Subgroups — C₁₃×#13279 #15699618

Order 3328.

366 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1387	C₂	1	4	yes	maximal
5	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₁₃×#500	—	2	1	no	—
8	C₁₃×#500	—	2	1	no	—
9	C₁₃×#500	C₄	1	2	yes	—
10	C₁₃×#500	C₄	1	2	yes	—
11	C₂×C₁₃×#108	C₂²	1	2	yes	—
12	C₂×C₁₃×#107	—	2	1	no	—
13	C₂×C₁₃×#107	C₂²	1	2	yes	—
14	C₄×C₁₃×M₁₆	—	2	1	no	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×C₄⋊C₁₆	—	2	1	no	—
17	C₁₃×C₄⋊C₁₆	—	2	1	no	—
18	C₁₃×#341	—	2	1	no	—
19	C₂²×Q₈×C₁₃	—	4	1	no	—
20	C₂×C₁₃×M₁₆	—	2	2	no	—
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	—	2	2	no	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	4	1	no	—
26	C₁₃×C₄⋊Q₈	—	4	1	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
29	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
30	C₁₃×M₃₂	—	2	4	no	—
31	C₂×C₁₃×C₁₆	—	2	2	no	—
32	C₁₃×#108	—	2	2	no	—
33	C₁₃×#108	Q₈	1	4	yes	complemented
34	C₁₃×#107	—	2	2	no	—
35	C₁₃×#107	—	2	2	no	—
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×#107	C₂×C₄	1	4	yes	—
38	C₁₃×#97	—	4	1	no	—
39	C₄×C₈×C₁₃	—	4	1	no	—
40	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
44	#13279	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×Q₈×C₁₃	—	4	2	no	—
46	C₂×Q₈×C₁₃	—	4	2	no	—
47	C₂×Q₈×C₁₃	—	8	4	no	—
48	C₂²×C₄×C₁₃	—	4	2	no	—
49	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₁₃×M₁₆	—	2	4	no	—
53	C₁₃×M₁₆	—	4	2	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	4	2	no	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
61	C₂×C₈×C₁₃	#41	1	2	yes	—
62	C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₃	D₈	1	1	yes	characteristic
69	C₄²×C₁₃	D₈	1	1	yes	characteristic
70	C₁₃×C₁₆	—	4	2	no	—
71	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
72	#2150	C₂×C₁₃	1	1	yes	characteristic
73	C₄×#108	C₂×C₁₃	1	1	yes	characteristic
74	#1387	C₂×C₁₃	1	4	yes	—
75	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
76	Q₈×C₁₃	—	8	4	no	—
77	Q₈×C₁₃	—	8	4	no	—
78	C₂×C₄×C₁₃	—	2	2	no	—
79	C₂×C₄×C₁₃	—	2	2	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	—	8	4	no	—
82	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
83	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	#137	1	2	yes	—
90	C₈×C₁₃	—	2	1	no	—
91	C₈×C₁₃	—	2	1	no	—
92	C₈×C₁₃	—	4	4	no	—
93	C₈×C₁₃	C₄×Q₈	1	2	yes	—
94	C₈×C₁₃	#124	1	1	yes	characteristic
95	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
96	C₂×C₄⋊Q₈	—	2	1	no	—
97	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
98	#500	—	2	1	no	—
99	#500	—	2	1	no	—
100	#500	C₄×C₁₃	1	2	yes	—
101	#500	C₄×C₁₃	1	2	yes	—
102	C₂×#108	C₂²×C₁₃	1	2	yes	—
103	C₂×#107	—	2	1	no	—
104	C₂×#107	C₂²×C₁₃	1	2	yes	—
105	C₄×M₁₆	—	2	1	no	—
106	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
107	C₄⋊C₁₆	—	2	1	no	—
108	C₄⋊C₁₆	—	2	1	no	—
109	#341	—	2	1	no	—
110	C₂²×C₁₃	—	2	1	no	—
111	C₂²×C₁₃	—	2	1	no	—
112	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
113	C₂²×C₁₃	#475	1	2	yes	—
114	C₄×C₁₃	—	2	1	no	—
115	C₄×C₁₃	—	2	1	no	—
116	C₄×C₁₃	—	8	4	no	—
117	C₄×C₁₃	#361	1	2	yes	—
118	C₄×C₁₃	#362	1	2	yes	—
119	C₄×C₁₃	#391	1	1	yes	characteristic
120	C₄×C₁₃	#419	1	1	yes	characteristic
121	C₄×C₁₃	#474	1	2	yes	—
122	C₂²×Q₈	—	4	1	no	—
123	C₂×M₁₆	—	2	2	no	—
124	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
125	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
126	C₄⋊Q₈	—	2	2	no	—
127	C₄⋊Q₈	—	2	2	no	—
128	C₄⋊Q₈	—	4	1	no	—
129	C₄⋊Q₈	—	4	1	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	4	1	no	—
132	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
133	M₃₂	—	2	4	no	—
134	C₂×C₁₆	—	2	2	no	—
135	#108	—	2	2	no	—
136	#108	Q₈×C₁₃	1	4	yes	complemented
137	#107	—	2	2	no	—
138	#107	—	2	2	no	—
139	#107	—	2	2	no	—
140	#107	C₂×C₄×C₁₃	1	4	yes	—
141	#97	—	4	1	no	—
142	C₄×C₈	—	4	1	no	—
143	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
144	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
145	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
146	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
147	C₂×C₁₃	—	2	2	no	—
148	C₂×C₁₃	#1988	1	1	yes	characteristic
149	C₂×C₁₃	C₂×#361	1	1	yes	characteristic
150	C₂×C₁₃	C₂×#362	1	1	yes	characteristic
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	4	2	no	—
153	C₂×Q₈	—	8	4	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
156	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
157	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
158	M₁₆	—	2	4	no	—
159	M₁₆	—	4	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
165	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
166	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
167	C₂×C₈	C₁₃×#41	1	2	yes	—
168	C₄⋊C₄	—	2	4	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
173	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
174	C₄²	C₁₃×D₈	1	1	yes	characteristic
175	C₄²	C₁₃×D₈	1	1	yes	characteristic
176	C₁₆	—	4	2	no	—
177	C₁₃	#13279	1	1	yes	characteristic, direct product factor, Sylow
178	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
179	Q₈	—	8	4	no	—
180	Q₈	—	8	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	8	4	no	—
185	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
186	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
187	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
188	C₂×C₄	C₁₃×#102	1	1	yes	characteristic
189	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
192	C₂×C₄	C₁₃×#137	1	2	yes	—
193	C₈	—	2	1	no	—
194	C₈	—	2	1	no	—
195	C₈	—	4	4	no	—
196	C₈	C₄×Q₈×C₁₃	1	2	yes	—
197	C₈	C₁₃×#124	1	1	yes	characteristic
198	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
199	C₂²	—	2	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
202	C₂²	C₁₃×#475	1	2	yes	—
203	C₄	—	2	1	no	—
204	C₄	—	2	1	no	—
205	C₄	—	8	4	no	—
206	C₄	C₁₃×#361	1	2	yes	—
207	C₄	C₁₃×#362	1	2	yes	—
208	C₄	C₁₃×#391	1	1	yes	characteristic
209	C₄	C₁₃×#419	1	1	yes	characteristic
210	C₄	C₁₃×#474	1	2	yes	—
211	C₂	—	2	2	no	—
212	C₂	C₁₃×#1988	1	1	yes	characteristic
213	C₂	C₂×C₁₃×#361	1	1	yes	characteristic
214	C₂	C₂×C₁₃×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
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
33. C₁₃×#108	Q₈	semidirect
44. #13279	C₁₃	direct (N × H)
136. #108	Q₈×C₁₃	semidirect
177. C₁₃	#13279	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#500	2
C₁₃×#2150	2
C₄×C₁₃×#108	2
C₁₃×#1387	2
#13279	13

Subgroups — C13×#13279 #15699618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13279 #15699618