Subgroups — C₁₃×#34971 #15721310

Order 3328.

2630 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2599	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2581	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2536	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2486	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2484	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2409	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2406	C₂	1	2	yes	maximal
10	C₁₃×#2399	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#123	C₂²	1	4	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₄×C₁₃×#41	—	2	8	no	—
20	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#400	C₂²	1	4	yes	—
39	C₁₃×#398	C₂²	1	4	yes	—
40	C₁₃×#398	C₂²	1	4	yes	—
41	C₁₃×#397	C₂²	1	4	yes	—
42	C₁₃×#395	C₂²	1	4	yes	—
43	C₁₃×#395	C₂²	1	4	yes	—
44	C₁₃×#394	C₂²	1	4	yes	—
45	C₁₃×#393	C₂²	1	4	yes	—
46	C₁₃×#391	C₂²	1	4	yes	—
47	C₁₃×#389	C₂²	1	4	yes	—
48	C₁₃×#388	C₂²	1	8	yes	—
49	C₁₃×#387	C₂²	1	8	yes	—
50	C₁₃×#387	C₂²	1	8	yes	—
51	C₁₃×#386	C₂²	1	4	yes	—
52	C₁₃×#385	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	8	yes	—
54	C₁₃×#383	C₂²	1	2	yes	—
55	C₁₃×#382	C₂²	1	2	yes	—
56	C₁₃×#381	C₂²	1	2	yes	—
57	C₁₃×#381	C₂²	1	4	yes	—
58	C₁₃×#380	C₂²	1	4	yes	—
59	C₁₃×#380	C₂²	1	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
64	C₁₃×#376	C₂²	1	2	yes	—
65	C₂×C₁₃×#41	—	2	8	no	—
66	C₂×C₁₃×#41	—	2	4	no	—
67	C₂²×Q₈×C₁₃	—	2	8	no	—
68	C₂²×Q₈×C₁₃	—	2	4	no	—
69	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#123	—	2	16	no	—
83	C₁₃×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₁₃	—	2	8	no	—
85	C₄×Q₈×C₁₃	—	2	8	no	—
86	C₄×Q₈×C₁₃	—	2	8	no	—
87	C₄×Q₈×C₁₃	—	2	8	no	—
88	C₄×Q₈×C₁₃	—	2	4	no	—
89	C₄×Q₈×C₁₃	—	2	4	no	—
90	C₄×D₄×C₁₃	—	2	8	no	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₁₃×#117	—	2	4	no	—
95	C₁₃×#117	—	2	8	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃	—	2	8	no	—
116	C₂×C₄²×C₁₃	—	2	8	no	—
117	C₂×C₄²×C₁₃	D₄	1	8	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#95	C₂³	1	8	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	8	yes	—
131	C₁₃×#95	C₂³	1	8	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	8	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	4	yes	—
136	#34971	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×#41	—	2	32	no	—
140	C₂×Q₈×C₁₃	—	2	32	no	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	2	8	no	—
145	C₂×Q₈×C₁₃	—	2	4	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	#41	1	8	yes	complemented
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	#41	1	8	yes	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	8	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	8	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	8	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	16	no	—
192	C₁₃×C₄⋊C₄	—	2	16	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	16	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	16	no	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	—	2	4	no	—
201	C₄²×C₁₃	—	2	4	no	—
202	C₄²×C₁₃	—	2	8	no	—
203	C₄²×C₁₃	—	2	8	no	—
204	C₄²×C₁₃	—	2	8	no	—
205	C₄²×C₁₃	C₂×D₄	1	4	yes	—
206	C₄²×C₁₃	C₂×D₄	1	4	yes	—
207	C₄²×C₁₃	C₂×D₄	1	4	yes	—
208	C₄²×C₁₃	C₂×D₄	1	4	yes	—
209	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
210	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#2599	C₂×C₁₃	1	4	yes	complemented
212	#2581	C₂×C₁₃	1	2	yes	complemented
213	#2536	C₂×C₁₃	1	2	yes	complemented
214	#2486	C₂×C₁₃	1	2	yes	complemented
215	#2484	C₂×C₁₃	1	2	yes	complemented
216	#2409	C₂×C₁₃	1	2	yes	complemented
217	#2406	C₂×C₁₃	1	2	yes	—
218	#2399	C₂×C₁₃	1	2	yes	complemented
219	#2398	C₂×C₁₃	1	2	yes	complemented
220	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
221	C₄×#123	C₂×C₁₃	1	4	yes	complemented
222	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₃	C₂×#41	1	4	yes	—
231	C₂³×C₁₃	C₂×#41	1	4	yes	—
232	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	16	no	—
234	Q₈×C₁₃	—	2	8	no	—
235	Q₈×C₁₃	—	2	16	no	—
236	D₄×C₁₃	—	2	8	no	—
237	D₄×C₁₃	—	2	16	no	—
238	C₂×C₄×C₁₃	—	2	16	no	—
239	C₂×C₄×C₁₃	—	2	16	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	8	no	—
250	C₂×C₄×C₁₃	—	2	8	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	8	no	—
255	C₂×C₄×C₁₃	—	2	8	no	—
256	C₂×C₄×C₁₃	—	2	8	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	4	8	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	4	8	no	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
270	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
271	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
272	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
273	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
274	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#123	C₂²×C₁₃	1	4	yes	—
276	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
277	C₄×#41	—	2	8	no	—
278	C₂×C₄×Q₈	—	2	8	no	—
279	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
281	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
282	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
283	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
289	C₂×#117	C₂²×C₁₃	1	2	yes	—
290	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
292	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
294	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
295	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
296	#400	C₂²×C₁₃	1	4	yes	—
297	#398	C₂²×C₁₃	1	4	yes	—
298	#398	C₂²×C₁₃	1	4	yes	—
299	#397	C₂²×C₁₃	1	4	yes	—
300	#395	C₂²×C₁₃	1	4	yes	—
301	#395	C₂²×C₁₃	1	4	yes	—
302	#394	C₂²×C₁₃	1	4	yes	—
303	#393	C₂²×C₁₃	1	4	yes	—
304	#391	C₂²×C₁₃	1	4	yes	—
305	#389	C₂²×C₁₃	1	4	yes	—
306	#388	C₂²×C₁₃	1	8	yes	—
307	#387	C₂²×C₁₃	1	8	yes	—
308	#387	C₂²×C₁₃	1	8	yes	—
309	#386	C₂²×C₁₃	1	4	yes	—
310	#385	C₂²×C₁₃	1	8	yes	—
311	#385	C₂²×C₁₃	1	4	yes	—
312	#383	C₂²×C₁₃	1	2	yes	—
313	#382	C₂²×C₁₃	1	2	yes	—
314	#381	C₂²×C₁₃	1	2	yes	—
315	#381	C₂²×C₁₃	1	4	yes	—
316	#380	C₂²×C₁₃	1	2	yes	—
317	#380	C₂²×C₁₃	1	4	yes	—
318	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
319	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
320	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
321	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
322	#376	C₂²×C₁₃	1	2	yes	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	8	no	—
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	2	8	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	#525	1	4	yes	—
332	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
333	C₂²×C₁₃	C₂²×#41	1	2	yes	—
334	C₂²×C₁₃	C₂²×#41	1	2	yes	—
335	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	4	no	—
340	C₄×C₁₃	—	2	8	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	2	no	—
345	C₄×C₁₃	—	4	8	no	—
346	C₄×C₁₃	#525	1	4	yes	—
347	C₄×C₁₃	#536	1	4	yes	—
348	C₂×#41	—	2	8	no	—
349	C₂×#41	—	2	4	no	—
350	C₂²×Q₈	—	2	8	no	—
351	C₂²×Q₈	—	2	4	no	—
352	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
353	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
355	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
359	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
360	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
365	#123	—	2	16	no	—
366	C₂²⋊Q₈	—	2	16	no	—
367	C₄×Q₈	—	2	8	no	—
368	C₄×Q₈	—	2	8	no	—
369	C₄×Q₈	—	2	8	no	—
370	C₄×Q₈	—	2	8	no	—
371	C₄×Q₈	—	2	4	no	—
372	C₄×Q₈	—	2	4	no	—
373	C₄×D₄	—	2	8	no	—
374	C₄×D₄	—	2	8	no	—
375	C₄×D₄	—	2	4	no	—
376	C₄×D₄	—	2	4	no	—
377	#117	—	2	4	no	—
378	#117	—	2	8	no	—
379	C₂×C₄⋊C₄	—	2	8	no	—
380	C₂×C₄⋊C₄	—	2	4	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
398	C₂×C₄²	—	2	8	no	—
399	C₂×C₄²	—	2	8	no	—
400	C₂×C₄²	D₄×C₁₃	1	8	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
405	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	#95	C₂³×C₁₃	1	4	yes	—
412	#95	C₂³×C₁₃	1	4	yes	—
413	#95	C₂³×C₁₃	1	8	yes	—
414	#95	C₂³×C₁₃	1	4	yes	—
415	#95	C₂³×C₁₃	1	8	yes	—
416	#95	C₂³×C₁₃	1	8	yes	—
417	#95	C₂³×C₁₃	1	4	yes	—
418	#95	C₂³×C₁₃	1	8	yes	—
419	C₂×C₁₃	—	2	4	no	—
420	C₂×C₁₃	—	4	4	no	—
421	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
422	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
424	C₂×C₁₃	#3482	1	4	yes	—
425	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
426	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
427	#41	—	2	32	no	—
428	C₂×Q₈	—	2	32	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	8	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	C₁₃×#41	1	8	yes	complemented
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	C₁₃×#41	1	8	yes	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	16	no	—
480	C₄⋊C₄	—	2	16	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	16	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	16	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	8	no	—
491	C₄²	—	2	8	no	—
492	C₄²	—	2	8	no	—
493	C₄²	C₂×D₄×C₁₃	1	4	yes	—
494	C₄²	C₂×D₄×C₁₃	1	4	yes	—
495	C₄²	C₂×D₄×C₁₃	1	4	yes	—
496	C₄²	C₂×D₄×C₁₃	1	4	yes	—
497	C₁₃	#34971	1	1	yes	characteristic, direct product factor, Sylow
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	4	no	—
504	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂³	C₂×C₁₃×#41	1	4	yes	—
506	C₂³	C₂×C₁₃×#41	1	4	yes	—
507	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
508	Q₈	—	2	16	no	—
509	Q₈	—	2	8	no	—
510	Q₈	—	2	16	no	—
511	D₄	—	2	8	no	—
512	D₄	—	2	16	no	—
513	C₂×C₄	—	2	16	no	—
514	C₂×C₄	—	2	16	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
544	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
545	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
546	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
547	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	C₁₃×#525	1	4	yes	—
557	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
558	C₂²	C₂²×C₁₃×#41	1	2	yes	—
559	C₂²	C₂²×C₁₃×#41	1	2	yes	—
560	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	4	no	—
565	C₄	—	2	8	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	8	no	—
571	C₄	C₁₃×#525	1	4	yes	—
572	C₄	C₁₃×#536	1	4	yes	—
573	C₂	—	2	4	no	—
574	C₂	—	4	4	no	—
575	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
576	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
577	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
578	C₂	C₁₃×#3482	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#2599	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
5. C₁₃×#2536	C₂	semidirect
6. C₁₃×#2486	C₂	semidirect
7. C₁₃×#2484	C₂	semidirect
8. C₁₃×#2409	C₂	semidirect
10. C₁₃×#2399	C₂	semidirect
11. C₁₃×#2398	C₂	semidirect
12. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
13. C₄×C₁₃×#123	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
136. #34971	C₁₃	direct (N × H)
147. C₂×Q₈×C₁₃	#41	semidirect
210. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
211. #2599	C₂×C₁₃	semidirect
212. #2581	C₂×C₁₃	semidirect
213. #2536	C₂×C₁₃	semidirect
214. #2486	C₂×C₁₃	semidirect
215. #2484	C₂×C₁₃	semidirect
216. #2409	C₂×C₁₃	semidirect
218. #2399	C₂×C₁₃	semidirect
219. #2398	C₂×C₁₃	semidirect
220. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
221. C₄×#123	C₂×C₁₃	semidirect
222. #2283	C₂×C₁₃	semidirect
435. C₂×Q₈	C₁₃×#41	semidirect
497. C₁₃	#34971	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×C₄×C₁₃×#41	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2599	2
C₁₃×#2581	2
C₁₃×#2536	2
C₁₃×#2486	2
C₁₃×#2484	2
C₁₃×#2409	2
C₁₃×#2406	2
C₁₃×#2399	2
C₁₃×#2398	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₁₃×#2283	2
#34971	13

Subgroups — C13×#34971 #15721310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34971 #15721310