Subgroups — C₁₃×#17961 #15704300

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 246 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×#1593	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1579	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1566	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1493	C₂	1	2	yes	maximal
7	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#533	C₂²	1	2	yes	—
9	C₁₃×#500	C₄	1	1	yes	characteristic
10	C₁₃×#494	C₄	1	1	yes	characteristic
11	C₁₃×#487	C₄	1	2	yes	—
12	C₁₃×#467	C₄	1	4	yes	—
13	C₁₃×#446	—	2	2	no	—
14	C₁₃×#446	C₂²	1	4	yes	—
15	C₈×Q₈×C₁₃	—	2	2	no	—
16	C₈×Q₈×C₁₃	C₂²	1	4	yes	—
17	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
18	C₁₃×#424	—	2	2	no	—
19	C₁₃×#423	C₂²	1	2	yes	—
20	C₁₃×#405	—	2	2	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#334	C₂²	1	4	yes	—
25	C₁₃×Q₈⋊C₈	C₂²	1	8	yes	—
26	C₁₃×#322	C₂²	1	2	yes	—
27	C₁₃×#322	C₂²	1	2	yes	—
28	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
29	C₂×C₁₃×M₁₆	—	2	2	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₃	D₄	1	2	yes	—
33	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
34	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
35	C₁₃×#125	—	2	2	no	—
36	C₁₃×C₂²⋊Q₈	—	2	2	no	—
37	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
38	C₄×Q₈×C₁₃	—	2	2	no	—
39	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×#117	—	2	2	no	—
41	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×#107	C₂×C₄	1	4	yes	—
43	C₁₃×C₄⋊C₈	—	2	4	no	—
44	C₁₃×C₄⋊C₈	—	2	4	no	—
45	C₁₃×C₄⋊C₈	—	2	2	no	—
46	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
47	C₁₃×#103	C₂×C₄	1	8	yes	—
48	C₁₃×#97	—	2	4	no	—
49	C₄×C₈×C₁₃	—	2	4	no	—
50	C₄×C₈×C₁₃	—	2	1	no	—
51	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₁₃	D₄	1	2	yes	—
54	C₄×C₈×C₁₃	C₂³	1	2	yes	—
55	C₄×C₈×C₁₃	C₂³	1	2	yes	—
56	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	#17961	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂×Q₈×C₁₃	—	2	2	no	—
60	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
61	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
64	C₁₃×Q₁₆	—	2	8	no	—
65	C₁₃×M₁₆	—	4	4	no	—
66	C₂×C₈×C₁₃	—	2	4	no	—
67	C₂×C₈×C₁₃	—	2	4	no	—
68	C₂×C₈×C₁₃	—	2	4	no	—
69	C₂×C₈×C₁₃	—	2	2	no	—
70	C₂×C₈×C₁₃	—	4	2	no	—
71	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
73	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
75	C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₁₃×C₄⋊C₄	—	2	4	no	—
79	C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
81	C₁₃×C₂²⋊C₄	—	2	4	no	—
82	C₄²×C₁₃	—	2	4	no	—
83	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₃	#41	1	1	yes	characteristic
86	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
87	#3170	C₂×C₁₃	1	1	yes	characteristic
88	#2960	C₂×C₁₃	1	2	yes	—
89	#1593	C₂×C₁₃	1	4	yes	complemented
90	#1579	C₂×C₁₃	1	4	yes	complemented
91	#1566	C₂×C₁₃	1	1	yes	characteristic
92	#1493	C₂×C₁₃	1	2	yes	—
93	C₂×#322	C₂×C₁₃	1	1	yes	characteristic
94	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
95	Q₈×C₁₃	—	2	8	no	—
96	Q₈×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	2	2	no	—
99	C₂×C₄×C₁₃	—	2	4	no	—
100	C₂×C₄×C₁₃	—	2	4	no	—
101	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#137	1	4	yes	—
105	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
108	C₈×C₁₃	—	2	2	no	—
109	C₈×C₁₃	—	2	2	no	—
110	C₈×C₁₃	—	2	2	no	—
111	C₈×C₁₃	—	4	2	no	—
112	C₈×C₁₃	—	4	4	no	—
113	C₈×C₁₃	#131	1	4	yes	—
114	#533	C₂²×C₁₃	1	2	yes	—
115	#500	C₄×C₁₃	1	1	yes	characteristic
116	#494	C₄×C₁₃	1	1	yes	characteristic
117	#487	C₄×C₁₃	1	2	yes	—
118	#467	C₄×C₁₃	1	4	yes	—
119	#446	—	2	2	no	—
120	#446	C₂²×C₁₃	1	4	yes	—
121	C₈×Q₈	—	2	2	no	—
122	C₈×Q₈	C₂²×C₁₃	1	4	yes	—
123	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
124	#424	—	2	2	no	—
125	#423	C₂²×C₁₃	1	2	yes	—
126	#405	—	2	2	no	—
127	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
130	#334	C₂²×C₁₃	1	4	yes	—
131	Q₈⋊C₈	C₂²×C₁₃	1	8	yes	—
132	#322	C₂²×C₁₃	1	2	yes	—
133	#322	C₂²×C₁₃	1	2	yes	—
134	C₂²×C₁₃	—	2	1	no	—
135	C₂²×C₁₃	—	2	1	no	—
136	C₂²×C₁₃	#441	1	2	yes	—
137	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
138	C₄×C₁₃	—	2	1	no	—
139	C₄×C₁₃	—	2	1	no	—
140	C₄×C₁₃	—	4	4	no	—
141	C₄×C₁₃	—	4	4	no	—
142	C₄×C₁₃	#441	1	2	yes	—
143	C₄×C₁₃	#444	1	2	yes	—
144	C₄×C₁₃	C₂×#131	1	2	yes	—
145	C₄×C₁₃	C₂×#137	1	2	yes	—
146	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
150	C₂²×C₈	D₄×C₁₃	1	2	yes	—
151	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
152	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
153	#125	—	2	2	no	—
154	C₂²⋊Q₈	—	2	2	no	—
155	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
156	C₄×Q₈	—	2	2	no	—
157	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
158	#117	—	2	2	no	—
159	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
160	#107	C₂×C₄×C₁₃	1	4	yes	—
161	C₄⋊C₈	—	2	4	no	—
162	C₄⋊C₈	—	2	4	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
165	#103	C₂×C₄×C₁₃	1	8	yes	—
166	#97	—	2	4	no	—
167	C₄×C₈	—	2	4	no	—
168	C₄×C₈	—	2	1	no	—
169	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
170	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
171	C₄×C₈	D₄×C₁₃	1	2	yes	—
172	C₄×C₈	C₂³×C₁₃	1	2	yes	—
173	C₄×C₈	C₂³×C₁₃	1	2	yes	—
174	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
175	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
176	C₂×C₁₃	—	2	2	no	—
177	C₂×C₁₃	#2931	1	1	yes	characteristic
178	C₂×C₁₃	C₂×#441	1	1	yes	characteristic
179	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
182	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
184	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
185	Q₁₆	—	2	8	no	—
186	M₁₆	—	4	4	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
193	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
194	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
195	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	2	4	no	—
201	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	—	2	4	no	—
204	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
205	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
206	C₄²	C₁₃×#41	1	1	yes	characteristic
207	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
208	C₁₃	#17961	1	1	yes	characteristic, direct product factor, Sylow
209	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
210	Q₈	—	2	8	no	—
211	Q₈	—	4	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
217	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
218	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
219	C₂×C₄	C₁₃×#137	1	4	yes	—
220	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
222	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	2	2	no	—
225	C₈	—	2	2	no	—
226	C₈	—	4	2	no	—
227	C₈	—	4	4	no	—
228	C₈	C₁₃×#131	1	4	yes	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	C₁₃×#441	1	2	yes	—
232	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	4	no	—
236	C₄	—	4	4	no	—
237	C₄	C₁₃×#441	1	2	yes	—
238	C₄	C₁₃×#444	1	2	yes	—
239	C₄	C₂×C₁₃×#131	1	2	yes	—
240	C₄	C₂×C₁₃×#137	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	C₁₃×#2931	1	1	yes	characteristic
243	C₂	C₂×C₁₃×#441	1	1	yes	characteristic
244	C₂	C₂×C₁₃×#444	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×#1593	C₂	semidirect
4. C₁₃×#1579	C₂	semidirect
58. #17961	C₁₃	direct (N × H)
89. #1593	C₂×C₁₃	semidirect
90. #1579	C₂×C₁₃	semidirect
208. C₁₃	#17961	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×#1593	2
C₁₃×#1579	2
C₁₃×#1566	2
C₁₃×#1493	2
C₂×C₁₃×#322	2
#17961	13

Subgroups — C13×#17961 #15704300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17961 #15704300