Subgroups — C₁₃×#19003 #15705342

Order 3328.

808 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3234	C₂	1	2	yes	maximal
3	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1663	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1658	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1534	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1528	C₂	1	2	yes	maximal, complemented
8	C₁₃×#564	—	2	4	no	—
9	C₁₃×#564	—	2	2	no	—
10	C₁₃×#564	C₂²	1	4	yes	—
11	C₁₃×#532	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#125	—	2	2	no	—
13	C₂×C₁₃×#125	—	2	2	no	—
14	C₂×C₁₃×#125	—	2	2	no	—
15	C₂×C₁₃×#125	C₂²	1	2	yes	—
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₁₃×#501	C₂²	1	4	yes	—
18	C₁₃×#491	C₂²	1	2	yes	—
19	C₁₃×#490	C₂²	1	2	yes	—
20	C₁₃×#490	C₂²	1	4	yes	—
21	C₁₃×#488	—	2	2	no	—
22	C₁₃×#481	—	2	2	no	—
23	C₁₃×#480	—	2	2	no	—
24	C₁₃×#478	—	2	4	no	—
25	C₁₃×#432	C₂²	1	2	yes	—
26	C₁₃×#417	—	2	2	no	—
27	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₁₃×#330	C₂²	1	8	yes	—
29	C₁₃×#330	C₂²	1	4	yes	—
30	C₂×C₁₃×#41	—	2	1	no	—
31	C₂×C₁₃×M₁₆	—	2	1	no	—
32	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
33	C₁₃×#127	C₂³	1	1	yes	characteristic
34	C₁₃×#125	—	2	8	no	—
35	C₁₃×#125	—	2	8	no	—
36	C₁₃×#125	—	2	8	no	—
37	C₁₃×#125	—	2	8	no	—
38	C₁₃×#125	—	2	8	no	—
39	C₁₃×#125	—	2	8	no	—
40	C₁₃×#125	—	2	2	no	—
41	C₁₃×#125	—	2	2	no	—
42	C₁₃×#125	—	2	2	no	—
43	C₁₃×#125	D₄	1	4	yes	—
44	C₁₃×#125	D₄	1	2	yes	—
45	C₁₃×#125	C₂³	1	2	yes	—
46	C₁₃×#125	C₂³	1	4	yes	—
47	C₁₃×#124	—	2	1	no	—
48	C₁₃×#121	—	2	2	no	—
49	C₄×D₄×C₁₃	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
59	C₂×C₄²×C₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#107	—	2	4	no	—
62	C₁₃×#106	—	2	4	no	—
63	C₁₃×C₄⋊C₈	—	2	2	no	—
64	C₁₃×#103	—	2	4	no	—
65	C₁₃×#102	—	2	4	no	—
66	C₁₃×#102	—	2	4	no	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×C₂²⋊C₈	—	2	2	no	—
69	C₁₃×#97	C₂³	1	2	yes	—
70	C₁₃×#97	C₂³	1	4	yes	—
71	C₄×C₈×C₁₃	—	2	1	no	—
72	#19003	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₁₃×#41	—	4	4	no	—
74	C₂×Q₈×C₁₃	—	2	1	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	1	no	—
77	C₂×D₄×C₁₃	—	4	1	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
84	C₁₃×M₁₆	—	4	2	no	—
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₁₃×C₄⋊C₄	—	2	8	no	—
88	C₁₃×C₄⋊C₄	—	2	8	no	—
89	C₁₃×C₄⋊C₄	—	2	8	no	—
90	C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₁₃×C₄⋊C₄	—	2	4	no	—
92	C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₁₃×C₄⋊C₄	—	2	4	no	—
98	C₁₃×C₄⋊C₄	—	2	4	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
101	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
102	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
103	C₁₃×C₂²⋊C₄	—	4	2	no	—
104	C₄²×C₁₃	—	2	8	no	—
105	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂×D₄	1	2	yes	—
107	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×#564	C₂×C₁₃	1	1	yes	characteristic, complemented
109	#3234	C₂×C₁₃	1	2	yes	—
110	#3142	C₂×C₁₃	1	1	yes	characteristic
111	#1663	C₂×C₁₃	1	4	yes	complemented
112	#1658	C₂×C₁₃	1	4	yes	complemented
113	#1534	C₂×C₁₃	1	1	yes	characteristic, complemented
114	#1528	C₂×C₁₃	1	2	yes	complemented
115	C₂³×C₁₃	—	4	1	no	—
116	C₂³×C₁₃	#120	1	1	yes	characteristic
117	Q₈×C₁₃	—	4	2	no	—
118	D₄×C₁₃	—	4	4	no	—
119	D₄×C₁₃	—	4	2	no	—
120	D₄×C₁₃	—	8	2	no	—
121	C₂×C₄×C₁₃	—	2	2	no	—
122	C₂×C₄×C₁₃	—	2	4	no	—
123	C₂×C₄×C₁₃	—	2	4	no	—
124	C₂×C₄×C₁₃	—	2	4	no	—
125	C₂×C₄×C₁₃	—	4	2	no	—
126	C₂×C₄×C₁₃	—	4	4	no	—
127	C₂×C₄×C₁₃	—	4	4	no	—
128	C₂×C₄×C₁₃	—	4	4	no	—
129	C₂×C₄×C₁₃	—	4	1	no	—
130	C₂×C₄×C₁₃	—	8	2	no	—
131	C₂×C₄×C₁₃	#120	1	2	yes	—
132	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
133	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
134	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
135	C₈×C₁₃	—	4	4	no	—
136	C₈×C₁₃	—	4	2	no	—
137	#564	—	2	4	no	—
138	#564	—	2	2	no	—
139	#564	C₂²×C₁₃	1	4	yes	—
140	#532	C₂²×C₁₃	1	1	yes	characteristic
141	C₂×#125	—	2	2	no	—
142	C₂×#125	—	2	2	no	—
143	C₂×#125	—	2	2	no	—
144	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
145	C₂×#125	C₂²×C₁₃	1	2	yes	—
146	#501	C₂²×C₁₃	1	4	yes	—
147	#491	C₂²×C₁₃	1	2	yes	—
148	#490	C₂²×C₁₃	1	2	yes	—
149	#490	C₂²×C₁₃	1	4	yes	—
150	#488	—	2	2	no	—
151	#481	—	2	2	no	—
152	#480	—	2	2	no	—
153	#478	—	2	4	no	—
154	#432	C₂²×C₁₃	1	2	yes	—
155	#417	—	2	2	no	—
156	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
157	#330	C₂²×C₁₃	1	8	yes	—
158	#330	C₂²×C₁₃	1	4	yes	—
159	C₂²×C₁₃	—	2	2	no	—
160	C₂²×C₁₃	—	8	1	no	—
161	C₂²×C₁₃	—	8	2	no	—
162	C₂²×C₁₃	#454	1	2	yes	—
163	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
164	C₄×C₁₃	—	2	1	no	—
165	C₄×C₁₃	—	2	1	no	—
166	C₄×C₁₃	—	2	2	no	—
167	C₄×C₁₃	—	2	2	no	—
168	C₄×C₁₃	—	4	4	no	—
169	C₄×C₁₃	—	4	4	no	—
170	C₄×C₁₃	—	4	4	no	—
171	C₄×C₁₃	—	8	1	no	—
172	C₂×#41	—	2	1	no	—
173	C₂×M₁₆	—	2	1	no	—
174	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
175	#127	C₂³×C₁₃	1	1	yes	characteristic
176	#125	—	2	8	no	—
177	#125	—	2	8	no	—
178	#125	—	2	8	no	—
179	#125	—	2	8	no	—
180	#125	—	2	8	no	—
181	#125	—	2	8	no	—
182	#125	—	2	2	no	—
183	#125	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	D₄×C₁₃	1	4	yes	—
186	#125	D₄×C₁₃	1	2	yes	—
187	#125	C₂³×C₁₃	1	2	yes	—
188	#125	C₂³×C₁₃	1	4	yes	—
189	#124	—	2	1	no	—
190	#121	—	2	2	no	—
191	C₄×D₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	2	no	—
195	C₂×C₄⋊C₄	—	2	2	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
199	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
200	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
201	C₂×C₄²	—	2	2	no	—
202	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
203	#107	—	2	4	no	—
204	#106	—	2	4	no	—
205	C₄⋊C₈	—	2	2	no	—
206	#103	—	2	4	no	—
207	#102	—	2	4	no	—
208	#102	—	2	4	no	—
209	#102	—	2	4	no	—
210	C₂²⋊C₈	—	2	2	no	—
211	#97	C₂³×C₁₃	1	2	yes	—
212	#97	C₂³×C₁₃	1	4	yes	—
213	C₄×C₈	—	2	1	no	—
214	C₂×C₁₃	—	2	2	no	—
215	C₂×C₁₃	—	16	1	no	—
216	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
217	C₂×C₁₃	#3020	1	2	yes	—
218	#41	—	4	4	no	—
219	C₂×Q₈	—	2	1	no	—
220	C₂×D₄	—	2	2	no	—
221	C₂×D₄	—	2	1	no	—
222	C₂×D₄	—	4	1	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	4	1	no	—
227	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
229	M₁₆	—	4	2	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	—	2	4	no	—
232	C₄⋊C₄	—	2	8	no	—
233	C₄⋊C₄	—	2	8	no	—
234	C₄⋊C₄	—	2	8	no	—
235	C₄⋊C₄	—	2	4	no	—
236	C₄⋊C₄	—	2	4	no	—
237	C₄⋊C₄	—	2	4	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	—	2	4	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
246	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
247	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
248	C₂²⋊C₄	—	4	2	no	—
249	C₄²	—	2	8	no	—
250	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
251	C₄²	C₂×D₄×C₁₃	1	2	yes	—
252	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
253	C₁₃	#19003	1	1	yes	characteristic, direct product factor, Sylow
254	C₂³	—	4	1	no	—
255	C₂³	C₁₃×#120	1	1	yes	characteristic
256	Q₈	—	4	2	no	—
257	D₄	—	4	4	no	—
258	D₄	—	4	2	no	—
259	D₄	—	8	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	4	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	2	4	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	4	no	—
266	C₂×C₄	—	4	4	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	4	1	no	—
269	C₂×C₄	—	8	2	no	—
270	C₂×C₄	C₁₃×#120	1	2	yes	—
271	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
272	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
273	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
274	C₈	—	4	4	no	—
275	C₈	—	4	2	no	—
276	C₂²	—	2	2	no	—
277	C₂²	—	8	1	no	—
278	C₂²	—	8	2	no	—
279	C₂²	C₁₃×#454	1	2	yes	—
280	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
281	C₄	—	2	1	no	—
282	C₄	—	2	1	no	—
283	C₄	—	2	2	no	—
284	C₄	—	2	2	no	—
285	C₄	—	4	4	no	—
286	C₄	—	4	4	no	—
287	C₄	—	4	4	no	—
288	C₄	—	8	1	no	—
289	C₂	—	2	2	no	—
290	C₂	—	16	1	no	—
291	C₂	C₂×C₁₃×#454	1	1	yes	characteristic
292	C₂	C₁₃×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#564	C₂	semidirect
4. C₁₃×#1663	C₂	semidirect
5. C₁₃×#1658	C₂	semidirect
6. C₁₃×#1534	C₂	semidirect
7. C₁₃×#1528	C₂	semidirect
72. #19003	C₁₃	direct (N × H)
108. C₂×#564	C₂×C₁₃	semidirect
111. #1663	C₂×C₁₃	semidirect
112. #1658	C₂×C₁₃	semidirect
113. #1534	C₂×C₁₃	semidirect
114. #1528	C₂×C₁₃	semidirect
253. C₁₃	#19003	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×#564	2
C₁₃×#3234	2
C₁₃×#3142	2
C₁₃×#1663	2
C₁₃×#1658	2
C₁₃×#1534	2
C₁₃×#1528	2
#19003	13

Subgroups — C13×#19003 #15705342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19003 #15705342