Subgroups — C₁₃×#10279 #15696618

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 238 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	C₂×C₁₃×#477	C₂	1	2	yes	maximal
3	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#333	C₂	1	2	yes	maximal
5	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#500	—	2	4	no	—
9	C₁₃×#477	—	2	4	no	—
10	C₁₃×#477	—	2	4	no	—
11	C₂×C₁₃×#107	—	2	2	no	—
12	C₂×C₁₃×#107	—	2	2	no	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#103	—	2	2	no	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#336	—	2	2	no	—
18	C₁₃×#333	—	2	4	no	—
19	C₂²×Q₈×C₁₃	—	2	2	no	—
20	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₂²×C₈×C₁₃	D₄	1	2	yes	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
28	C₄×Q₈×C₁₃	—	2	2	no	—
29	C₄×Q₈×C₁₃	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	—	2	1	no	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×#107	—	2	8	no	—
37	C₁₃×#107	—	2	8	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	2	no	—
40	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
41	C₁₃×#103	—	2	8	no	—
42	C₄×C₈×C₁₃	—	2	2	no	—
43	#10279	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₃	—	2	1	no	—
45	C₂×Q₈×C₁₃	—	2	2	no	—
46	C₂×Q₈×C₁₃	—	2	4	no	—
47	C₂×Q₈×C₁₃	—	2	2	no	—
48	C₂×Q₈×C₁₃	—	4	2	no	—
49	C₂×Q₈×C₁₃	—	8	4	no	—
50	C₂×Q₈×C₁₃	Q₁₆	1	2	yes	—
51	C₂²×C₄×C₁₃	—	2	1	no	—
52	C₂²×C₄×C₁₃	—	2	1	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	2	2	no	—
59	C₂×C₈×C₁₃	—	2	4	no	—
60	C₂×C₈×C₁₃	—	4	2	no	—
61	C₂×C₈×C₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	—	4	1	no	—
63	C₂×C₈×C₁₃	—	4	2	no	—
64	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₄²×C₁₃	—	4	1	no	—
72	C₄²×C₁₃	—	4	1	no	—
73	C₄²×C₁₃	C₂×D₄	1	2	yes	—
74	C₄²×C₁₃	C₂×D₄	1	2	yes	—
75	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
76	C₂×#477	C₂×C₁₃	1	2	yes	—
77	#1984	C₂×C₁₃	1	1	yes	characteristic
78	C₂×#333	C₂×C₁₃	1	2	yes	—
79	#1277	C₂×C₁₃	1	1	yes	characteristic
80	C₂³×C₁₃	#121	1	1	yes	characteristic
81	Q₈×C₁₃	—	2	4	no	—
82	Q₈×C₁₃	—	4	2	no	—
83	Q₈×C₁₃	—	8	4	no	—
84	Q₈×C₁₃	—	8	4	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	4	1	no	—
88	C₂×C₄×C₁₃	—	4	1	no	—
89	C₂×C₄×C₁₃	—	4	1	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	8	4	no	—
93	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#120	1	2	yes	—
95	C₂×C₄×C₁₃	#121	1	2	yes	—
96	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
99	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#137	1	2	yes	—
101	C₂×C₄×C₁₃	#137	1	2	yes	—
102	C₈×C₁₃	—	2	4	no	—
103	C₈×C₁₃	—	4	4	no	—
104	C₈×C₁₃	—	8	1	no	—
105	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
106	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
107	#500	—	2	4	no	—
108	#477	—	2	4	no	—
109	#477	—	2	4	no	—
110	C₂×#107	—	2	2	no	—
111	C₂×#107	—	2	2	no	—
112	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
113	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
114	C₂×#103	—	2	2	no	—
115	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
116	#336	—	2	2	no	—
117	#333	—	2	4	no	—
118	C₂²×C₁₃	#392	1	1	yes	characteristic
119	C₂²×C₁₃	#462	1	2	yes	—
120	C₂²×C₁₃	#467	1	1	yes	characteristic
121	C₂²×C₁₃	#470	1	1	yes	characteristic
122	C₂²×C₁₃	#472	1	2	yes	—
123	C₄×C₁₃	—	2	2	no	—
124	C₄×C₁₃	—	4	2	no	—
125	C₄×C₁₃	—	8	1	no	—
126	C₄×C₁₃	—	8	4	no	—
127	C₄×C₁₃	#451	1	2	yes	—
128	C₄×C₁₃	#451	1	2	yes	—
129	C₄×C₁₃	#452	1	2	yes	—
130	C₄×C₁₃	#494	1	1	yes	characteristic
131	C₄×C₁₃	#497	1	1	yes	characteristic
132	C₂²×Q₈	—	2	2	no	—
133	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
134	C₂²×C₈	—	2	2	no	—
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	D₄×C₁₃	1	2	yes	—
137	C₄⋊Q₈	—	2	2	no	—
138	C₄⋊Q₈	—	2	2	no	—
139	C₄⋊Q₈	—	2	2	no	—
140	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
141	C₄×Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
147	C₂×C₄²	—	2	1	no	—
148	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
149	#107	—	2	8	no	—
150	#107	—	2	8	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
154	#103	—	2	8	no	—
155	C₄×C₈	—	2	2	no	—
156	C₂×C₁₃	#1676	1	2	yes	—
157	C₂×C₁₃	#1696	1	2	yes	—
158	C₂×C₁₃	#2001	1	1	yes	characteristic
159	C₂×C₁₃	#2016	1	1	yes	characteristic
160	C₂×C₁₃	#2018	1	1	yes	characteristic
161	C₂×Q₈	—	2	1	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	—	2	4	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	8	4	no	—
167	C₂×Q₈	C₁₃×Q₁₆	1	2	yes	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	4	2	no	—
171	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
173	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	C₁₃×Q₁₆	1	4	yes	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄²	—	4	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	C₂×D₄×C₁₃	1	2	yes	—
191	C₄²	C₂×D₄×C₁₃	1	2	yes	—
192	C₁₃	#10279	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	C₁₃×#121	1	1	yes	characteristic
194	Q₈	—	2	4	no	—
195	Q₈	—	4	2	no	—
196	Q₈	—	8	4	no	—
197	Q₈	—	8	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	8	4	no	—
206	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
207	C₂×C₄	C₁₃×#120	1	2	yes	—
208	C₂×C₄	C₁₃×#121	1	2	yes	—
209	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
210	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
211	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
212	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
213	C₂×C₄	C₁₃×#137	1	2	yes	—
214	C₂×C₄	C₁₃×#137	1	2	yes	—
215	C₈	—	2	4	no	—
216	C₈	—	4	4	no	—
217	C₈	—	8	1	no	—
218	C₂²	C₁₃×#392	1	1	yes	characteristic
219	C₂²	C₁₃×#462	1	2	yes	—
220	C₂²	C₁₃×#467	1	1	yes	characteristic
221	C₂²	C₁₃×#470	1	1	yes	characteristic
222	C₂²	C₁₃×#472	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	4	2	no	—
225	C₄	—	8	1	no	—
226	C₄	—	8	4	no	—
227	C₄	C₁₃×#451	1	2	yes	—
228	C₄	C₁₃×#451	1	2	yes	—
229	C₄	C₁₃×#452	1	2	yes	—
230	C₄	C₁₃×#494	1	1	yes	characteristic
231	C₄	C₁₃×#497	1	1	yes	characteristic
232	C₂	C₁₃×#1676	1	2	yes	—
233	C₂	C₁₃×#1696	1	2	yes	—
234	C₂	C₁₃×#2001	1	1	yes	characteristic
235	C₂	C₁₃×#2016	1	1	yes	characteristic
236	C₂	C₁₃×#2018	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×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
43. #10279	C₁₃	direct (N × H)
192. C₁₃	#10279	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
C₂×C₁₃×#477	2
C₁₃×#1984	2
C₂×C₁₃×#333	2
C₁₃×#1277	2
#10279	13

Subgroups — C13×#10279 #15696618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10279 #15696618