Subgroups — C₁₃×#18703 #15705042

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3556	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3255	C₂	1	2	yes	maximal
3	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1653	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1648	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1561	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1493	C₂	1	2	yes	maximal
8	C₁₃×#564	—	2	2	no	—
9	C₁₃×#557	—	2	2	no	—
10	C₁₃×#557	—	2	2	no	—
11	C₁₃×#557	C₂²	1	4	yes	—
12	C₁₃×#541	—	2	4	no	—
13	C₁₃×#541	—	2	2	no	—
14	C₁₃×#533	C₂²	1	1	yes	characteristic
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#533	C₂²	1	1	yes	characteristic
17	C₁₃×#500	C₂²	1	2	yes	—
18	C₁₃×#499	—	2	2	no	—
19	C₁₃×#498	C₂²	1	2	yes	—
20	C₁₃×#475	—	2	2	no	—
21	C₁₃×#475	C₂²	1	4	yes	—
22	C₁₃×#470	—	2	4	no	—
23	C₁₃×#462	—	2	2	no	—
24	C₁₃×#462	C₂²	1	4	yes	—
25	C₁₃×#427	—	2	2	no	—
26	C₁₃×#423	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#332	C₂²	1	4	yes	—
29	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
30	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₂×C₁₃×Q₁₆	—	2	4	no	—
32	C₂×C₁₃×M₁₆	—	2	2	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₁₃×C₄⋊Q₈	—	2	2	no	—
35	C₁₃×C₄⋊Q₈	—	2	4	no	—
36	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
37	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
38	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
39	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
40	C₁₃×#126	—	2	8	no	—
41	C₁₃×#125	—	2	2	no	—
42	C₁₃×#125	—	2	8	no	—
43	C₁₃×#125	—	2	8	no	—
44	C₁₃×#125	—	2	4	no	—
45	C₁₃×#125	—	2	8	no	—
46	C₁₃×#125	—	2	2	no	—
47	C₁₃×#125	—	2	1	no	—
48	C₁₃×#125	D₄	1	2	yes	—
49	C₁₃×C₂²⋊Q₈	—	2	2	no	—
50	C₁₃×C₂²⋊Q₈	—	2	2	no	—
51	C₁₃×C₂²⋊Q₈	—	2	2	no	—
52	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
53	C₄×Q₈×C₁₃	—	2	4	no	—
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
60	C₁₃×#117	—	2	2	no	—
61	C₁₃×#117	—	2	1	no	—
62	C₁₃×#117	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#107	—	2	4	no	—
65	C₁₃×#106	—	2	4	no	—
66	C₁₃×#106	—	2	4	no	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
69	C₁₃×#103	—	2	4	no	—
70	C₁₃×#103	—	2	4	no	—
71	C₄×C₈×C₁₃	—	2	1	no	—
72	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	#18703	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
79	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
81	C₁₃×Q₁₆	—	8	4	no	—
82	C₁₃×M₁₆	—	8	2	no	—
83	C₂×C₈×C₁₃	—	2	4	no	—
84	C₂×C₈×C₁₃	—	2	1	no	—
85	C₂×C₈×C₁₃	—	2	1	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	2	no	—
91	C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₁₃×C₄⋊C₄	—	2	2	no	—
93	C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	4	2	no	—
100	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
101	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
102	C₁₃×C₂²⋊C₄	—	2	4	no	—
103	C₁₃×C₂²⋊C₄	—	2	2	no	—
104	C₁₃×C₂²⋊C₄	—	4	1	no	—
105	C₄²×C₁₃	—	2	8	no	—
106	C₄²×C₁₃	—	2	2	no	—
107	C₄²×C₁₃	—	2	4	no	—
108	C₄²×C₁₃	—	4	1	no	—
109	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂×D₄	1	2	yes	—
111	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
112	#3556	C₂×C₁₃	1	1	yes	characteristic
113	#3255	C₂×C₁₃	1	2	yes	—
114	#3160	C₂×C₁₃	1	1	yes	characteristic
115	#1653	C₂×C₁₃	1	4	yes	complemented
116	#1648	C₂×C₁₃	1	4	yes	complemented
117	#1561	C₂×C₁₃	1	1	yes	characteristic
118	#1493	C₂×C₁₃	1	2	yes	—
119	C₂³×C₁₃	#120	1	1	yes	characteristic
120	Q₈×C₁₃	—	2	4	no	—
121	Q₈×C₁₃	—	2	4	no	—
122	Q₈×C₁₃	—	4	2	no	—
123	Q₈×C₁₃	—	4	2	no	—
124	Q₈×C₁₃	—	4	4	no	—
125	Q₈×C₁₃	—	4	2	no	—
126	Q₈×C₁₃	—	4	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	#120	1	2	yes	—
135	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
138	C₈×C₁₃	—	2	2	no	—
139	C₈×C₁₃	—	2	2	no	—
140	C₈×C₁₃	—	4	4	no	—
141	#564	—	2	2	no	—
142	#557	—	2	2	no	—
143	#557	—	2	2	no	—
144	#557	C₂²×C₁₃	1	4	yes	—
145	#541	—	2	4	no	—
146	#541	—	2	2	no	—
147	#533	C₂²×C₁₃	1	1	yes	characteristic
148	#533	C₂²×C₁₃	1	2	yes	—
149	#533	C₂²×C₁₃	1	1	yes	characteristic
150	#500	C₂²×C₁₃	1	2	yes	—
151	#499	—	2	2	no	—
152	#498	C₂²×C₁₃	1	2	yes	—
153	#475	—	2	2	no	—
154	#475	C₂²×C₁₃	1	4	yes	—
155	#470	—	2	4	no	—
156	#462	—	2	2	no	—
157	#462	C₂²×C₁₃	1	4	yes	—
158	#427	—	2	2	no	—
159	#423	C₂²×C₁₃	1	2	yes	—
160	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
161	#332	C₂²×C₁₃	1	4	yes	—
162	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
163	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
164	C₂²×C₁₃	—	2	2	no	—
165	C₂²×C₁₃	—	2	1	no	—
166	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
167	C₄×C₁₃	—	2	2	no	—
168	C₄×C₁₃	—	2	1	no	—
169	C₄×C₁₃	—	4	4	no	—
170	C₄×C₁₃	—	4	4	no	—
171	C₄×C₁₃	—	4	4	no	—
172	C₄×C₁₃	—	8	2	no	—
173	C₄×C₁₃	#456	1	2	yes	—
174	C₄×C₁₃	#577	1	2	yes	—
175	C₄×C₁₃	#578	1	2	yes	—
176	C₂×Q₁₆	—	2	4	no	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂²×C₈	—	2	1	no	—
179	C₄⋊Q₈	—	2	2	no	—
180	C₄⋊Q₈	—	2	4	no	—
181	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
182	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
183	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
184	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
185	#126	—	2	8	no	—
186	#125	—	2	2	no	—
187	#125	—	2	8	no	—
188	#125	—	2	8	no	—
189	#125	—	2	4	no	—
190	#125	—	2	8	no	—
191	#125	—	2	2	no	—
192	#125	—	2	1	no	—
193	#125	D₄×C₁₃	1	2	yes	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
198	C₄×Q₈	—	2	4	no	—
199	C₄×Q₈	—	2	4	no	—
200	C₄×Q₈	—	2	4	no	—
201	C₄×Q₈	—	2	2	no	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×Q₈	—	2	2	no	—
204	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
205	#117	—	2	2	no	—
206	#117	—	2	1	no	—
207	#117	D₄×C₁₃	1	2	yes	—
208	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
209	#107	—	2	4	no	—
210	#106	—	2	4	no	—
211	#106	—	2	4	no	—
212	C₄⋊C₈	—	2	2	no	—
213	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
214	#103	—	2	4	no	—
215	#103	—	2	4	no	—
216	C₄×C₈	—	2	1	no	—
217	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
218	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
219	C₂×C₁₃	—	4	1	no	—
220	C₂×C₁₃	#3013	1	2	yes	—
221	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
222	C₂×Q₈	—	2	2	no	—
223	C₂×Q₈	—	2	2	no	—
224	C₂×Q₈	—	2	2	no	—
225	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
226	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
227	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
228	Q₁₆	—	8	4	no	—
229	M₁₆	—	8	2	no	—
230	C₂×C₈	—	2	4	no	—
231	C₂×C₈	—	2	1	no	—
232	C₂×C₈	—	2	1	no	—
233	C₂×C₈	—	2	4	no	—
234	C₄⋊C₄	—	2	8	no	—
235	C₄⋊C₄	—	2	8	no	—
236	C₄⋊C₄	—	2	8	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	2	4	no	—
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	—	2	2	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	4	2	no	—
247	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
248	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
249	C₂²⋊C₄	—	2	4	no	—
250	C₂²⋊C₄	—	2	2	no	—
251	C₂²⋊C₄	—	4	1	no	—
252	C₄²	—	2	8	no	—
253	C₄²	—	2	2	no	—
254	C₄²	—	2	4	no	—
255	C₄²	—	4	1	no	—
256	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
257	C₄²	C₂×D₄×C₁₃	1	2	yes	—
258	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
259	C₁₃	#18703	1	1	yes	characteristic, direct product factor, Sylow
260	C₂³	C₁₃×#120	1	1	yes	characteristic
261	Q₈	—	2	4	no	—
262	Q₈	—	2	4	no	—
263	Q₈	—	4	4	no	—
264	Q₈	—	4	2	no	—
265	Q₈	—	4	2	no	—
266	Q₈	—	4	2	no	—
267	Q₈	—	4	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	C₁₃×#120	1	2	yes	—
276	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
277	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
279	C₈	—	2	2	no	—
280	C₈	—	2	2	no	—
281	C₈	—	4	4	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	2	1	no	—
284	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
285	C₄	—	2	2	no	—
286	C₄	—	2	1	no	—
287	C₄	—	4	4	no	—
288	C₄	—	4	4	no	—
289	C₄	—	4	4	no	—
290	C₄	—	8	2	no	—
291	C₄	C₁₃×#456	1	2	yes	—
292	C₄	C₁₃×#577	1	2	yes	—
293	C₄	C₁₃×#578	1	2	yes	—
294	C₂	—	4	1	no	—
295	C₂	C₁₃×#3013	1	2	yes	—
296	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	#120
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
4. C₁₃×#1653	C₂	semidirect
5. C₁₃×#1648	C₂	semidirect
74. #18703	C₁₃	direct (N × H)
115. #1653	C₂×C₁₃	semidirect
116. #1648	C₂×C₁₃	semidirect
259. C₁₃	#18703	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×#3556	2
C₁₃×#3255	2
C₁₃×#3160	2
C₁₃×#1653	2
C₁₃×#1648	2
C₁₃×#1561	2
C₁₃×#1493	2
#18703	13

Subgroups — C13×#18703 #15705042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18703 #15705042