Subgroups — C₁₃×#18672 #15705011

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 742 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, complemented
2	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1651	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×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1624	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1623	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×#532	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×#498	C₂²	1	1	yes	characteristic
35	C₁₃×#495	—	2	1	no	—
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×#482	—	2	1	no	—
41	C₁₃×#475	C₂²	1	1	yes	characteristic
42	C₁₃×#474	C₂²	1	1	yes	characteristic
43	C₁₃×#465	—	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×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×#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	—	2	1	no	—
72	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
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×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	1	no	—
80	C₂×C₁₃×D₈	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₃×#127	C₂³	1	1	yes	characteristic
90	C₁₃×#126	—	2	2	no	—
91	C₁₃×#126	—	2	2	no	—
92	C₁₃×#126	—	2	2	no	—
93	C₁₃×#126	—	2	2	no	—
94	C₁₃×#126	—	2	1	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	D₄	1	1	yes	characteristic
97	C₁₃×#124	—	2	2	no	—
98	C₁₃×#124	—	2	2	no	—
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	—	2	2	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	D₄	1	1	yes	characteristic
104	C₁₃×#123	—	2	2	no	—
105	C₁₃×#123	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	—	2	1	no	—
109	C₁₃×C₂²⋊Q₈	—	2	1	no	—
110	C₁₃×C₂²⋊Q₈	—	2	1	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	—	2	1	no	—
118	C₁₃×#121	—	2	1	no	—
119	C₁₃×#121	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	—	2	2	no	—
121	C₄×Q₈×C₁₃	—	2	2	no	—
122	C₄×Q₈×C₁₃	—	2	2	no	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
125	C₄×Q₈×C₁₃	—	2	1	no	—
126	C₄×Q₈×C₁₃	—	2	1	no	—
127	C₄×Q₈×C₁₃	D₄	1	2	yes	—
128	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
129	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
139	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	—	2	2	no	—
143	C₁₃×#117	—	2	1	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	—	2	1	no	—
149	C₁₃×#117	D₄	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	—	2	1	no	—
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₁₃×#107	—	2	1	no	—
153	C₁₃×#106	—	2	2	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×#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	#18672	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	—	8	1	no	—
180	C₁₃×#41	—	8	1	no	—
181	C₂×Q₈×C₁₃	—	2	2	no	—
182	C₂×Q₈×C₁₃	—	2	2	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	4	2	no	—
186	C₂×Q₈×C₁₃	—	4	2	no	—
187	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	4	1	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	4	1	no	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₁₃×Q₁₆	—	8	1	no	—
209	C₁₃×SD₁₆	—	4	4	no	—
210	C₁₃×SD₁₆	—	4	2	no	—
211	C₁₃×SD₁₆	—	8	1	no	—
212	C₁₃×SD₁₆	—	8	1	no	—
213	C₁₃×D₈	—	4	2	no	—
214	C₁₃×D₈	—	8	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	4	2	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
243	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
257	C₁₃×C₂²⋊C₄	—	2	1	no	—
258	C₁₃×C₂²⋊C₄	—	4	1	no	—
259	C₁₃×C₂²⋊C₄	—	4	1	no	—
260	C₄²×C₁₃	—	2	2	no	—
261	C₄²×C₁₃	—	2	2	no	—
262	C₄²×C₁₃	—	2	2	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	2	2	no	—
266	C₄²×C₁₃	—	2	1	no	—
267	C₄²×C₁₃	—	2	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	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1646	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1645	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1628	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1627	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1624	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1623	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1554	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	—	4	1	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	4	no	—
295	Q₈×C₁₃	—	4	2	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	4	1	no	—
299	Q₈×C₁₃	—	4	1	no	—
300	Q₈×C₁₃	—	8	2	no	—
301	Q₈×C₁₃	#135	1	2	yes	—
302	D₄×C₁₃	—	2	1	no	—
303	D₄×C₁₃	—	2	1	no	—
304	D₄×C₁₃	—	2	1	no	—
305	D₄×C₁₃	—	2	1	no	—
306	D₄×C₁₃	—	4	2	no	—
307	D₄×C₁₃	—	4	2	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	8	1	no	—
313	D₄×C₁₃	—	8	2	no	—
314	D₄×C₁₃	—	8	2	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	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	2	no	—
329	C₂×C₄×C₁₃	—	4	4	no	—
330	C₂×C₄×C₁₃	—	4	1	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	—	8	1	no	—
336	C₂×C₄×C₁₃	—	8	2	no	—
337	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
338	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
339	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₈×C₁₃	—	2	2	no	—
344	C₈×C₁₃	—	4	1	no	—
345	C₈×C₁₃	—	4	1	no	—
346	C₈×C₁₃	—	4	1	no	—
347	C₈×C₁₃	—	4	1	no	—
348	C₈×C₁₃	—	4	1	no	—
349	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
350	#556	—	2	1	no	—
351	#556	—	2	2	no	—
352	#556	—	2	1	no	—
353	#556	C₂²×C₁₃	1	1	yes	characteristic
354	#555	—	2	1	no	—
355	#555	C₂²×C₁₃	1	1	yes	characteristic
356	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
357	#548	—	2	1	no	—
358	#542	—	2	2	no	—
359	#542	—	2	1	no	—
360	#533	—	2	1	no	—
361	#533	C₂²×C₁₃	1	1	yes	characteristic
362	#532	C₂²×C₁₃	1	1	yes	characteristic
363	#529	—	2	1	no	—
364	#529	C₂²×C₁₃	1	1	yes	characteristic
365	#519	—	2	1	no	—
366	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
367	#498	C₂²×C₁₃	1	1	yes	characteristic
368	#495	—	2	1	no	—
369	#492	C₂²×C₁₃	1	1	yes	characteristic
370	#488	—	2	1	no	—
371	#487	C₂²×C₁₃	1	1	yes	characteristic
372	#486	C₂²×C₁₃	1	1	yes	characteristic
373	#482	—	2	1	no	—
374	#475	C₂²×C₁₃	1	1	yes	characteristic
375	#474	C₂²×C₁₃	1	1	yes	characteristic
376	#465	—	2	2	no	—
377	#462	C₂²×C₁₃	1	1	yes	characteristic
378	#461	C₂²×C₁₃	1	1	yes	characteristic
379	#460	C₂²×C₁₃	1	1	yes	characteristic
380	#460	C₂²×C₁₃	1	1	yes	characteristic
381	#459	C₂²×C₁₃	1	1	yes	characteristic
382	#459	C₂²×C₁₃	1	1	yes	characteristic
383	#452	—	2	1	no	—
384	#449	—	2	1	no	—
385	#449	—	2	1	no	—
386	#442	—	2	1	no	—
387	#440	—	2	1	no	—
388	C₄×SD₁₆	—	2	2	no	—
389	#432	C₂²×C₁₃	1	1	yes	characteristic
390	#431	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
392	#333	C₂²×C₁₃	1	1	yes	characteristic
393	#333	C₂²×C₁₃	1	1	yes	characteristic
394	#332	C₂²×C₁₃	1	1	yes	characteristic
395	#332	C₂²×C₁₃	1	1	yes	characteristic
396	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
397	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
398	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
399	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
400	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
401	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
402	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
403	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂²×C₁₃	—	2	1	no	—
405	C₂²×C₁₃	—	2	1	no	—
406	C₂²×C₁₃	—	2	1	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	—	4	1	no	—
409	C₂²×C₁₃	—	4	1	no	—
410	C₂²×C₁₃	—	4	1	no	—
411	C₂²×C₁₃	—	4	1	no	—
412	C₂²×C₁₃	—	4	1	no	—
413	C₂²×C₁₃	—	8	1	no	—
414	C₂²×C₁₃	—	8	1	no	—
415	C₂²×C₁₃	—	8	1	no	—
416	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
417	C₄×C₁₃	—	2	1	no	—
418	C₄×C₁₃	—	2	2	no	—
419	C₄×C₁₃	—	2	1	no	—
420	C₄×C₁₃	—	2	1	no	—
421	C₄×C₁₃	—	2	1	no	—
422	C₄×C₁₃	—	4	2	no	—
423	C₄×C₁₃	—	4	1	no	—
424	C₄×C₁₃	—	4	1	no	—
425	C₄×C₁₃	—	4	1	no	—
426	C₄×C₁₃	—	4	1	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	1	no	—
429	C₄×C₁₃	—	8	1	no	—
430	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
431	C₄×C₁₃	#575	1	1	yes	characteristic
432	C₄×C₁₃	#577	1	1	yes	characteristic
433	C₄×C₁₃	#577	1	1	yes	characteristic
434	C₂×#41	—	2	1	no	—
435	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
436	C₂²×Q₈	—	2	1	no	—
437	C₂×Q₁₆	—	2	1	no	—
438	C₂×SD₁₆	—	2	2	no	—
439	C₂×SD₁₆	—	2	1	no	—
440	C₂×SD₁₆	—	2	1	no	—
441	C₂×SD₁₆	—	2	1	no	—
442	C₂×D₈	—	2	1	no	—
443	C₂×D₈	—	2	1	no	—
444	C₂²×C₈	—	2	1	no	—
445	C₄⋊Q₈	—	2	2	no	—
446	C₄⋊Q₈	—	2	1	no	—
447	C₄⋊Q₈	—	2	1	no	—
448	C₄⋊Q₈	—	2	1	no	—
449	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
451	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
452	#127	C₂³×C₁₃	1	1	yes	characteristic
453	#126	—	2	2	no	—
454	#126	—	2	2	no	—
455	#126	—	2	2	no	—
456	#126	—	2	2	no	—
457	#126	—	2	1	no	—
458	#125	—	2	1	no	—
459	#125	D₄×C₁₃	1	1	yes	characteristic
460	#124	—	2	2	no	—
461	#124	—	2	2	no	—
462	#124	—	2	2	no	—
463	#124	—	2	2	no	—
464	#124	—	2	1	no	—
465	#124	—	2	1	no	—
466	#124	D₄×C₁₃	1	1	yes	characteristic
467	#123	—	2	2	no	—
468	#123	—	2	1	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
476	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
477	#121	—	2	2	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	D₄×C₁₃	1	1	yes	characteristic
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
491	C₄×Q₈	D₄×C₁₃	1	2	yes	—
492	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	1	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	D₄×C₁₃	1	1	yes	characteristic
502	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
504	#117	—	2	2	no	—
505	#117	—	2	2	no	—
506	#117	—	2	1	no	—
507	#117	—	2	1	no	—
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	D₄×C₁₃	1	1	yes	characteristic
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
515	#107	—	2	1	no	—
516	#106	—	2	2	no	—
517	#106	—	2	1	no	—
518	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
522	#103	—	2	2	no	—
523	#103	—	2	1	no	—
524	#103	—	2	1	no	—
525	#103	—	2	1	no	—
526	#102	—	2	1	no	—
527	#102	—	2	2	no	—
528	#102	—	2	1	no	—
529	#102	—	2	1	no	—
530	#102	—	2	1	no	—
531	#102	—	2	1	no	—
532	C₂²⋊C₈	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	#97	—	2	1	no	—
535	C₄×C₈	—	2	1	no	—
536	C₄×C₈	—	2	1	no	—
537	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₁₃	—	4	1	no	—
540	C₂×C₁₃	—	8	1	no	—
541	C₂×C₁₃	—	8	1	no	—
542	C₂×C₁₃	—	16	1	no	—
543	C₂×C₁₃	#3002	1	1	yes	characteristic
544	C₂×C₁₃	#3010	1	1	yes	characteristic
545	C₂×C₁₃	#3018	1	1	yes	characteristic
546	#41	—	2	2	no	—
547	#41	—	4	1	no	—
548	#41	—	8	1	no	—
549	#41	—	8	1	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	4	2	no	—
555	C₂×Q₈	—	4	2	no	—
556	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
558	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	4	1	no	—
574	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	Q₁₆	—	8	1	no	—
578	SD₁₆	—	4	4	no	—
579	SD₁₆	—	4	2	no	—
580	SD₁₆	—	8	1	no	—
581	SD₁₆	—	8	1	no	—
582	D₈	—	4	2	no	—
583	D₈	—	8	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	4	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	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	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
610	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	4	1	no	—
628	C₂²⋊C₄	—	4	1	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
641	C₁₃	#18672	1	1	yes	characteristic, direct product factor, Sylow
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	C₁₃×#120	1	1	yes	characteristic
646	Q₈	—	2	1	no	—
647	Q₈	—	2	1	no	—
648	Q₈	—	2	1	no	—
649	Q₈	—	4	2	no	—
650	Q₈	—	4	4	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	8	2	no	—
656	Q₈	C₁₃×#135	1	2	yes	—
657	D₄	—	2	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	8	1	no	—
668	D₄	—	8	2	no	—
669	D₄	—	8	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	8	1	no	—
691	C₂×C₄	—	8	2	no	—
692	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
693	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
694	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	1	no	—
729	C₄	—	8	1	no	—
730	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
731	C₄	C₁₃×#575	1	1	yes	characteristic
732	C₄	C₁₃×#577	1	1	yes	characteristic
733	C₄	C₁₃×#577	1	1	yes	characteristic
734	C₂	—	4	1	no	—
735	C₂	—	8	1	no	—
736	C₂	—	8	1	no	—
737	C₂	—	16	1	no	—
738	C₂	C₁₃×#3002	1	1	yes	characteristic
739	C₂	C₁₃×#3010	1	1	yes	characteristic
740	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×#3518	C₂	semidirect
2. C₁₃×#3212	C₂	semidirect
3. C₁₃×#3167	C₂	semidirect
4. C₁₃×#3115	C₂	semidirect
5. C₁₃×#1652	C₂	semidirect
6. C₁₃×#1651	C₂	semidirect
7. C₁₃×#1646	C₂	semidirect
8. C₁₃×#1645	C₂	semidirect
9. C₁₃×#1628	C₂	semidirect
10. C₁₃×#1627	C₂	semidirect
11. C₁₃×#1624	C₂	semidirect
12. C₁₃×#1623	C₂	semidirect
13. C₁₃×#1554	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1476	C₂	semidirect
176. #18672	C₁₃	direct (N × H)
272. #3518	C₂×C₁₃	semidirect
273. #3212	C₂×C₁₃	semidirect
274. #3167	C₂×C₁₃	semidirect
275. #3115	C₂×C₁₃	semidirect
276. #1652	C₂×C₁₃	semidirect
277. #1651	C₂×C₁₃	semidirect
278. #1646	C₂×C₁₃	semidirect
279. #1645	C₂×C₁₃	semidirect
280. #1628	C₂×C₁₃	semidirect
281. #1627	C₂×C₁₃	semidirect
282. #1624	C₂×C₁₃	semidirect
283. #1623	C₂×C₁₃	semidirect
284. #1554	C₂×C₁₃	semidirect
285. #1494	C₂×C₁₃	semidirect
286. #1476	C₂×C₁₃	semidirect
641. C₁₃	#18672	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×#3212	2
C₁₃×#3167	2
C₁₃×#3115	2
C₁₃×#1652	2
C₁₃×#1651	2
C₁₃×#1646	2
C₁₃×#1645	2
C₁₃×#1628	2
C₁₃×#1627	2
C₁₃×#1624	2
C₁₃×#1623	2
C₁₃×#1554	2
C₁₃×#1494	2
C₁₃×#1476	2
#18672	13

Subgroups — C13×#18672 #15705011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18672 #15705011