Subgroups — C₁₃×#18673 #15705012

Order 3328.

872 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3518	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1633	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#556	—	2	1	no	—
18	C₁₃×#556	—	2	2	no	—
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#556	C₂²	1	1	yes	characteristic
21	C₁₃×#555	—	2	1	no	—
22	C₁₃×#555	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#548	—	2	1	no	—
25	C₁₃×#542	—	2	2	no	—
26	C₁₃×#542	—	2	1	no	—
27	C₁₃×#533	—	2	1	no	—
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#533	C₂²	1	1	yes	characteristic
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	C₂²	1	1	yes	characteristic
32	C₁₃×#519	—	2	1	no	—
33	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
34	C₁₃×#500	C₂²	1	1	yes	characteristic
35	C₁₃×#499	—	2	1	no	—
36	C₁₃×#494	C₂²	1	1	yes	characteristic
37	C₁₃×#488	—	2	1	no	—
38	C₁₃×#487	C₂²	1	1	yes	characteristic
39	C₁₃×#487	C₂²	1	1	yes	characteristic
40	C₁₃×#485	—	2	1	no	—
41	C₁₃×#485	—	2	1	no	—
42	C₁₃×#482	—	2	1	no	—
43	C₁₃×#477	C₂²	1	1	yes	characteristic
44	C₁₃×#477	C₂²	1	1	yes	characteristic
45	C₁₃×#476	C₂²	1	1	yes	characteristic
46	C₁₃×#476	C₂²	1	1	yes	characteristic
47	C₁₃×#475	C₂²	1	1	yes	characteristic
48	C₁₃×#474	C₂²	1	1	yes	characteristic
49	C₁₃×#467	—	2	2	no	—
50	C₁₃×#462	C₂²	1	1	yes	characteristic
51	C₁₃×#461	C₂²	1	1	yes	characteristic
52	C₁₃×#452	—	2	1	no	—
53	C₁₃×#441	—	2	1	no	—
54	C₁₃×#440	—	2	1	no	—
55	C₄×C₁₃×Q₁₆	—	2	2	no	—
56	C₁₃×#432	C₂²	1	1	yes	characteristic
57	C₁₃×#431	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#333	C₂²	1	1	yes	characteristic
61	C₁₃×#332	C₂²	1	1	yes	characteristic
62	C₁₃×#332	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	—	2	1	no	—
73	C₂×C₁₃×Q₁₆	—	2	2	no	—
74	C₂×C₁₃×Q₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×#126	—	2	2	no	—
86	C₁₃×#126	—	2	2	no	—
87	C₁₃×#126	—	2	2	no	—
88	C₁₃×#126	—	2	2	no	—
89	C₁₃×#126	—	2	1	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	D₄	1	1	yes	characteristic
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	—	2	2	no	—
95	C₁₃×#124	—	2	2	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	1	no	—
98	C₁₃×#124	D₄	1	1	yes	characteristic
99	C₁₃×#123	—	2	2	no	—
100	C₁₃×#123	—	2	1	no	—
101	C₁₃×C₂²⋊Q₈	—	2	2	no	—
102	C₁₃×C₂²⋊Q₈	—	2	2	no	—
103	C₁₃×C₂²⋊Q₈	—	2	1	no	—
104	C₁₃×C₂²⋊Q₈	—	2	1	no	—
105	C₁₃×C₂²⋊Q₈	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	—	2	1	no	—
108	C₁₃×C₂²⋊Q₈	—	2	1	no	—
109	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
110	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	1	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₁₃	—	2	2	no	—
116	C₄×Q₈×C₁₃	—	2	2	no	—
117	C₄×Q₈×C₁₃	—	2	2	no	—
118	C₄×Q₈×C₁₃	—	2	1	no	—
119	C₄×Q₈×C₁₃	—	2	1	no	—
120	C₄×Q₈×C₁₃	—	2	1	no	—
121	C₄×Q₈×C₁₃	—	2	1	no	—
122	C₄×Q₈×C₁₃	—	2	1	no	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	D₄	1	2	yes	—
125	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
126	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₁₃	—	2	2	no	—
129	C₄×D₄×C₁₃	—	2	1	no	—
130	C₄×D₄×C₁₃	—	2	1	no	—
131	C₄×D₄×C₁₃	—	2	1	no	—
132	C₄×D₄×C₁₃	—	2	1	no	—
133	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
134	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₁₃×#117	—	2	2	no	—
137	C₁₃×#117	—	2	2	no	—
138	C₁₃×#117	—	2	1	no	—
139	C₁₃×#117	—	2	1	no	—
140	C₁₃×#117	—	2	1	no	—
141	C₁₃×#117	—	2	1	no	—
142	C₁₃×#117	—	2	1	no	—
143	C₁₃×#117	—	2	1	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	—	2	1	no	—
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#107	—	2	2	no	—
149	C₁₃×#107	—	2	1	no	—
150	C₁₃×#107	—	2	1	no	—
151	C₁₃×#107	—	2	1	no	—
152	C₁₃×#106	—	2	1	no	—
153	C₁₃×#106	—	2	1	no	—
154	C₁₃×#106	—	2	1	no	—
155	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₃×#103	—	2	2	no	—
160	C₁₃×#103	—	2	1	no	—
161	C₁₃×#103	—	2	1	no	—
162	C₁₃×#103	—	2	1	no	—
163	C₁₃×#103	—	2	2	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#103	—	2	1	no	—
166	C₁₃×#102	—	2	1	no	—
167	C₁₃×#102	—	2	1	no	—
168	C₁₃×#102	—	2	1	no	—
169	C₁₃×C₂²⋊C₈	—	2	1	no	—
170	C₁₃×C₂²⋊C₈	—	2	1	no	—
171	C₁₃×#97	—	2	1	no	—
172	C₄×C₈×C₁₃	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	#18673	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃×#41	—	2	2	no	—
178	C₁₃×#41	—	4	1	no	—
179	C₂×Q₈×C₁₃	—	2	2	no	—
180	C₂×Q₈×C₁₃	—	2	2	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	4	2	no	—
185	C₂×Q₈×C₁₃	—	4	2	no	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₁₃×Q₁₆	—	4	4	no	—
203	C₁₃×Q₁₆	—	4	2	no	—
204	C₁₃×SD₁₆	—	4	2	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	4	2	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	4	1	no	—
232	C₁₃×C₄⋊C₄	—	4	1	no	—
233	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₁₃×C₂²⋊C₄	—	2	2	no	—
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	—	2	2	no	—
241	C₁₃×C₂²⋊C₄	—	2	2	no	—
242	C₁₃×C₂²⋊C₄	—	2	2	no	—
243	C₁₃×C₂²⋊C₄	—	2	2	no	—
244	C₁₃×C₂²⋊C₄	—	2	1	no	—
245	C₁₃×C₂²⋊C₄	—	2	1	no	—
246	C₁₃×C₂²⋊C₄	—	2	1	no	—
247	C₁₃×C₂²⋊C₄	—	2	1	no	—
248	C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₁₃×C₂²⋊C₄	—	2	1	no	—
250	C₁₃×C₂²⋊C₄	—	2	1	no	—
251	C₁₃×C₂²⋊C₄	—	2	1	no	—
252	C₁₃×C₂²⋊C₄	—	4	1	no	—
253	C₄²×C₁₃	—	2	2	no	—
254	C₄²×C₁₃	—	2	2	no	—
255	C₄²×C₁₃	—	2	2	no	—
256	C₄²×C₁₃	—	2	1	no	—
257	C₄²×C₁₃	—	2	1	no	—
258	C₄²×C₁₃	—	2	2	no	—
259	C₄²×C₁₃	—	2	1	no	—
260	C₄²×C₁₃	—	2	1	no	—
261	C₄²×C₁₃	—	4	1	no	—
262	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
266	#3518	C₂×C₁₃	1	1	yes	characteristic
267	#3233	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1650	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1649	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1646	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1645	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1637	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1634	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1633	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1554	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂³×C₁₃	—	2	1	no	—
282	C₂³×C₁₃	—	2	1	no	—
283	C₂³×C₁₃	#120	1	1	yes	characteristic
284	Q₈×C₁₃	—	2	1	no	—
285	Q₈×C₁₃	—	2	1	no	—
286	Q₈×C₁₃	—	2	1	no	—
287	Q₈×C₁₃	—	4	4	no	—
288	Q₈×C₁₃	—	4	2	no	—
289	Q₈×C₁₃	—	4	2	no	—
290	Q₈×C₁₃	—	4	1	no	—
291	Q₈×C₁₃	—	4	1	no	—
292	Q₈×C₁₃	—	4	1	no	—
293	Q₈×C₁₃	—	4	1	no	—
294	Q₈×C₁₃	—	8	2	no	—
295	Q₈×C₁₃	#135	1	2	yes	—
296	D₄×C₁₃	—	2	1	no	—
297	D₄×C₁₃	—	2	1	no	—
298	D₄×C₁₃	—	2	1	no	—
299	D₄×C₁₃	—	2	1	no	—
300	D₄×C₁₃	—	4	2	no	—
301	D₄×C₁₃	—	8	1	no	—
302	D₄×C₁₃	—	8	2	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	2	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	8	1	no	—
325	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
326	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
327	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
328	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	C₈×C₁₃	—	2	2	no	—
332	C₈×C₁₃	—	4	1	no	—
333	C₈×C₁₃	—	4	1	no	—
334	C₈×C₁₃	—	4	1	no	—
335	C₈×C₁₃	—	4	1	no	—
336	C₈×C₁₃	—	4	1	no	—
337	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
338	#556	—	2	1	no	—
339	#556	—	2	2	no	—
340	#556	—	2	1	no	—
341	#556	C₂²×C₁₃	1	1	yes	characteristic
342	#555	—	2	1	no	—
343	#555	C₂²×C₁₃	1	1	yes	characteristic
344	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
345	#548	—	2	1	no	—
346	#542	—	2	2	no	—
347	#542	—	2	1	no	—
348	#533	—	2	1	no	—
349	#533	C₂²×C₁₃	1	1	yes	characteristic
350	#533	C₂²×C₁₃	1	1	yes	characteristic
351	#529	—	2	1	no	—
352	#529	C₂²×C₁₃	1	1	yes	characteristic
353	#519	—	2	1	no	—
354	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
355	#500	C₂²×C₁₃	1	1	yes	characteristic
356	#499	—	2	1	no	—
357	#494	C₂²×C₁₃	1	1	yes	characteristic
358	#488	—	2	1	no	—
359	#487	C₂²×C₁₃	1	1	yes	characteristic
360	#487	C₂²×C₁₃	1	1	yes	characteristic
361	#485	—	2	1	no	—
362	#485	—	2	1	no	—
363	#482	—	2	1	no	—
364	#477	C₂²×C₁₃	1	1	yes	characteristic
365	#477	C₂²×C₁₃	1	1	yes	characteristic
366	#476	C₂²×C₁₃	1	1	yes	characteristic
367	#476	C₂²×C₁₃	1	1	yes	characteristic
368	#475	C₂²×C₁₃	1	1	yes	characteristic
369	#474	C₂²×C₁₃	1	1	yes	characteristic
370	#467	—	2	2	no	—
371	#462	C₂²×C₁₃	1	1	yes	characteristic
372	#461	C₂²×C₁₃	1	1	yes	characteristic
373	#452	—	2	1	no	—
374	#441	—	2	1	no	—
375	#440	—	2	1	no	—
376	C₄×Q₁₆	—	2	2	no	—
377	#432	C₂²×C₁₃	1	1	yes	characteristic
378	#431	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
380	#333	C₂²×C₁₃	1	1	yes	characteristic
381	#333	C₂²×C₁₃	1	1	yes	characteristic
382	#332	C₂²×C₁₃	1	1	yes	characteristic
383	#332	C₂²×C₁₃	1	1	yes	characteristic
384	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
385	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
386	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
387	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
388	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
389	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
391	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×C₁₃	—	2	1	no	—
393	C₂²×C₁₃	—	2	1	no	—
394	C₂²×C₁₃	—	2	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	1	no	—
397	C₂²×C₁₃	—	4	1	no	—
398	C₂²×C₁₃	—	4	1	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	1	no	—
401	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
402	C₄×C₁₃	—	2	1	no	—
403	C₄×C₁₃	—	2	2	no	—
404	C₄×C₁₃	—	2	1	no	—
405	C₄×C₁₃	—	2	1	no	—
406	C₄×C₁₃	—	2	1	no	—
407	C₄×C₁₃	—	4	2	no	—
408	C₄×C₁₃	—	4	1	no	—
409	C₄×C₁₃	—	4	1	no	—
410	C₄×C₁₃	—	4	1	no	—
411	C₄×C₁₃	—	4	1	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	1	no	—
414	C₄×C₁₃	—	8	1	no	—
415	C₄×C₁₃	—	8	1	no	—
416	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
417	C₄×C₁₃	#575	1	1	yes	characteristic
418	C₄×C₁₃	#578	1	1	yes	characteristic
419	C₄×C₁₃	#578	1	1	yes	characteristic
420	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
421	C₂²×Q₈	—	2	1	no	—
422	C₂×Q₁₆	—	2	2	no	—
423	C₂×Q₁₆	—	2	1	no	—
424	C₂×SD₁₆	—	2	1	no	—
425	C₂²×C₈	—	2	1	no	—
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	2	1	no	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
434	#126	—	2	2	no	—
435	#126	—	2	2	no	—
436	#126	—	2	2	no	—
437	#126	—	2	2	no	—
438	#126	—	2	1	no	—
439	#125	—	2	1	no	—
440	#125	—	2	1	no	—
441	#125	D₄×C₁₃	1	1	yes	characteristic
442	#124	—	2	2	no	—
443	#124	—	2	2	no	—
444	#124	—	2	2	no	—
445	#124	—	2	2	no	—
446	#124	—	2	1	no	—
447	#124	D₄×C₁₃	1	1	yes	characteristic
448	#123	—	2	2	no	—
449	#123	—	2	1	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	1	no	—
453	C₂²⋊Q₈	—	2	1	no	—
454	C₂²⋊Q₈	—	2	1	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
459	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
460	#121	—	2	2	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	D₄×C₁₃	1	1	yes	characteristic
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
474	C₄×Q₈	D₄×C₁₃	1	2	yes	—
475	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	1	no	—
479	C₄×D₄	—	2	1	no	—
480	C₄×D₄	—	2	1	no	—
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
483	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
485	#117	—	2	2	no	—
486	#117	—	2	2	no	—
487	#117	—	2	1	no	—
488	#117	—	2	1	no	—
489	#117	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	—	2	1	no	—
492	#117	—	2	1	no	—
493	#117	—	2	1	no	—
494	#117	D₄×C₁₃	1	1	yes	characteristic
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
497	#107	—	2	2	no	—
498	#107	—	2	1	no	—
499	#107	—	2	1	no	—
500	#107	—	2	1	no	—
501	#106	—	2	1	no	—
502	#106	—	2	1	no	—
503	#106	—	2	1	no	—
504	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
505	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
508	#103	—	2	2	no	—
509	#103	—	2	1	no	—
510	#103	—	2	1	no	—
511	#103	—	2	1	no	—
512	#103	—	2	2	no	—
513	#103	—	2	1	no	—
514	#103	—	2	1	no	—
515	#102	—	2	1	no	—
516	#102	—	2	1	no	—
517	#102	—	2	1	no	—
518	C₂²⋊C₈	—	2	1	no	—
519	C₂²⋊C₈	—	2	1	no	—
520	#97	—	2	1	no	—
521	C₄×C₈	—	2	1	no	—
522	C₄×C₈	—	2	1	no	—
523	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₂×C₁₃	—	4	1	no	—
526	C₂×C₁₃	—	8	1	no	—
527	C₂×C₁₃	—	8	1	no	—
528	C₂×C₁₃	#3002	1	1	yes	characteristic
529	C₂×C₁₃	#3011	1	1	yes	characteristic
530	C₂×C₁₃	#3018	1	1	yes	characteristic
531	#41	—	2	2	no	—
532	#41	—	4	1	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	Q₁₆	—	4	4	no	—
557	Q₁₆	—	4	2	no	—
558	SD₁₆	—	4	2	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	4	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	4	1	no	—
586	C₄⋊C₄	—	4	1	no	—
587	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
590	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
591	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	4	1	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	4	1	no	—
616	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
620	C₁₃	#18673	1	1	yes	characteristic, direct product factor, Sylow
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	C₁₃×#120	1	1	yes	characteristic
624	Q₈	—	2	1	no	—
625	Q₈	—	2	1	no	—
626	Q₈	—	2	1	no	—
627	Q₈	—	4	2	no	—
628	Q₈	—	4	4	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	8	2	no	—
635	Q₈	C₁₃×#135	1	2	yes	—
636	D₄	—	2	1	no	—
637	D₄	—	2	1	no	—
638	D₄	—	2	1	no	—
639	D₄	—	2	1	no	—
640	D₄	—	4	2	no	—
641	D₄	—	8	1	no	—
642	D₄	—	8	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	8	1	no	—
665	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
666	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
667	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	C₈	—	2	2	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
702	C₄	C₁₃×#575	1	1	yes	characteristic
703	C₄	C₁₃×#578	1	1	yes	characteristic
704	C₄	C₁₃×#578	1	1	yes	characteristic
705	C₂	—	4	1	no	—
706	C₂	—	8	1	no	—
707	C₂	—	8	1	no	—
708	C₂	C₁₃×#3002	1	1	yes	characteristic
709	C₂	C₁₃×#3011	1	1	yes	characteristic
710	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3518	C₂
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
2. C₁₃×#3233	C₂	semidirect
3. C₁₃×#3170	C₂	semidirect
4. C₁₃×#3116	C₂	semidirect
5. C₁₃×#1650	C₂	semidirect
6. C₁₃×#1649	C₂	semidirect
7. C₁₃×#1646	C₂	semidirect
8. C₁₃×#1645	C₂	semidirect
9. C₁₃×#1638	C₂	semidirect
10. C₁₃×#1637	C₂	semidirect
11. C₁₃×#1634	C₂	semidirect
12. C₁₃×#1633	C₂	semidirect
13. C₁₃×#1554	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1476	C₂	semidirect
176. #18673	C₁₃	direct (N × H)
267. #3233	C₂×C₁₃	semidirect
268. #3170	C₂×C₁₃	semidirect
269. #3116	C₂×C₁₃	semidirect
270. #1650	C₂×C₁₃	semidirect
271. #1649	C₂×C₁₃	semidirect
272. #1646	C₂×C₁₃	semidirect
273. #1645	C₂×C₁₃	semidirect
274. #1638	C₂×C₁₃	semidirect
275. #1637	C₂×C₁₃	semidirect
276. #1634	C₂×C₁₃	semidirect
277. #1633	C₂×C₁₃	semidirect
278. #1554	C₂×C₁₃	semidirect
279. #1494	C₂×C₁₃	semidirect
280. #1476	C₂×C₁₃	semidirect
620. C₁₃	#18673	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×#3518	2
C₁₃×#3233	2
C₁₃×#3170	2
C₁₃×#3116	2
C₁₃×#1650	2
C₁₃×#1649	2
C₁₃×#1646	2
C₁₃×#1645	2
C₁₃×#1638	2
C₁₃×#1637	2
C₁₃×#1634	2
C₁₃×#1633	2
C₁₃×#1554	2
C₁₃×#1494	2
C₁₃×#1476	2
#18673	13

Subgroups — C13×#18673 #15705012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18673 #15705012