Subgroups — C₁₃×#21062 #15707401

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1928	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#428	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₁₃×#417	C₄	1	8	yes	complemented
23	C₁₃×#416	—	2	4	no	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#386	—	2	2	no	—
33	C₁₃×#380	—	2	1	no	—
34	C₁₃×#380	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×M₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	2	no	—
67	C₁₃×#117	—	2	2	no	—
68	C₁₃×#117	—	2	2	no	—
69	C₁₃×#117	D₄	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
86	C₂×C₄²×C₁₃	—	2	1	no	—
87	C₂×C₄²×C₁₃	—	2	2	no	—
88	C₂×C₄²×C₁₃	—	2	2	no	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₁₃×#107	—	2	4	no	—
91	C₁₃×#106	—	2	4	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	C₂×C₄	1	8	yes	complemented
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	C₂×C₄	1	8	yes	complemented
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	#21062	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₁₃×#41	—	2	8	no	—
106	C₁₃×#41	—	2	8	no	—
107	C₁₃×#41	—	4	4	no	—
108	C₁₃×#41	—	4	4	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	4	2	no	—
122	C₂×D₄×C₁₃	—	4	2	no	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	8	1	no	—
135	C₂²×C₄×C₁₃	—	8	1	no	—
136	C₂²×C₄×C₁₃	—	8	1	no	—
137	C₂²×C₄×C₁₃	—	8	1	no	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	#41	1	2	yes	—
144	C₂²×C₄×C₁₃	#41	1	2	yes	—
145	C₂²×C₄×C₁₃	#41	1	2	yes	—
146	C₂²×C₄×C₁₃	#41	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×M₁₆	—	2	8	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	4	4	no	—
158	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	8	2	no	—
174	C₁₃×C₂²⋊C₄	—	8	2	no	—
175	C₄²×C₁₃	—	2	4	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	8	2	no	—
179	C₄²×C₁₃	—	8	2	no	—
180	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
182	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
183	#2311	C₂×C₁₃	1	1	yes	characteristic
184	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1928	C₂×C₁₃	1	2	yes	complemented
186	#1927	C₂×C₁₃	1	2	yes	complemented
187	#1926	C₂×C₁₃	1	2	yes	complemented
188	#1925	C₂×C₁₃	1	2	yes	complemented
189	C₂×#340	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	C₄×D₄	1	2	yes	—
203	C₂³×C₁₃	#121	1	2	yes	—
204	C₂³×C₁₃	#123	1	2	yes	—
205	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₁₃	—	2	2	no	—
207	Q₈×C₁₃	—	2	2	no	—
208	Q₈×C₁₃	—	4	1	no	—
209	Q₈×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	4	8	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	8	4	no	—
238	C₂×C₄×C₁₃	—	8	4	no	—
239	C₂×C₄×C₁₃	#117	1	4	yes	—
240	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
241	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	#121	1	2	yes	—
243	C₂×C₄×C₁₃	#123	1	2	yes	—
244	C₂×C₄×C₁₃	#124	1	4	yes	—
245	C₂×C₄×C₁₃	#126	1	4	yes	—
246	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
252	C₈×C₁₃	—	2	4	no	—
253	C₈×C₁₃	—	4	1	no	—
254	C₈×C₁₃	—	4	1	no	—
255	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	#428	—	2	4	no	—
263	C₂×#107	C₂²×C₁₃	1	2	yes	—
264	C₂×#106	C₂²×C₁₃	1	2	yes	—
265	#417	C₄×C₁₃	1	8	yes	complemented
266	#416	—	2	4	no	—
267	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#103	C₂²×C₁₃	1	2	yes	—
270	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#102	C₂²×C₁₃	1	2	yes	—
273	#391	C₂²×C₁₃	1	2	yes	—
274	#390	C₂²×C₁₃	1	2	yes	—
275	#386	—	2	2	no	—
276	#380	—	2	1	no	—
277	#380	—	2	1	no	—
278	C₄×C₄⋊C₄	—	2	1	no	—
279	C₄×C₄⋊C₄	—	2	1	no	—
280	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
282	C₄×C₂²⋊C₄	—	2	2	no	—
283	#340	C₂²×C₁₃	1	2	yes	—
284	#340	C₂²×C₁₃	1	2	yes	—
285	#336	C₂²×C₁₃	1	2	yes	—
286	#336	C₂²×C₁₃	1	2	yes	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	8	1	no	—
297	C₂²×C₁₃	—	8	1	no	—
298	C₂²×C₁₃	—	8	1	no	—
299	C₂²×C₁₃	—	8	1	no	—
300	C₂²×C₁₃	#388	1	4	yes	—
301	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
303	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
304	C₂²×C₁₃	#576	1	1	yes	characteristic
305	C₂²×C₁₃	#577	1	1	yes	characteristic
306	C₂²×C₁₃	#577	1	1	yes	characteristic
307	C₂²×C₁₃	#578	1	1	yes	characteristic
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	4	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	8	2	no	—
315	C₄×C₁₃	#388	1	4	yes	—
316	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
317	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
319	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
326	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	D₄×C₁₃	1	4	yes	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
352	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
366	#107	—	2	4	no	—
367	#106	—	2	4	no	—
368	#103	—	2	2	no	—
369	#103	—	2	2	no	—
370	#103	C₂×C₄×C₁₃	1	8	yes	complemented
371	#102	—	2	2	no	—
372	#102	—	2	2	no	—
373	#102	C₂×C₄×C₁₃	1	8	yes	complemented
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	—	2	2	no	—
377	#95	—	2	2	no	—
378	C₂×C₁₃	—	2	4	no	—
379	C₂×C₁₃	—	8	2	no	—
380	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
381	C₂×C₁₃	#2946	1	1	yes	characteristic
382	C₂×C₁₃	#2947	1	1	yes	characteristic
383	C₂×C₁₃	#3045	1	1	yes	characteristic
384	C₂×C₁₃	#3046	1	1	yes	characteristic
385	C₂×C₁₃	#3098	1	1	yes	characteristic
386	C₂×C₁₃	#3099	1	1	yes	characteristic
387	C₂⁴	—	2	1	no	—
388	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
389	#41	—	2	8	no	—
390	#41	—	2	8	no	—
391	#41	—	4	4	no	—
392	#41	—	4	4	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	8	1	no	—
419	C₂²×C₄	—	8	1	no	—
420	C₂²×C₄	—	8	1	no	—
421	C₂²×C₄	—	8	1	no	—
422	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²×C₄	C₁₃×#41	1	2	yes	—
428	C₂²×C₄	C₁₃×#41	1	2	yes	—
429	C₂²×C₄	C₁₃×#41	1	2	yes	—
430	C₂²×C₄	C₁₃×#41	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
432	M₁₆	—	2	8	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	4	4	no	—
442	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
453	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	8	2	no	—
458	C₂²⋊C₄	—	8	2	no	—
459	C₄²	—	2	4	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	8	2	no	—
463	C₄²	—	8	2	no	—
464	C₁₃	#21062	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	C₄×D₄×C₁₃	1	2	yes	—
477	C₂³	C₁₃×#121	1	2	yes	—
478	C₂³	C₁₃×#123	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	Q₈	—	2	2	no	—
481	Q₈	—	2	2	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	8	4	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	C₁₃×#117	1	4	yes	—
514	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
515	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
516	C₂×C₄	C₁₃×#121	1	2	yes	—
517	C₂×C₄	C₁₃×#123	1	2	yes	—
518	C₂×C₄	C₁₃×#124	1	4	yes	—
519	C₂×C₄	C₁₃×#126	1	4	yes	—
520	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
523	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
524	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
525	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
526	C₈	—	2	4	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	C₁₃×#388	1	4	yes	—
543	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
544	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
545	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
546	C₂²	C₁₃×#576	1	1	yes	characteristic
547	C₂²	C₁₃×#577	1	1	yes	characteristic
548	C₂²	C₁₃×#577	1	1	yes	characteristic
549	C₂²	C₁₃×#578	1	1	yes	characteristic
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	4	no	—
556	C₄	—	8	2	no	—
557	C₄	C₁₃×#388	1	4	yes	—
558	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
559	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
560	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
561	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
562	C₂	—	2	4	no	—
563	C₂	—	8	2	no	—
564	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
565	C₂	C₁₃×#2946	1	1	yes	characteristic
566	C₂	C₁₃×#2947	1	1	yes	characteristic
567	C₂	C₁₃×#3045	1	1	yes	characteristic
568	C₂	C₁₃×#3046	1	1	yes	characteristic
569	C₂	C₁₃×#3098	1	1	yes	characteristic
570	C₂	C₁₃×#3099	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#428	C₂	semidirect
5. C₁₃×#2274	C₂	semidirect
6. C₁₃×#1928	C₂	semidirect
7. C₁₃×#1927	C₂	semidirect
8. C₁₃×#1926	C₂	semidirect
9. C₁₃×#1925	C₂	semidirect
10. C₂×C₁₃×#340	C₂	semidirect
11. C₁₃×#1729	C₂	semidirect
22. C₁₃×#417	C₄	semidirect
94. C₁₃×#103	C₂×C₄	semidirect
97. C₁₃×#102	C₂×C₄	semidirect
102. #21062	C₁₃	direct (N × H)
180. C₂×#428	C₂×C₁₃	semidirect
184. #2274	C₂×C₁₃	semidirect
185. #1928	C₂×C₁₃	semidirect
186. #1927	C₂×C₁₃	semidirect
187. #1926	C₂×C₁₃	semidirect
188. #1925	C₂×C₁₃	semidirect
189. C₂×#340	C₂×C₁₃	semidirect
190. #1729	C₂×C₁₃	semidirect
265. #417	C₄×C₁₃	semidirect
370. #103	C₂×C₄×C₁₃	semidirect
373. #102	C₂×C₄×C₁₃	semidirect
464. C₁₃	#21062	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#428	2
C₂×C₁₃×#417	2
C₂×C₁₃×#416	2
C₁₃×#2311	2
C₁₃×#2274	2
C₁₃×#1928	2
C₁₃×#1927	2
C₁₃×#1926	2
C₁₃×#1925	2
C₂×C₁₃×#340	2
C₁₃×#1729	2
#21062	13

Subgroups — C13×#21062 #15707401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21062 #15707401