1	4	yes	complemented
111	C₂²×C₁₃	#389	1	1	yes	characteristic
112	C₂²×C₁₃	#460	1	1	yes	characteristic
113	C₂²×C₁₃	#461	1	1	yes	characteristic
114	C₂²×C₁₃	#468	1	2	yes	—
115	C₂²×C₁₃	#471	1	2	yes	—
116	C₄×C₁₃	—	2	1	no	—
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	—	8	2	no	—
119	C₄×C₁₃	—	16	2	no	—
120	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
121	C₄×C₁₃	#428	1	1	yes	characteristic
122	C₄×C₁₃	#441	1	1	yes	characteristic
123	C₄×C₁₃	#442	1	1	yes	characteristic
124	C₄×C₁₃	#475	1	1	yes	characteristic
125	C₄×C₁₃	#476	1	1	yes	characteristic
126	C₄×C₁₃	#501	1	2	yes	—
127	C₂²×C₈	—	2	1	no	—
128	C₂²×C₈	—	2	2	no	—
129	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
130	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
135	C₂×C₄²	—	2	1	no	—
136	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
137	#106	—	4	4	no	—
138	#106	—	4	2	no	—
139	#106	—	4	2	no	—
140	C₄⋊C₈	—	2	2	no	—
141	C₄⋊C₈	—	2	1	no	—
142	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
143	C₄⋊C₈	Q₈×C₁₃	1	2	yes	—
144	#97	—	4	2	no	—
145	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
146	C₄×C₈	Q₈×C₁₃	1	2	yes	—
147	#95	—	2	1	no	—
148	C₂×C₁₃	#1686	1	2	yes	—
149	C₂×C₁₃	#1691	1	2	yes	—
150	C₂×C₁₃	#1943	1	1	yes	characteristic
151	C₂×C₁₃	#1948	1	1	yes	characteristic
152	C₂×C₁₃	#1951	1	1	yes	characteristic
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
156	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
157	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	4	1	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	—	4	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
167	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
168	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
169	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	2	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	8	2	no	—
177	C₄²	—	4	1	no	—
178	C₄²	—	4	1	no	—
179	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
180	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
181	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
182	C₄²	C₁₃×#41	1	1	yes	characteristic
183	C₁₃	#9618	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	C₁₃×#121	1	1	yes	characteristic
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
194	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
195	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
196	C₂×C₄	C₁₃×#125	1	1	yes	characteristic
197	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
199	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
200	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
202	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
203	C₂×C₄	C₁₃×#137	1	2	yes	—
204	C₈	—	2	2	no	—
205	C₈	—	4	4	no	—
206	C₈	—	4	2	no	—
207	C₈	C₁₃×#106	1	4	yes	complemented
208	C₂²	C₁₃×#389	1	1	yes	characteristic
209	C₂²	C₁₃×#460	1	1	yes	characteristic
210	C₂²	C₁₃×#461	1	1	yes	characteristic
211	C₂²	C₁₃×#468	1	2	yes	—
212	C₂²	C₁₃×#471	1	2	yes	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	8	2	no	—
216	C₄	—	16	2	no	—
217	C₄	C₂×C₁₃×#106	1	1	yes	characteristic
218	C₄	C₁₃×#428	1	1	yes	characteristic
219	C₄	C₁₃×#441	1	1	yes	characteristic
220	C₄	C₁₃×#442	1	1	yes	characteristic
221	C₄	C₁₃×#475	1	1	yes	characteristic
222	C₄	C₁₃×#476	1	1	yes	characteristic
223	C₄	C₁₃×#501	1	2	yes	—
224	C₂	C₁₃×#1686	1	2	yes	—
225	C₂	C₁₃×#1691	1	2	yes	—
226	C₂	C₁₃×#1943	1	1	yes	characteristic
227	C₂	C₁₃×#1948	1	1	yes	characteristic
228	C₂	C₁₃×#1951	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#121
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₁₃×#335	C₄	semidirect
39. #9618	C₁₃	direct (N × H)
98. C₈×C₁₃	#106	semidirect
110. #335	C₄×C₁₃	semidirect
183. C₁₃	#9618	direct (N × H)
207. C₈	C₁₃×#106	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#1948	2
C₁₃×#1844	2
C₁₃×#1770	2
C₂×C₁₃×#335	2
C₁₃×#1296	2
#9618	13

Subgroups — C13×#9618 #15695957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9618 #15695957