Subgroups — C₁₃×#17980 #15704319

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2960	C₂	1	2	yes	maximal
3	C₁₃×#1587	C₂	1	8	yes	maximal, complemented
4	C₁₃×#1566	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1493	C₂	1	2	yes	maximal
6	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	C₂²	1	2	yes	—
8	C₁₃×#500	C₄	1	1	yes	characteristic
9	C₁₃×#494	C₄	1	1	yes	characteristic
10	C₁₃×#487	C₄	1	2	yes	—
11	C₁₃×#467	C₄	1	4	yes	—
12	C₁₃×#446	—	2	2	no	—
13	C₁₃×#446	C₂²	1	4	yes	—
14	C₈×Q₈×C₁₃	—	2	2	no	—
15	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
16	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
17	C₁₃×#424	—	2	2	no	—
18	C₁₃×#423	C₂²	1	2	yes	—
19	C₁₃×#405	—	2	2	no	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#334	C₂²	1	4	yes	—
24	C₁₃×Q₈⋊C₈	C₂²	1	8	yes	—
25	C₁₃×#322	C₂²	1	4	yes	—
26	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂²×C₈×C₁₃	—	2	1	no	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₁₃	D₄	1	2	yes	—
31	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
32	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
33	C₁₃×#125	—	2	2	no	—
34	C₁₃×C₂²⋊Q₈	—	2	2	no	—
35	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
36	C₄×Q₈×C₁₃	—	2	2	no	—
37	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
38	C₁₃×#117	—	2	2	no	—
39	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
40	C₁₃×#107	C₂×C₄	1	4	yes	—
41	C₁₃×C₄⋊C₈	—	2	4	no	—
42	C₁₃×C₄⋊C₈	—	2	4	no	—
43	C₁₃×C₄⋊C₈	—	2	2	no	—
44	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
45	C₁₃×#103	C₂×C₄	1	8	yes	—
46	C₁₃×#97	—	2	4	no	—
47	C₄×C₈×C₁₃	—	2	4	no	—
48	C₄×C₈×C₁₃	—	2	1	no	—
49	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₄×C₈×C₁₃	C₂³	1	2	yes	—
54	C₄×C₈×C₁₃	C₂³	1	2	yes	—
55	C₄×C₈×C₁₃	C₂³	1	2	yes	—
56	#17980	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂×Q₈×C₁₃	—	2	2	no	—
58	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
62	C₁₃×Q₁₆	—	4	4	no	—
63	C₁₃×M₁₆	—	4	4	no	—
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₂×C₈×C₁₃	—	2	4	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	4	no	—
68	C₂×C₈×C₁₃	—	4	2	no	—
69	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
70	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
71	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
73	C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₁₃×C₄⋊C₄	—	2	4	no	—
78	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
79	C₁₃×C₂²⋊C₄	—	2	4	no	—
80	C₄²×C₁₃	—	2	4	no	—
81	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₃	#41	1	1	yes	characteristic
84	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
85	#3170	C₂×C₁₃	1	1	yes	characteristic
86	#2960	C₂×C₁₃	1	2	yes	—
87	#1587	C₂×C₁₃	1	8	yes	complemented
88	#1566	C₂×C₁₃	1	1	yes	characteristic
89	#1493	C₂×C₁₃	1	2	yes	—
90	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
91	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
92	Q₈×C₁₃	—	2	8	no	—
93	Q₈×C₁₃	—	4	4	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	2	4	no	—
97	C₂×C₄×C₁₃	—	2	4	no	—
98	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#137	1	4	yes	—
102	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
105	C₈×C₁₃	—	2	4	no	—
106	C₈×C₁₃	—	2	2	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	—	2	2	no	—
109	C₈×C₁₃	—	2	2	no	—
110	C₈×C₁₃	—	4	4	no	—
111	#533	C₂²×C₁₃	1	2	yes	—
112	#500	C₄×C₁₃	1	1	yes	characteristic
113	#494	C₄×C₁₃	1	1	yes	characteristic
114	#487	C₄×C₁₃	1	2	yes	—
115	#467	C₄×C₁₃	1	4	yes	—
116	#446	—	2	2	no	—
117	#446	C₂²×C₁₃	1	4	yes	—
118	C₈×Q₈	—	2	2	no	—
119	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
120	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
121	#424	—	2	2	no	—
122	#423	C₂²×C₁₃	1	2	yes	—
123	#405	—	2	2	no	—
124	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
127	#334	C₂²×C₁₃	1	4	yes	—
128	Q₈⋊C₈	C₂²×C₁₃	1	8	yes	—
129	#322	C₂²×C₁₃	1	4	yes	—
130	C₂²×C₁₃	—	2	1	no	—
131	C₂²×C₁₃	—	2	1	no	—
132	C₂²×C₁₃	#441	1	2	yes	—
133	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	4	4	no	—
137	C₄×C₁₃	—	4	4	no	—
138	C₄×C₁₃	#441	1	2	yes	—
139	C₄×C₁₃	#443	1	2	yes	—
140	C₄×C₁₃	#568	1	2	yes	—
141	C₄×C₁₃	C₂×#137	1	2	yes	—
142	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
143	C₂×M₁₆	—	2	2	no	—
144	C₂²×C₈	—	2	1	no	—
145	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
146	C₂²×C₈	D₄×C₁₃	1	2	yes	—
147	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
148	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
149	#125	—	2	2	no	—
150	C₂²⋊Q₈	—	2	2	no	—
151	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
152	C₄×Q₈	—	2	2	no	—
153	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
154	#117	—	2	2	no	—
155	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
156	#107	C₂×C₄×C₁₃	1	4	yes	—
157	C₄⋊C₈	—	2	4	no	—
158	C₄⋊C₈	—	2	4	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
161	#103	C₂×C₄×C₁₃	1	8	yes	—
162	#97	—	2	4	no	—
163	C₄×C₈	—	2	4	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
166	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
167	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
168	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
169	C₄×C₈	C₂³×C₁₃	1	2	yes	—
170	C₄×C₈	C₂³×C₁₃	1	2	yes	—
171	C₄×C₈	C₂³×C₁₃	1	2	yes	—
172	C₂×C₁₃	—	2	2	no	—
173	C₂×C₁₃	#2932	1	1	yes	characteristic
174	C₂×C₁₃	C₂×#441	1	1	yes	characteristic
175	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
178	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
180	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
181	Q₁₆	—	4	4	no	—
182	M₁₆	—	4	4	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	2	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
189	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
190	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
191	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	2	4	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
198	C₂²⋊C₄	—	2	4	no	—
199	C₄²	—	2	4	no	—
200	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
201	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
202	C₄²	C₁₃×#41	1	1	yes	characteristic
203	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
204	C₁₃	#17980	1	1	yes	characteristic, direct product factor, Sylow
205	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
206	Q₈	—	2	8	no	—
207	Q₈	—	4	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
213	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
215	C₂×C₄	C₁₃×#137	1	4	yes	—
216	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
217	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
218	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
219	C₈	—	2	4	no	—
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	2	2	no	—
223	C₈	—	2	2	no	—
224	C₈	—	4	4	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	C₁₃×#441	1	2	yes	—
228	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	4	4	no	—
232	C₄	—	4	4	no	—
233	C₄	C₁₃×#441	1	2	yes	—
234	C₄	C₁₃×#443	1	2	yes	—
235	C₄	C₁₃×#568	1	2	yes	—
236	C₄	C₂×C₁₃×#137	1	2	yes	—
237	C₂	—	2	2	no	—
238	C₂	C₁₃×#2932	1	1	yes	characteristic
239	C₂	C₂×C₁₃×#441	1	1	yes	characteristic
240	C₂	C₂×C₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×C₁₃	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1587	C₂	semidirect
56. #17980	C₁₃	direct (N × H)
87. #1587	C₂×C₁₃	semidirect
204. C₁₃	#17980	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×#3170	2
C₁₃×#2960	2
C₁₃×#1587	2
C₁₃×#1566	2
C₁₃×#1493	2
C₂×C₁₃×#322	2
#17980	13

Subgroups — C13×#17980 #15704319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17980 #15704319