Subgroups — C₁₃×#33732 #15720071

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2255	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2253	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2159	C₂	1	4	yes	maximal
6	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	—	2	1	no	—
8	C₂×C₁₃×#125	—	2	1	no	—
9	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
10	C₁₃×#500	C₂²	1	2	yes	—
11	C₁₃×#499	—	2	1	no	—
12	C₁₃×#499	—	2	1	no	—
13	C₁₃×#499	—	2	1	no	—
14	C₁₃×#499	C₂²	1	2	yes	—
15	C₁₃×#499	C₂²	1	2	yes	—
16	C₁₃×#499	C₂²	1	2	yes	—
17	C₁₃×#498	—	2	1	no	—
18	C₁₃×#427	—	2	1	no	—
19	C₁₃×#427	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	—	2	1	no	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#367	C₂²	1	8	yes	—
24	C₁₃×#366	C₂²	1	8	yes	—
25	C₁₃×#346	C₂²	1	2	yes	—
26	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
27	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₁₃×C₄⋊Q₈	—	2	2	no	—
30	C₁₃×#125	—	2	2	no	—
31	C₁₃×#125	—	2	2	no	—
32	C₁₃×#125	—	2	2	no	—
33	C₁₃×#125	—	4	2	no	—
34	C₁₃×C₂²⋊Q₈	—	4	2	no	—
35	C₄×Q₈×C₁₃	—	4	2	no	—
36	C₁₃×#117	—	2	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₁₃×M₃₂	Q₈	1	8	yes	complemented
41	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
42	C₁₃×#107	—	2	2	no	—
43	C₁₃×#107	—	2	2	no	—
44	C₁₃×#107	C₂³	1	4	yes	—
45	C₁₃×#107	C₂³	1	4	yes	—
46	C₁₃×#106	—	2	2	no	—
47	C₁₃×#106	—	2	2	no	—
48	C₁₃×#106	—	2	2	no	—
49	C₁₃×#106	—	2	2	no	—
50	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	#33732	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×Q₈×C₁₃	—	4	2	no	—
56	C₂²×C₄×C₁₃	—	4	2	no	—
57	C₂²×C₄×C₁₃	D₈	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
60	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
64	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₁₃×C₄⋊C₄	—	4	2	no	—
68	C₁₃×C₄⋊C₄	—	4	4	no	—
69	C₁₃×C₄⋊C₄	—	4	4	no	—
70	C₁₃×C₄⋊C₄	—	4	4	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₁₃×C₂²⋊C₄	—	4	2	no	—
73	C₄²×C₁₃	—	4	2	no	—
74	C₄²×C₁₃	D₈	1	2	yes	—
75	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₁₃×C₁₆	C₂×Q₈	1	8	yes	—
78	#3160	C₂×C₁₃	1	1	yes	characteristic
79	C₂×#499	C₂×C₁₃	1	1	yes	characteristic
80	#2255	C₂×C₁₃	1	4	yes	complemented
81	#2253	C₂×C₁₃	1	4	yes	complemented
82	#2159	C₂×C₁₃	1	4	yes	—
83	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
84	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
85	Q₈×C₁₃	—	8	4	no	—
86	C₂×C₄×C₁₃	—	4	2	no	—
87	C₂×C₄×C₁₃	—	4	4	no	—
88	C₂×C₄×C₁₃	—	4	4	no	—
89	C₂×C₄×C₁₃	—	8	4	no	—
90	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
96	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
97	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
98	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
99	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
100	#533	—	2	1	no	—
101	C₂×#125	—	2	1	no	—
102	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
103	#500	C₂²×C₁₃	1	2	yes	—
104	#499	—	2	1	no	—
105	#499	—	2	1	no	—
106	#499	—	2	1	no	—
107	#499	C₂²×C₁₃	1	2	yes	—
108	#499	C₂²×C₁₃	1	2	yes	—
109	#499	C₂²×C₁₃	1	2	yes	—
110	#498	—	2	1	no	—
111	#427	—	2	1	no	—
112	#427	C₂²×C₁₃	1	2	yes	—
113	C₂×#107	C₂²×C₁₃	1	2	yes	—
114	C₂×#106	—	2	1	no	—
115	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
116	#367	C₂²×C₁₃	1	8	yes	—
117	#366	C₂²×C₁₃	1	8	yes	—
118	#346	C₂²×C₁₃	1	2	yes	—
119	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
120	C₂²×C₁₃	—	2	2	no	—
121	C₂²×C₁₃	#500	1	2	yes	—
122	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
123	C₄×C₁₃	—	2	2	no	—
124	C₄×C₁₃	—	2	2	no	—
125	C₄×C₁₃	—	8	4	no	—
126	C₄×C₁₃	—	8	4	no	—
127	C₄×C₁₃	#500	1	2	yes	—
128	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
129	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
130	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
132	C₄⋊Q₈	—	2	2	no	—
133	#125	—	2	2	no	—
134	#125	—	2	2	no	—
135	#125	—	2	2	no	—
136	#125	—	4	2	no	—
137	C₂²⋊Q₈	—	4	2	no	—
138	C₄×Q₈	—	4	2	no	—
139	#117	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	4	2	no	—
142	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
143	M₃₂	Q₈×C₁₃	1	8	yes	complemented
144	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
145	#107	—	2	2	no	—
146	#107	—	2	2	no	—
147	#107	C₂³×C₁₃	1	4	yes	—
148	#107	C₂³×C₁₃	1	4	yes	—
149	#106	—	2	2	no	—
150	#106	—	2	2	no	—
151	#106	—	2	2	no	—
152	#106	—	2	2	no	—
153	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
154	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
155	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
156	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
157	C₂×C₁₃	—	2	2	no	—
158	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
159	C₂×C₁₃	#3414	1	2	yes	—
160	C₂×Q₈	—	4	2	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	C₁₃×D₈	1	2	yes	—
163	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
164	C₂×C₈	C₁₃×Q₁₆	1	4	yes	—
165	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
166	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
167	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
168	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
169	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	4	no	—
174	C₄⋊C₄	—	4	4	no	—
175	C₄⋊C₄	—	4	4	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₂²⋊C₄	—	4	2	no	—
178	C₄²	—	4	2	no	—
179	C₄²	C₁₃×D₈	1	2	yes	—
180	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
181	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
182	C₁₆	C₂×Q₈×C₁₃	1	8	yes	—
183	C₁₃	#33732	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
185	Q₈	—	8	4	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	8	4	no	—
190	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
191	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
192	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
193	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
194	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
195	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
196	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
197	C₈	C₂×C₁₃×Q₁₆	1	2	yes	—
198	C₈	C₂×C₁₃×Q₁₆	1	2	yes	—
199	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
200	C₂²	—	2	2	no	—
201	C₂²	C₁₃×#500	1	2	yes	—
202	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	8	4	no	—
206	C₄	—	8	4	no	—
207	C₄	C₁₃×#500	1	2	yes	—
208	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
209	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
210	C₂	—	2	2	no	—
211	C₂	C₂×C₁₃×#500	1	1	yes	characteristic
212	C₂	C₁₃×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2255	C₂	semidirect
4. C₁₃×#2253	C₂	semidirect
40. C₁₃×M₃₂	Q₈	semidirect
54. #33732	C₁₃	direct (N × H)
80. #2255	C₂×C₁₃	semidirect
81. #2253	C₂×C₁₃	semidirect
143. M₃₂	Q₈×C₁₃	semidirect
183. C₁₃	#33732	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×#3160	2
C₂×C₁₃×#499	2
C₁₃×#2255	2
C₁₃×#2253	2
C₁₃×#2159	2
C₄×C₁₃×M₃₂	2
#33732	13

Subgroups — C13×#33732 #15720071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33732 #15720071