Subgroups — C₁₃×#24677 #15711016

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2054	C₂	1	2	yes	maximal
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	—	2	1	no	—
17	C₁₃×#476	—	2	4	no	—
18	C₄×C₁₃×D₈	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#393	—	2	2	no	—
29	C₁₃×#390	C₂²	1	2	yes	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#388	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₁₃×#380	—	2	1	no	—
35	C₁₃×#380	—	2	1	no	—
36	C₁₃×#380	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	D₄	1	4	yes	—
60	C₁₃×#117	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	2	no	—
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#102	—	2	4	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	D₄	1	2	yes	—
92	#24677	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂⁴×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	8	1	no	—
97	C₂×Q₈×C₁₃	—	8	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₃	#41	1	2	yes	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×D₈	—	2	8	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	8	1	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₁₃×C₂²⋊C₄	—	2	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	2	no	—
151	C₁₃×C₂²⋊C₄	—	8	2	no	—
152	C₁₃×C₂²⋊C₄	—	8	2	no	—
153	C₁₃×C₂²⋊C₄	—	8	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	4	4	no	—
157	C₄²×C₁₃	C₂×D₄	1	2	yes	—
158	C₄²×C₁₃	#41	1	2	yes	—
159	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
161	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2073	C₂×C₁₃	1	2	yes	complemented
164	#2054	C₂×C₁₃	1	2	yes	—
165	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1949	C₂×C₁₃	1	2	yes	complemented
167	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1926	C₂×C₁₃	1	2	yes	complemented
169	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	8	4	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	4	1	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	1	no	—
193	D₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	8	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	8	4	no	—
216	C₂×C₄×C₁₃	#121	1	2	yes	—
217	C₂×C₄×C₁₃	#121	1	2	yes	—
218	C₂×C₄×C₁₃	#135	1	2	yes	—
219	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
225	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	—	4	2	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#117	—	2	1	no	—
234	#476	—	2	4	no	—
235	C₄×D₈	—	2	4	no	—
236	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
239	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#102	C₂²×C₁₃	1	2	yes	—
241	C₂×#102	C₂²×C₁₃	1	2	yes	—
242	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
245	#393	—	2	2	no	—
246	#390	C₂²×C₁₃	1	2	yes	—
247	#390	C₂²×C₁₃	1	2	yes	—
248	#388	—	2	2	no	—
249	#384	C₂²×C₁₃	1	1	yes	characteristic
250	#382	C₂²×C₁₃	1	2	yes	—
251	#380	—	2	1	no	—
252	#380	—	2	1	no	—
253	#380	—	2	1	no	—
254	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
256	#340	C₂²×C₁₃	1	2	yes	—
257	#340	C₂²×C₁₃	1	2	yes	—
258	#340	C₂²×C₁₃	1	2	yes	—
259	#336	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	—	8	1	no	—
269	C₂²×C₁₃	—	8	1	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	—	8	1	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
275	C₂²×C₁₃	#547	1	1	yes	characteristic
276	C₂²×C₁₃	#548	1	1	yes	characteristic
277	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₂²×C₁₃	#576	1	1	yes	characteristic
280	C₂²×C₁₃	#577	1	1	yes	characteristic
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	8	2	no	—
286	C₄×C₁₃	—	8	1	no	—
287	C₄×C₁₃	—	8	2	no	—
288	C₄×C₁₃	#463	1	4	yes	—
289	C₄×C₁₃	#525	1	1	yes	characteristic
290	C₄×C₁₃	#536	1	1	yes	characteristic
291	C₄×C₁₃	#552	1	1	yes	characteristic
292	C₄×C₁₃	#556	1	1	yes	characteristic
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	2	no	—
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	D₄×C₁₃	1	4	yes	—
310	#117	—	4	4	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	#107	—	2	2	no	—
330	#106	—	2	4	no	—
331	C₄⋊C₈	—	2	4	no	—
332	C₄⋊C₈	—	2	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	D₄×C₁₃	1	2	yes	—
342	C₂×C₁₃	—	8	2	no	—
343	C₂×C₁₃	—	8	2	no	—
344	C₂×C₁₃	#2415	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
346	C₂×C₁₃	#3045	1	1	yes	characteristic
347	C₂×C₁₃	#3341	1	1	yes	characteristic
348	C₂×C₁₃	#3354	1	1	yes	characteristic
349	C₂×C₁₃	#3360	1	1	yes	characteristic
350	C₂×C₁₃	#3366	1	1	yes	characteristic
351	C₂⁴	—	2	1	no	—
352	C₂⁴	—	2	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	—	8	1	no	—
355	C₂×Q₈	—	8	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂×D₄	C₁₃×#41	1	2	yes	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
383	D₈	—	2	8	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	C₁₃×#41	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	8	1	no	—
405	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₂²⋊C₄	—	8	2	no	—
411	C₂²⋊C₄	—	8	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	4	4	no	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₄²	C₁₃×#41	1	2	yes	—
417	C₁₃	#24677	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	Q₈	—	8	4	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	8	4	no	—
464	C₂×C₄	C₁₃×#121	1	2	yes	—
465	C₂×C₄	C₁₃×#121	1	2	yes	—
466	C₂×C₄	C₁₃×#135	1	2	yes	—
467	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
470	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
472	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	1	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
492	C₂²	C₁₃×#547	1	1	yes	characteristic
493	C₂²	C₁₃×#548	1	1	yes	characteristic
494	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
495	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
496	C₂²	C₁₃×#576	1	1	yes	characteristic
497	C₂²	C₁₃×#577	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	8	1	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	2	no	—
505	C₄	C₁₃×#463	1	4	yes	—
506	C₄	C₁₃×#525	1	1	yes	characteristic
507	C₄	C₁₃×#536	1	1	yes	characteristic
508	C₄	C₁₃×#552	1	1	yes	characteristic
509	C₄	C₁₃×#556	1	1	yes	characteristic
510	C₂	—	8	2	no	—
511	C₂	—	8	2	no	—
512	C₂	C₁₃×#2415	1	1	yes	characteristic
513	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
514	C₂	C₁₃×#3045	1	1	yes	characteristic
515	C₂	C₁₃×#3341	1	1	yes	characteristic
516	C₂	C₁₃×#3354	1	1	yes	characteristic
517	C₂	C₁₃×#3360	1	1	yes	characteristic
518	C₂	C₁₃×#3366	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#476	C₂	semidirect
3. C₁₃×#2563	C₂	semidirect
4. C₁₃×#2354	C₂	semidirect
5. C₁₃×#2073	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1949	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
92. #24677	C₁₃	direct (N × H)
159. C₂×#476	C₂×C₁₃	semidirect
161. #2563	C₂×C₁₃	semidirect
162. #2354	C₂×C₁₃	semidirect
163. #2073	C₂×C₁₃	semidirect
165. #1990	C₂×C₁₃	semidirect
166. #1949	C₂×C₁₃	semidirect
167. #1939	C₂×C₁₃	semidirect
168. #1926	C₂×C₁₃	semidirect
169. #1802	C₂×C₁₃	semidirect
417. C₁₃	#24677	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×#476	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2563	2
C₁₃×#2354	2
C₁₃×#2073	2
C₁₃×#2054	2
C₁₃×#1990	2
C₁₃×#1949	2
C₁₃×#1939	2
C₁₃×#1926	2
C₁₃×#1802	2
#24677	13

Subgroups — C13×#24677 #15711016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24677 #15711016