Subgroups — C₁₃×#22565 #15708904

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1763	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₁₃×#416	C₄	1	8	yes	complemented
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#97	C₂²	1	2	yes	—
26	C₁₃×#390	—	2	2	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#388	—	2	2	no	—
30	C₁₃×#382	—	2	1	no	—
31	C₁₃×#380	—	2	1	no	—
32	C₁₃×#380	C₂²	1	1	yes	characteristic
33	C₁₃×#380	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#376	—	2	1	no	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	4	2	no	—
45	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	—	4	2	no	—
52	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	4	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	C₂×C₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₁₃×#106	—	4	2	no	—
77	C₁₃×#103	—	2	4	no	—
78	C₁₃×#103	C₂×C₄	1	4	yes	—
79	C₁₃×#103	C₂×C₄	1	4	yes	—
80	C₁₃×#102	—	4	2	no	—
81	C₁₃×#102	C₂×C₄	1	4	yes	—
82	C₁₃×#102	C₂×C₄	1	4	yes	—
83	C₁₃×C₂²⋊C₈	—	2	2	no	—
84	C₁₃×#97	—	4	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	#22565	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	1	no	—
93	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₁₃×#41	—	2	8	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₁₃×#41	—	4	8	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×Q₈×C₁₃	#41	1	4	yes	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	4	4	no	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₄⋊C₄	—	8	2	no	—
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	8	2	no	—
144	C₁₃×C₂²⋊C₄	—	8	1	no	—
145	C₁₃×C₂²⋊C₄	—	8	1	no	—
146	C₄²×C₁₃	—	2	4	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	4	4	no	—
150	C₄²×C₁₃	—	4	4	no	—
151	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
152	#2346	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2341	C₂×C₁₃	1	1	yes	characteristic
154	#1936	C₂×C₁₃	1	2	yes	complemented
155	#1926	C₂×C₁₃	1	2	yes	complemented
156	#1865	C₂×C₁₃	1	2	yes	complemented
157	#1825	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1788	C₂×C₁₃	1	1	yes	characteristic
160	#1763	C₂×C₁₃	1	2	yes	complemented
161	#1752	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	1	no	—
171	C₂³×C₁₃	C₄×D₄	1	2	yes	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	4	no	—
175	Q₈×C₁₃	#117	1	4	yes	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	4	8	no	—
179	D₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
213	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#106	C₂²×C₁₃	1	2	yes	—
217	#416	C₄×C₁₃	1	8	yes	complemented
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#97	C₂²×C₁₃	1	2	yes	—
226	#390	—	2	2	no	—
227	#390	C₂²×C₁₃	1	2	yes	—
228	#389	C₂²×C₁₃	1	2	yes	—
229	#388	—	2	2	no	—
230	#382	—	2	1	no	—
231	#380	—	2	1	no	—
232	#380	C₂²×C₁₃	1	1	yes	characteristic
233	#380	C₂²×C₁₃	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
235	C₄×C₂²⋊C₄	—	2	1	no	—
236	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	#376	—	2	1	no	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	2	yes	—
241	#336	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₁₃	#546	1	2	yes	—
254	C₂²×C₁₃	#575	1	2	yes	—
255	C₂²×C₁₃	#577	1	1	yes	characteristic
256	C₂²×C₁₃	#577	1	1	yes	characteristic
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
266	C₄×C₁₃	#518	1	1	yes	characteristic
267	C₄×C₁₃	#551	1	2	yes	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	4	no	—
270	C₂×#41	—	4	2	no	—
271	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
272	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂²×C₈	—	4	2	no	—
278	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	4	2	no	—
284	#117	—	2	2	no	—
285	#117	C₂×C₄×C₁₃	1	4	yes	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
302	#106	—	4	2	no	—
303	#103	—	2	4	no	—
304	#103	C₂×C₄×C₁₃	1	4	yes	—
305	#103	C₂×C₄×C₁₃	1	4	yes	—
306	#102	—	4	2	no	—
307	#102	C₂×C₄×C₁₃	1	4	yes	—
308	#102	C₂×C₄×C₁₃	1	4	yes	—
309	C₂²⋊C₈	—	2	2	no	—
310	#97	—	4	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	2	no	—
315	#95	D₄×C₁₃	1	1	yes	characteristic
316	#95	D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₁₃	—	4	2	no	—
318	C₂×C₁₃	—	8	2	no	—
319	C₂×C₁₃	#2342	1	1	yes	characteristic
320	C₂×C₁₃	#2943	1	1	yes	characteristic
321	C₂×C₁₃	#2952	1	1	yes	characteristic
322	C₂×C₁₃	#3317	1	2	yes	—
323	C₂×C₁₃	#3321	1	2	yes	—
324	C₂⁴	—	2	1	no	—
325	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
326	#41	—	2	8	no	—
327	#41	—	4	4	no	—
328	#41	—	4	8	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
332	C₂×Q₈	C₁₃×#41	1	4	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₁₃×#41	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
361	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
371	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	8	2	no	—
376	C₂²⋊C₄	—	8	1	no	—
377	C₂²⋊C₄	—	8	1	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	4	no	—
382	C₄²	—	4	4	no	—
383	C₁₃	#22565	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	C₄×D₄×C₁₃	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	4	no	—
397	Q₈	C₁₃×#117	1	4	yes	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	4	8	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
429	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
430	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
445	C₂²	C₁₃×#546	1	2	yes	—
446	C₂²	C₁₃×#575	1	2	yes	—
447	C₂²	C₁₃×#577	1	1	yes	characteristic
448	C₂²	C₁₃×#577	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
458	C₄	C₁₃×#518	1	1	yes	characteristic
459	C₄	C₁₃×#551	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	8	2	no	—
462	C₂	C₁₃×#2342	1	1	yes	characteristic
463	C₂	C₁₃×#2943	1	1	yes	characteristic
464	C₂	C₁₃×#2952	1	1	yes	characteristic
465	C₂	C₁₃×#3317	1	2	yes	—
466	C₂	C₁₃×#3321	1	2	yes	—

	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 ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2346	C₂	semidirect
4. C₁₃×#1936	C₂	semidirect
5. C₁₃×#1926	C₂	semidirect
6. C₁₃×#1865	C₂	semidirect
7. C₁₃×#1825	C₂	semidirect
8. C₁₃×#1807	C₂	semidirect
10. C₁₃×#1763	C₂	semidirect
11. C₁₃×#1752	C₂	semidirect
17. C₁₃×#416	C₄	semidirect
91. #22565	C₁₃	direct (N × H)
152. #2346	C₂×C₁₃	semidirect
154. #1936	C₂×C₁₃	semidirect
155. #1926	C₂×C₁₃	semidirect
156. #1865	C₂×C₁₃	semidirect
157. #1825	C₂×C₁₃	semidirect
158. #1807	C₂×C₁₃	semidirect
160. #1763	C₂×C₁₃	semidirect
161. #1752	C₂×C₁₃	semidirect
217. #416	C₄×C₁₃	semidirect
383. C₁₃	#22565	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×#416	2
C₁₃×#2346	2
C₁₃×#2341	2
C₁₃×#1936	2
C₁₃×#1926	2
C₁₃×#1865	2
C₁₃×#1825	2
C₁₃×#1807	2
C₁₃×#1788	2
C₁₃×#1763	2
C₁₃×#1752	2
#22565	13

Subgroups — C13×#22565 #15708904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22565 #15708904