Subgroups — C₁₃×#60870 #15747209

Order 3328.

1690 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3244	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3243	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3165	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3095	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3094	C₂	1	2	yes	maximal
9	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#544	—	2	1	no	—
13	C₁₃×#544	—	2	1	no	—
14	C₁₃×#544	C₂²	1	4	yes	complemented
15	C₁₃×#544	C₂²	1	4	yes	complemented
16	C₁₃×#543	—	2	1	no	—
17	C₁₃×#543	—	2	1	no	—
18	C₁₃×#542	—	2	4	no	—
19	C₁₃×#542	C₂²	1	8	yes	—
20	C₁₃×#533	—	2	4	no	—
21	C₁₃×#533	C₂²	1	2	yes	—
22	C₁₃×#533	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#126	—	2	1	no	—
25	C₂×C₁₃×#124	—	2	1	no	—
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#123	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₁₃×#501	C₂²	1	8	yes	complemented
36	C₁₃×#500	C₂²	1	4	yes	complemented
37	C₁₃×#498	C₂²	1	4	yes	complemented
38	C₁₃×#489	C₂²	1	4	yes	complemented
39	C₁₃×#489	C₂²	1	4	yes	complemented
40	C₁₃×#488	C₂²	1	8	yes	complemented
41	C₁₃×#485	C₂²	1	8	yes	complemented
42	C₁₃×#484	C₂²	1	4	yes	complemented
43	C₁₃×#483	C₂²	1	4	yes	complemented
44	C₁₃×#482	C₂²	1	8	yes	—
45	C₁₃×#481	C₂²	1	4	yes	—
46	C₁₃×#480	C₂²	1	4	yes	—
47	C₁₃×#479	C₂²	1	8	yes	complemented
48	C₁₃×#478	C₂²	1	8	yes	complemented
49	C₁₃×#477	C₂²	1	4	yes	complemented
50	C₁₃×#476	C₂²	1	4	yes	complemented
51	C₁₃×#475	C₂²	1	4	yes	complemented
52	C₁₃×#474	C₂²	1	4	yes	complemented
53	C₁₃×#433	C₂²	1	8	yes	complemented
54	C₁₃×#428	C₂²	1	4	yes	—
55	C₁₃×#428	C₂²	1	4	yes	—
56	C₁₃×#423	C₂²	1	2	yes	—
57	C₁₃×#419	C₂²	1	4	yes	—
58	C₁₃×#418	C₂²	1	4	yes	—
59	C₁₃×#407	C₂²	1	2	yes	—
60	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	—	2	4	no	—
69	C₁₃×C₄⋊Q₈	—	2	4	no	—
70	C₁₃×C₄⋊Q₈	—	2	2	no	—
71	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×#126	—	2	8	no	—
77	C₁₃×#125	—	2	4	no	—
78	C₁₃×#125	—	2	4	no	—
79	C₁₃×#125	C₂³	1	4	yes	—
80	C₁₃×#125	C₂³	1	4	yes	—
81	C₁₃×#124	—	2	8	no	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	C₂³	1	4	yes	—
84	C₁₃×#123	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	8	no	—
91	C₁₃×C₂²⋊Q₈	—	2	4	no	—
92	C₁₃×C₂²⋊Q₈	—	2	4	no	—
93	C₁₃×C₂²⋊Q₈	—	2	4	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	C₂³	1	4	yes	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	C₂³	1	4	yes	—
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	2	2	no	—
108	C₁₃×#117	D₄	1	4	yes	—
109	C₁₃×#117	C₂³	1	4	yes	—
110	C₁₃×#117	C₂³	1	4	yes	—
111	C₁₃×#117	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	—	2	2	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₁₃×#107	C₂³	1	8	yes	—
134	C₁₃×#107	C₂³	1	8	yes	—
135	C₁₃×#106	C₂³	1	8	yes	—
136	C₁₃×#106	C₂³	1	8	yes	—
137	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
138	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
139	C₁₃×#103	C₂³	1	8	yes	—
140	C₁₃×#103	C₂³	1	8	yes	—
141	C₁₃×#102	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₁₃×#97	C₂³	1	4	yes	—
146	C₄×C₈×C₁₃	C₂³	1	4	yes	—
147	#60870	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂⁴×C₁₃	—	2	1	no	—
149	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	—	2	2	no	—
154	C₂×Q₈×C₁₃	—	2	2	no	—
155	C₂×Q₈×C₁₃	—	2	4	no	—
156	C₂×Q₈×C₁₃	—	2	4	no	—
157	C₂×Q₈×C₁₃	—	8	2	no	—
158	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	8	2	no	—
163	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	8	2	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×M₁₆	—	2	8	no	—
181	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
211	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂⁴	1	2	yes	—
218	C₄²×C₁₃	C₂⁴	1	2	yes	—
219	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#542	C₂×C₁₃	1	1	yes	characteristic
221	#3244	C₂×C₁₃	1	8	yes	complemented
222	#3243	C₂×C₁₃	1	8	yes	complemented
223	#3165	C₂×C₁₃	1	2	yes	complemented
224	#3140	C₂×C₁₃	1	2	yes	complemented
225	#3095	C₂×C₁₃	1	2	yes	complemented
226	#3094	C₂×C₁₃	1	2	yes	—
227	#3078	C₂×C₁₃	1	2	yes	complemented
228	#3077	C₂×C₁₃	1	2	yes	complemented
229	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	—	4	2	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
238	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	2	4	no	—
240	Q₈×C₁₃	—	4	2	no	—
241	Q₈×C₁₃	—	8	2	no	—
242	Q₈×C₁₃	—	8	2	no	—
243	Q₈×C₁₃	—	8	2	no	—
244	Q₈×C₁₃	—	8	2	no	—
245	Q₈×C₁₃	—	8	4	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	8	4	no	—
265	C₂×C₄×C₁₃	—	8	2	no	—
266	C₂×C₄×C₁₃	—	8	2	no	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
275	C₈×C₁₃	—	2	8	no	—
276	#544	—	2	1	no	—
277	#544	—	2	1	no	—
278	#544	C₂²×C₁₃	1	4	yes	complemented
279	#544	C₂²×C₁₃	1	4	yes	complemented
280	#543	—	2	1	no	—
281	#543	—	2	1	no	—
282	#542	—	2	4	no	—
283	#542	C₂²×C₁₃	1	8	yes	—
284	#533	—	2	4	no	—
285	#533	C₂²×C₁₃	1	2	yes	—
286	#533	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#126	—	2	1	no	—
289	C₂×#124	—	2	1	no	—
290	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#123	—	2	1	no	—
292	C₂×C₂²⋊Q₈	—	2	1	no	—
293	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#117	C₂²×C₁₃	1	2	yes	—
298	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
299	#501	C₂²×C₁₃	1	8	yes	complemented
300	#500	C₂²×C₁₃	1	4	yes	complemented
301	#498	C₂²×C₁₃	1	4	yes	complemented
302	#489	C₂²×C₁₃	1	4	yes	complemented
303	#489	C₂²×C₁₃	1	4	yes	complemented
304	#488	C₂²×C₁₃	1	8	yes	complemented
305	#485	C₂²×C₁₃	1	8	yes	complemented
306	#484	C₂²×C₁₃	1	4	yes	complemented
307	#483	C₂²×C₁₃	1	4	yes	complemented
308	#482	C₂²×C₁₃	1	8	yes	—
309	#481	C₂²×C₁₃	1	4	yes	—
310	#480	C₂²×C₁₃	1	4	yes	—
311	#479	C₂²×C₁₃	1	8	yes	complemented
312	#478	C₂²×C₁₃	1	8	yes	complemented
313	#477	C₂²×C₁₃	1	4	yes	complemented
314	#476	C₂²×C₁₃	1	4	yes	complemented
315	#475	C₂²×C₁₃	1	4	yes	complemented
316	#474	C₂²×C₁₃	1	4	yes	complemented
317	#433	C₂²×C₁₃	1	8	yes	complemented
318	#428	C₂²×C₁₃	1	4	yes	—
319	#428	C₂²×C₁₃	1	4	yes	—
320	#423	C₂²×C₁₃	1	2	yes	—
321	#419	C₂²×C₁₃	1	4	yes	—
322	#418	C₂²×C₁₃	1	4	yes	—
323	#407	C₂²×C₁₃	1	2	yes	—
324	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	2	no	—
333	C₂²×C₁₃	—	8	2	no	—
334	C₂²×C₁₃	—	8	4	no	—
335	C₂²×C₁₃	#536	1	2	yes	—
336	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	—	4	2	no	—
344	C₄×C₁₃	—	4	4	no	—
345	C₄×C₁₃	—	4	4	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	#536	1	2	yes	—
348	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
349	C₂²×Q₈	—	2	1	no	—
350	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
356	C₄⋊Q₈	—	2	4	no	—
357	C₄⋊Q₈	—	2	4	no	—
358	C₄⋊Q₈	—	2	2	no	—
359	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
360	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
361	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
362	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
363	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
364	#126	—	2	8	no	—
365	#125	—	2	4	no	—
366	#125	—	2	4	no	—
367	#125	C₂³×C₁₃	1	4	yes	—
368	#125	C₂³×C₁₃	1	4	yes	—
369	#124	—	2	8	no	—
370	#124	—	2	2	no	—
371	#124	C₂³×C₁₃	1	4	yes	—
372	#123	—	2	8	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	8	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	4	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	C₂²⋊Q₈	—	2	4	no	—
383	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
384	#121	—	2	2	no	—
385	#121	C₂³×C₁₃	1	4	yes	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	C₂³×C₁₃	1	4	yes	—
394	#117	—	2	2	no	—
395	#117	—	2	2	no	—
396	#117	D₄×C₁₃	1	4	yes	—
397	#117	C₂³×C₁₃	1	4	yes	—
398	#117	C₂³×C₁₃	1	4	yes	—
399	#117	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	2	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
421	#107	C₂³×C₁₃	1	8	yes	—
422	#107	C₂³×C₁₃	1	8	yes	—
423	#106	C₂³×C₁₃	1	8	yes	—
424	#106	C₂³×C₁₃	1	8	yes	—
425	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
426	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
427	#103	C₂³×C₁₃	1	8	yes	—
428	#103	C₂³×C₁₃	1	8	yes	—
429	#102	C₂³×C₁₃	1	8	yes	—
430	#102	C₂³×C₁₃	1	8	yes	—
431	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
432	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
433	#97	C₂³×C₁₃	1	4	yes	—
434	C₄×C₈	C₂³×C₁₃	1	4	yes	—
435	C₂×C₁₃	—	2	2	no	—
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	—	8	2	no	—
438	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
439	C₂×C₁₃	#3585	1	1	yes	characteristic
440	C₂×C₁₃	#3586	1	1	yes	characteristic
441	C₂⁴	—	2	1	no	—
442	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	8	2	no	—
451	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	8	2	no	—
456	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	8	2	no	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	M₁₆	—	2	8	no	—
474	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
491	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
492	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
494	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
495	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
504	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
505	C₄²	—	2	4	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	C₂×D₄×C₁₃	1	2	yes	—
509	C₄²	C₂×D₄×C₁₃	1	2	yes	—
510	C₄²	C₂⁴×C₁₃	1	2	yes	—
511	C₄²	C₂⁴×C₁₃	1	2	yes	—
512	C₁₃	#60870	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
521	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	8	4	no	—
525	Q₈	—	8	2	no	—
526	Q₈	—	8	2	no	—
527	Q₈	—	8	2	no	—
528	Q₈	—	8	2	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	4	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
557	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
558	C₈	—	2	8	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	4	no	—
569	C₂²	C₁₃×#536	1	2	yes	—
570	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	2	no	—
581	C₄	C₁₃×#536	1	2	yes	—
582	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	2	no	—
586	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
587	C₂	C₁₃×#3585	1	1	yes	characteristic
588	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3458	C₂	semidirect
3. C₁₃×#3244	C₂	semidirect
4. C₁₃×#3243	C₂	semidirect
5. C₁₃×#3165	C₂	semidirect
6. C₁₃×#3140	C₂	semidirect
7. C₁₃×#3095	C₂	semidirect
9. C₁₃×#3078	C₂	semidirect
10. C₁₃×#3077	C₂	semidirect
11. C₁₃×#2921	C₂	semidirect
14. C₁₃×#544	C₂²	semidirect
15. C₁₃×#544	C₂²	semidirect
35. C₁₃×#501	C₂²	semidirect
36. C₁₃×#500	C₂²	semidirect
37. C₁₃×#498	C₂²	semidirect
38. C₁₃×#489	C₂²	semidirect
39. C₁₃×#489	C₂²	semidirect
40. C₁₃×#488	C₂²	semidirect
41. C₁₃×#485	C₂²	semidirect
42. C₁₃×#484	C₂²	semidirect
43. C₁₃×#483	C₂²	semidirect
47. C₁₃×#479	C₂²	semidirect
48. C₁₃×#478	C₂²	semidirect
49. C₁₃×#477	C₂²	semidirect
50. C₁₃×#476	C₂²	semidirect
51. C₁₃×#475	C₂²	semidirect
52. C₁₃×#474	C₂²	semidirect
53. C₁₃×#433	C₂²	semidirect
147. #60870	C₁₃	direct (N × H)
219. #3458	C₂×C₁₃	semidirect
221. #3244	C₂×C₁₃	semidirect
222. #3243	C₂×C₁₃	semidirect
223. #3165	C₂×C₁₃	semidirect
224. #3140	C₂×C₁₃	semidirect
225. #3095	C₂×C₁₃	semidirect
227. #3078	C₂×C₁₃	semidirect
228. #3077	C₂×C₁₃	semidirect
229. #2921	C₂×C₁₃	semidirect
278. #544	C₂²×C₁₃	semidirect
279. #544	C₂²×C₁₃	semidirect
299. #501	C₂²×C₁₃	semidirect
300. #500	C₂²×C₁₃	semidirect
301. #498	C₂²×C₁₃	semidirect
302. #489	C₂²×C₁₃	semidirect
303. #489	C₂²×C₁₃	semidirect
304. #488	C₂²×C₁₃	semidirect
305. #485	C₂²×C₁₃	semidirect
306. #484	C₂²×C₁₃	semidirect
307. #483	C₂²×C₁₃	semidirect
311. #479	C₂²×C₁₃	semidirect
312. #478	C₂²×C₁₃	semidirect
313. #477	C₂²×C₁₃	semidirect
314. #476	C₂²×C₁₃	semidirect
315. #475	C₂²×C₁₃	semidirect
316. #474	C₂²×C₁₃	semidirect
317. #433	C₂²×C₁₃	semidirect
512. C₁₃	#60870	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×#3458	2
C₂×C₁₃×#542	2
C₁₃×#3244	2
C₁₃×#3243	2
C₁₃×#3165	2
C₁₃×#3140	2
C₁₃×#3095	2
C₁₃×#3094	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#2921	2
#60870	13

Subgroups — C13×#60870 #15747209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60870 #15747209