Subgroups — C₁₃×#60879 #15747218

Order 3328.

1654 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3243	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3233	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3232	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3096	C₂	1	2	yes	maximal
13	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#557	—	2	2	no	—
18	C₁₃×#556	—	2	2	no	—
19	C₁₃×#554	—	2	4	no	—
20	C₁₃×#554	—	2	2	no	—
21	C₁₃×#551	—	2	4	no	—
22	C₁₃×#544	C₂²	1	2	yes	—
23	C₁₃×#544	C₂²	1	4	yes	complemented
24	C₁₃×#542	C₂²	1	4	yes	—
25	C₁₃×#536	C₂²	1	1	yes	characteristic
26	C₁₃×#535	C₂²	1	1	yes	characteristic
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#533	C₂²	1	2	yes	complemented
30	C₁₃×#529	C₂²	1	4	yes	—
31	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
34	C₁₃×#520	C₂²	1	2	yes	—
35	C₁₃×#519	C₂²	1	1	yes	characteristic
36	C₁₃×#518	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₁₃×#501	C₂²	1	4	yes	complemented
39	C₁₃×#500	C₂²	1	2	yes	complemented
40	C₁₃×#499	C₂²	1	2	yes	complemented
41	C₁₃×#499	C₂²	1	2	yes	complemented
42	C₁₃×#499	C₂²	1	4	yes	complemented
43	C₁₃×#498	C₂²	1	2	yes	complemented
44	C₁₃×#489	C₂²	1	4	yes	—
45	C₁₃×#488	C₂²	1	4	yes	—
46	C₁₃×#488	C₂²	1	2	yes	—
47	C₁₃×#488	C₂²	1	2	yes	—
48	C₁₃×#488	C₂²	1	2	yes	—
49	C₁₃×#488	C₂²	1	2	yes	—
50	C₁₃×#485	C₂²	1	4	yes	complemented
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#484	C₂²	1	4	yes	complemented
53	C₁₃×#483	C₂²	1	4	yes	complemented
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#482	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	—
57	C₁₃×#480	C₂²	1	4	yes	—
58	C₁₃×#479	C₂²	1	4	yes	complemented
59	C₁₃×#479	C₂²	1	4	yes	complemented
60	C₁₃×#478	C₂²	1	4	yes	—
61	C₁₃×#478	C₂²	1	4	yes	—
62	C₁₃×#477	C₂²	1	4	yes	complemented
63	C₁₃×#476	C₂²	1	4	yes	—
64	C₁₃×#475	C₂²	1	4	yes	complemented
65	C₁₃×#474	C₂²	1	4	yes	—
66	C₁₃×#433	C₂²	1	2	yes	complemented
67	C₁₃×#433	C₂²	1	2	yes	complemented
68	C₁₃×#431	C₂²	1	4	yes	complemented
69	C₁₃×#428	C₂²	1	2	yes	—
70	C₁₃×#428	C₂²	1	2	yes	—
71	C₁₃×#427	C₂²	1	2	yes	—
72	C₁₃×#427	C₂²	1	2	yes	—
73	C₁₃×#424	C₂²	1	2	yes	—
74	C₁₃×#419	C₂²	1	2	yes	—
75	C₁₃×#418	C₂²	1	2	yes	—
76	C₂×C₁₃×#103	C₂²	1	2	yes	—
77	C₂×C₁₃×#102	C₂²	1	2	yes	—
78	C₁₃×#408	C₂²	1	2	yes	—
79	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
85	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
86	C₁₃×C₄⋊Q₈	—	2	1	no	—
87	C₁₃×C₄⋊Q₈	—	2	2	no	—
88	C₁₃×C₄⋊Q₈	—	2	4	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×#127	—	2	1	no	—
93	C₁₃×#126	—	2	4	no	—
94	C₁₃×#126	—	2	4	no	—
95	C₁₃×#125	—	2	2	no	—
96	C₁₃×#125	—	2	4	no	—
97	C₁₃×#125	—	2	2	no	—
98	C₁₃×#125	—	2	4	no	—
99	C₁₃×#125	C₂³	1	4	yes	—
100	C₁₃×#125	C₂³	1	2	yes	—
101	C₁₃×#125	C₂³	1	1	yes	characteristic
102	C₁₃×#125	C₂³	1	1	yes	characteristic
103	C₁₃×#125	C₂³	1	2	yes	—
104	C₁₃×#125	C₂³	1	2	yes	—
105	C₁₃×#124	—	2	1	no	—
106	C₁₃×#124	—	2	1	no	—
107	C₁₃×#124	—	2	4	no	—
108	C₁₃×#124	—	2	2	no	—
109	C₁₃×#124	C₂³	1	2	yes	—
110	C₁₃×#124	C₂³	1	2	yes	—
111	C₁₃×#123	—	2	2	no	—
112	C₁₃×#123	—	2	4	no	—
113	C₁₃×#123	—	2	4	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	4	no	—
117	C₁₃×C₂²⋊Q₈	—	2	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	2	4	no	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×#121	C₂³	1	4	yes	—
123	C₁₃×#120	—	2	2	no	—
124	C₄×Q₈×C₁₃	—	2	2	no	—
125	C₄×Q₈×C₁₃	—	2	2	no	—
126	C₄×Q₈×C₁₃	—	2	2	no	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	4	no	—
129	C₄×Q₈×C₁₃	D₄	1	2	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
131	C₄×D₄×C₁₃	—	2	4	no	—
132	C₄×D₄×C₁₃	—	2	2	no	—
133	C₄×D₄×C₁₃	—	2	4	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	D₄	1	4	yes	—
136	C₄×D₄×C₁₃	D₄	1	2	yes	—
137	C₄×D₄×C₁₃	C₂³	1	4	yes	—
138	C₁₃×#117	—	2	2	no	—
139	C₁₃×#117	—	2	4	no	—
140	C₁₃×#117	C₂³	1	2	yes	—
141	C₁₃×#117	C₂³	1	1	yes	characteristic
142	C₁₃×#117	C₂³	1	1	yes	characteristic
143	C₁₃×#117	C₂³	1	4	yes	—
144	C₁₃×#117	C₂³	1	1	yes	characteristic
145	C₁₃×#117	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
154	C₁₃×#107	C₂³	1	2	yes	—
155	C₁₃×#107	C₂³	1	2	yes	—
156	C₁₃×#107	C₂³	1	2	yes	—
157	C₁₃×#107	C₂³	1	2	yes	—
158	C₁₃×#107	C₂³	1	4	yes	—
159	C₁₃×#107	C₂³	1	4	yes	—
160	C₁₃×#106	C₂³	1	2	yes	—
161	C₁₃×#106	C₂³	1	2	yes	—
162	C₁₃×#106	C₂³	1	2	yes	—
163	C₁₃×#106	C₂³	1	2	yes	—
164	C₁₃×#106	C₂³	1	4	yes	—
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
167	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
168	C₁₃×#103	C₂³	1	4	yes	—
169	C₁₃×#103	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×#97	C₂³	1	2	yes	—
179	C₄×C₈×C₁₃	C₂³	1	2	yes	—
180	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₁₃	C₂³	1	2	yes	—
183	#60879	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂⁴×C₁₃	—	2	1	no	—
185	C₁₃×#41	—	2	4	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	4	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
193	C₂×D₄×C₁₃	—	2	4	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×M₁₆	—	2	4	no	—
208	C₂×C₈×C₁₃	—	2	4	no	—
209	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	4	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	4	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	4	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	2	no	—
227	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
228	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
233	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
234	C₁₃×C₂²⋊C₄	—	2	1	no	—
235	C₁₃×C₂²⋊C₄	—	2	1	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	2	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
244	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
245	C₄²×C₁₃	—	2	4	no	—
246	C₄²×C₁₃	—	2	1	no	—
247	C₄²×C₁₃	—	2	4	no	—
248	C₄²×C₁₃	—	2	2	no	—
249	C₄²×C₁₃	—	2	1	no	—
250	C₄²×C₁₃	C₂×D₄	1	4	yes	—
251	C₄²×C₁₃	C₂×D₄	1	2	yes	—
252	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₄²×C₁₃	C₂⁴	1	2	yes	—
255	#3510	C₂×C₁₃	1	1	yes	characteristic
256	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3244	C₂×C₁₃	1	4	yes	complemented
258	#3243	C₂×C₁₃	1	4	yes	complemented
259	#3233	C₂×C₁₃	1	4	yes	complemented
260	#3232	C₂×C₁₃	1	4	yes	complemented
261	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#3097	C₂×C₁₃	1	2	yes	complemented
266	#3096	C₂×C₁₃	1	2	yes	—
267	#3082	C₂×C₁₃	1	2	yes	complemented
268	#3081	C₂×C₁₃	1	2	yes	complemented
269	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	4	2	no	—
272	C₂³×C₁₃	—	8	2	no	—
273	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	Q₈×C₁₃	—	2	2	no	—
276	Q₈×C₁₃	—	2	4	no	—
277	Q₈×C₁₃	—	4	2	no	—
278	Q₈×C₁₃	—	8	4	no	—
279	Q₈×C₁₃	—	8	2	no	—
280	Q₈×C₁₃	—	8	2	no	—
281	D₄×C₁₃	—	2	4	no	—
282	D₄×C₁₃	—	2	2	no	—
283	D₄×C₁₃	—	2	4	no	—
284	D₄×C₁₃	—	4	2	no	—
285	D₄×C₁₃	—	8	4	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	4	4	no	—
294	C₂×C₄×C₁₃	—	4	2	no	—
295	C₂×C₄×C₁₃	—	4	2	no	—
296	C₂×C₄×C₁₃	—	8	4	no	—
297	C₂×C₄×C₁₃	—	8	2	no	—
298	C₂×C₄×C₁₃	—	8	4	no	—
299	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
305	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
306	C₈×C₁₃	—	2	2	no	—
307	C₈×C₁₃	—	2	2	no	—
308	C₈×C₁₃	—	2	4	no	—
309	#559	—	2	2	no	—
310	#557	—	2	2	no	—
311	#556	—	2	2	no	—
312	#554	—	2	4	no	—
313	#554	—	2	2	no	—
314	#551	—	2	4	no	—
315	#544	C₂²×C₁₃	1	2	yes	—
316	#544	C₂²×C₁₃	1	4	yes	complemented
317	#542	C₂²×C₁₃	1	4	yes	—
318	#536	C₂²×C₁₃	1	1	yes	characteristic
319	#535	C₂²×C₁₃	1	1	yes	characteristic
320	#533	C₂²×C₁₃	1	1	yes	characteristic
321	#533	C₂²×C₁₃	1	1	yes	characteristic
322	#533	C₂²×C₁₃	1	2	yes	complemented
323	#529	C₂²×C₁₃	1	4	yes	—
324	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
326	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
327	#520	C₂²×C₁₃	1	2	yes	—
328	#519	C₂²×C₁₃	1	1	yes	characteristic
329	#518	C₂²×C₁₃	1	1	yes	characteristic
330	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
331	#501	C₂²×C₁₃	1	4	yes	complemented
332	#500	C₂²×C₁₃	1	2	yes	complemented
333	#499	C₂²×C₁₃	1	2	yes	complemented
334	#499	C₂²×C₁₃	1	2	yes	complemented
335	#499	C₂²×C₁₃	1	4	yes	complemented
336	#498	C₂²×C₁₃	1	2	yes	complemented
337	#489	C₂²×C₁₃	1	4	yes	—
338	#488	C₂²×C₁₃	1	4	yes	—
339	#488	C₂²×C₁₃	1	2	yes	—
340	#488	C₂²×C₁₃	1	2	yes	—
341	#488	C₂²×C₁₃	1	2	yes	—
342	#488	C₂²×C₁₃	1	2	yes	—
343	#485	C₂²×C₁₃	1	4	yes	complemented
344	#485	C₂²×C₁₃	1	4	yes	complemented
345	#484	C₂²×C₁₃	1	4	yes	complemented
346	#483	C₂²×C₁₃	1	4	yes	complemented
347	#482	C₂²×C₁₃	1	4	yes	—
348	#482	C₂²×C₁₃	1	4	yes	—
349	#481	C₂²×C₁₃	1	4	yes	—
350	#480	C₂²×C₁₃	1	4	yes	—
351	#479	C₂²×C₁₃	1	4	yes	complemented
352	#479	C₂²×C₁₃	1	4	yes	complemented
353	#478	C₂²×C₁₃	1	4	yes	—
354	#478	C₂²×C₁₃	1	4	yes	—
355	#477	C₂²×C₁₃	1	4	yes	complemented
356	#476	C₂²×C₁₃	1	4	yes	—
357	#475	C₂²×C₁₃	1	4	yes	complemented
358	#474	C₂²×C₁₃	1	4	yes	—
359	#433	C₂²×C₁₃	1	2	yes	complemented
360	#433	C₂²×C₁₃	1	2	yes	complemented
361	#431	C₂²×C₁₃	1	4	yes	complemented
362	#428	C₂²×C₁₃	1	2	yes	—
363	#428	C₂²×C₁₃	1	2	yes	—
364	#427	C₂²×C₁₃	1	2	yes	—
365	#427	C₂²×C₁₃	1	2	yes	—
366	#424	C₂²×C₁₃	1	2	yes	—
367	#419	C₂²×C₁₃	1	2	yes	—
368	#418	C₂²×C₁₃	1	2	yes	—
369	C₂×#103	C₂²×C₁₃	1	2	yes	—
370	C₂×#102	C₂²×C₁₃	1	2	yes	—
371	#408	C₂²×C₁₃	1	2	yes	—
372	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×C₁₃	—	2	2	no	—
375	C₂²×C₁₃	—	2	4	no	—
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	4	4	no	—
378	C₂²×C₁₃	—	4	2	no	—
379	C₂²×C₁₃	—	16	2	no	—
380	C₂²×C₁₃	#536	1	2	yes	—
381	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₁₃	—	2	2	no	—
383	C₄×C₁₃	—	2	4	no	—
384	C₄×C₁₃	—	2	2	no	—
385	C₄×C₁₃	—	2	2	no	—
386	C₄×C₁₃	—	4	2	no	—
387	C₄×C₁₃	—	4	4	no	—
388	C₄×C₁₃	—	4	2	no	—
389	C₄×C₁₃	—	4	2	no	—
390	C₄×C₁₃	—	4	2	no	—
391	C₄×C₁₃	—	4	2	no	—
392	C₄×C₁₃	#536	1	2	yes	—
393	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
394	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
398	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	—	2	2	no	—
401	C₄⋊Q₈	—	2	4	no	—
402	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
403	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
404	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
405	#127	—	2	1	no	—
406	#126	—	2	4	no	—
407	#126	—	2	4	no	—
408	#125	—	2	2	no	—
409	#125	—	2	4	no	—
410	#125	—	2	2	no	—
411	#125	—	2	4	no	—
412	#125	C₂³×C₁₃	1	2	yes	—
413	#125	C₂³×C₁₃	1	2	yes	—
414	#125	C₂³×C₁₃	1	1	yes	characteristic
415	#125	C₂³×C₁₃	1	4	yes	—
416	#125	C₂³×C₁₃	1	2	yes	—
417	#125	C₂³×C₁₃	1	1	yes	characteristic
418	#124	—	2	1	no	—
419	#124	—	2	1	no	—
420	#124	—	2	4	no	—
421	#124	—	2	2	no	—
422	#124	C₂³×C₁₃	1	2	yes	—
423	#124	C₂³×C₁₃	1	2	yes	—
424	#123	—	2	2	no	—
425	#123	—	2	4	no	—
426	#123	—	2	4	no	—
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	4	no	—
430	C₂²⋊Q₈	—	2	4	no	—
431	C₂²⋊Q₈	—	2	4	no	—
432	C₂²⋊Q₈	—	2	4	no	—
433	C₂²⋊Q₈	—	2	4	no	—
434	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
435	#121	C₂³×C₁₃	1	4	yes	—
436	#120	—	2	2	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	2	2	no	—
439	C₄×Q₈	—	2	2	no	—
440	C₄×Q₈	—	2	2	no	—
441	C₄×Q₈	—	2	4	no	—
442	C₄×Q₈	D₄×C₁₃	1	2	yes	—
443	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
444	C₄×D₄	—	2	4	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	4	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	D₄×C₁₃	1	4	yes	—
449	C₄×D₄	D₄×C₁₃	1	2	yes	—
450	C₄×D₄	C₂³×C₁₃	1	4	yes	—
451	#117	—	2	2	no	—
452	#117	—	2	4	no	—
453	#117	C₂³×C₁₃	1	1	yes	characteristic
454	#117	C₂³×C₁₃	1	1	yes	characteristic
455	#117	C₂³×C₁₃	1	2	yes	—
456	#117	C₂³×C₁₃	1	4	yes	—
457	#117	C₂³×C₁₃	1	1	yes	characteristic
458	#117	C₂³×C₁₃	1	2	yes	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	—	2	4	no	—
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
467	#107	C₂³×C₁₃	1	2	yes	—
468	#107	C₂³×C₁₃	1	2	yes	—
469	#107	C₂³×C₁₃	1	2	yes	—
470	#107	C₂³×C₁₃	1	2	yes	—
471	#107	C₂³×C₁₃	1	4	yes	—
472	#107	C₂³×C₁₃	1	4	yes	—
473	#106	C₂³×C₁₃	1	2	yes	—
474	#106	C₂³×C₁₃	1	2	yes	—
475	#106	C₂³×C₁₃	1	2	yes	—
476	#106	C₂³×C₁₃	1	2	yes	—
477	#106	C₂³×C₁₃	1	4	yes	—
478	#106	C₂³×C₁₃	1	4	yes	—
479	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
480	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
481	#103	C₂³×C₁₃	1	4	yes	—
482	#103	C₂³×C₁₃	1	4	yes	—
483	#103	C₂³×C₁₃	1	4	yes	—
484	#103	C₂³×C₁₃	1	4	yes	—
485	#102	C₂³×C₁₃	1	4	yes	—
486	#102	C₂³×C₁₃	1	4	yes	—
487	#102	C₂³×C₁₃	1	4	yes	—
488	#102	C₂³×C₁₃	1	4	yes	—
489	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
490	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
491	#97	C₂³×C₁₃	1	2	yes	—
492	C₄×C₈	C₂³×C₁₃	1	2	yes	—
493	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₄×C₈	C₂³×C₁₃	1	2	yes	—
496	C₂×C₁₃	—	2	2	no	—
497	C₂×C₁₃	—	4	2	no	—
498	C₂×C₁₃	—	8	2	no	—
499	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
500	C₂×C₁₃	#3584	1	2	yes	—
501	C₂⁴	—	2	1	no	—
502	#41	—	2	4	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	2	4	no	—
508	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
521	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	M₁₆	—	2	4	no	—
525	C₂×C₈	—	2	4	no	—
526	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
527	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
528	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
545	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
546	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
547	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
548	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
549	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
550	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
561	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	1	no	—
567	C₄²	C₂×D₄×C₁₃	1	4	yes	—
568	C₄²	C₂×D₄×C₁₃	1	2	yes	—
569	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
570	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
571	C₄²	C₂⁴×C₁₃	1	2	yes	—
572	C₁₃	#60879	1	1	yes	characteristic, direct product factor, Sylow
573	C₂³	—	2	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	8	2	no	—
576	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
577	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	4	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	8	4	no	—
582	Q₈	—	8	2	no	—
583	Q₈	—	8	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	4	no	—
587	D₄	—	4	2	no	—
588	D₄	—	8	4	no	—
589	C₂×C₄	—	2	4	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	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	8	4	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
603	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
604	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
605	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
607	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
608	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	2	2	no	—
611	C₈	—	2	4	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	16	2	no	—
618	C₂²	C₁₃×#536	1	2	yes	—
619	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	4	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	C₁₃×#536	1	2	yes	—
631	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	8	2	no	—
635	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
636	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3244	C₂	semidirect
4. C₁₃×#3243	C₂	semidirect
5. C₁₃×#3233	C₂	semidirect
6. C₁₃×#3232	C₂	semidirect
7. C₁₃×#3166	C₂	semidirect
8. C₁₃×#3160	C₂	semidirect
9. C₁₃×#3140	C₂	semidirect
10. C₂×C₁₃×#488	C₂	semidirect
11. C₁₃×#3097	C₂	semidirect
13. C₁₃×#3082	C₂	semidirect
14. C₁₃×#3081	C₂	semidirect
15. C₁₃×#2922	C₂	semidirect
23. C₁₃×#544	C₂²	semidirect
29. C₁₃×#533	C₂²	semidirect
32. C₂×C₁₃×#125	C₂²	semidirect
38. C₁₃×#501	C₂²	semidirect
39. C₁₃×#500	C₂²	semidirect
40. C₁₃×#499	C₂²	semidirect
41. C₁₃×#499	C₂²	semidirect
42. C₁₃×#499	C₂²	semidirect
43. C₁₃×#498	C₂²	semidirect
50. C₁₃×#485	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
52. C₁₃×#484	C₂²	semidirect
53. C₁₃×#483	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
62. C₁₃×#477	C₂²	semidirect
64. C₁₃×#475	C₂²	semidirect
66. C₁₃×#433	C₂²	semidirect
67. C₁₃×#433	C₂²	semidirect
68. C₁₃×#431	C₂²	semidirect
183. #60879	C₁₃	direct (N × H)
256. #3504	C₂×C₁₃	semidirect
257. #3244	C₂×C₁₃	semidirect
258. #3243	C₂×C₁₃	semidirect
259. #3233	C₂×C₁₃	semidirect
260. #3232	C₂×C₁₃	semidirect
261. #3166	C₂×C₁₃	semidirect
262. #3160	C₂×C₁₃	semidirect
263. #3140	C₂×C₁₃	semidirect
264. C₂×#488	C₂×C₁₃	semidirect
265. #3097	C₂×C₁₃	semidirect
267. #3082	C₂×C₁₃	semidirect
268. #3081	C₂×C₁₃	semidirect
269. #2922	C₂×C₁₃	semidirect
316. #544	C₂²×C₁₃	semidirect
322. #533	C₂²×C₁₃	semidirect
325. C₂×#125	C₂²×C₁₃	semidirect
331. #501	C₂²×C₁₃	semidirect
332. #500	C₂²×C₁₃	semidirect
333. #499	C₂²×C₁₃	semidirect
334. #499	C₂²×C₁₃	semidirect
335. #499	C₂²×C₁₃	semidirect
336. #498	C₂²×C₁₃	semidirect
343. #485	C₂²×C₁₃	semidirect
344. #485	C₂²×C₁₃	semidirect
345. #484	C₂²×C₁₃	semidirect
346. #483	C₂²×C₁₃	semidirect
351. #479	C₂²×C₁₃	semidirect
352. #479	C₂²×C₁₃	semidirect
355. #477	C₂²×C₁₃	semidirect
357. #475	C₂²×C₁₃	semidirect
359. #433	C₂²×C₁₃	semidirect
360. #433	C₂²×C₁₃	semidirect
361. #431	C₂²×C₁₃	semidirect
572. C₁₃	#60879	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×#3510	2
C₁₃×#3504	2
C₁₃×#3244	2
C₁₃×#3243	2
C₁₃×#3233	2
C₁₃×#3232	2
C₁₃×#3166	2
C₁₃×#3160	2
C₁₃×#3140	2
C₂×C₁₃×#488	2
C₁₃×#3097	2
C₁₃×#3096	2
C₁₃×#3082	2
C₁₃×#3081	2
C₁₃×#2922	2
#60879	13

Subgroups — C13×#60879 #15747218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60879 #15747218