Subgroups — C₁₃×#22545 #15708884

Order 3328.

1366 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1982	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1961	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1804	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1762	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₁₃×#550	—	2	4	no	—
14	C₁₃×#550	C₄	1	8	yes	complemented
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#127	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₁₃×#121	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#446	—	2	4	no	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#97	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#391	—	2	1	no	—
35	C₁₃×#387	—	2	2	no	—
36	C₁₃×#384	C₂²	1	1	yes	characteristic
37	C₁₃×#382	C₂²	1	2	yes	—
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	1	yes	characteristic
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	8	no	—
45	C₂×C₁₃×#41	—	4	4	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#127	—	2	2	no	—
60	C₁₃×#127	—	2	4	no	—
61	C₁₃×#127	C₂×C₄	1	4	yes	—
62	C₁₃×#127	C₂×C₄	1	8	yes	—
63	C₁₃×#121	—	2	16	no	—
64	C₁₃×#121	—	2	8	no	—
65	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
66	C₄×Q₈×C₁₃	D₄	1	4	yes	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	2	4	no	—
69	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
70	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	4	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×#102	—	2	4	no	—
89	C₁₃×#102	—	2	2	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	4	2	no	—
92	C₁₃×#102	—	4	2	no	—
93	C₁₃×#102	—	4	2	no	—
94	C₁₃×#97	—	2	4	no	—
95	C₄×C₈×C₁₃	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	#22545	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	2	2	no	—
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₁₃×#41	—	4	32	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	C₂²⋊C₄	1	4	yes	—
107	C₂×D₄×C₁₃	—	2	8	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	4	no	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	8	2	no	—
126	C₂×D₄×C₁₃	—	8	1	no	—
127	C₂×D₄×C₁₃	—	8	2	no	—
128	C₂×D₄×C₁₃	—	8	1	no	—
129	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	4	4	no	—
138	C₂²×C₄×C₁₃	—	4	4	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	#41	1	2	yes	complemented
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	4	2	no	—
162	C₁₃×C₄⋊C₄	—	8	1	no	—
163	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
164	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
166	C₁₃×C₄⋊C₄	#41	1	2	yes	complemented
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₄²×C₁₃	—	4	2	no	—
170	C₄²×C₁₃	—	8	2	no	—
171	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
172	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₃	C₂×D₄	1	4	yes	—
175	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
176	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1982	C₂×C₁₃	1	2	yes	complemented
180	#1961	C₂×C₁₃	1	2	yes	complemented
181	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1804	C₂×C₁₃	1	2	yes	complemented
183	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1762	C₂×C₁₃	1	2	yes	complemented
185	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	4	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₃	—	2	8	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	4	no	—
204	D₄×C₁₃	—	2	2	no	—
205	D₄×C₁₃	—	2	4	no	—
206	D₄×C₁₃	—	4	16	no	—
207	D₄×C₁₃	—	4	1	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	8	no	—
212	D₄×C₁₃	—	8	8	no	—
213	D₄×C₁₃	—	8	4	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	4	16	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	8	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
237	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
246	C₈×C₁₃	—	2	2	no	—
247	C₈×C₁₃	—	4	1	no	—
248	C₈×C₁₃	—	4	2	no	—
249	C₂²×#41	—	2	1	no	—
250	#550	—	2	4	no	—
251	#550	C₄×C₁₃	1	8	yes	complemented
252	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#127	C₂²×C₁₃	1	2	yes	—
254	C₂×#121	—	2	1	no	—
255	C₂×#121	—	2	2	no	—
256	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
259	#446	—	2	4	no	—
260	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
262	C₂×#102	C₂²×C₁₃	1	2	yes	—
263	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#102	C₂²×C₁₃	1	2	yes	—
266	C₂×#102	C₂²×C₁₃	1	2	yes	—
267	C₂×#102	C₂²×C₁₃	1	2	yes	—
268	C₂×#102	C₂²×C₁₃	1	2	yes	—
269	C₂×#97	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
271	#391	—	2	1	no	—
272	#387	—	2	2	no	—
273	#384	C₂²×C₁₃	1	1	yes	characteristic
274	#382	C₂²×C₁₃	1	2	yes	—
275	C₄×C₄⋊C₄	—	2	1	no	—
276	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
278	#340	C₂²×C₁₃	1	2	yes	—
279	#340	C₂²×C₁₃	1	1	yes	characteristic
280	#340	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	8	2	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	1	no	—
291	C₂²×C₁₃	—	8	2	no	—
292	C₂²×C₁₃	—	8	1	no	—
293	C₂²×C₁₃	—	8	2	no	—
294	C₂²×C₁₃	—	8	1	no	—
295	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×C₁₃	#548	1	1	yes	characteristic
297	C₂²×C₁₃	#550	1	1	yes	characteristic
298	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₂²×C₁₃	#576	1	1	yes	characteristic
301	C₂²×C₁₃	#577	1	1	yes	characteristic
302	C₄×C₁₃	—	2	4	no	—
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	4	2	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	8	1	no	—
308	C₄×C₁₃	—	8	2	no	—
309	C₄×C₁₃	#418	1	4	yes	—
310	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
311	C₄×C₁₃	#520	1	1	yes	characteristic
312	C₄×C₁₃	#548	1	1	yes	characteristic
313	C₄×C₁₃	#550	1	1	yes	characteristic
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	4	4	no	—
316	C₂×#41	—	4	4	no	—
317	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	#127	—	2	2	no	—
330	#127	—	2	4	no	—
331	#127	C₂×C₄×C₁₃	1	4	yes	—
332	#127	C₂×C₄×C₁₃	1	8	yes	—
333	#121	—	2	16	no	—
334	#121	—	2	8	no	—
335	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
336	C₄×Q₈	D₄×C₁₃	1	4	yes	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
340	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	4	no	—
357	#102	—	2	4	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	#102	—	2	4	no	—
361	#102	—	4	2	no	—
362	#102	—	4	2	no	—
363	#102	—	4	2	no	—
364	#97	—	2	4	no	—
365	C₄×C₈	—	2	2	no	—
366	#95	—	2	2	no	—
367	#95	—	2	1	no	—
368	#95	—	2	2	no	—
369	#95	—	2	2	no	—
370	C₂×C₁₃	—	8	4	no	—
371	C₂×C₁₃	—	8	2	no	—
372	C₂×C₁₃	#2341	1	1	yes	characteristic
373	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
374	C₂×C₁₃	#2897	1	1	yes	characteristic
375	C₂×C₁₃	#3366	1	1	yes	characteristic
376	C₂×C₁₃	#3368	1	1	yes	characteristic
377	C₂×C₁₃	#3397	1	1	yes	characteristic
378	C₂×C₁₃	#3399	1	1	yes	characteristic
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	1	no	—
381	#41	—	4	32	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	C₁₃×C₂²⋊C₄	1	4	yes	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂×D₄	—	8	1	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂×D₄	—	8	1	no	—
407	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
408	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	C₁₃×#41	1	2	yes	complemented
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	—	8	1	no	—
441	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
442	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
443	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
444	C₄⋊C₄	C₁₃×#41	1	2	yes	complemented
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₄²	—	4	2	no	—
448	C₄²	—	8	2	no	—
449	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
450	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
451	C₄²	C₂×D₄×C₁₃	1	2	yes	—
452	C₄²	C₂×D₄×C₁₃	1	4	yes	—
453	C₁₃	#22545	1	1	yes	characteristic, direct product factor, Sylow
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	4	no	—
474	D₄	—	4	16	no	—
475	D₄	—	4	8	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	2	no	—
480	D₄	—	8	8	no	—
481	D₄	—	8	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
503	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
504	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
505	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
506	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
507	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
508	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
511	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
512	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	2	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	1	no	—
531	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
532	C₂²	C₁₃×#548	1	1	yes	characteristic
533	C₂²	C₁₃×#550	1	1	yes	characteristic
534	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
535	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
536	C₂²	C₁₃×#576	1	1	yes	characteristic
537	C₂²	C₁₃×#577	1	1	yes	characteristic
538	C₄	—	2	4	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	2	no	—
545	C₄	C₁₃×#418	1	4	yes	—
546	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
547	C₄	C₁₃×#520	1	1	yes	characteristic
548	C₄	C₁₃×#548	1	1	yes	characteristic
549	C₄	C₁₃×#550	1	1	yes	characteristic
550	C₂	—	8	4	no	—
551	C₂	—	8	2	no	—
552	C₂	C₁₃×#2341	1	1	yes	characteristic
553	C₂	C₂×C₁₃×#418	1	1	yes	characteristic
554	C₂	C₁₃×#2897	1	1	yes	characteristic
555	C₂	C₁₃×#3366	1	1	yes	characteristic
556	C₂	C₁₃×#3368	1	1	yes	characteristic
557	C₂	C₁₃×#3397	1	1	yes	characteristic
558	C₂	C₁₃×#3399	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	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#446	C₂	semidirect
3. C₁₃×#2355	C₂	semidirect
4. C₁₃×#1982	C₂	semidirect
5. C₁₃×#1982	C₂	semidirect
6. C₁₃×#1961	C₂	semidirect
7. C₁₃×#1957	C₂	semidirect
8. C₁₃×#1804	C₂	semidirect
9. C₁₃×#1802	C₂	semidirect
10. C₁₃×#1762	C₂	semidirect
11. C₄×C₁₃×#102	C₂	semidirect
14. C₁₃×#550	C₄	semidirect
100. #22545	C₁₃	direct (N × H)
154. C₂×C₈×C₁₃	#41	semidirect
166. C₁₃×C₄⋊C₄	#41	semidirect
176. C₂×#446	C₂×C₁₃	semidirect
177. #2355	C₂×C₁₃	semidirect
178. #1982	C₂×C₁₃	semidirect
179. #1982	C₂×C₁₃	semidirect
180. #1961	C₂×C₁₃	semidirect
181. #1957	C₂×C₁₃	semidirect
182. #1804	C₂×C₁₃	semidirect
183. #1802	C₂×C₁₃	semidirect
184. #1762	C₂×C₁₃	semidirect
185. C₄×#102	C₂×C₁₃	semidirect
251. #550	C₄×C₁₃	semidirect
432. C₂×C₈	C₁₃×#41	semidirect
444. C₄⋊C₄	C₁₃×#41	semidirect
453. C₁₃	#22545	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×#550	2
C₂×C₁₃×#446	2
C₁₃×#2355	2
C₁₃×#1982	2
C₁₃×#1961	2
C₁₃×#1957	2
C₁₃×#1804	2
C₁₃×#1802	2
C₁₃×#1762	2
C₄×C₁₃×#102	2
#22545	13

Subgroups — C13×#22545 #15708884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22545 #15708884