Subgroups — C₁₃×#18671 #15705010

Order 3328.

928 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1642	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1636	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1553	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	C₁₃×#557	C₂²	1	1	yes	characteristic
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#553	—	2	1	no	—
19	C₁₃×#550	—	2	1	no	—
20	C₁₃×#550	—	2	1	no	—
21	C₁₃×#550	C₂²	1	1	yes	characteristic
22	C₁₃×#550	C₂²	1	1	yes	characteristic
23	C₁₃×#547	—	2	1	no	—
24	C₁₃×#547	C₂²	1	1	yes	characteristic
25	C₁₃×#540	—	2	2	no	—
26	C₁₃×#540	—	2	1	no	—
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#532	—	2	1	no	—
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	C₂²	1	1	yes	characteristic
32	C₁₃×#520	—	2	1	no	—
33	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
34	C₁₃×#499	—	2	1	no	—
35	C₁₃×#498	C₂²	1	1	yes	characteristic
36	C₁₃×#492	C₂²	1	1	yes	characteristic
37	C₁₃×#488	—	2	1	no	—
38	C₁₃×#487	C₂²	1	1	yes	characteristic
39	C₁₃×#486	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×#465	—	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×SD₁₆	—	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×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×#331	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	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	2	1	no	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
76	C₂×C₁₃×Q₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	2	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	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×#127	—	2	2	no	—
85	C₁₃×#127	—	2	1	no	—
86	C₁₃×#127	—	2	1	no	—
87	C₁₃×#127	C₂³	1	1	yes	characteristic
88	C₁₃×#126	—	2	2	no	—
89	C₁₃×#126	—	2	1	no	—
90	C₁₃×#125	—	2	2	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₁₃×#125	D₄	1	1	yes	characteristic
94	C₁₃×#124	—	2	1	no	—
95	C₁₃×#124	D₄	1	1	yes	characteristic
96	C₁₃×#123	—	2	2	no	—
97	C₁₃×#123	—	2	2	no	—
98	C₁₃×#123	—	2	2	no	—
99	C₁₃×#123	—	2	1	no	—
100	C₁₃×#123	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	—	2	1	no	—
102	C₁₃×C₂²⋊Q₈	—	2	1	no	—
103	C₁₃×C₂²⋊Q₈	—	2	1	no	—
104	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
105	C₁₃×#121	—	2	2	no	—
106	C₁₃×#121	—	2	2	no	—
107	C₁₃×#121	—	2	2	no	—
108	C₁₃×#121	—	2	2	no	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	1	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	2	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	—	2	1	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#121	D₄	1	2	yes	—
117	C₁₃×#121	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
123	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₄×D₄×C₁₃	—	2	2	no	—
126	C₄×D₄×C₁₃	—	2	2	no	—
127	C₄×D₄×C₁₃	—	2	2	no	—
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	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	D₄	1	2	yes	—
136	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
137	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₁₃×#117	—	2	2	no	—
140	C₁₃×#117	—	2	1	no	—
141	C₁₃×#117	—	2	1	no	—
142	C₁₃×#117	—	2	1	no	—
143	C₁₃×#117	D₄	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄²×C₁₃	—	2	1	no	—
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#107	—	2	1	no	—
149	C₁₃×#107	—	2	1	no	—
150	C₁₃×#107	—	2	1	no	—
151	C₁₃×#106	—	2	2	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	1	no	—
160	C₁₃×#103	—	2	1	no	—
161	C₁₃×#103	—	2	1	no	—
162	C₁₃×#103	—	2	2	no	—
163	C₁₃×#103	—	2	1	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#102	—	2	2	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	#18671	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃×#41	—	2	2	no	—
178	C₁₃×#41	—	4	1	no	—
179	C₁₃×#41	—	4	2	no	—
180	C₁₃×#41	—	4	2	no	—
181	C₁₃×#41	—	8	1	no	—
182	C₁₃×#41	—	8	1	no	—
183	C₁₃×#41	—	8	1	no	—
184	C₁₃×#41	—	8	1	no	—
185	C₁₃×#41	—	8	1	no	—
186	C₁₃×#41	—	8	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₁₃×Q₁₆	—	4	2	no	—
217	C₁₃×SD₁₆	—	4	4	no	—
218	C₁₃×SD₁₆	—	4	2	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	4	2	no	—
226	C₁₃×C₄⋊C₄	—	2	2	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	4	1	no	—
242	C₁₃×C₄⋊C₄	—	4	1	no	—
243	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
245	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
246	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	1	no	—
252	C₁₃×C₂²⋊C₄	—	2	1	no	—
253	C₁₃×C₂²⋊C₄	—	2	1	no	—
254	C₁₃×C₂²⋊C₄	—	2	1	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	2	1	no	—
257	C₁₃×C₂²⋊C₄	—	2	1	no	—
258	C₁₃×C₂²⋊C₄	—	2	2	no	—
259	C₁₃×C₂²⋊C₄	—	2	1	no	—
260	C₁₃×C₂²⋊C₄	—	2	1	no	—
261	C₁₃×C₂²⋊C₄	—	4	1	no	—
262	C₄²×C₁₃	—	2	2	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	2	1	no	—
266	C₄²×C₁₃	—	2	1	no	—
267	C₄²×C₁₃	—	4	1	no	—
268	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
272	#3517	C₂×C₁₃	1	1	yes	characteristic
273	#3233	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1654	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1642	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1636	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1635	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1553	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂³×C₁₃	—	2	1	no	—
288	C₂³×C₁₃	—	2	1	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	#120	1	1	yes	characteristic
291	Q₈×C₁₃	—	2	1	no	—
292	Q₈×C₁₃	—	2	1	no	—
293	Q₈×C₁₃	—	2	1	no	—
294	Q₈×C₁₃	—	4	2	no	—
295	Q₈×C₁₃	—	4	1	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	4	1	no	—
299	Q₈×C₁₃	#135	1	2	yes	—
300	D₄×C₁₃	—	2	1	no	—
301	D₄×C₁₃	—	2	1	no	—
302	D₄×C₁₃	—	2	1	no	—
303	D₄×C₁₃	—	2	1	no	—
304	D₄×C₁₃	—	4	2	no	—
305	D₄×C₁₃	—	4	4	no	—
306	D₄×C₁₃	—	4	2	no	—
307	D₄×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	8	1	no	—
312	D₄×C₁₃	—	8	2	no	—
313	D₄×C₁₃	—	8	2	no	—
314	D₄×C₁₃	—	8	2	no	—
315	D₄×C₁₃	—	8	2	no	—
316	D₄×C₁₃	—	8	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	2	no	—
330	C₂×C₄×C₁₃	—	4	4	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	8	1	no	—
338	C₂×C₄×C₁₃	—	8	2	no	—
339	C₂×C₄×C₁₃	—	8	2	no	—
340	C₂×C₄×C₁₃	—	8	2	no	—
341	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
342	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
343	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₈×C₁₃	—	2	2	no	—
348	C₈×C₁₃	—	4	1	no	—
349	C₈×C₁₃	—	4	1	no	—
350	C₈×C₁₃	—	4	1	no	—
351	C₈×C₁₃	—	4	1	no	—
352	C₈×C₁₃	—	4	1	no	—
353	#557	C₂²×C₁₃	1	1	yes	characteristic
354	#553	—	2	2	no	—
355	#553	—	2	1	no	—
356	#550	—	2	1	no	—
357	#550	—	2	1	no	—
358	#550	C₂²×C₁₃	1	1	yes	characteristic
359	#550	C₂²×C₁₃	1	1	yes	characteristic
360	#547	—	2	1	no	—
361	#547	C₂²×C₁₃	1	1	yes	characteristic
362	#540	—	2	2	no	—
363	#540	—	2	1	no	—
364	#533	C₂²×C₁₃	1	1	yes	characteristic
365	#532	—	2	1	no	—
366	#532	C₂²×C₁₃	1	1	yes	characteristic
367	#529	—	2	1	no	—
368	#529	C₂²×C₁₃	1	1	yes	characteristic
369	#520	—	2	1	no	—
370	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
371	#499	—	2	1	no	—
372	#498	C₂²×C₁₃	1	1	yes	characteristic
373	#492	C₂²×C₁₃	1	1	yes	characteristic
374	#488	—	2	1	no	—
375	#487	C₂²×C₁₃	1	1	yes	characteristic
376	#486	C₂²×C₁₃	1	1	yes	characteristic
377	#485	—	2	1	no	—
378	#485	—	2	1	no	—
379	#482	—	2	1	no	—
380	#477	C₂²×C₁₃	1	1	yes	characteristic
381	#477	C₂²×C₁₃	1	1	yes	characteristic
382	#476	C₂²×C₁₃	1	1	yes	characteristic
383	#476	C₂²×C₁₃	1	1	yes	characteristic
384	#475	C₂²×C₁₃	1	1	yes	characteristic
385	#474	C₂²×C₁₃	1	1	yes	characteristic
386	#465	—	2	2	no	—
387	#462	C₂²×C₁₃	1	1	yes	characteristic
388	#461	C₂²×C₁₃	1	1	yes	characteristic
389	#452	—	2	1	no	—
390	#441	—	2	1	no	—
391	#440	—	2	1	no	—
392	C₄×SD₁₆	—	2	2	no	—
393	#432	C₂²×C₁₃	1	1	yes	characteristic
394	#431	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
396	#332	C₂²×C₁₃	1	1	yes	characteristic
397	#332	C₂²×C₁₃	1	1	yes	characteristic
398	#331	C₂²×C₁₃	1	1	yes	characteristic
399	#331	C₂²×C₁₃	1	1	yes	characteristic
400	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
401	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
402	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
403	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
404	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
405	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
406	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
407	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₁₃	—	2	1	no	—
409	C₂²×C₁₃	—	2	1	no	—
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	4	1	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	1	no	—
414	C₂²×C₁₃	—	4	1	no	—
415	C₂²×C₁₃	—	4	1	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	1	no	—
418	C₂²×C₁₃	—	4	2	no	—
419	C₂²×C₁₃	—	4	1	no	—
420	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
421	C₄×C₁₃	—	2	1	no	—
422	C₄×C₁₃	—	2	2	no	—
423	C₄×C₁₃	—	2	1	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	4	1	no	—
427	C₄×C₁₃	—	4	1	no	—
428	C₄×C₁₃	—	4	1	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	—	4	1	no	—
431	C₄×C₁₃	—	4	1	no	—
432	C₄×C₁₃	—	8	1	no	—
433	C₄×C₁₃	—	8	1	no	—
434	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
435	C₄×C₁₃	#575	1	1	yes	characteristic
436	C₄×C₁₃	#577	1	1	yes	characteristic
437	C₄×C₁₃	#577	1	1	yes	characteristic
438	C₂×#41	—	2	1	no	—
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
443	C₂×Q₁₆	—	2	1	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	2	1	no	—
446	C₂²×C₈	—	2	1	no	—
447	C₄⋊Q₈	—	2	1	no	—
448	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
451	#127	—	2	2	no	—
452	#127	—	2	1	no	—
453	#127	—	2	1	no	—
454	#127	C₂³×C₁₃	1	1	yes	characteristic
455	#126	—	2	2	no	—
456	#126	—	2	1	no	—
457	#125	—	2	2	no	—
458	#125	—	2	1	no	—
459	#125	—	2	1	no	—
460	#125	D₄×C₁₃	1	1	yes	characteristic
461	#124	—	2	1	no	—
462	#124	D₄×C₁₃	1	1	yes	characteristic
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	#123	—	2	2	no	—
466	#123	—	2	1	no	—
467	#123	—	2	2	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	1	no	—
478	#121	—	2	2	no	—
479	#121	—	2	2	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	—	2	1	no	—
483	#121	D₄×C₁₃	1	1	yes	characteristic
484	#121	D₄×C₁₃	1	2	yes	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
490	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	—	2	1	no	—
498	C₄×D₄	—	2	1	no	—
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
503	C₄×D₄	D₄×C₁₃	1	2	yes	—
504	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
506	#117	—	2	2	no	—
507	#117	—	2	1	no	—
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	—	2	2	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
515	#107	—	2	1	no	—
516	#107	—	2	1	no	—
517	#107	—	2	1	no	—
518	#106	—	2	2	no	—
519	#106	—	2	1	no	—
520	#106	—	2	1	no	—
521	#106	—	2	1	no	—
522	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
526	#103	—	2	1	no	—
527	#103	—	2	1	no	—
528	#103	—	2	1	no	—
529	#103	—	2	2	no	—
530	#103	—	2	1	no	—
531	#103	—	2	1	no	—
532	#102	—	2	2	no	—
533	#102	—	2	1	no	—
534	#102	—	2	1	no	—
535	#102	—	2	1	no	—
536	C₂²⋊C₈	—	2	1	no	—
537	C₂²⋊C₈	—	2	1	no	—
538	#97	—	2	1	no	—
539	C₄×C₈	—	2	1	no	—
540	C₄×C₈	—	2	1	no	—
541	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₁₃	—	4	1	no	—
544	C₂×C₁₃	—	8	1	no	—
545	C₂×C₁₃	—	8	1	no	—
546	C₂×C₁₃	—	8	2	no	—
547	C₂×C₁₃	#3002	1	1	yes	characteristic
548	C₂×C₁₃	#3009	1	1	yes	characteristic
549	C₂×C₁₃	#3018	1	1	yes	characteristic
550	#41	—	2	2	no	—
551	#41	—	4	1	no	—
552	#41	—	4	2	no	—
553	#41	—	4	2	no	—
554	#41	—	8	1	no	—
555	#41	—	8	1	no	—
556	#41	—	8	1	no	—
557	#41	—	8	1	no	—
558	#41	—	8	1	no	—
559	#41	—	8	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	Q₁₆	—	4	2	no	—
590	SD₁₆	—	4	4	no	—
591	SD₁₆	—	4	2	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	4	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	4	1	no	—
615	C₄⋊C₄	—	4	1	no	—
616	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	4	1	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	4	1	no	—
641	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
645	C₁₃	#18671	1	1	yes	characteristic, direct product factor, Sylow
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	2	no	—
649	C₂³	C₁₃×#120	1	1	yes	characteristic
650	Q₈	—	2	1	no	—
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	C₁₃×#135	1	2	yes	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	2	1	no	—
662	D₄	—	2	1	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	8	1	no	—
671	D₄	—	8	2	no	—
672	D₄	—	8	2	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	8	1	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
701	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
702	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₈	—	4	1	no	—
711	C₈	—	4	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	1	no	—
724	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	8	1	no	—
737	C₄	—	8	1	no	—
738	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
739	C₄	C₁₃×#575	1	1	yes	characteristic
740	C₄	C₁₃×#577	1	1	yes	characteristic
741	C₄	C₁₃×#577	1	1	yes	characteristic
742	C₂	—	4	1	no	—
743	C₂	—	8	1	no	—
744	C₂	—	8	1	no	—
745	C₂	—	8	2	no	—
746	C₂	C₁₃×#3002	1	1	yes	characteristic
747	C₂	C₁₃×#3009	1	1	yes	characteristic
748	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×#3517	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×#3167	C₂	semidirect
4. C₁₃×#3116	C₂	semidirect
5. C₁₃×#1654	C₂	semidirect
6. C₁₃×#1653	C₂	semidirect
7. C₁₃×#1642	C₂	semidirect
8. C₁₃×#1641	C₂	semidirect
9. C₁₃×#1636	C₂	semidirect
10. C₁₃×#1635	C₂	semidirect
11. C₁₃×#1631	C₂	semidirect
12. C₁₃×#1631	C₂	semidirect
13. C₁₃×#1553	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1476	C₂	semidirect
176. #18671	C₁₃	direct (N × H)
273. #3233	C₂×C₁₃	semidirect
274. #3167	C₂×C₁₃	semidirect
275. #3116	C₂×C₁₃	semidirect
276. #1654	C₂×C₁₃	semidirect
277. #1653	C₂×C₁₃	semidirect
278. #1642	C₂×C₁₃	semidirect
279. #1641	C₂×C₁₃	semidirect
280. #1636	C₂×C₁₃	semidirect
281. #1635	C₂×C₁₃	semidirect
282. #1631	C₂×C₁₃	semidirect
283. #1631	C₂×C₁₃	semidirect
284. #1553	C₂×C₁₃	semidirect
285. #1494	C₂×C₁₃	semidirect
286. #1476	C₂×C₁₃	semidirect
645. C₁₃	#18671	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×#3517	2
C₁₃×#3233	2
C₁₃×#3167	2
C₁₃×#3116	2
C₁₃×#1654	2
C₁₃×#1653	2
C₁₃×#1642	2
C₁₃×#1641	2
C₁₃×#1636	2
C₁₃×#1635	2
C₁₃×#1631	2
C₁₃×#1553	2
C₁₃×#1494	2
C₁₃×#1476	2
#18671	13

Subgroups — C13×#18671 #15705010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18671 #15705010