Subgroups — C₁₃×#61886 #15748225

Order 3328.

1796 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3396	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3394	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3361	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3360	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3212	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3207	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3106	C₂	1	3	yes	maximal, complemented
14	C₁₃×#3102	C₂	1	3	yes	maximal, complemented
15	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	3	yes	—
17	C₁₃×#559	C₂²	1	3	yes	—
18	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#556	C₂²	1	3	yes	—
21	C₁₃×#554	C₂²	1	3	yes	—
22	C₁₃×#553	—	2	3	no	—
23	C₁₃×#550	C₂²	1	1	yes	characteristic
24	C₁₃×#550	C₂²	1	1	yes	characteristic
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#548	—	2	1	no	—
27	C₁₃×#547	—	2	3	no	—
28	C₁₃×#542	—	2	3	no	—
29	C₁₃×#532	C₂²	1	3	yes	—
30	C₁₃×#532	C₂²	1	3	yes	—
31	C₁₃×#529	—	2	3	no	—
32	C₁₃×#529	C₂²	1	3	yes	—
33	C₁₃×#520	—	2	1	no	—
34	C₄×C₁₃×#41	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	3	yes	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#495	C₂²	1	6	yes	—
38	C₁₃×#493	C₂²	1	3	yes	—
39	C₁₃×#492	C₂²	1	3	yes	—
40	C₁₃×#488	C₂²	1	6	yes	—
41	C₁₃×#487	C₂²	1	3	yes	—
42	C₁₃×#486	C₂²	1	3	yes	—
43	C₁₃×#485	C₂²	1	1	yes	characteristic
44	C₁₃×#482	C₂²	1	3	yes	—
45	C₁₃×#479	C₂²	1	3	yes	—
46	C₁₃×#478	C₂²	1	3	yes	—
47	C₁₃×#477	C₂²	1	3	yes	—
48	C₁₃×#476	C₂²	1	3	yes	—
49	C₁₃×#464	C₂²	1	3	yes	—
50	C₁₃×#463	C₂²	1	3	yes	—
51	C₁₃×#463	C₂²	1	6	yes	—
52	C₁₃×#463	C₂²	1	6	yes	—
53	C₁₃×#462	C₂²	1	3	yes	—
54	C₁₃×#461	C₂²	1	3	yes	—
55	C₁₃×#460	C₂²	1	3	yes	—
56	C₁₃×#460	C₂²	1	3	yes	—
57	C₁₃×#459	C₂²	1	3	yes	—
58	C₁₃×#459	C₂²	1	3	yes	—
59	C₁₃×#452	C₂²	1	3	yes	—
60	C₁₃×#449	C₂²	1	3	yes	—
61	C₁₃×#449	C₂²	1	6	yes	—
62	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
63	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
64	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
67	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
68	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
69	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
70	C₄×C₁₃×D₈	C₂²	1	3	yes	—
71	C₄×C₁₃×D₈	C₂²	1	6	yes	—
72	C₁₃×#431	C₂²	1	3	yes	—
73	C₁₃×#431	C₂²	1	3	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	3	no	—
77	C₂×C₁₃×#41	C₂³	1	3	yes	—
78	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
83	C₂×C₁₃×D₈	C₂³	1	6	yes	—
84	C₂×C₁₃×D₈	C₂³	1	3	yes	—
85	C₁₃×C₄⋊Q₈	—	2	3	no	—
86	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
87	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
88	C₁₃×#127	C₂³	1	3	yes	—
89	C₁₃×#127	C₂³	1	3	yes	—
90	C₁₃×#126	—	2	6	no	—
91	C₁₃×#126	—	2	3	no	—
92	C₁₃×#125	—	2	3	no	—
93	C₁₃×#125	C₂³	1	3	yes	—
94	C₁₃×#124	—	2	3	no	—
95	C₁₃×#124	—	2	3	no	—
96	C₁₃×#124	—	2	3	no	—
97	C₁₃×#124	C₂³	1	6	yes	—
98	C₁₃×#124	C₂³	1	3	yes	—
99	C₁₃×#123	—	2	3	no	—
100	C₁₃×#123	—	2	6	no	—
101	C₁₃×#123	—	2	6	no	—
102	C₁₃×C₂²⋊Q₈	—	2	3	no	—
103	C₁₃×C₂²⋊Q₈	—	2	3	no	—
104	C₁₃×C₂²⋊Q₈	—	2	6	no	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
106	C₁₃×#121	—	2	3	no	—
107	C₁₃×#121	—	2	3	no	—
108	C₁₃×#121	—	2	3	no	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	C₂³	1	3	yes	—
112	C₄×Q₈×C₁₃	—	2	1	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₁₃	D₄	1	3	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
117	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
121	C₄×D₄×C₁₃	—	2	3	no	—
122	C₄×D₄×C₁₃	—	2	3	no	—
123	C₄×D₄×C₁₃	—	2	3	no	—
124	C₄×D₄×C₁₃	—	2	3	no	—
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	—	2	3	no	—
129	C₄×D₄×C₁₃	C₂³	1	3	yes	—
130	C₄×D₄×C₁₃	C₂³	1	3	yes	—
131	C₄×D₄×C₁₃	C₂³	1	3	yes	—
132	C₄×D₄×C₁₃	C₂³	1	6	yes	—
133	C₁₃×#117	—	2	3	no	—
134	C₁₃×#117	—	2	3	no	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
138	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
139	C₂×C₄²×C₁₃	—	2	3	no	—
140	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
141	C₁₃×#107	C₂³	1	1	yes	characteristic
142	C₁₃×#107	C₂³	1	3	yes	—
143	C₁₃×#106	C₂³	1	3	yes	—
144	C₁₃×#106	C₂³	1	1	yes	characteristic
145	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
146	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
147	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×#103	C₂³	1	1	yes	characteristic
150	C₁₃×#103	C₂³	1	6	yes	—
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	1	yes	characteristic
153	C₁₃×#103	C₂³	1	3	yes	—
154	C₁₃×#102	C₂³	1	3	yes	—
155	C₁₃×#102	C₂³	1	3	yes	—
156	C₁₃×#102	C₂³	1	6	yes	—
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
161	C₄×C₈×C₁₃	C₂³	1	6	yes	—
162	C₄×C₈×C₁₃	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	#61886	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₁₃×#41	—	4	3	no	—
166	C₁₃×#41	—	4	3	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	8	6	no	—
170	C₂×Q₈×C₁₃	—	2	4	no	—
171	C₂×Q₈×C₁₃	—	2	3	no	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
173	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
175	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×D₄×C₁₃	—	2	3	no	—
177	C₂×D₄×C₁₃	—	2	3	no	—
178	C₂×D₄×C₁₃	—	2	3	no	—
179	C₂×D₄×C₁₃	—	2	3	no	—
180	C₂×D₄×C₁₃	—	2	3	no	—
181	C₂×D₄×C₁₃	—	2	3	no	—
182	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
184	C₂²×C₄×C₁₃	—	2	3	no	—
185	C₂²×C₄×C₁₃	—	2	3	no	—
186	C₂²×C₄×C₁₃	—	2	3	no	—
187	C₂²×C₄×C₁₃	—	2	3	no	—
188	C₂²×C₄×C₁₃	—	2	6	no	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
190	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₁₃×Q₁₆	—	4	3	no	—
193	C₁₃×SD₁₆	—	4	3	no	—
194	C₁₃×SD₁₆	—	4	6	no	—
195	C₁₃×SD₁₆	—	4	3	no	—
196	C₁₃×D₈	—	4	3	no	—
197	C₁₃×D₈	—	4	6	no	—
198	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
199	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
201	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	—	2	3	no	—
203	C₁₃×C₄⋊C₄	—	2	3	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	3	no	—
206	C₁₃×C₄⋊C₄	—	2	3	no	—
207	C₁₃×C₄⋊C₄	—	2	3	no	—
208	C₁₃×C₄⋊C₄	—	2	3	no	—
209	C₁₃×C₄⋊C₄	—	2	3	no	—
210	C₁₃×C₄⋊C₄	—	2	3	no	—
211	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
212	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
216	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
218	C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	6	no	—
221	C₁₃×C₂²⋊C₄	—	2	3	no	—
222	C₁₃×C₂²⋊C₄	—	2	3	no	—
223	C₁₃×C₂²⋊C₄	—	2	3	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	6	no	—
226	C₁₃×C₂²⋊C₄	—	2	3	no	—
227	C₁₃×C₂²⋊C₄	—	2	3	no	—
228	C₁₃×C₂²⋊C₄	—	2	6	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	3	no	—
231	C₄²×C₁₃	—	2	3	no	—
232	C₄²×C₁₃	—	2	3	no	—
233	C₄²×C₁₃	C₂×D₄	1	3	yes	—
234	C₄²×C₁₃	C₂×D₄	1	3	yes	—
235	C₄²×C₁₃	C₂⁴	1	3	yes	—
236	C₄²×C₁₃	C₂⁴	1	3	yes	—
237	#3522	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#3396	C₂×C₁₃	1	3	yes	complemented
240	#3394	C₂×C₁₃	1	3	yes	complemented
241	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3361	C₂×C₁₃	1	3	yes	complemented
246	#3360	C₂×C₁₃	1	3	yes	complemented
247	#3212	C₂×C₁₃	1	3	yes	complemented
248	#3207	C₂×C₁₃	1	3	yes	complemented
249	#3106	C₂×C₁₃	1	3	yes	complemented
250	#3102	C₂×C₁₃	1	3	yes	complemented
251	#2982	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂³×C₁₃	—	2	3	no	—
253	C₂³×C₁₃	—	2	3	no	—
254	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₃	—	2	6	no	—
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	2	3	no	—
258	Q₈×C₁₃	—	2	3	no	—
259	Q₈×C₁₃	—	2	1	no	—
260	Q₈×C₁₃	—	8	3	no	—
261	Q₈×C₁₃	#135	1	4	yes	—
262	D₄×C₁₃	—	2	3	no	—
263	D₄×C₁₃	—	2	3	no	—
264	D₄×C₁₃	—	2	3	no	—
265	D₄×C₁₃	—	2	3	no	—
266	D₄×C₁₃	—	4	6	no	—
267	D₄×C₁₃	—	4	6	no	—
268	D₄×C₁₃	—	4	6	no	—
269	D₄×C₁₃	—	4	6	no	—
270	D₄×C₁₃	—	8	3	no	—
271	D₄×C₁₃	—	8	3	no	—
272	C₂×C₄×C₁₃	—	2	6	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	3	no	—
279	C₂×C₄×C₁₃	—	2	3	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	4	3	no	—
282	C₂×C₄×C₁₃	—	4	6	no	—
283	C₂×C₄×C₁₃	—	4	6	no	—
284	C₂×C₄×C₁₃	—	4	6	no	—
285	C₂×C₄×C₁₃	—	8	3	no	—
286	C₂×C₄×C₁₃	—	8	6	no	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
291	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₁₃	—	2	1	no	—
294	C₈×C₁₃	—	2	3	no	—
295	C₈×C₁₃	—	2	3	no	—
296	C₈×C₁₃	—	2	1	no	—
297	#559	C₂²×C₁₃	1	3	yes	—
298	#559	C₂²×C₁₃	1	3	yes	—
299	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
300	#557	C₂²×C₁₃	1	1	yes	characteristic
301	#556	C₂²×C₁₃	1	3	yes	—
302	#554	C₂²×C₁₃	1	3	yes	—
303	#553	—	2	3	no	—
304	#550	C₂²×C₁₃	1	1	yes	characteristic
305	#550	C₂²×C₁₃	1	1	yes	characteristic
306	#548	—	2	1	no	—
307	#548	—	2	1	no	—
308	#547	—	2	3	no	—
309	#542	—	2	3	no	—
310	#532	C₂²×C₁₃	1	3	yes	—
311	#532	C₂²×C₁₃	1	3	yes	—
312	#529	—	2	3	no	—
313	#529	C₂²×C₁₃	1	3	yes	—
314	#520	—	2	1	no	—
315	C₄×#41	—	2	1	no	—
316	C₄×#41	C₂²×C₁₃	1	3	yes	—
317	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
318	#495	C₂²×C₁₃	1	6	yes	—
319	#493	C₂²×C₁₃	1	3	yes	—
320	#492	C₂²×C₁₃	1	3	yes	—
321	#488	C₂²×C₁₃	1	6	yes	—
322	#487	C₂²×C₁₃	1	3	yes	—
323	#486	C₂²×C₁₃	1	3	yes	—
324	#485	C₂²×C₁₃	1	1	yes	characteristic
325	#482	C₂²×C₁₃	1	3	yes	—
326	#479	C₂²×C₁₃	1	3	yes	—
327	#478	C₂²×C₁₃	1	3	yes	—
328	#477	C₂²×C₁₃	1	3	yes	—
329	#476	C₂²×C₁₃	1	3	yes	—
330	#464	C₂²×C₁₃	1	3	yes	—
331	#463	C₂²×C₁₃	1	3	yes	—
332	#463	C₂²×C₁₃	1	6	yes	—
333	#463	C₂²×C₁₃	1	6	yes	—
334	#462	C₂²×C₁₃	1	3	yes	—
335	#461	C₂²×C₁₃	1	3	yes	—
336	#460	C₂²×C₁₃	1	3	yes	—
337	#460	C₂²×C₁₃	1	3	yes	—
338	#459	C₂²×C₁₃	1	3	yes	—
339	#459	C₂²×C₁₃	1	3	yes	—
340	#452	C₂²×C₁₃	1	3	yes	—
341	#449	C₂²×C₁₃	1	3	yes	—
342	#449	C₂²×C₁₃	1	6	yes	—
343	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
344	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
345	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
346	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
348	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
349	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
350	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
351	C₄×D₈	C₂²×C₁₃	1	3	yes	—
352	C₄×D₈	C₂²×C₁₃	1	6	yes	—
353	#431	C₂²×C₁₃	1	3	yes	—
354	#431	C₂²×C₁₃	1	3	yes	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	1	no	—
357	C₂²×C₁₃	—	2	1	no	—
358	C₂²×C₁₃	—	4	3	no	—
359	C₂²×C₁₃	—	4	3	no	—
360	C₂²×C₁₃	—	4	3	no	—
361	C₂²×C₁₃	—	4	3	no	—
362	C₂²×C₁₃	—	4	3	no	—
363	C₂²×C₁₃	—	4	3	no	—
364	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₁₃	—	2	3	no	—
366	C₄×C₁₃	—	2	3	no	—
367	C₄×C₁₃	—	2	1	no	—
368	C₄×C₁₃	—	2	3	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	3	no	—
371	C₄×C₁₃	—	4	3	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	1	no	—
374	C₄×C₁₃	—	4	1	no	—
375	C₄×C₁₃	C₂×#135	1	6	yes	—
376	C₄×C₁₃	#585	1	1	yes	characteristic
377	C₄×C₁₃	#585	1	1	yes	characteristic
378	C₂×#41	—	2	1	no	—
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	3	no	—
381	C₂×#41	C₂³×C₁₃	1	3	yes	—
382	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
383	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
384	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
385	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
386	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
387	C₂×D₈	C₂³×C₁₃	1	6	yes	—
388	C₂×D₈	C₂³×C₁₃	1	3	yes	—
389	C₄⋊Q₈	—	2	3	no	—
390	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
391	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
392	#127	C₂³×C₁₃	1	3	yes	—
393	#127	C₂³×C₁₃	1	3	yes	—
394	#126	—	2	6	no	—
395	#126	—	2	3	no	—
396	#125	—	2	3	no	—
397	#125	C₂³×C₁₃	1	3	yes	—
398	#124	—	2	3	no	—
399	#124	—	2	3	no	—
400	#124	—	2	3	no	—
401	#124	C₂³×C₁₃	1	3	yes	—
402	#124	C₂³×C₁₃	1	6	yes	—
403	#123	—	2	3	no	—
404	#123	—	2	6	no	—
405	#123	—	2	6	no	—
406	C₂²⋊Q₈	—	2	3	no	—
407	C₂²⋊Q₈	—	2	3	no	—
408	C₂²⋊Q₈	—	2	6	no	—
409	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
410	#121	—	2	3	no	—
411	#121	—	2	3	no	—
412	#121	—	2	3	no	—
413	#121	—	2	3	no	—
414	#121	—	2	3	no	—
415	#121	C₂³×C₁₃	1	3	yes	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
419	C₄×Q₈	D₄×C₁₃	1	3	yes	—
420	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
421	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
422	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
425	C₄×D₄	—	2	3	no	—
426	C₄×D₄	—	2	3	no	—
427	C₄×D₄	—	2	3	no	—
428	C₄×D₄	—	2	3	no	—
429	C₄×D₄	—	2	3	no	—
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	C₂³×C₁₃	1	3	yes	—
434	C₄×D₄	C₂³×C₁₃	1	3	yes	—
435	C₄×D₄	C₂³×C₁₃	1	3	yes	—
436	C₄×D₄	C₂³×C₁₃	1	6	yes	—
437	#117	—	2	3	no	—
438	#117	—	2	3	no	—
439	#117	—	2	3	no	—
440	#117	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	—	2	3	no	—
442	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
443	C₂×C₄²	—	2	3	no	—
444	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
445	#107	C₂³×C₁₃	1	1	yes	characteristic
446	#107	C₂³×C₁₃	1	3	yes	—
447	#106	C₂³×C₁₃	1	3	yes	—
448	#106	C₂³×C₁₃	1	1	yes	characteristic
449	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
450	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
451	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
452	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
453	#103	C₂³×C₁₃	1	1	yes	characteristic
454	#103	C₂³×C₁₃	1	6	yes	—
455	#103	C₂³×C₁₃	1	3	yes	—
456	#103	C₂³×C₁₃	1	1	yes	characteristic
457	#103	C₂³×C₁₃	1	3	yes	—
458	#102	C₂³×C₁₃	1	3	yes	—
459	#102	C₂³×C₁₃	1	3	yes	—
460	#102	C₂³×C₁₃	1	6	yes	—
461	#102	C₂³×C₁₃	1	3	yes	—
462	#102	C₂³×C₁₃	1	3	yes	—
463	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
465	C₄×C₈	C₂³×C₁₃	1	6	yes	—
466	C₄×C₈	C₂³×C₁₃	1	3	yes	—
467	C₄×C₈	C₂³×C₁₃	1	3	yes	—
468	C₂×C₁₃	—	4	1	no	—
469	C₂×C₁₃	—	8	3	no	—
470	C₂×C₁₃	—	8	3	no	—
471	C₂×C₁₃	#3487	1	1	yes	characteristic
472	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
473	C₂×C₁₃	#3585	1	1	yes	characteristic
474	#41	—	4	3	no	—
475	#41	—	4	3	no	—
476	#41	—	4	4	no	—
477	#41	—	4	4	no	—
478	#41	—	8	6	no	—
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	2	3	no	—
481	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
482	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
484	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
485	C₂×D₄	—	2	3	no	—
486	C₂×D₄	—	2	3	no	—
487	C₂×D₄	—	2	3	no	—
488	C₂×D₄	—	2	3	no	—
489	C₂×D₄	—	2	3	no	—
490	C₂×D₄	—	2	3	no	—
491	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
492	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
493	C₂²×C₄	—	2	3	no	—
494	C₂²×C₄	—	2	3	no	—
495	C₂²×C₄	—	2	3	no	—
496	C₂²×C₄	—	2	3	no	—
497	C₂²×C₄	—	2	6	no	—
498	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
499	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	Q₁₆	—	4	3	no	—
502	SD₁₆	—	4	3	no	—
503	SD₁₆	—	4	6	no	—
504	SD₁₆	—	4	3	no	—
505	D₈	—	4	3	no	—
506	D₈	—	4	6	no	—
507	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
508	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
509	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
510	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	3	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	3	no	—
520	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
521	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
522	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
523	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
525	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	6	no	—
530	C₂²⋊C₄	—	2	3	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₂²⋊C₄	—	2	3	no	—
534	C₂²⋊C₄	—	2	6	no	—
535	C₂²⋊C₄	—	2	3	no	—
536	C₂²⋊C₄	—	2	3	no	—
537	C₂²⋊C₄	—	2	6	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	3	no	—
540	C₄²	—	2	3	no	—
541	C₄²	—	2	3	no	—
542	C₄²	C₂×D₄×C₁₃	1	3	yes	—
543	C₄²	C₂×D₄×C₁₃	1	3	yes	—
544	C₄²	C₂⁴×C₁₃	1	3	yes	—
545	C₄²	C₂⁴×C₁₃	1	3	yes	—
546	C₁₃	#61886	1	1	yes	characteristic, direct product factor, Sylow
547	C₂³	—	2	3	no	—
548	C₂³	—	2	3	no	—
549	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	Q₈	—	2	6	no	—
551	Q₈	—	2	1	no	—
552	Q₈	—	2	3	no	—
553	Q₈	—	2	3	no	—
554	Q₈	—	2	1	no	—
555	Q₈	—	8	3	no	—
556	Q₈	C₁₃×#135	1	4	yes	—
557	D₄	—	2	3	no	—
558	D₄	—	2	3	no	—
559	D₄	—	2	3	no	—
560	D₄	—	2	3	no	—
561	D₄	—	4	6	no	—
562	D₄	—	4	6	no	—
563	D₄	—	4	6	no	—
564	D₄	—	4	6	no	—
565	D₄	—	8	3	no	—
566	D₄	—	8	3	no	—
567	C₂×C₄	—	2	6	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	3	no	—
574	C₂×C₄	—	2	3	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	4	3	no	—
577	C₂×C₄	—	4	6	no	—
578	C₂×C₄	—	4	6	no	—
579	C₂×C₄	—	4	6	no	—
580	C₂×C₄	—	8	3	no	—
581	C₂×C₄	—	8	6	no	—
582	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
584	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
585	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
586	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
587	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
588	C₈	—	2	1	no	—
589	C₈	—	2	3	no	—
590	C₈	—	2	3	no	—
591	C₈	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	3	no	—
596	C₂²	—	4	3	no	—
597	C₂²	—	4	3	no	—
598	C₂²	—	4	3	no	—
599	C₂²	—	4	3	no	—
600	C₂²	—	4	3	no	—
601	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
602	C₄	—	2	3	no	—
603	C₄	—	2	3	no	—
604	C₄	—	2	3	no	—
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	3	no	—
610	C₄	—	4	3	no	—
611	C₄	—	4	1	no	—
612	C₄	C₂×C₁₃×#135	1	6	yes	—
613	C₄	C₁₃×#585	1	1	yes	characteristic
614	C₄	C₁₃×#585	1	1	yes	characteristic
615	C₂	—	4	1	no	—
616	C₂	—	8	3	no	—
617	C₂	—	8	3	no	—
618	C₂	C₁₃×#3487	1	1	yes	characteristic
619	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
620	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3522	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3394	C₂	semidirect
5. C₁₃×#3392	C₂	semidirect
6. C₁₃×#3391	C₂	semidirect
7. C₁₃×#3363	C₂	semidirect
8. C₁₃×#3362	C₂	semidirect
9. C₁₃×#3361	C₂	semidirect
10. C₁₃×#3360	C₂	semidirect
11. C₁₃×#3212	C₂	semidirect
12. C₁₃×#3207	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₁₃×#3102	C₂	semidirect
15. C₁₃×#2982	C₂	semidirect
164. #61886	C₁₃	direct (N × H)
237. #3522	C₂×C₁₃	semidirect
238. #3480	C₂×C₁₃	semidirect
239. #3396	C₂×C₁₃	semidirect
240. #3394	C₂×C₁₃	semidirect
241. #3392	C₂×C₁₃	semidirect
242. #3391	C₂×C₁₃	semidirect
243. #3363	C₂×C₁₃	semidirect
244. #3362	C₂×C₁₃	semidirect
245. #3361	C₂×C₁₃	semidirect
246. #3360	C₂×C₁₃	semidirect
247. #3212	C₂×C₁₃	semidirect
248. #3207	C₂×C₁₃	semidirect
249. #3106	C₂×C₁₃	semidirect
250. #3102	C₂×C₁₃	semidirect
251. #2982	C₂×C₁₃	semidirect
546. C₁₃	#61886	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×#3522	2
C₁₃×#3480	2
C₁₃×#3396	2
C₁₃×#3394	2
C₁₃×#3392	2
C₁₃×#3391	2
C₁₃×#3363	2
C₁₃×#3362	2
C₁₃×#3361	2
C₁₃×#3360	2
C₁₃×#3212	2
C₁₃×#3207	2
C₁₃×#3106	2
C₁₃×#3102	2
C₁₃×#2982	2
#61886	13

Subgroups — C13×#61886 #15748225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61886 #15748225