Subgroups — C₁₃×#61885 #15748224

Order 3328.

1814 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3396	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3394	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3365	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3361	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#3105	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	—	2	2	no	—
15	C₁₃×#559	—	2	2	no	—
16	C₁₃×#559	C₂²	1	4	yes	—
17	C₁₃×#559	C₂²	1	4	yes	—
18	C₁₃×#559	C₂²	1	2	yes	complemented
19	C₁₃×#557	C₂²	1	2	yes	complemented
20	C₁₃×#556	—	2	2	no	—
21	C₁₃×#556	C₂²	1	2	yes	complemented
22	C₁₃×#554	C₂²	1	2	yes	complemented
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#539	—	2	2	no	—
25	C₁₃×#536	—	2	1	no	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
29	C₁₃×#529	C₂²	1	4	yes	—
30	C₂×C₁₃×#124	—	2	1	no	—
31	C₂×C₁₃×#124	C₂²	1	2	yes	—
32	C₂×C₁₃×#123	—	2	2	no	—
33	C₁₃×#520	—	2	1	no	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
38	C₁₃×#495	C₂²	1	8	yes	complemented
39	C₁₃×#493	C₂²	1	2	yes	—
40	C₁₃×#492	C₂²	1	2	yes	—
41	C₁₃×#488	C₂²	1	8	yes	complemented
42	C₁₃×#486	C₂²	1	2	yes	—
43	C₁₃×#486	C₂²	1	2	yes	—
44	C₁₃×#484	C₂²	1	2	yes	—
45	C₁₃×#481	C₂²	1	2	yes	—
46	C₁₃×#478	C₂²	1	8	yes	complemented
47	C₁₃×#477	C₂²	1	2	yes	complemented
48	C₁₃×#475	C₂²	1	2	yes	complemented
49	C₁₃×#464	C₂²	1	8	yes	complemented
50	C₁₃×#463	C₂²	1	8	yes	complemented
51	C₁₃×#463	C₂²	1	8	yes	complemented
52	C₁₃×#462	C₂²	1	2	yes	complemented
53	C₁₃×#460	C₂²	1	4	yes	—
54	C₁₃×#460	C₂²	1	2	yes	complemented
55	C₁₃×#459	C₂²	1	4	yes	—
56	C₁₃×#451	C₂²	1	2	yes	—
57	C₁₃×#450	C₂²	1	4	yes	—
58	C₁₃×#448	C₂²	1	2	yes	—
59	C₁₃×#447	C₂²	1	4	yes	—
60	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
61	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
62	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
63	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
64	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
65	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
66	C₁₃×#431	C₂²	1	1	yes	characteristic
67	C₁₃×#431	C₂²	1	1	yes	characteristic
68	C₁₃×#431	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	—	2	2	no	—
76	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
79	C₂×C₁₃×D₈	C₂³	1	8	yes	—
80	C₁₃×C₄⋊Q₈	—	2	2	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	1	no	—
85	C₁₃×#127	—	2	1	no	—
86	C₁₃×#127	C₂³	1	2	yes	—
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#127	C₂³	1	1	yes	characteristic
89	C₁₃×#126	—	2	4	no	—
90	C₁₃×#126	—	2	4	no	—
91	C₁₃×#125	—	2	4	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₁₃×#125	C₂³	1	4	yes	—
94	C₁₃×#124	—	2	4	no	—
95	C₁₃×#124	—	2	4	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	4	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	C₂³	1	4	yes	—
100	C₁₃×#124	C₂³	1	8	yes	—
101	C₁₃×#123	—	2	4	no	—
102	C₁₃×#123	—	2	8	no	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×#123	—	2	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	2	no	—
106	C₁₃×C₂²⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	—	2	1	no	—
108	C₁₃×C₂²⋊Q₈	—	2	4	no	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×#121	—	2	1	no	—
111	C₁₃×#121	C₂³	1	2	yes	—
112	C₄×Q₈×C₁₃	—	2	2	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	D₄	1	2	yes	—
117	C₄×Q₈×C₁₃	D₄	1	2	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₄×D₄×C₁₃	—	2	4	no	—
125	C₄×D₄×C₁₃	—	2	4	no	—
126	C₄×D₄×C₁₃	—	2	4	no	—
127	C₄×D₄×C₁₃	—	2	2	no	—
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	1	no	—
130	C₄×D₄×C₁₃	C₂³	1	4	yes	—
131	C₄×D₄×C₁₃	C₂³	1	8	yes	—
132	C₄×D₄×C₁₃	C₂³	1	2	yes	—
133	C₁₃×#117	—	2	1	no	—
134	C₁₃×#117	—	2	2	no	—
135	C₁₃×#117	—	2	4	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₄²×C₁₃	—	2	1	no	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₁₃×#107	C₂³	1	4	yes	—
148	C₁₃×#106	C₂³	1	4	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	4	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#102	C₂³	1	4	yes	—
156	C₁₃×#102	C₂³	1	8	yes	—
157	C₁₃×#102	C₂³	1	8	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
160	C₄×C₈×C₁₃	C₂³	1	8	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	2	yes	—
163	#61885	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	2	no	—
165	C₁₃×#41	—	4	4	no	—
166	C₂×Q₈×C₁₃	—	2	4	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	4	2	no	—
171	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	2	no	—
178	C₂×D₄×C₁₃	—	2	2	no	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	2	no	—
182	C₂×D₄×C₁₃	—	2	2	no	—
183	C₂×D₄×C₁₃	—	4	4	no	—
184	C₂×D₄×C₁₃	—	4	4	no	—
185	C₂×D₄×C₁₃	—	8	2	no	—
186	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	8	no	—
193	C₂²×C₄×C₁₃	—	8	4	no	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₁₃×Q₁₆	—	4	4	no	—
200	C₁₃×SD₁₆	—	4	4	no	—
201	C₁₃×SD₁₆	—	4	8	no	—
202	C₁₃×D₈	—	4	8	no	—
203	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
204	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
219	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
220	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
222	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
223	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	8	no	—
226	C₁₃×C₂²⋊C₄	—	2	8	no	—
227	C₁₃×C₂²⋊C₄	—	2	8	no	—
228	C₁₃×C₂²⋊C₄	—	2	2	no	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	2	no	—
232	C₁₃×C₂²⋊C₄	—	2	4	no	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	—	2	2	no	—
235	C₄²×C₁₃	—	2	4	no	—
236	C₄²×C₁₃	—	2	2	no	—
237	C₄²×C₁₃	C₂×D₄	1	4	yes	—
238	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₁₃	C₂⁴	1	4	yes	—
241	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
243	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
244	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3396	C₂×C₁₃	1	4	yes	complemented
246	#3394	C₂×C₁₃	1	4	yes	complemented
247	#3365	C₂×C₁₃	1	4	yes	complemented
248	#3361	C₂×C₁₃	1	4	yes	complemented
249	#3211	C₂×C₁₃	1	4	yes	complemented
250	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3205	C₂×C₁₃	1	1	yes	characteristic
252	#3105	C₂×C₁₃	1	4	yes	complemented
253	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2982	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	4	no	—
258	C₂³×C₁₃	—	4	4	no	—
259	C₂³×C₁₃	—	4	4	no	—
260	C₂³×C₁₃	—	4	4	no	—
261	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	Q₈×C₁₃	—	2	4	no	—
263	Q₈×C₁₃	—	2	4	no	—
264	Q₈×C₁₃	—	2	4	no	—
265	Q₈×C₁₃	—	2	2	no	—
266	Q₈×C₁₃	—	2	2	no	—
267	Q₈×C₁₃	—	4	2	no	—
268	Q₈×C₁₃	—	4	2	no	—
269	Q₈×C₁₃	—	8	1	no	—
270	D₄×C₁₃	—	2	4	no	—
271	D₄×C₁₃	—	2	8	no	—
272	D₄×C₁₃	—	4	4	no	—
273	D₄×C₁₃	—	4	4	no	—
274	D₄×C₁₃	—	4	4	no	—
275	D₄×C₁₃	—	4	4	no	—
276	D₄×C₁₃	—	4	2	no	—
277	D₄×C₁₃	—	8	1	no	—
278	D₄×C₁₃	—	8	2	no	—
279	D₄×C₁₃	—	8	2	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	4	2	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	2	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	4	no	—
292	C₂×C₄×C₁₃	—	8	4	no	—
293	C₂×C₄×C₁₃	—	8	8	no	—
294	C₂×C₄×C₁₃	#135	1	4	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
303	C₈×C₁₃	—	2	4	no	—
304	C₈×C₁₃	—	2	4	no	—
305	#559	—	2	2	no	—
306	#559	—	2	2	no	—
307	#559	C₂²×C₁₃	1	4	yes	—
308	#559	C₂²×C₁₃	1	4	yes	—
309	#559	C₂²×C₁₃	1	2	yes	complemented
310	#557	C₂²×C₁₃	1	2	yes	complemented
311	#556	—	2	2	no	—
312	#556	C₂²×C₁₃	1	2	yes	complemented
313	#554	C₂²×C₁₃	1	2	yes	complemented
314	#552	—	2	2	no	—
315	#539	—	2	2	no	—
316	#536	—	2	1	no	—
317	#533	C₂²×C₁₃	1	1	yes	characteristic
318	#532	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
320	#529	C₂²×C₁₃	1	4	yes	—
321	C₂×#124	—	2	1	no	—
322	C₂×#124	C₂²×C₁₃	1	2	yes	—
323	C₂×#123	—	2	2	no	—
324	#520	—	2	1	no	—
325	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×D₄	—	2	1	no	—
328	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
329	#495	C₂²×C₁₃	1	8	yes	complemented
330	#493	C₂²×C₁₃	1	2	yes	—
331	#492	C₂²×C₁₃	1	2	yes	—
332	#488	C₂²×C₁₃	1	8	yes	complemented
333	#486	C₂²×C₁₃	1	2	yes	—
334	#486	C₂²×C₁₃	1	2	yes	—
335	#484	C₂²×C₁₃	1	2	yes	—
336	#481	C₂²×C₁₃	1	2	yes	—
337	#478	C₂²×C₁₃	1	8	yes	complemented
338	#477	C₂²×C₁₃	1	2	yes	complemented
339	#475	C₂²×C₁₃	1	2	yes	complemented
340	#464	C₂²×C₁₃	1	8	yes	complemented
341	#463	C₂²×C₁₃	1	8	yes	complemented
342	#463	C₂²×C₁₃	1	8	yes	complemented
343	#462	C₂²×C₁₃	1	2	yes	complemented
344	#460	C₂²×C₁₃	1	4	yes	—
345	#460	C₂²×C₁₃	1	2	yes	complemented
346	#459	C₂²×C₁₃	1	4	yes	—
347	#451	C₂²×C₁₃	1	2	yes	—
348	#450	C₂²×C₁₃	1	4	yes	—
349	#448	C₂²×C₁₃	1	2	yes	—
350	#447	C₂²×C₁₃	1	4	yes	—
351	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
352	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
353	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
354	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
355	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
356	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
357	#431	C₂²×C₁₃	1	1	yes	characteristic
358	#431	C₂²×C₁₃	1	1	yes	characteristic
359	#431	C₂²×C₁₃	1	4	yes	—
360	C₂²×C₁₃	—	2	1	no	—
361	C₂²×C₁₃	—	2	1	no	—
362	C₂²×C₁₃	—	4	4	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	4	no	—
365	C₂²×C₁₃	—	4	2	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	4	4	no	—
368	C₂²×C₁₃	—	8	8	no	—
369	C₂²×C₁₃	C₂×#135	1	2	yes	—
370	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₁₃	—	2	4	no	—
372	C₄×C₁₃	—	2	1	no	—
373	C₄×C₁₃	—	2	1	no	—
374	C₄×C₁₃	—	2	1	no	—
375	C₄×C₁₃	—	2	4	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	2	no	—
378	C₄×C₁₃	—	4	2	no	—
379	C₄×C₁₃	—	4	2	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	C₂×#135	1	2	yes	—
382	C₄×C₁₃	C₂×#135	1	2	yes	—
383	C₄×C₁₃	#585	1	2	yes	—
384	C₂×#41	—	2	1	no	—
385	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
390	C₂³×C₄	—	2	2	no	—
391	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
392	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
393	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
394	C₂×D₈	C₂³×C₁₃	1	8	yes	—
395	C₄⋊Q₈	—	2	2	no	—
396	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
399	#127	—	2	1	no	—
400	#127	—	2	1	no	—
401	#127	C₂³×C₁₃	1	2	yes	—
402	#127	C₂³×C₁₃	1	2	yes	—
403	#127	C₂³×C₁₃	1	1	yes	characteristic
404	#126	—	2	4	no	—
405	#126	—	2	4	no	—
406	#125	—	2	4	no	—
407	#125	—	2	1	no	—
408	#125	C₂³×C₁₃	1	4	yes	—
409	#124	—	2	4	no	—
410	#124	—	2	4	no	—
411	#124	—	2	2	no	—
412	#124	—	2	4	no	—
413	#124	—	2	1	no	—
414	#124	C₂³×C₁₃	1	8	yes	—
415	#124	C₂³×C₁₃	1	4	yes	—
416	#123	—	2	4	no	—
417	#123	—	2	8	no	—
418	#123	—	2	8	no	—
419	#123	—	2	4	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	4	no	—
424	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
425	#121	—	2	1	no	—
426	#121	C₂³×C₁₃	1	2	yes	—
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	D₄×C₁₃	1	2	yes	—
432	C₄×Q₈	D₄×C₁₃	1	2	yes	—
433	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
434	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
435	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
436	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
437	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
438	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
439	C₄×D₄	—	2	4	no	—
440	C₄×D₄	—	2	4	no	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	4	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	C₂³×C₁₃	1	8	yes	—
446	C₄×D₄	C₂³×C₁₃	1	4	yes	—
447	C₄×D₄	C₂³×C₁₃	1	2	yes	—
448	#117	—	2	1	no	—
449	#117	—	2	2	no	—
450	#117	—	2	4	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	2	no	—
453	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₂²⋊C₄	—	2	2	no	—
458	C₂×C₂²⋊C₄	—	2	2	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
462	#107	C₂³×C₁₃	1	4	yes	—
463	#106	C₂³×C₁₃	1	4	yes	—
464	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
465	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
466	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
467	#103	C₂³×C₁₃	1	4	yes	—
468	#103	C₂³×C₁₃	1	4	yes	—
469	#103	C₂³×C₁₃	1	4	yes	—
470	#102	C₂³×C₁₃	1	4	yes	—
471	#102	C₂³×C₁₃	1	8	yes	—
472	#102	C₂³×C₁₃	1	8	yes	—
473	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
474	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
475	C₄×C₈	C₂³×C₁₃	1	8	yes	—
476	C₄×C₈	C₂³×C₁₃	1	2	yes	—
477	C₄×C₈	C₂³×C₁₃	1	2	yes	—
478	C₂×C₁₃	—	2	2	no	—
479	C₂×C₁₃	—	8	2	no	—
480	C₂×C₁₃	—	8	4	no	—
481	C₂×C₁₃	#3487	1	1	yes	characteristic
482	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
483	C₂×C₁₃	#3585	1	1	yes	characteristic
484	C₂⁴	—	2	2	no	—
485	#41	—	4	4	no	—
486	C₂×Q₈	—	2	4	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
492	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
493	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
494	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	4	4	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
507	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	8	4	no	—
514	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
515	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
516	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
519	Q₁₆	—	4	4	no	—
520	SD₁₆	—	4	4	no	—
521	SD₁₆	—	4	8	no	—
522	D₈	—	4	8	no	—
523	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
524	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
538	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
539	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
540	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
541	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
542	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
543	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	4	no	—
556	C₄²	—	2	2	no	—
557	C₄²	C₂×D₄×C₁₃	1	4	yes	—
558	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
559	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
560	C₄²	C₂⁴×C₁₃	1	4	yes	—
561	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
562	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₁₃	#61885	1	1	yes	characteristic, direct product factor, Sylow
564	C₂³	—	2	2	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	4	4	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	4	4	no	—
569	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
570	Q₈	—	2	4	no	—
571	Q₈	—	2	4	no	—
572	Q₈	—	2	4	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	8	1	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	8	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	4	no	—
582	D₄	—	4	4	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	2	no	—
585	D₄	—	8	2	no	—
586	D₄	—	8	2	no	—
587	D₄	—	8	1	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	8	8	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	C₁₃×#135	1	4	yes	—
603	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
604	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
606	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
611	C₈	—	2	4	no	—
612	C₈	—	2	4	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	8	no	—
622	C₂²	C₂×C₁₃×#135	1	2	yes	—
623	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	C₂×C₁₃×#135	1	2	yes	—
635	C₄	C₂×C₁₃×#135	1	2	yes	—
636	C₄	C₁₃×#585	1	2	yes	—
637	C₂	—	2	2	no	—
638	C₂	—	8	4	no	—
639	C₂	—	8	2	no	—
640	C₂	C₁₃×#3487	1	1	yes	characteristic
641	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
642	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3205	C₂
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×#3507	C₂	semidirect
2. C₂×C₁₃×#559	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3394	C₂	semidirect
5. C₁₃×#3365	C₂	semidirect
6. C₁₃×#3361	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3208	C₂	semidirect
10. C₁₃×#3105	C₂	semidirect
11. C₁₃×#3104	C₂	semidirect
12. C₁₃×#3103	C₂	semidirect
13. C₁₃×#2982	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
46. C₁₃×#478	C₂²	semidirect
47. C₁₃×#477	C₂²	semidirect
48. C₁₃×#475	C₂²	semidirect
49. C₁₃×#464	C₂²	semidirect
50. C₁₃×#463	C₂²	semidirect
51. C₁₃×#463	C₂²	semidirect
52. C₁₃×#462	C₂²	semidirect
54. C₁₃×#460	C₂²	semidirect
60. C₈×Q₈×C₁₃	C₂²	semidirect
61. C₈×Q₈×C₁₃	C₂²	semidirect
62. C₄×C₁₃×Q₁₆	C₂²	semidirect
63. C₄×C₁₃×SD₁₆	C₂²	semidirect
64. C₄×C₁₃×SD₁₆	C₂²	semidirect
65. C₄×C₁₃×D₈	C₂²	semidirect
163. #61885	C₁₃	direct (N × H)
243. #3507	C₂×C₁₃	semidirect
244. C₂×#559	C₂×C₁₃	semidirect
245. #3396	C₂×C₁₃	semidirect
246. #3394	C₂×C₁₃	semidirect
247. #3365	C₂×C₁₃	semidirect
248. #3361	C₂×C₁₃	semidirect
249. #3211	C₂×C₁₃	semidirect
250. #3208	C₂×C₁₃	semidirect
252. #3105	C₂×C₁₃	semidirect
253. #3104	C₂×C₁₃	semidirect
254. #3103	C₂×C₁₃	semidirect
255. #2982	C₂×C₁₃	semidirect
309. #559	C₂²×C₁₃	semidirect
310. #557	C₂²×C₁₃	semidirect
312. #556	C₂²×C₁₃	semidirect
313. #554	C₂²×C₁₃	semidirect
329. #495	C₂²×C₁₃	semidirect
332. #488	C₂²×C₁₃	semidirect
337. #478	C₂²×C₁₃	semidirect
338. #477	C₂²×C₁₃	semidirect
339. #475	C₂²×C₁₃	semidirect
340. #464	C₂²×C₁₃	semidirect
341. #463	C₂²×C₁₃	semidirect
342. #463	C₂²×C₁₃	semidirect
343. #462	C₂²×C₁₃	semidirect
345. #460	C₂²×C₁₃	semidirect
351. C₈×Q₈	C₂²×C₁₃	semidirect
352. C₈×Q₈	C₂²×C₁₃	semidirect
353. C₄×Q₁₆	C₂²×C₁₃	semidirect
354. C₄×SD₁₆	C₂²×C₁₃	semidirect
355. C₄×SD₁₆	C₂²×C₁₃	semidirect
356. C₄×D₈	C₂²×C₁₃	semidirect
563. C₁₃	#61885	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×#3507	2
C₂×C₁₃×#559	2
C₁₃×#3396	2
C₁₃×#3394	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3211	2
C₁₃×#3208	2
C₁₃×#3205	2
C₁₃×#3105	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#2982	2
#61885	13

Subgroups — C13×#61885 #15748224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61885 #15748224