Subgroups — C₁₃×#18709 #15705048

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3554	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1642	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1636	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1630	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1557	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#562	—	2	2	no	—
17	C₁₃×#559	—	2	1	no	—
18	C₁₃×#559	C₂²	1	1	yes	characteristic
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#554	—	2	1	no	—
21	C₁₃×#550	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#548	—	2	1	no	—
24	C₁₃×#547	—	2	1	no	—
25	C₁₃×#542	—	2	1	no	—
26	C₁₃×#542	—	2	1	no	—
27	C₁₃×#540	—	2	1	no	—
28	C₁₃×#539	—	2	2	no	—
29	C₁₃×#536	—	2	1	no	—
30	C₁₃×#533	C₂²	1	1	yes	characteristic
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#501	—	2	1	no	—
35	C₁₃×#498	C₂²	1	1	yes	characteristic
36	C₁₃×#492	C₂²	1	1	yes	characteristic
37	C₁₃×#491	—	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×#479	—	2	1	no	—
43	C₁₃×#477	C₂²	1	1	yes	characteristic
44	C₁₃×#477	C₂²	1	1	yes	characteristic
45	C₁₃×#477	C₂²	1	1	yes	characteristic
46	C₁₃×#476	C₂²	1	1	yes	characteristic
47	C₁₃×#475	C₂²	1	1	yes	characteristic
48	C₁₃×#475	C₂²	1	1	yes	characteristic
49	C₁₃×#470	—	2	1	no	—
50	C₁₃×#468	—	2	1	no	—
51	C₁₃×#465	—	2	2	no	—
52	C₁₃×#464	—	2	1	no	—
53	C₁₃×#462	C₂²	1	1	yes	characteristic
54	C₁₃×#461	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×SD₁₆	—	2	2	no	—
56	C₁₃×#432	C₂²	1	1	yes	characteristic
57	C₁₃×#423	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₃×Q₈⋊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	C₂²×Q₈×C₁₃	—	2	1	no	—
74	C₂×C₁₃×Q₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
94	C₁₃×#125	D₄	1	1	yes	characteristic
95	C₁₃×#124	—	2	2	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	1	no	—
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	2	no	—
105	C₁₃×#123	—	2	2	no	—
106	C₁₃×#123	—	2	2	no	—
107	C₁₃×#123	—	2	1	no	—
108	C₁₃×C₂²⋊Q₈	—	2	2	no	—
109	C₁₃×C₂²⋊Q₈	—	2	2	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
119	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	1	no	—
124	C₁₃×#121	—	2	1	no	—
125	C₁₃×#121	D₄	1	2	yes	—
126	C₁₃×#121	D₄	1	1	yes	characteristic
127	C₄×Q₈×C₁₃	—	2	1	no	—
128	C₄×Q₈×C₁₃	—	2	1	no	—
129	C₄×Q₈×C₁₃	—	2	1	no	—
130	C₄×Q₈×C₁₃	—	2	1	no	—
131	C₄×Q₈×C₁₃	—	2	1	no	—
132	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₁₃	—	2	2	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	—	2	1	no	—
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	D₄	1	2	yes	—
143	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₁₃×#107	—	2	1	no	—
150	C₁₃×#107	—	2	1	no	—
151	C₁₃×#107	—	2	1	no	—
152	C₁₃×#106	—	2	2	no	—
153	C₁₃×#106	—	2	1	no	—
154	C₁₃×#106	—	2	1	no	—
155	C₁₃×#106	—	2	1	no	—
156	C₁₃×C₄⋊C₈	—	2	1	no	—
157	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₃×#103	—	2	1	no	—
162	C₁₃×#103	—	2	1	no	—
163	C₁₃×#103	—	2	1	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#103	—	2	1	no	—
166	C₁₃×#103	—	2	2	no	—
167	C₁₃×#103	—	2	1	no	—
168	C₁₃×#103	—	2	1	no	—
169	C₁₃×#102	—	2	2	no	—
170	C₁₃×#102	—	2	1	no	—
171	C₁₃×C₂²⋊C₈	—	2	1	no	—
172	C₁₃×#97	—	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	#18709	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃×#41	—	8	1	no	—
178	C₁₃×#41	—	8	1	no	—
179	C₁₃×#41	—	8	1	no	—
180	C₁₃×#41	—	8	1	no	—
181	C₂×Q₈×C₁₃	—	2	2	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	8	1	no	—
187	C₂×Q₈×C₁₃	—	8	1	no	—
188	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₁₃	—	2	2	no	—
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	1	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₁₃×Q₁₆	—	8	1	no	—
208	C₁₃×SD₁₆	—	4	4	no	—
209	C₁₃×SD₁₆	—	8	1	no	—
210	C₁₃×M₁₆	—	8	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	4	2	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	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	—	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	—	4	1	no	—
239	C₁₃×C₄⋊C₄	—	4	1	no	—
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₁₃×C₂²⋊C₄	—	2	2	no	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₁₃×C₂²⋊C₄	—	2	2	no	—
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	1	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	1	no	—
256	C₁₃×C₂²⋊C₄	—	2	2	no	—
257	C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₁₃×C₂²⋊C₄	—	2	1	no	—
259	C₁₃×C₂²⋊C₄	—	4	1	no	—
260	C₄²×C₁₃	—	2	2	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₄²×C₁₃	—	2	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	4	1	no	—
265	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
269	#3554	C₂×C₁₃	1	1	yes	characteristic
270	#3252	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1642	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1640	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1637	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1636	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1630	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1557	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	#120	1	1	yes	characteristic
287	Q₈×C₁₃	—	2	1	no	—
288	Q₈×C₁₃	—	2	1	no	—
289	Q₈×C₁₃	—	2	1	no	—
290	Q₈×C₁₃	—	2	1	no	—
291	Q₈×C₁₃	—	2	1	no	—
292	Q₈×C₁₃	—	2	1	no	—
293	Q₈×C₁₃	—	4	2	no	—
294	Q₈×C₁₃	—	4	1	no	—
295	Q₈×C₁₃	—	4	1	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	8	1	no	—
299	Q₈×C₁₃	—	8	2	no	—
300	D₄×C₁₃	—	2	1	no	—
301	D₄×C₁₃	—	2	1	no	—
302	D₄×C₁₃	—	4	2	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	4	1	no	—
306	D₄×C₁₃	—	4	1	no	—
307	D₄×C₁₃	—	8	1	no	—
308	D₄×C₁₃	—	8	2	no	—
309	D₄×C₁₃	—	8	2	no	—
310	D₄×C₁₃	—	8	2	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	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	2	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	8	2	no	—
329	C₂×C₄×C₁₃	—	8	2	no	—
330	C₂×C₄×C₁₃	—	8	2	no	—
331	C₂×C₄×C₁₃	—	8	2	no	—
332	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
333	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
334	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₈×C₁₃	—	2	2	no	—
339	C₈×C₁₃	—	4	1	no	—
340	C₈×C₁₃	—	4	1	no	—
341	C₈×C₁₃	—	4	1	no	—
342	C₈×C₁₃	—	4	1	no	—
343	C₈×C₁₃	—	4	1	no	—
344	#562	—	2	2	no	—
345	#559	—	2	1	no	—
346	#559	C₂²×C₁₃	1	1	yes	characteristic
347	#557	C₂²×C₁₃	1	1	yes	characteristic
348	#554	—	2	1	no	—
349	#550	C₂²×C₁₃	1	1	yes	characteristic
350	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
351	#548	—	2	1	no	—
352	#547	—	2	1	no	—
353	#542	—	2	1	no	—
354	#542	—	2	1	no	—
355	#540	—	2	1	no	—
356	#539	—	2	2	no	—
357	#536	—	2	1	no	—
358	#533	C₂²×C₁₃	1	1	yes	characteristic
359	#533	C₂²×C₁₃	1	1	yes	characteristic
360	#532	C₂²×C₁₃	1	1	yes	characteristic
361	#529	C₂²×C₁₃	1	1	yes	characteristic
362	#501	—	2	1	no	—
363	#498	C₂²×C₁₃	1	1	yes	characteristic
364	#492	C₂²×C₁₃	1	1	yes	characteristic
365	#491	—	2	1	no	—
366	#487	C₂²×C₁₃	1	1	yes	characteristic
367	#486	C₂²×C₁₃	1	1	yes	characteristic
368	#485	—	2	1	no	—
369	#485	—	2	1	no	—
370	#479	—	2	1	no	—
371	#477	C₂²×C₁₃	1	1	yes	characteristic
372	#477	C₂²×C₁₃	1	1	yes	characteristic
373	#477	C₂²×C₁₃	1	1	yes	characteristic
374	#476	C₂²×C₁₃	1	1	yes	characteristic
375	#475	C₂²×C₁₃	1	1	yes	characteristic
376	#475	C₂²×C₁₃	1	1	yes	characteristic
377	#470	—	2	1	no	—
378	#468	—	2	1	no	—
379	#465	—	2	2	no	—
380	#464	—	2	1	no	—
381	#462	C₂²×C₁₃	1	1	yes	characteristic
382	#461	C₂²×C₁₃	1	1	yes	characteristic
383	C₄×SD₁₆	—	2	2	no	—
384	#432	C₂²×C₁₃	1	1	yes	characteristic
385	#423	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
387	#332	C₂²×C₁₃	1	1	yes	characteristic
388	#332	C₂²×C₁₃	1	1	yes	characteristic
389	#331	C₂²×C₁₃	1	1	yes	characteristic
390	#331	C₂²×C₁₃	1	1	yes	characteristic
391	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
392	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
393	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
394	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
395	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
396	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
397	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
398	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×C₁₃	—	2	1	no	—
400	C₂²×C₁₃	—	2	1	no	—
401	C₂²×C₁₃	—	2	1	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	—	4	1	no	—
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	—	4	2	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
409	C₄×C₁₃	—	2	1	no	—
410	C₄×C₁₃	—	2	1	no	—
411	C₄×C₁₃	—	2	1	no	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	4	1	no	—
414	C₄×C₁₃	—	4	1	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	1	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	4	1	no	—
420	C₄×C₁₃	—	4	1	no	—
421	C₄×C₁₃	—	8	1	no	—
422	C₄×C₁₃	—	8	1	no	—
423	C₄×C₁₃	#577	1	1	yes	characteristic
424	C₄×C₁₃	#577	1	1	yes	characteristic
425	C₄×C₁₃	#577	1	1	yes	characteristic
426	C₄×C₁₃	#578	1	1	yes	characteristic
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂×Q₁₆	—	2	1	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₂²×C₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
438	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
439	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
442	#127	—	2	1	no	—
443	#127	C₂³×C₁₃	1	1	yes	characteristic
444	#126	—	2	2	no	—
445	#126	—	2	1	no	—
446	#125	—	2	2	no	—
447	#125	—	2	1	no	—
448	#125	—	2	1	no	—
449	#125	—	2	1	no	—
450	#125	D₄×C₁₃	1	1	yes	characteristic
451	#124	—	2	2	no	—
452	#124	—	2	2	no	—
453	#124	—	2	1	no	—
454	#124	—	2	1	no	—
455	#124	—	2	1	no	—
456	#124	D₄×C₁₃	1	1	yes	characteristic
457	#123	—	2	2	no	—
458	#123	—	2	2	no	—
459	#123	—	2	2	no	—
460	#123	—	2	2	no	—
461	#123	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	1	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
474	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
475	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	2	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	D₄×C₁₃	1	1	yes	characteristic
482	#121	D₄×C₁₃	1	2	yes	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	—	2	1	no	—
498	C₄×D₄	D₄×C₁₃	1	2	yes	—
499	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	#117	—	2	1	no	—
501	#117	—	2	1	no	—
502	#117	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
505	#107	—	2	1	no	—
506	#107	—	2	1	no	—
507	#107	—	2	1	no	—
508	#106	—	2	2	no	—
509	#106	—	2	1	no	—
510	#106	—	2	1	no	—
511	#106	—	2	1	no	—
512	C₄⋊C₈	—	2	1	no	—
513	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
517	#103	—	2	1	no	—
518	#103	—	2	1	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#103	—	2	2	no	—
523	#103	—	2	1	no	—
524	#103	—	2	1	no	—
525	#102	—	2	2	no	—
526	#102	—	2	1	no	—
527	C₂²⋊C₈	—	2	1	no	—
528	#97	—	2	1	no	—
529	C₄×C₈	—	2	1	no	—
530	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₁₃	—	4	1	no	—
533	C₂×C₁₃	—	8	1	no	—
534	C₂×C₁₃	—	8	2	no	—
535	C₂×C₁₃	#3009	1	1	yes	characteristic
536	C₂×C₁₃	#3013	1	1	yes	characteristic
537	C₂×C₁₃	#3018	1	1	yes	characteristic
538	#41	—	8	1	no	—
539	#41	—	8	1	no	—
540	#41	—	8	1	no	—
541	#41	—	8	1	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	8	1	no	—
548	C₂×Q₈	—	8	1	no	—
549	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
559	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
568	Q₁₆	—	8	1	no	—
569	SD₁₆	—	4	4	no	—
570	SD₁₆	—	8	1	no	—
571	M₁₆	—	8	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	4	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	4	1	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
603	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	4	1	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	4	1	no	—
626	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₁₃	#18709	1	1	yes	characteristic, direct product factor, Sylow
631	C₂³	—	2	1	no	—
632	C₂³	—	2	2	no	—
633	C₂³	C₁₃×#120	1	1	yes	characteristic
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	2	1	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	4	2	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	8	1	no	—
646	Q₈	—	8	2	no	—
647	D₄	—	2	1	no	—
648	D₄	—	2	1	no	—
649	D₄	—	4	2	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	8	1	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	2	no	—
657	D₄	—	8	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	8	2	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
680	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
681	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₁₃×#577	1	1	yes	characteristic
716	C₄	C₁₃×#577	1	1	yes	characteristic
717	C₄	C₁₃×#577	1	1	yes	characteristic
718	C₄	C₁₃×#578	1	1	yes	characteristic
719	C₂	—	4	1	no	—
720	C₂	—	8	1	no	—
721	C₂	—	8	2	no	—
722	C₂	C₁₃×#3009	1	1	yes	characteristic
723	C₂	C₁₃×#3013	1	1	yes	characteristic
724	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×#3554	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×#3252	C₂	semidirect
3. C₁₃×#3237	C₂	semidirect
4. C₁₃×#3167	C₂	semidirect
5. C₁₃×#1653	C₂	semidirect
6. C₁₃×#1651	C₂	semidirect
7. C₁₃×#1642	C₂	semidirect
8. C₁₃×#1640	C₂	semidirect
9. C₁₃×#1637	C₂	semidirect
10. C₁₃×#1636	C₂	semidirect
11. C₁₃×#1631	C₂	semidirect
12. C₁₃×#1630	C₂	semidirect
13. C₁₃×#1557	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1493	C₂	semidirect
176. #18709	C₁₃	direct (N × H)
270. #3252	C₂×C₁₃	semidirect
271. #3237	C₂×C₁₃	semidirect
272. #3167	C₂×C₁₃	semidirect
273. #1653	C₂×C₁₃	semidirect
274. #1651	C₂×C₁₃	semidirect
275. #1642	C₂×C₁₃	semidirect
276. #1640	C₂×C₁₃	semidirect
277. #1637	C₂×C₁₃	semidirect
278. #1636	C₂×C₁₃	semidirect
279. #1631	C₂×C₁₃	semidirect
280. #1630	C₂×C₁₃	semidirect
281. #1557	C₂×C₁₃	semidirect
282. #1494	C₂×C₁₃	semidirect
283. #1493	C₂×C₁₃	semidirect
630. C₁₃	#18709	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×#3554	2
C₁₃×#3252	2
C₁₃×#3237	2
C₁₃×#3167	2
C₁₃×#1653	2
C₁₃×#1651	2
C₁₃×#1642	2
C₁₃×#1640	2
C₁₃×#1637	2
C₁₃×#1636	2
C₁₃×#1631	2
C₁₃×#1630	2
C₁₃×#1557	2
C₁₃×#1494	2
C₁₃×#1493	2
#18709	13

Subgroups — C13×#18709 #15705048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18709 #15705048