Subgroups — C₁₃×#60863 #15747202

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3237	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3235	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3233	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3166	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3093	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3079	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#533	—	2	2	no	—
12	C₁₃×#533	—	2	2	no	—
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	1	yes	characteristic
15	C₁₃×#533	C₂²	1	4	yes	—
16	C₁₃×#533	C₂²	1	4	yes	—
17	C₁₃×#532	C₂²	1	1	yes	characteristic
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	C₂²	1	4	yes	—
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₁₃×#525	—	2	2	no	—
25	C₁₃×#525	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
27	C₄×C₁₃×#41	—	2	2	no	—
28	C₄×C₁₃×#41	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#501	C₂²	1	8	yes	complemented
33	C₁₃×#499	C₂²	1	8	yes	complemented
34	C₁₃×#491	C₂²	1	4	yes	complemented
35	C₁₃×#490	C₂²	1	4	yes	complemented
36	C₁₃×#488	C₂²	1	8	yes	complemented
37	C₁₃×#485	C₂²	1	16	yes	—
38	C₁₃×#482	C₂²	1	16	yes	—
39	C₁₃×#477	C₂²	1	8	yes	complemented
40	C₁₃×#476	C₂²	1	8	yes	complemented
41	C₁₃×#475	C₂²	1	8	yes	complemented
42	C₁₃×#474	C₂²	1	8	yes	complemented
43	C₁₃×#432	C₂²	1	4	yes	—
44	C₁₃×#431	C₂²	1	4	yes	—
45	C₁₃×#428	C₂²	1	8	yes	—
46	C₁₃×#423	C₂²	1	2	yes	—
47	C₁₃×#417	C₂²	1	8	yes	—
48	C₁₃×#407	C₂²	1	2	yes	—
49	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	C₂³	1	2	yes	—
52	C₂²×Q₈×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	D₄	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₃×#127	C₂³	1	1	yes	characteristic
63	C₁₃×#126	—	2	4	no	—
64	C₁₃×#125	—	2	4	no	—
65	C₁₃×#125	—	2	2	no	—
66	C₁₃×#125	C₂³	1	4	yes	—
67	C₁₃×#125	C₂³	1	4	yes	—
68	C₁₃×#125	C₂³	1	2	yes	—
69	C₁₃×#124	—	2	2	no	—
70	C₁₃×#124	C₂³	1	2	yes	—
71	C₁₃×#123	—	2	4	no	—
72	C₁₃×#123	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
80	C₁₃×#121	—	2	2	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	C₂³	1	4	yes	—
83	C₁₃×#120	—	2	2	no	—
84	C₄×Q₈×C₁₃	—	2	4	no	—
85	C₄×Q₈×C₁₃	—	2	4	no	—
86	C₄×Q₈×C₁₃	—	2	4	no	—
87	C₄×Q₈×C₁₃	—	2	4	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	—	2	4	no	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	C₂³	1	4	yes	—
97	C₁₃×#117	—	2	4	no	—
98	C₁₃×#117	—	2	2	no	—
99	C₁₃×#117	—	2	4	no	—
100	C₁₃×#117	—	2	2	no	—
101	C₁₃×#117	C₂³	1	2	yes	—
102	C₁₃×#117	C₂³	1	8	yes	—
103	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₄²×C₁₃	—	2	2	no	—
108	C₂×C₄²×C₁₃	—	2	2	no	—
109	C₂×C₄²×C₁₃	D₄	1	2	yes	—
110	C₂×C₄²×C₁₃	D₄	1	2	yes	—
111	C₂×C₄²×C₁₃	D₄	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₁₃×#107	C₂³	1	16	yes	—
117	C₁₃×#106	C₂³	1	16	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
119	C₁₃×#103	C₂³	1	16	yes	—
120	C₁₃×#102	C₂³	1	16	yes	—
121	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	#60863	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×#41	—	2	8	no	—
127	C₁₃×#41	—	4	8	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	4	8	no	—
132	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	4	4	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×M₁₆	—	2	8	no	—
153	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₄²×C₁₃	—	2	4	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	—	2	8	no	—
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	2	yes	—
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂×D₄	1	2	yes	—
181	C₄²×C₁₃	C₂×D₄	1	2	yes	—
182	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₄²×C₁₃	C₂⁴	1	2	yes	—
185	#3444	C₂×C₁₃	1	1	yes	characteristic
186	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#3237	C₂×C₁₃	1	4	yes	complemented
188	#3235	C₂×C₁₃	1	4	yes	complemented
189	#3233	C₂×C₁₃	1	8	yes	complemented
190	#3166	C₂×C₁₃	1	2	yes	complemented
191	#3142	C₂×C₁₃	1	2	yes	complemented
192	#3093	C₂×C₁₃	1	4	yes	complemented
193	#3079	C₂×C₁₃	1	4	yes	complemented
194	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	4	no	—
201	Q₈×C₁₃	—	4	8	no	—
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	4	8	no	—
204	D₄×C₁₃	—	2	4	no	—
205	D₄×C₁₃	—	4	4	no	—
206	D₄×C₁₃	—	4	8	no	—
207	D₄×C₁₃	—	4	4	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	8	no	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₃	—	2	8	no	—
232	#533	—	2	2	no	—
233	#533	—	2	2	no	—
234	#533	C₂²×C₁₃	1	2	yes	—
235	#533	C₂²×C₁₃	1	1	yes	characteristic
236	#533	C₂²×C₁₃	1	4	yes	—
237	#533	C₂²×C₁₃	1	4	yes	—
238	#532	C₂²×C₁₃	1	1	yes	characteristic
239	#532	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	#529	—	2	2	no	—
242	#529	—	2	2	no	—
243	#529	C₂²×C₁₃	1	4	yes	—
244	C₂×#125	C₂²×C₁₃	1	2	yes	—
245	#525	—	2	2	no	—
246	#525	C₂²×C₁₃	1	2	yes	—
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	C₄×#41	—	2	2	no	—
249	C₄×#41	C₂²×C₁₃	1	2	yes	—
250	C₂×C₄×Q₈	—	2	2	no	—
251	C₂×#117	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
253	#501	C₂²×C₁₃	1	8	yes	complemented
254	#499	C₂²×C₁₃	1	8	yes	complemented
255	#491	C₂²×C₁₃	1	4	yes	complemented
256	#490	C₂²×C₁₃	1	4	yes	complemented
257	#488	C₂²×C₁₃	1	8	yes	complemented
258	#485	C₂²×C₁₃	1	16	yes	—
259	#482	C₂²×C₁₃	1	16	yes	—
260	#477	C₂²×C₁₃	1	8	yes	complemented
261	#476	C₂²×C₁₃	1	8	yes	complemented
262	#475	C₂²×C₁₃	1	8	yes	complemented
263	#474	C₂²×C₁₃	1	8	yes	complemented
264	#432	C₂²×C₁₃	1	4	yes	—
265	#431	C₂²×C₁₃	1	4	yes	—
266	#428	C₂²×C₁₃	1	8	yes	—
267	#423	C₂²×C₁₃	1	2	yes	—
268	#417	C₂²×C₁₃	1	8	yes	—
269	#407	C₂²×C₁₃	1	2	yes	—
270	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	4	4	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	#536	1	2	yes	—
279	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	4	4	no	—
286	C₄×C₁₃	—	4	8	no	—
287	C₄×C₁₃	#536	1	2	yes	—
288	C₄×C₁₃	#575	1	4	yes	—
289	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	C₂³×C₁₃	1	2	yes	—
292	C₂²×Q₈	—	2	2	no	—
293	C₂³×C₄	D₄×C₁₃	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
300	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
301	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
302	#127	C₂³×C₁₃	1	1	yes	characteristic
303	#126	—	2	4	no	—
304	#125	—	2	4	no	—
305	#125	—	2	2	no	—
306	#125	C₂³×C₁₃	1	4	yes	—
307	#125	C₂³×C₁₃	1	4	yes	—
308	#125	C₂³×C₁₃	1	2	yes	—
309	#124	—	2	2	no	—
310	#124	C₂³×C₁₃	1	2	yes	—
311	#123	—	2	4	no	—
312	#123	—	2	2	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
320	#121	—	2	2	no	—
321	#121	—	2	2	no	—
322	#121	C₂³×C₁₃	1	4	yes	—
323	#120	—	2	2	no	—
324	C₄×Q₈	—	2	4	no	—
325	C₄×Q₈	—	2	4	no	—
326	C₄×Q₈	—	2	4	no	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	C₂³×C₁₃	1	4	yes	—
337	#117	—	2	4	no	—
338	#117	—	2	2	no	—
339	#117	—	2	4	no	—
340	#117	—	2	2	no	—
341	#117	C₂³×C₁₃	1	8	yes	—
342	#117	C₂³×C₁₃	1	2	yes	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	D₄×C₁₃	1	2	yes	—
350	C₂×C₄²	D₄×C₁₃	1	2	yes	—
351	C₂×C₄²	D₄×C₁₃	1	2	yes	—
352	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
356	#107	C₂³×C₁₃	1	16	yes	—
357	#106	C₂³×C₁₃	1	16	yes	—
358	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
359	#103	C₂³×C₁₃	1	16	yes	—
360	#102	C₂³×C₁₃	1	16	yes	—
361	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
362	#97	C₂³×C₁₃	1	4	yes	—
363	C₄×C₈	C₂³×C₁₃	1	4	yes	—
364	C₂×C₁₃	—	2	2	no	—
365	C₂×C₁₃	—	4	2	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#575	1	2	yes	—
369	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
370	#41	—	2	8	no	—
371	#41	—	4	8	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	4	8	no	—
376	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	M₁₆	—	2	8	no	—
397	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
409	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	8	no	—
419	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₁₃	1	2	yes	—
421	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₄²	C₂×D₄×C₁₃	1	2	yes	—
423	C₄²	C₂×D₄×C₁₃	1	2	yes	—
424	C₄²	C₂×D₄×C₁₃	1	2	yes	—
425	C₄²	C₂×D₄×C₁₃	1	2	yes	—
426	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
427	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₄²	C₂⁴×C₁₃	1	2	yes	—
429	C₁₃	#60863	1	1	yes	characteristic, direct product factor, Sylow
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
434	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	4	8	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	4	8	no	—
439	D₄	—	2	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	8	no	—
442	D₄	—	4	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
464	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
465	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
466	C₈	—	2	8	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	C₁₃×#536	1	2	yes	—
475	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	8	no	—
482	C₄	—	4	2	no	—
483	C₄	C₁₃×#536	1	2	yes	—
484	C₄	C₁₃×#575	1	4	yes	—
485	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
486	C₂	—	2	2	no	—
487	C₂	—	4	2	no	—
488	C₂	—	8	2	no	—
489	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
490	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3237	C₂	semidirect
4. C₁₃×#3235	C₂	semidirect
5. C₁₃×#3233	C₂	semidirect
6. C₁₃×#3166	C₂	semidirect
7. C₁₃×#3142	C₂	semidirect
8. C₁₃×#3093	C₂	semidirect
9. C₁₃×#3079	C₂	semidirect
10. C₁₃×#2920	C₂	semidirect
32. C₁₃×#501	C₂²	semidirect
33. C₁₃×#499	C₂²	semidirect
34. C₁₃×#491	C₂²	semidirect
35. C₁₃×#490	C₂²	semidirect
36. C₁₃×#488	C₂²	semidirect
39. C₁₃×#477	C₂²	semidirect
40. C₁₃×#476	C₂²	semidirect
41. C₁₃×#475	C₂²	semidirect
42. C₁₃×#474	C₂²	semidirect
124. #60863	C₁₃	direct (N × H)
186. C₂×#533	C₂×C₁₃	semidirect
187. #3237	C₂×C₁₃	semidirect
188. #3235	C₂×C₁₃	semidirect
189. #3233	C₂×C₁₃	semidirect
190. #3166	C₂×C₁₃	semidirect
191. #3142	C₂×C₁₃	semidirect
192. #3093	C₂×C₁₃	semidirect
193. #3079	C₂×C₁₃	semidirect
194. #2920	C₂×C₁₃	semidirect
253. #501	C₂²×C₁₃	semidirect
254. #499	C₂²×C₁₃	semidirect
255. #491	C₂²×C₁₃	semidirect
256. #490	C₂²×C₁₃	semidirect
257. #488	C₂²×C₁₃	semidirect
260. #477	C₂²×C₁₃	semidirect
261. #476	C₂²×C₁₃	semidirect
262. #475	C₂²×C₁₃	semidirect
263. #474	C₂²×C₁₃	semidirect
429. C₁₃	#60863	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×#3444	2
C₂×C₁₃×#533	2
C₁₃×#3237	2
C₁₃×#3235	2
C₁₃×#3233	2
C₁₃×#3166	2
C₁₃×#3142	2
C₁₃×#3093	2
C₁₃×#3079	2
C₁₃×#2920	2
#60863	13

Subgroups — C13×#60863 #15747202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60863 #15747202