Subgroups — C₁₃×#9624 #15695963

Order 3328.

298 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1950	C₂	1	2	yes	maximal
2	C₁₃×#1567	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic
4	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1301	C₂	1	2	yes	maximal
6	C₁₃×#431	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	—	2	2	no	—
8	C₁₃×#423	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#341	—	2	2	no	—
13	C₁₃×#335	—	2	1	no	—
14	C₁₃×#335	—	2	1	no	—
15	C₁₃×#335	C₄	1	2	yes	—
16	C₁₃×#335	C₄	1	2	yes	—
17	C₁₃×#322	—	2	1	no	—
18	C₈²×C₁₃	—	2	1	no	—
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₁₃×#108	—	4	4	no	—
27	C₁₃×C₄⋊C₈	—	2	2	no	—
28	C₁₃×C₄⋊C₈	—	2	2	no	—
29	C₁₃×C₄⋊C₈	—	2	1	no	—
30	C₁₃×C₄⋊C₈	—	2	2	no	—
31	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
32	C₁₃×C₂²⋊C₈	Q₈	1	2	yes	—
33	C₁₃×#97	—	2	1	no	—
34	C₄×C₈×C₁₃	—	2	1	no	—
35	C₄×C₈×C₁₃	—	2	1	no	—
36	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
40	#9624	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₁₃×M₁₆	—	2	1	no	—
45	C₁₃×M₁₆	—	2	1	no	—
46	C₁₃×M₁₆	—	4	2	no	—
47	C₁₃×M₁₆	—	4	2	no	—
48	C₁₃×M₁₆	D₈	1	2	yes	—
49	C₁₃×M₁₆	Q₁₆	1	2	yes	—
50	C₂×C₈×C₁₃	—	2	1	no	—
51	C₂×C₈×C₁₃	—	2	1	no	—
52	C₂×C₈×C₁₃	—	2	2	no	—
53	C₂×C₈×C₁₃	—	2	4	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	4	1	no	—
56	C₂×C₈×C₁₃	—	4	2	no	—
57	C₂×C₈×C₁₃	—	4	2	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₃	#41	1	1	yes	characteristic
66	C₄²×C₁₃	#41	1	1	yes	characteristic
67	#1950	C₂×C₁₃	1	2	yes	—
68	#1567	C₂×C₁₃	1	1	yes	characteristic
69	C₂×#335	C₂×C₁₃	1	1	yes	characteristic
70	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic
71	#1301	C₂×C₁₃	1	2	yes	—
72	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₃	—	2	1	no	—
74	C₂×C₄×C₁₃	—	2	1	no	—
75	C₂×C₄×C₁₃	—	4	1	no	—
76	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
86	C₈×C₁₃	—	2	1	no	—
87	C₈×C₁₃	—	2	1	no	—
88	C₈×C₁₃	—	2	1	no	—
89	C₈×C₁₃	—	2	2	no	—
90	C₈×C₁₃	—	2	2	no	—
91	C₈×C₁₃	—	4	2	no	—
92	C₈×C₁₃	—	4	4	no	—
93	C₈×C₁₃	—	8	2	no	—
94	C₈×C₁₃	#108	1	2	yes	complemented
95	#431	C₂²×C₁₃	1	1	yes	characteristic
96	C₂×#108	—	2	2	no	—
97	#423	C₂²×C₁₃	1	2	yes	—
98	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
99	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
100	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
101	#341	—	2	2	no	—
102	#335	—	2	1	no	—
103	#335	—	2	1	no	—
104	#335	C₄×C₁₃	1	2	yes	—
105	#335	C₄×C₁₃	1	2	yes	—
106	#322	—	2	1	no	—
107	C₈²	—	2	1	no	—
108	C₂²×C₁₃	—	2	1	no	—
109	C₂²×C₁₃	—	2	1	no	—
110	C₂²×C₁₃	#389	1	1	yes	characteristic
111	C₂²×C₁₃	#499	1	1	yes	characteristic
112	C₂²×C₁₃	#500	1	1	yes	characteristic
113	C₄×C₁₃	—	2	1	no	—
114	C₄×C₁₃	—	2	1	no	—
115	C₄×C₁₃	—	2	1	no	—
116	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
117	C₄×C₁₃	#430	1	1	yes	characteristic
118	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
119	C₄×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
120	C₄×C₁₃	#466	1	1	yes	characteristic
121	C₄×C₁₃	#467	1	1	yes	characteristic
122	C₂×M₁₆	—	2	2	no	—
123	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
124	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
125	C₂²×C₈	—	2	2	no	—
126	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
127	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
128	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
129	#108	—	4	4	no	—
130	C₄⋊C₈	—	2	2	no	—
131	C₄⋊C₈	—	2	2	no	—
132	C₄⋊C₈	—	2	1	no	—
133	C₄⋊C₈	—	2	2	no	—
134	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
135	C₂²⋊C₈	Q₈×C₁₃	1	2	yes	—
136	#97	—	2	1	no	—
137	C₄×C₈	—	2	1	no	—
138	C₄×C₈	—	2	1	no	—
139	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
140	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
141	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
142	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
143	C₂×C₁₃	—	2	1	no	—
144	C₂×C₁₃	—	2	1	no	—
145	C₂×C₁₃	#1942	1	1	yes	characteristic
146	C₂×C₁₃	#1950	1	1	yes	characteristic
147	C₂×C₁₃	#1953	1	1	yes	characteristic
148	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
149	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
150	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
151	M₁₆	—	2	1	no	—
152	M₁₆	—	2	1	no	—
153	M₁₆	—	4	2	no	—
154	M₁₆	—	4	2	no	—
155	M₁₆	C₁₃×D₈	1	2	yes	—
156	M₁₆	C₁₃×Q₁₆	1	2	yes	—
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	2	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	2	no	—
166	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
170	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
171	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
172	C₄²	C₁₃×#41	1	1	yes	characteristic
173	C₄²	C₁₃×#41	1	1	yes	characteristic
174	C₁₃	#9624	1	1	yes	characteristic, direct product factor, Sylow
175	C₂³	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	4	1	no	—
179	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
181	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
182	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
183	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄	C₁₃×#125	1	1	yes	characteristic
185	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
186	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
187	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
188	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
189	C₈	—	2	1	no	—
190	C₈	—	2	1	no	—
191	C₈	—	2	1	no	—
192	C₈	—	2	2	no	—
193	C₈	—	2	2	no	—
194	C₈	—	4	2	no	—
195	C₈	—	4	4	no	—
196	C₈	—	8	2	no	—
197	C₈	C₁₃×#108	1	2	yes	complemented
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	C₁₃×#389	1	1	yes	characteristic
201	C₂²	C₁₃×#499	1	1	yes	characteristic
202	C₂²	C₁₃×#500	1	1	yes	characteristic
203	C₄	—	2	1	no	—
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	C₂×C₁₃×#108	1	1	yes	characteristic
207	C₄	C₁₃×#430	1	1	yes	characteristic
208	C₄	C₄×C₁₃×D₈	1	1	yes	characteristic
209	C₄	C₄×C₁₃×Q₁₆	1	1	yes	characteristic
210	C₄	C₁₃×#466	1	1	yes	characteristic
211	C₄	C₁₃×#467	1	1	yes	characteristic
212	C₂	—	2	1	no	—
213	C₂	—	2	1	no	—
214	C₂	C₁₃×#1942	1	1	yes	characteristic
215	C₂	C₁₃×#1950	1	1	yes	characteristic
216	C₂	C₁₃×#1953	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#121
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#389
prime radical	C₂³×C₁₃	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
40. #9624	C₁₃	direct (N × H)
94. C₈×C₁₃	#108	semidirect
174. C₁₃	#9624	direct (N × H)
197. C₈	C₁₃×#108	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#1950	2
C₁₃×#1567	2
C₂×C₁₃×#335	2
C₈×C₁₃×M₁₆	2
C₁₃×#1301	2
#9624	13

Subgroups — C13×#9624 #15695963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9624 #15695963