Subgroups — C₁₃×#25939 #15712278

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1879	C₂	1	2	yes	maximal
10	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	—	2	1	no	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₁₃	—	2	4	no	—
16	D₄×Q₈×C₁₃	—	2	4	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#489	—	2	4	no	—
26	C₁₃×#463	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#397	—	2	1	no	—
35	C₁₃×#393	—	2	1	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#388	—	2	2	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	8	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	4	8	no	—
49	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	4	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	—	2	4	no	—
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	4	no	—
63	C₁₃×C₄⋊Q₈	—	2	4	no	—
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#124	—	2	2	no	—
68	C₁₃×C₂²⋊Q₈	—	2	8	no	—
69	C₁₃×C₂²⋊Q₈	—	2	16	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	4	no	—
73	C₄×D₄×C₁₃	—	2	4	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₄×D₄×C₁₃	D₄	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	4	no	—
98	C₁₃×#97	—	2	2	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	#25939	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂⁴×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	—	4	4	no	—
115	C₂×Q₈×C₁₃	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₃	#41	1	4	yes	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	—	4	4	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×SD₁₆	—	4	4	no	—
140	C₁₃×D₈	—	4	4	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
157	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	2	no	—
161	C₁₃×C₂²⋊C₄	—	4	2	no	—
162	C₁₃×C₂²⋊C₄	—	4	4	no	—
163	C₁₃×C₂²⋊C₄	—	8	2	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	8	1	no	—
167	C₄²×C₁₃	C₂×D₄	1	2	yes	—
168	C₄²×C₁₃	C₂×D₄	1	2	yes	—
169	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂×#463	C₂×C₁₃	1	1	yes	characteristic
172	#2592	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2024	C₂×C₁₃	1	2	yes	complemented
174	#2023	C₂×C₁₃	1	2	yes	complemented
175	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1879	C₂×C₁₃	1	2	yes	—
178	#1877	C₂×C₁₃	1	2	yes	complemented
179	#1762	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	8	no	—
192	Q₈×C₁₃	—	4	8	no	—
193	Q₈×C₁₃	—	4	16	no	—
194	Q₈×C₁₃	—	4	1	no	—
195	Q₈×C₁₃	—	4	1	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	2	2	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	—	4	1	no	—
200	D₄×C₁₃	—	4	1	no	—
201	D₄×C₁₃	—	4	2	no	—
202	D₄×C₁₃	#124	1	4	yes	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	4	8	no	—
214	C₂×C₄×C₁₃	—	4	16	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	#120	1	2	yes	—
224	C₂×C₄×C₁₃	#120	1	2	yes	—
225	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
230	C₈×C₁₃	—	4	1	no	—
231	C₈×C₁₃	—	4	1	no	—
232	C₈×C₁₃	—	4	2	no	—
233	C₂³×Q₈	—	2	1	no	—
234	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
236	D₄×Q₈	—	2	4	no	—
237	D₄×Q₈	—	2	4	no	—
238	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	—	2	2	no	—
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
246	#489	—	2	4	no	—
247	#463	—	2	4	no	—
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#103	C₂²×C₁₃	1	2	yes	—
250	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×#102	C₂²×C₁₃	1	2	yes	—
252	C₂×#102	C₂²×C₁₃	1	2	yes	—
253	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
255	#397	—	2	1	no	—
256	#393	—	2	1	no	—
257	#391	C₂²×C₁₃	1	2	yes	—
258	#390	C₂²×C₁₃	1	2	yes	—
259	#388	—	2	2	no	—
260	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
261	#340	C₂²×C₁₃	1	2	yes	—
262	#340	C₂²×C₁₃	1	2	yes	—
263	#340	C₂²×C₁₃	1	2	yes	—
264	#336	C₂²×C₁₃	1	2	yes	—
265	#336	C₂²×C₁₃	1	2	yes	—
266	C₂²×C₁₃	—	2	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	8	2	no	—
272	C₂²×C₁₃	—	8	2	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	—	8	1	no	—
275	C₂²×C₁₃	—	8	1	no	—
276	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
277	C₂²×C₁₃	#548	1	2	yes	—
278	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
279	C₂²×C₁₃	#577	1	1	yes	characteristic
280	C₂²×C₁₃	#578	1	1	yes	characteristic
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	4	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	8	2	no	—
288	C₄×C₁₃	—	8	1	no	—
289	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
290	C₄×C₁₃	#536	1	1	yes	characteristic
291	C₄×C₁₃	#548	1	2	yes	—
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	—	4	8	no	—
296	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
297	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×D₈	—	2	2	no	—
305	C₂×D₈	—	2	4	no	—
306	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
309	C₄⋊Q₈	—	2	4	no	—
310	C₄⋊Q₈	—	2	4	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
313	#124	—	2	2	no	—
314	#124	—	2	2	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	—	2	16	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	D₄×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	C₄⋊C₈	—	2	2	no	—
340	#103	—	2	2	no	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#102	—	2	2	no	—
344	#102	—	2	4	no	—
345	#97	—	2	2	no	—
346	#95	—	2	1	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	C₂×C₁₃	—	4	4	no	—
350	C₂×C₁₃	—	16	1	no	—
351	C₂×C₁₃	#2436	1	1	yes	characteristic
352	C₂×C₁₃	#3003	1	1	yes	characteristic
353	C₂×C₁₃	#3013	1	1	yes	characteristic
354	C₂×C₁₃	#3367	1	2	yes	—
355	C₂×C₁₃	#3373	1	2	yes	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	—	2	1	no	—
358	C₂×Q₈	—	2	8	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	32	no	—
369	C₂×Q₈	—	4	4	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂×D₄	C₁₃×#41	1	4	yes	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	SD₁₆	—	4	4	no	—
393	D₈	—	4	4	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
410	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	8	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	8	1	no	—
420	C₄²	C₂×D₄×C₁₃	1	2	yes	—
421	C₄²	C₂×D₄×C₁₃	1	2	yes	—
422	C₁₃	#25939	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
434	Q₈	—	2	8	no	—
435	Q₈	—	4	8	no	—
436	Q₈	—	4	16	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	4	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	2	no	—
445	D₄	C₁₃×#124	1	4	yes	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	C₁₃×#120	1	2	yes	—
467	C₂×C₄	C₁₃×#120	1	2	yes	—
468	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
472	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	—	4	2	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
487	C₂²	C₁₃×#548	1	2	yes	—
488	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
489	C₂²	C₁₃×#577	1	1	yes	characteristic
490	C₂²	C₁₃×#578	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	1	no	—
499	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
500	C₄	C₁₃×#536	1	1	yes	characteristic
501	C₄	C₁₃×#548	1	2	yes	—
502	C₂	—	4	4	no	—
503	C₂	—	16	1	no	—
504	C₂	C₁₃×#2436	1	1	yes	characteristic
505	C₂	C₁₃×#3003	1	1	yes	characteristic
506	C₂	C₁₃×#3013	1	1	yes	characteristic
507	C₂	C₁₃×#3367	1	2	yes	—
508	C₂	C₁₃×#3373	1	2	yes	—

	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₁₃	C₂	semidirect
2. C₂×C₁₃×#489	C₂	semidirect
4. C₁₃×#2592	C₂	semidirect
5. C₁₃×#2024	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1987	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1877	C₂	semidirect
11. C₁₃×#1762	C₂	semidirect
102. #25939	C₁₃	direct (N × H)
169. C₂×D₄×Q₈	C₂×C₁₃	semidirect
170. C₂×#489	C₂×C₁₃	semidirect
172. #2592	C₂×C₁₃	semidirect
173. #2024	C₂×C₁₃	semidirect
174. #2023	C₂×C₁₃	semidirect
175. #1987	C₂×C₁₃	semidirect
176. #1985	C₂×C₁₃	semidirect
178. #1877	C₂×C₁₃	semidirect
179. #1762	C₂×C₁₃	semidirect
422. C₁₃	#25939	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×D₄×Q₈×C₁₃	2
C₂×C₁₃×#489	2
C₂×C₁₃×#463	2
C₁₃×#2592	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1987	2
C₁₃×#1985	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1762	2
#25939	13

Subgroups — C13×#25939 #15712278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25939 #15712278