Subgroups — C₁₃×#10607 #15696946

Order 3328.

374 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
9	C₁₃×#431	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#108	—	2	1	no	—
11	C₁₃×#423	C₂²	1	1	yes	characteristic
12	C₁₃×#423	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#100	—	2	1	no	—
16	C₂×C₁₃×#100	—	2	1	no	—
17	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#341	—	2	1	no	—
19	C₁₃×#335	—	2	1	no	—
20	C₁₃×#334	—	2	1	no	—
21	C₁₃×#334	—	2	2	no	—
22	C₁₃×#331	—	2	2	no	—
23	C₁₃×#331	—	2	1	no	—
24	C₁₃×#331	—	2	1	no	—
25	C₂²×D₄×C₁₃	—	2	1	no	—
26	C₂²×D₄×C₁₃	—	2	1	no	—
27	C₂²×D₄×C₁₃	Q₈	1	2	yes	—
28	C₂×C₁₃×M₁₆	—	2	1	no	—
29	C₂×C₁₃×M₁₆	—	2	1	no	—
30	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
31	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₁₃×#127	—	2	1	no	—
35	C₁₃×#127	—	2	1	no	—
36	C₁₃×#127	—	2	1	no	—
37	C₁₃×#127	—	2	1	no	—
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₁₃×#108	—	4	2	no	—
40	C₁₃×C₄⋊C₈	—	2	1	no	—
41	C₁₃×C₄⋊C₈	—	2	1	no	—
42	C₁₃×C₄⋊C₈	—	2	1	no	—
43	C₁₃×C₄⋊C₈	—	2	1	no	—
44	C₁₃×C₄⋊C₈	—	2	1	no	—
45	C₁₃×C₄⋊C₈	—	2	1	no	—
46	C₁₃×C₄⋊C₈	—	2	1	no	—
47	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
48	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
49	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
50	C₁₃×#100	—	4	2	no	—
51	C₁₃×#100	—	4	2	no	—
52	C₁₃×C₂²⋊C₈	—	2	1	no	—
53	C₁₃×#97	—	2	1	no	—
54	C₄×C₈×C₁₃	—	2	1	no	—
55	C₄×C₈×C₁₃	—	2	1	no	—
56	#10607	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂⁴×C₁₃	—	2	2	no	—
58	C₂×D₄×C₁₃	—	2	2	no	—
59	C₂×D₄×C₁₃	—	2	2	no	—
60	C₂×D₄×C₁₃	—	4	1	no	—
61	C₂×D₄×C₁₃	—	4	1	no	—
62	C₂×D₄×C₁₃	—	4	1	no	—
63	C₂×D₄×C₁₃	—	4	1	no	—
64	C₂×D₄×C₁₃	—	4	1	no	—
65	C₂×D₄×C₁₃	—	4	1	no	—
66	C₂×D₄×C₁₃	—	4	1	no	—
67	C₂×D₄×C₁₃	—	4	1	no	—
68	C₂×D₄×C₁₃	—	8	1	no	—
69	C₂×D₄×C₁₃	—	8	1	no	—
70	C₂×D₄×C₁₃	—	8	2	no	—
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
74	C₁₃×M₁₆	—	2	1	no	—
75	C₁₃×M₁₆	—	2	1	no	—
76	C₁₃×M₁₆	—	2	1	no	—
77	C₁₃×M₁₆	—	4	1	no	—
78	C₁₃×M₁₆	—	4	1	no	—
79	C₁₃×M₁₆	—	4	1	no	—
80	C₁₃×M₁₆	—	4	1	no	—
81	C₁₃×M₁₆	SD₁₆	1	2	yes	—
82	C₂×C₈×C₁₃	—	2	1	no	—
83	C₂×C₈×C₁₃	—	2	1	no	—
84	C₂×C₈×C₁₃	—	2	1	no	—
85	C₂×C₈×C₁₃	—	2	1	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	4	1	no	—
88	C₂×C₈×C₁₃	—	4	1	no	—
89	C₂×C₈×C₁₃	—	4	1	no	—
90	C₂×C₈×C₁₃	—	4	1	no	—
91	C₂×C₈×C₁₃	—	4	1	no	—
92	C₂×C₈×C₁₃	—	8	1	no	—
93	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₄²×C₁₃	#41	1	1	yes	characteristic
96	C₄²×C₁₃	#41	1	1	yes	characteristic
97	#1965	C₂×C₁₃	1	1	yes	characteristic
98	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
99	#1570	C₂×C₁₃	1	1	yes	characteristic, complemented
100	#1565	C₂×C₁₃	1	1	yes	characteristic, complemented
101	#1545	C₂×C₁₃	1	1	yes	characteristic
102	C₂×#331	C₂×C₁₃	1	1	yes	characteristic
103	#1292	C₂×C₁₃	1	1	yes	characteristic, complemented
104	C₂³×C₁₃	—	4	2	no	—
105	C₂³×C₁₃	—	4	2	no	—
106	C₂³×C₁₃	—	4	2	no	—
107	C₂³×C₁₃	—	8	2	no	—
108	C₂³×C₁₃	—	8	2	no	—
109	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
110	D₄×C₁₃	—	8	2	no	—
111	D₄×C₁₃	—	8	2	no	—
112	D₄×C₁₃	—	8	2	no	—
113	D₄×C₁₃	—	8	1	no	—
114	D₄×C₁₃	—	8	1	no	—
115	D₄×C₁₃	—	8	1	no	—
116	D₄×C₁₃	—	8	1	no	—
117	D₄×C₁₃	—	8	1	no	—
118	D₄×C₁₃	—	8	1	no	—
119	C₂×C₄×C₁₃	—	2	1	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	4	1	no	—
122	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
123	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
124	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
125	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
128	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
129	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
130	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
131	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
132	C₈×C₁₃	—	2	2	no	—
133	C₈×C₁₃	—	4	2	no	—
134	C₈×C₁₃	—	4	1	no	—
135	C₈×C₁₃	—	4	1	no	—
136	C₈×C₁₃	—	4	1	no	—
137	C₈×C₁₃	—	8	1	no	—
138	C₈×C₁₃	—	8	1	no	—
139	C₈×C₁₃	—	8	1	no	—
140	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
141	#431	C₂²×C₁₃	1	1	yes	characteristic
142	C₂×#108	—	2	1	no	—
143	#423	C₂²×C₁₃	1	1	yes	characteristic
144	#423	C₂²×C₁₃	1	1	yes	characteristic
145	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
147	C₂×#100	—	2	1	no	—
148	C₂×#100	—	2	1	no	—
149	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
150	#341	—	2	1	no	—
151	#335	—	2	1	no	—
152	#334	—	2	1	no	—
153	#334	—	2	2	no	—
154	#331	—	2	2	no	—
155	#331	—	2	1	no	—
156	#331	—	2	1	no	—
157	C₂²×C₁₃	—	2	1	no	—
158	C₂²×C₁₃	—	2	1	no	—
159	C₂²×C₁₃	—	8	2	no	—
160	C₂²×C₁₃	—	8	2	no	—
161	C₂²×C₁₃	—	8	2	no	—
162	C₂²×C₁₃	—	16	2	no	—
163	C₂²×C₁₃	—	16	2	no	—
164	C₂²×C₁₃	#396	1	1	yes	characteristic
165	C₂²×C₁₃	#476	1	1	yes	characteristic
166	C₂²×C₁₃	#478	1	1	yes	characteristic
167	C₄×C₁₃	—	2	1	no	—
168	C₄×C₁₃	—	2	1	no	—
169	C₄×C₁₃	—	2	1	no	—
170	C₄×C₁₃	#460	1	1	yes	characteristic
171	C₄×C₁₃	#463	1	1	yes	characteristic
172	C₄×C₁₃	#465	1	1	yes	characteristic
173	C₄×C₁₃	#469	1	1	yes	characteristic
174	C₄×C₁₃	#471	1	1	yes	characteristic
175	C₄×C₁₃	#472	1	1	yes	characteristic
176	C₂²×D₄	—	2	1	no	—
177	C₂²×D₄	—	2	1	no	—
178	C₂²×D₄	Q₈×C₁₃	1	2	yes	—
179	C₂×M₁₆	—	2	1	no	—
180	C₂×M₁₆	—	2	1	no	—
181	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
182	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
183	C₂²×C₈	—	2	1	no	—
184	C₂²×C₈	—	2	1	no	—
185	#127	—	2	1	no	—
186	#127	—	2	1	no	—
187	#127	—	2	1	no	—
188	#127	—	2	1	no	—
189	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
190	#108	—	4	2	no	—
191	C₄⋊C₈	—	2	1	no	—
192	C₄⋊C₈	—	2	1	no	—
193	C₄⋊C₈	—	2	1	no	—
194	C₄⋊C₈	—	2	1	no	—
195	C₄⋊C₈	—	2	1	no	—
196	C₄⋊C₈	—	2	1	no	—
197	C₄⋊C₈	—	2	1	no	—
198	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
199	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
200	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
201	#100	—	4	2	no	—
202	#100	—	4	2	no	—
203	C₂²⋊C₈	—	2	1	no	—
204	#97	—	2	1	no	—
205	C₄×C₈	—	2	1	no	—
206	C₄×C₈	—	2	1	no	—
207	C₂×C₁₃	—	2	1	no	—
208	C₂×C₁₃	—	2	1	no	—
209	C₂×C₁₃	—	16	2	no	—
210	C₂×C₁₃	#2063	1	1	yes	characteristic
211	C₂×C₁₃	#2065	1	1	yes	characteristic
212	C₂×C₁₃	#2069	1	1	yes	characteristic
213	C₂⁴	—	2	2	no	—
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	—	2	2	no	—
216	C₂×D₄	—	4	1	no	—
217	C₂×D₄	—	4	1	no	—
218	C₂×D₄	—	4	1	no	—
219	C₂×D₄	—	4	1	no	—
220	C₂×D₄	—	4	1	no	—
221	C₂×D₄	—	4	1	no	—
222	C₂×D₄	—	4	1	no	—
223	C₂×D₄	—	4	1	no	—
224	C₂×D₄	—	8	1	no	—
225	C₂×D₄	—	8	1	no	—
226	C₂×D₄	—	8	2	no	—
227	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
228	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
229	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
230	M₁₆	—	2	1	no	—
231	M₁₆	—	2	1	no	—
232	M₁₆	—	2	1	no	—
233	M₁₆	—	4	1	no	—
234	M₁₆	—	4	1	no	—
235	M₁₆	—	4	1	no	—
236	M₁₆	—	4	1	no	—
237	M₁₆	C₁₃×SD₁₆	1	2	yes	—
238	C₂×C₈	—	2	1	no	—
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	—	2	1	no	—
241	C₂×C₈	—	2	1	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	4	1	no	—
244	C₂×C₈	—	4	1	no	—
245	C₂×C₈	—	4	1	no	—
246	C₂×C₈	—	4	1	no	—
247	C₂×C₈	—	4	1	no	—
248	C₂×C₈	—	8	1	no	—
249	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
250	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
251	C₄²	C₁₃×#41	1	1	yes	characteristic
252	C₄²	C₁₃×#41	1	1	yes	characteristic
253	C₁₃	#10607	1	1	yes	characteristic, direct product factor, Sylow
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	4	2	no	—
257	C₂³	—	8	2	no	—
258	C₂³	—	8	2	no	—
259	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
260	D₄	—	8	2	no	—
261	D₄	—	8	2	no	—
262	D₄	—	8	2	no	—
263	D₄	—	8	1	no	—
264	D₄	—	8	1	no	—
265	D₄	—	8	1	no	—
266	D₄	—	8	1	no	—
267	D₄	—	8	1	no	—
268	D₄	—	8	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	4	1	no	—
272	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
273	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
274	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
275	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
277	C₂×C₄	C₁₃×#126	1	1	yes	characteristic
278	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
279	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
280	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₈	—	2	2	no	—
283	C₈	—	4	2	no	—
284	C₈	—	4	1	no	—
285	C₈	—	4	1	no	—
286	C₈	—	4	1	no	—
287	C₈	—	8	1	no	—
288	C₈	—	8	1	no	—
289	C₈	—	8	1	no	—
290	C₂²	—	2	1	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	8	2	no	—
293	C₂²	—	8	2	no	—
294	C₂²	—	8	2	no	—
295	C₂²	—	16	2	no	—
296	C₂²	—	16	2	no	—
297	C₂²	C₁₃×#396	1	1	yes	characteristic
298	C₂²	C₁₃×#476	1	1	yes	characteristic
299	C₂²	C₁₃×#478	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	1	no	—
303	C₄	C₁₃×#460	1	1	yes	characteristic
304	C₄	C₁₃×#463	1	1	yes	characteristic
305	C₄	C₁₃×#465	1	1	yes	characteristic
306	C₄	C₁₃×#469	1	1	yes	characteristic
307	C₄	C₁₃×#471	1	1	yes	characteristic
308	C₄	C₁₃×#472	1	1	yes	characteristic
309	C₂	—	2	1	no	—
310	C₂	—	2	1	no	—
311	C₂	—	16	2	no	—
312	C₂	C₁₃×#2063	1	1	yes	characteristic
313	C₂	C₁₃×#2065	1	1	yes	characteristic
314	C₂	C₁₃×#2069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×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
2. C₁₃×#1950	C₂	semidirect
3. C₁₃×#1570	C₂	semidirect
4. C₁₃×#1565	C₂	semidirect
7. C₁₃×#1292	C₂	semidirect
56. #10607	C₁₃	direct (N × H)
98. #1950	C₂×C₁₃	semidirect
99. #1570	C₂×C₁₃	semidirect
100. #1565	C₂×C₁₃	semidirect
103. #1292	C₂×C₁₃	semidirect
253. C₁₃	#10607	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×#1965	2
C₁₃×#1950	2
C₁₃×#1570	2
C₁₃×#1565	2
C₁₃×#1545	2
C₂×C₁₃×#331	2
C₁₃×#1292	2
#10607	13

Subgroups — C13×#10607 #15696946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10607 #15696946