Subgroups — C₁₃×#25970 #15712309

Order 3328.

1032 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₁₃×#474	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#417	—	2	4	no	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×#398	—	2	1	no	—
41	C₁₃×#395	—	2	1	no	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#386	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₁₃×#381	—	2	1	no	—
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#95	—	2	1	no	—
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	4	1	no	—
65	C₂×C₁₃×#41	—	4	1	no	—
66	C₂×C₁₃×#41	Q₈	1	4	yes	complemented
67	C₂²×Q₈×C₁₃	—	2	1	no	—
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	—	2	2	no	—
77	C₂×C₁₃×M₁₆	—	2	2	no	—
78	C₂×C₁₃×M₁₆	—	4	1	no	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	—	4	1	no	—
85	C₁₃×C₂²⋊Q₈	—	4	4	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	4	1	no	—
89	C₄×D₄×C₁₃	—	4	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	—	2	2	no	—
113	C₁₃×#107	—	2	2	no	—
114	C₁₃×#107	—	4	1	no	—
115	C₁₃×#106	—	4	1	no	—
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	4	1	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	—	2	2	no	—
125	C₁₃×#102	D₄	1	4	yes	—
126	C₁₃×C₂²⋊C₈	—	2	2	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	D₄	1	1	yes	characteristic
136	C₁₃×#95	D₄	1	1	yes	characteristic
137	#25970	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	1	no	—
139	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₁₃×#41	—	2	8	no	—
141	C₁₃×#41	—	4	4	no	—
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	4	2	no	—
150	C₂×Q₈×C₁₃	—	4	2	no	—
151	C₂×Q₈×C₁₃	—	8	1	no	—
152	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	4	2	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
161	C₂×D₄×C₁₃	#41	1	2	yes	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	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	4	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	4	2	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	—	4	2	no	—
182	C₂²×C₄×C₁₃	—	8	1	no	—
183	C₂²×C₄×C₁₃	—	8	1	no	—
184	C₂²×C₄×C₁₃	—	8	1	no	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
191	C₂²×C₄×C₁₃	#41	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₁₃×M₁₆	—	4	4	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₄⋊C₄	—	4	2	no	—
219	C₁₃×C₄⋊C₄	—	4	2	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₄⋊C₄	—	4	2	no	—
222	C₁₃×C₄⋊C₄	—	8	1	no	—
223	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	2	no	—
226	C₁₃×C₂²⋊C₄	—	4	2	no	—
227	C₁₃×C₂²⋊C₄	—	4	2	no	—
228	C₁₃×C₂²⋊C₄	—	4	2	no	—
229	C₁₃×C₂²⋊C₄	—	8	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
236	#2440	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2339	C₂×C₁₃	1	1	yes	characteristic
238	#2095	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1788	C₂×C₁₃	1	1	yes	characteristic
249	C₂³×C₁₃	—	2	2	no	—
250	C₂³×C₁₃	—	2	2	no	—
251	C₂³×C₁₃	—	2	1	no	—
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
263	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	Q₈×C₁₃	—	2	2	no	—
265	Q₈×C₁₃	—	2	2	no	—
266	Q₈×C₁₃	—	4	1	no	—
267	Q₈×C₁₃	—	4	1	no	—
268	Q₈×C₁₃	—	8	4	no	—
269	D₄×C₁₃	—	2	2	no	—
270	D₄×C₁₃	—	2	2	no	—
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	4	8	no	—
273	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	4	8	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	8	4	no	—
313	C₂×C₄×C₁₃	—	8	4	no	—
314	C₂×C₄×C₁₃	—	8	4	no	—
315	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
316	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
317	C₂×C₄×C₁₃	#137	1	2	yes	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
324	C₈×C₁₃	—	2	2	no	—
325	C₈×C₁₃	—	4	1	no	—
326	C₈×C₁₃	—	4	1	no	—
327	C₈×C₁₃	—	4	1	no	—
328	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₂²⋊Q₈	—	2	1	no	—
332	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
335	#474	—	2	4	no	—
336	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	#417	—	2	4	no	—
343	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
352	#398	—	2	1	no	—
353	#395	—	2	1	no	—
354	#391	C₂²×C₁₃	1	1	yes	characteristic
355	#391	C₂²×C₁₃	1	1	yes	characteristic
356	#389	C₂²×C₁₃	1	1	yes	characteristic
357	#389	C₂²×C₁₃	1	1	yes	characteristic
358	#386	—	2	1	no	—
359	#386	—	2	1	no	—
360	#385	—	2	1	no	—
361	#384	C₂²×C₁₃	1	1	yes	characteristic
362	#381	—	2	1	no	—
363	#380	C₂²×C₁₃	1	1	yes	characteristic
364	#380	C₂²×C₁₃	1	1	yes	characteristic
365	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#95	—	2	1	no	—
367	#340	C₂²×C₁₃	1	1	yes	characteristic
368	#340	C₂²×C₁₃	1	1	yes	characteristic
369	#340	C₂²×C₁₃	1	1	yes	characteristic
370	#340	C₂²×C₁₃	1	1	yes	characteristic
371	#336	C₂²×C₁₃	1	1	yes	characteristic
372	#336	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₁₃	—	2	2	no	—
374	C₂²×C₁₃	—	2	2	no	—
375	C₂²×C₁₃	—	2	2	no	—
376	C₂²×C₁₃	—	2	4	no	—
377	C₂²×C₁₃	—	4	1	no	—
378	C₂²×C₁₃	—	4	2	no	—
379	C₂²×C₁₃	—	4	2	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	1	no	—
382	C₂²×C₁₃	—	4	2	no	—
383	C₂²×C₁₃	—	4	1	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	1	no	—
387	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
388	C₂²×C₁₃	D₄²	1	1	yes	characteristic
389	C₂²×C₁₃	#546	1	1	yes	characteristic
390	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
392	C₂²×C₁₃	#576	1	1	yes	characteristic
393	C₂²×C₁₃	#578	1	1	yes	characteristic
394	C₄×C₁₃	—	2	2	no	—
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	4	1	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	1	no	—
401	C₄×C₁₃	—	8	1	no	—
402	C₄×C₁₃	—	8	1	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	—	8	1	no	—
406	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
407	C₄×C₁₃	#543	1	1	yes	characteristic
408	C₄×C₁₃	#546	1	1	yes	characteristic
409	C₄×C₁₃	#551	1	1	yes	characteristic
410	C₂×#41	—	2	2	no	—
411	C₂×#41	—	2	2	no	—
412	C₂×#41	—	2	2	no	—
413	C₂×#41	—	4	1	no	—
414	C₂×#41	—	4	1	no	—
415	C₂×#41	Q₈×C₁₃	1	4	yes	complemented
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂²×D₄	—	2	1	no	—
419	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂³×C₄	—	2	1	no	—
421	C₂³×C₄	—	2	1	no	—
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	—	2	1	no	—
424	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×M₁₆	—	2	2	no	—
426	C₂×M₁₆	—	2	2	no	—
427	C₂×M₁₆	—	4	1	no	—
428	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄⋊Q₈	—	2	2	no	—
433	C₄⋊Q₈	—	4	1	no	—
434	C₂²⋊Q₈	—	4	4	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	4	1	no	—
438	C₄×D₄	—	4	1	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	4	1	no	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
461	#107	—	2	2	no	—
462	#107	—	2	2	no	—
463	#107	—	4	1	no	—
464	#106	—	4	1	no	—
465	C₄⋊C₈	—	2	2	no	—
466	C₄⋊C₈	—	4	1	no	—
467	#103	—	2	2	no	—
468	#103	—	2	2	no	—
469	#103	—	4	1	no	—
470	#103	—	4	1	no	—
471	#102	—	2	2	no	—
472	#102	—	2	2	no	—
473	#102	—	2	2	no	—
474	#102	D₄×C₁₃	1	4	yes	—
475	C₂²⋊C₈	—	2	2	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	D₄×C₁₃	1	1	yes	characteristic
485	#95	D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₁₃	—	4	2	no	—
487	C₂×C₁₃	—	4	4	no	—
488	C₂×C₁₃	#2437	1	1	yes	characteristic
489	C₂×C₁₃	#3079	1	1	yes	characteristic
490	C₂×C₁₃	#3083	1	1	yes	characteristic
491	C₂×C₁₃	#3264	1	1	yes	characteristic
492	C₂×C₁₃	#3276	1	1	yes	characteristic
493	C₂×C₁₃	#3314	1	1	yes	characteristic
494	C₂×C₁₃	#3330	1	1	yes	characteristic
495	C₂⁴	—	2	1	no	—
496	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
497	#41	—	2	8	no	—
498	#41	—	4	4	no	—
499	#41	—	4	4	no	—
500	#41	—	4	4	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×Q₈	—	4	2	no	—
508	C₂×Q₈	—	8	1	no	—
509	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
517	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
518	C₂×D₄	C₁₃×#41	1	2	yes	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	8	1	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
548	C₂²×C₄	C₁₃×#41	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	M₁₆	—	4	4	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	8	1	no	—
580	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₁₃	#25970	1	1	yes	characteristic, direct product factor, Sylow
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
606	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	8	4	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	4	8	no	—
616	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	4	8	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	8	4	no	—
656	C₂×C₄	—	8	4	no	—
657	C₂×C₄	—	8	4	no	—
658	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
659	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
660	C₂×C₄	C₁₃×#137	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
662	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
663	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
664	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
665	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
686	C₂²	D₄²×C₁₃	1	1	yes	characteristic
687	C₂²	C₁₃×#546	1	1	yes	characteristic
688	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
689	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
690	C₂²	C₁₃×#576	1	1	yes	characteristic
691	C₂²	C₁₃×#578	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	2	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
705	C₄	C₁₃×#543	1	1	yes	characteristic
706	C₄	C₁₃×#546	1	1	yes	characteristic
707	C₄	C₁₃×#551	1	1	yes	characteristic
708	C₂	—	4	2	no	—
709	C₂	—	4	4	no	—
710	C₂	C₁₃×#2437	1	1	yes	characteristic
711	C₂	C₁₃×#3079	1	1	yes	characteristic
712	C₂	C₁₃×#3083	1	1	yes	characteristic
713	C₂	C₁₃×#3264	1	1	yes	characteristic
714	C₂	C₁₃×#3276	1	1	yes	characteristic
715	C₂	C₁₃×#3314	1	1	yes	characteristic
716	C₂	C₁₃×#3330	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#474	C₂	semidirect
3. C₁₃×#2440	C₂	semidirect
5. C₁₃×#2095	C₂	semidirect
6. C₁₃×#2068	C₂	semidirect
7. C₁₃×#2066	C₂	semidirect
8. C₁₃×#2024	C₂	semidirect
9. C₁₃×#1864	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₁₃×#1852	C₂	semidirect
12. C₁₃×#1851	C₂	semidirect
13. C₁₃×#1809	C₂	semidirect
14. C₁₃×#1802	C₂	semidirect
66. C₂×C₁₃×#41	Q₈	semidirect
137. #25970	C₁₃	direct (N × H)
234. C₂×#474	C₂×C₁₃	semidirect
236. #2440	C₂×C₁₃	semidirect
238. #2095	C₂×C₁₃	semidirect
239. #2068	C₂×C₁₃	semidirect
240. #2066	C₂×C₁₃	semidirect
241. #2024	C₂×C₁₃	semidirect
242. #1864	C₂×C₁₃	semidirect
243. #1862	C₂×C₁₃	semidirect
244. #1852	C₂×C₁₃	semidirect
245. #1851	C₂×C₁₃	semidirect
246. #1809	C₂×C₁₃	semidirect
247. #1802	C₂×C₁₃	semidirect
273. D₄×C₁₃	C₂²⋊Q₈	semidirect
415. C₂×#41	Q₈×C₁₃	semidirect
591. C₁₃	#25970	direct (N × H)
616. D₄	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#474	2
C₂×C₁₃×#417	2
C₁₃×#2440	2
C₁₃×#2339	2
C₁₃×#2095	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#2024	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1852	2
C₁₃×#1851	2
C₁₃×#1809	2
C₁₃×#1802	2
C₁₃×#1788	2
#25970	13

Subgroups — C13×#25970 #15712309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25970 #15712309