Subgroups — C₁₃×#18670 #15705009

Order 3328.

962 conjugacy classes of subgroups.

The subgroup lattice has 780 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, complemented
2	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1648	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1647	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×#1626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1621	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×#532	—	2	1	no	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
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×#500	C₂²	1	1	yes	characteristic
35	C₁₃×#495	—	2	1	no	—
36	C₁₃×#493	C₂²	1	1	yes	characteristic
37	C₁₃×#488	—	2	1	no	—
38	C₁₃×#486	C₂²	1	1	yes	characteristic
39	C₁₃×#486	C₂²	1	1	yes	characteristic
40	C₁₃×#482	—	2	1	no	—
41	C₁₃×#475	C₂²	1	1	yes	characteristic
42	C₁₃×#474	C₂²	1	1	yes	characteristic
43	C₁₃×#466	—	2	2	no	—
44	C₁₃×#462	C₂²	1	1	yes	characteristic
45	C₁₃×#461	C₂²	1	1	yes	characteristic
46	C₁₃×#460	C₂²	1	1	yes	characteristic
47	C₁₃×#460	C₂²	1	1	yes	characteristic
48	C₁₃×#459	C₂²	1	1	yes	characteristic
49	C₁₃×#459	C₂²	1	1	yes	characteristic
50	C₁₃×#452	—	2	1	no	—
51	C₁₃×#449	—	2	1	no	—
52	C₁₃×#449	—	2	1	no	—
53	C₁₃×#442	—	2	1	no	—
54	C₁₃×#440	—	2	1	no	—
55	C₄×C₁₃×D₈	—	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	—	2	1	no	—
76	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
77	C₂×C₁₃×Q₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	1	no	—
81	C₂×C₁₃×D₈	—	2	2	no	—
82	C₂×C₁₃×D₈	—	2	1	no	—
83	C₂×C₁₃×D₈	—	2	1	no	—
84	C₂²×C₈×C₁₃	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₃×#127	—	2	2	no	—
89	C₁₃×#127	—	2	1	no	—
90	C₁₃×#127	—	2	1	no	—
91	C₁₃×#127	C₂³	1	1	yes	characteristic
92	C₁₃×#127	C₂³	1	1	yes	characteristic
93	C₁₃×#126	—	2	2	no	—
94	C₁₃×#126	—	2	1	no	—
95	C₁₃×#125	—	2	2	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×#125	D₄	1	1	yes	characteristic
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	—	2	1	no	—
100	C₁₃×#124	D₄	1	1	yes	characteristic
101	C₁₃×#123	—	2	2	no	—
102	C₁₃×#123	—	2	2	no	—
103	C₁₃×#123	—	2	2	no	—
104	C₁₃×#123	—	2	1	no	—
105	C₁₃×#123	—	2	2	no	—
106	C₁₃×C₂²⋊Q₈	—	2	1	no	—
107	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
108	C₁₃×#121	—	2	2	no	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	2	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	2	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	—	2	1	no	—
118	C₁₃×#121	—	2	1	no	—
119	C₁₃×#121	—	2	1	no	—
120	C₁₃×#121	—	2	1	no	—
121	C₁₃×#121	D₄	1	1	yes	characteristic
122	C₁₃×#121	D₄	1	2	yes	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
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	2	no	—
130	C₄×D₄×C₁₃	—	2	2	no	—
131	C₄×D₄×C₁₃	—	2	2	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	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₄×D₄×C₁₃	—	2	1	no	—
138	C₄×D₄×C₁₃	—	2	1	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	D₄	1	2	yes	—
141	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
142	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×#117	—	2	2	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	D₄	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄²×C₁₃	—	2	1	no	—
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₁₃×#107	—	2	2	no	—
153	C₁₃×#107	—	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×#102	—	2	2	no	—
163	C₁₃×#102	—	2	1	no	—
164	C₁₃×#102	—	2	2	no	—
165	C₁₃×#102	—	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	#18670	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	C₁₃×#41	—	8	1	no	—
188	C₁₃×#41	—	8	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	1	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	2	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	2	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	4	1	no	—
207	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	4	1	no	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₁₃×Q₁₆	—	8	1	no	—
223	C₁₃×SD₁₆	—	4	2	no	—
224	C₁₃×SD₁₆	—	8	1	no	—
225	C₁₃×SD₁₆	—	8	1	no	—
226	C₁₃×D₈	—	4	4	no	—
227	C₁₃×D₈	—	4	2	no	—
228	C₁₃×D₈	—	8	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	4	2	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
251	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
254	C₁₃×C₂²⋊C₄	—	2	2	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	2	2	no	—
257	C₁₃×C₂²⋊C₄	—	2	1	no	—
258	C₁₃×C₂²⋊C₄	—	2	1	no	—
259	C₁₃×C₂²⋊C₄	—	2	1	no	—
260	C₁₃×C₂²⋊C₄	—	2	1	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	no	—
262	C₁₃×C₂²⋊C₄	—	2	1	no	—
263	C₁₃×C₂²⋊C₄	—	2	1	no	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	1	no	—
266	C₁₃×C₂²⋊C₄	—	2	1	no	—
267	C₁₃×C₂²⋊C₄	—	4	1	no	—
268	C₁₃×C₂²⋊C₄	—	4	1	no	—
269	C₄²×C₁₃	—	2	2	no	—
270	C₄²×C₁₃	—	2	1	no	—
271	C₄²×C₁₃	—	2	1	no	—
272	C₄²×C₁₃	—	2	1	no	—
273	C₄²×C₁₃	—	2	1	no	—
274	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
278	#3517	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1648	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1647	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1642	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1626	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1625	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1621	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1621	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1553	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	4	1	no	—
297	C₂³×C₁₃	#120	1	1	yes	characteristic
298	Q₈×C₁₃	—	2	1	no	—
299	Q₈×C₁₃	—	2	1	no	—
300	Q₈×C₁₃	—	2	1	no	—
301	Q₈×C₁₃	—	4	1	no	—
302	Q₈×C₁₃	—	4	1	no	—
303	Q₈×C₁₃	—	4	1	no	—
304	Q₈×C₁₃	—	4	1	no	—
305	Q₈×C₁₃	#135	1	2	yes	—
306	D₄×C₁₃	—	2	1	no	—
307	D₄×C₁₃	—	2	1	no	—
308	D₄×C₁₃	—	2	1	no	—
309	D₄×C₁₃	—	2	1	no	—
310	D₄×C₁₃	—	4	2	no	—
311	D₄×C₁₃	—	4	4	no	—
312	D₄×C₁₃	—	4	2	no	—
313	D₄×C₁₃	—	4	2	no	—
314	D₄×C₁₃	—	4	1	no	—
315	D₄×C₁₃	—	4	1	no	—
316	D₄×C₁₃	—	4	1	no	—
317	D₄×C₁₃	—	4	1	no	—
318	D₄×C₁₃	—	4	1	no	—
319	D₄×C₁₃	—	4	1	no	—
320	D₄×C₁₃	—	4	1	no	—
321	D₄×C₁₃	—	4	1	no	—
322	D₄×C₁₃	—	8	1	no	—
323	D₄×C₁₃	—	8	2	no	—
324	D₄×C₁₃	—	8	2	no	—
325	D₄×C₁₃	—	8	2	no	—
326	D₄×C₁₃	—	8	2	no	—
327	D₄×C₁₃	—	8	2	no	—
328	D₄×C₁₃	—	8	2	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	2	no	—
342	C₂×C₄×C₁₃	—	4	4	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	8	1	no	—
349	C₂×C₄×C₁₃	—	8	2	no	—
350	C₂×C₄×C₁₃	—	8	2	no	—
351	C₂×C₄×C₁₃	—	8	2	no	—
352	C₂×C₄×C₁₃	—	8	2	no	—
353	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
354	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
355	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₈×C₁₃	—	2	2	no	—
360	C₈×C₁₃	—	4	1	no	—
361	C₈×C₁₃	—	4	1	no	—
362	C₈×C₁₃	—	4	1	no	—
363	C₈×C₁₃	—	4	1	no	—
364	C₈×C₁₃	—	4	1	no	—
365	#557	C₂²×C₁₃	1	1	yes	characteristic
366	#553	—	2	2	no	—
367	#553	—	2	1	no	—
368	#550	—	2	1	no	—
369	#550	—	2	1	no	—
370	#550	C₂²×C₁₃	1	1	yes	characteristic
371	#550	C₂²×C₁₃	1	1	yes	characteristic
372	#547	—	2	1	no	—
373	#547	C₂²×C₁₃	1	1	yes	characteristic
374	#540	—	2	2	no	—
375	#540	—	2	1	no	—
376	#532	—	2	1	no	—
377	#532	C₂²×C₁₃	1	1	yes	characteristic
378	#532	C₂²×C₁₃	1	1	yes	characteristic
379	#529	—	2	1	no	—
380	#529	C₂²×C₁₃	1	1	yes	characteristic
381	#520	—	2	1	no	—
382	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
383	#500	C₂²×C₁₃	1	1	yes	characteristic
384	#495	—	2	1	no	—
385	#493	C₂²×C₁₃	1	1	yes	characteristic
386	#488	—	2	1	no	—
387	#486	C₂²×C₁₃	1	1	yes	characteristic
388	#486	C₂²×C₁₃	1	1	yes	characteristic
389	#482	—	2	1	no	—
390	#475	C₂²×C₁₃	1	1	yes	characteristic
391	#474	C₂²×C₁₃	1	1	yes	characteristic
392	#466	—	2	2	no	—
393	#462	C₂²×C₁₃	1	1	yes	characteristic
394	#461	C₂²×C₁₃	1	1	yes	characteristic
395	#460	C₂²×C₁₃	1	1	yes	characteristic
396	#460	C₂²×C₁₃	1	1	yes	characteristic
397	#459	C₂²×C₁₃	1	1	yes	characteristic
398	#459	C₂²×C₁₃	1	1	yes	characteristic
399	#452	—	2	1	no	—
400	#449	—	2	1	no	—
401	#449	—	2	1	no	—
402	#442	—	2	1	no	—
403	#440	—	2	1	no	—
404	C₄×D₈	—	2	2	no	—
405	#432	C₂²×C₁₃	1	1	yes	characteristic
406	#431	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
408	#332	C₂²×C₁₃	1	1	yes	characteristic
409	#332	C₂²×C₁₃	1	1	yes	characteristic
410	#331	C₂²×C₁₃	1	1	yes	characteristic
411	#331	C₂²×C₁₃	1	1	yes	characteristic
412	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
413	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
414	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
415	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
416	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
417	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
418	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
419	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×C₁₃	—	2	1	no	—
421	C₂²×C₁₃	—	2	1	no	—
422	C₂²×C₁₃	—	2	1	no	—
423	C₂²×C₁₃	—	4	1	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	1	no	—
427	C₂²×C₁₃	—	4	1	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	1	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	1	no	—
432	C₂²×C₁₃	—	8	1	no	—
433	C₂²×C₁₃	—	8	1	no	—
434	C₂²×C₁₃	—	8	1	no	—
435	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
436	C₄×C₁₃	—	2	1	no	—
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	1	no	—
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	1	no	—
441	C₄×C₁₃	—	4	1	no	—
442	C₄×C₁₃	—	4	1	no	—
443	C₄×C₁₃	—	4	1	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	1	no	—
446	C₄×C₁₃	—	4	1	no	—
447	C₄×C₁₃	—	8	1	no	—
448	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
449	C₄×C₁₃	#575	1	1	yes	characteristic
450	C₄×C₁₃	#576	1	1	yes	characteristic
451	C₄×C₁₃	#576	1	1	yes	characteristic
452	C₂×#41	—	2	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
458	C₂×Q₁₆	—	2	1	no	—
459	C₂×SD₁₆	—	2	1	no	—
460	C₂×SD₁₆	—	2	1	no	—
461	C₂×SD₁₆	—	2	1	no	—
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	1	no	—
464	C₂×D₈	—	2	1	no	—
465	C₂²×C₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
469	#127	—	2	2	no	—
470	#127	—	2	1	no	—
471	#127	—	2	1	no	—
472	#127	C₂³×C₁₃	1	1	yes	characteristic
473	#127	C₂³×C₁₃	1	1	yes	characteristic
474	#126	—	2	2	no	—
475	#126	—	2	1	no	—
476	#125	—	2	2	no	—
477	#125	—	2	1	no	—
478	#125	D₄×C₁₃	1	1	yes	characteristic
479	#124	—	2	1	no	—
480	#124	—	2	1	no	—
481	#124	D₄×C₁₃	1	1	yes	characteristic
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	1	no	—
486	#123	—	2	2	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	1	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	1	no	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	D₄×C₁₃	1	1	yes	characteristic
503	#121	D₄×C₁₃	1	2	yes	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
507	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
522	C₄×D₄	D₄×C₁₃	1	2	yes	—
523	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
525	#117	—	2	2	no	—
526	#117	—	2	1	no	—
527	#117	—	2	1	no	—
528	#117	D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
533	#107	—	2	2	no	—
534	#107	—	2	1	no	—
535	#106	—	2	1	no	—
536	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
537	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
540	#103	—	2	1	no	—
541	#103	—	2	1	no	—
542	#103	—	2	1	no	—
543	#102	—	2	2	no	—
544	#102	—	2	1	no	—
545	#102	—	2	2	no	—
546	#102	—	2	1	no	—
547	#102	—	2	1	no	—
548	#102	—	2	1	no	—
549	#102	—	2	1	no	—
550	C₂²⋊C₈	—	2	1	no	—
551	C₂²⋊C₈	—	2	1	no	—
552	#97	—	2	1	no	—
553	C₄×C₈	—	2	1	no	—
554	C₄×C₈	—	2	1	no	—
555	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₁₃	—	4	1	no	—
558	C₂×C₁₃	—	8	1	no	—
559	C₂×C₁₃	—	8	1	no	—
560	C₂×C₁₃	—	8	2	no	—
561	C₂×C₁₃	—	16	1	no	—
562	C₂×C₁₃	#3002	1	1	yes	characteristic
563	C₂×C₁₃	#3008	1	1	yes	characteristic
564	C₂×C₁₃	#3018	1	1	yes	characteristic
565	#41	—	2	2	no	—
566	#41	—	4	1	no	—
567	#41	—	4	2	no	—
568	#41	—	4	2	no	—
569	#41	—	8	1	no	—
570	#41	—	8	1	no	—
571	#41	—	8	1	no	—
572	#41	—	8	1	no	—
573	#41	—	8	1	no	—
574	#41	—	8	1	no	—
575	#41	—	8	1	no	—
576	#41	—	8	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	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	2	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
610	Q₁₆	—	8	1	no	—
611	SD₁₆	—	4	2	no	—
612	SD₁₆	—	8	1	no	—
613	SD₁₆	—	8	1	no	—
614	D₈	—	4	4	no	—
615	D₈	—	4	2	no	—
616	D₈	—	8	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	4	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	4	1	no	—
656	C₂²⋊C₄	—	4	1	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
665	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
666	C₁₃	#18670	1	1	yes	characteristic, direct product factor, Sylow
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	1	no	—
671	C₂³	C₁₃×#120	1	1	yes	characteristic
672	Q₈	—	2	1	no	—
673	Q₈	—	2	1	no	—
674	Q₈	—	2	1	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	C₁₃×#135	1	2	yes	—
680	D₄	—	2	1	no	—
681	D₄	—	2	1	no	—
682	D₄	—	2	1	no	—
683	D₄	—	2	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	8	1	no	—
697	D₄	—	8	2	no	—
698	D₄	—	8	2	no	—
699	D₄	—	8	2	no	—
700	D₄	—	8	2	no	—
701	D₄	—	8	2	no	—
702	D₄	—	8	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	—	8	2	no	—
724	C₂×C₄	—	8	2	no	—
725	C₂×C₄	—	8	2	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
728	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
729	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
733	C₈	—	2	2	no	—
734	C₈	—	4	1	no	—
735	C₈	—	4	1	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	1	no	—
766	C₄	—	8	1	no	—
767	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
768	C₄	C₁₃×#575	1	1	yes	characteristic
769	C₄	C₁₃×#576	1	1	yes	characteristic
770	C₄	C₁₃×#576	1	1	yes	characteristic
771	C₂	—	4	1	no	—
772	C₂	—	8	1	no	—
773	C₂	—	8	1	no	—
774	C₂	—	8	2	no	—
775	C₂	—	16	1	no	—
776	C₂	C₁₃×#3002	1	1	yes	characteristic
777	C₂	C₁₃×#3008	1	1	yes	characteristic
778	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
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. C₁₃×#3517	C₂	semidirect
2. C₁₃×#3212	C₂	semidirect
3. C₁₃×#3169	C₂	semidirect
4. C₁₃×#3115	C₂	semidirect
5. C₁₃×#1648	C₂	semidirect
6. C₁₃×#1647	C₂	semidirect
7. C₁₃×#1642	C₂	semidirect
8. C₁₃×#1641	C₂	semidirect
9. C₁₃×#1626	C₂	semidirect
10. C₁₃×#1625	C₂	semidirect
11. C₁₃×#1621	C₂	semidirect
12. C₁₃×#1621	C₂	semidirect
13. C₁₃×#1553	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1476	C₂	semidirect
176. #18670	C₁₃	direct (N × H)
278. #3517	C₂×C₁₃	semidirect
279. #3212	C₂×C₁₃	semidirect
280. #3169	C₂×C₁₃	semidirect
281. #3115	C₂×C₁₃	semidirect
282. #1648	C₂×C₁₃	semidirect
283. #1647	C₂×C₁₃	semidirect
284. #1642	C₂×C₁₃	semidirect
285. #1641	C₂×C₁₃	semidirect
286. #1626	C₂×C₁₃	semidirect
287. #1625	C₂×C₁₃	semidirect
288. #1621	C₂×C₁₃	semidirect
289. #1621	C₂×C₁₃	semidirect
290. #1553	C₂×C₁₃	semidirect
291. #1494	C₂×C₁₃	semidirect
292. #1476	C₂×C₁₃	semidirect
666. C₁₃	#18670	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×#3212	2
C₁₃×#3169	2
C₁₃×#3115	2
C₁₃×#1648	2
C₁₃×#1647	2
C₁₃×#1642	2
C₁₃×#1641	2
C₁₃×#1626	2
C₁₃×#1625	2
C₁₃×#1621	2
C₁₃×#1553	2
C₁₃×#1494	2
C₁₃×#1476	2
#18670	13

Subgroups — C13×#18670 #15705009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18670 #15705009