Subgroups — C₁₃×#24694 #15711033

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2072	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2055	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1947	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	2	yes	maximal
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#477	—	2	4	no	—
18	C₁₃×#440	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₁₃×#399	—	2	1	no	—
29	C₁₃×#399	—	2	1	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#384	C₂²	1	2	yes	—
34	C₁₃×#383	—	2	1	no	—
35	C₁₃×#382	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#376	—	2	1	no	—
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	8	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	D₄	1	4	yes	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#107	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#97	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	C₁₃×#95	D₄	1	1	yes	characteristic
92	#24694	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	4	4	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
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	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×SD₁₆	—	2	8	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	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	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	4	4	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	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	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
154	#2542	C₂×C₁₃	1	1	yes	characteristic
155	#2356	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2072	C₂×C₁₃	1	2	yes	complemented
157	#2055	C₂×C₁₃	1	2	yes	—
158	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1947	C₂×C₁₃	1	2	yes	complemented
160	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1925	C₂×C₁₃	1	2	yes	—
162	#1804	C₂×C₁₃	1	1	yes	characteristic
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	Q₈×C₁₃	—	4	1	no	—
173	Q₈×C₁₃	—	8	4	no	—
174	D₄×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	4	1	no	—
177	D₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	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	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	8	4	no	—
199	C₂×C₄×C₁₃	#121	1	2	yes	—
200	C₂×C₄×C₁₃	#121	1	2	yes	—
201	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	—	2	2	no	—
214	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
216	#477	—	2	4	no	—
217	#440	—	2	4	no	—
218	C₂×#107	C₂²×C₁₃	1	2	yes	—
219	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
222	C₂×#103	C₂²×C₁₃	1	2	yes	—
223	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
227	#399	—	2	1	no	—
228	#399	—	2	1	no	—
229	#391	C₂²×C₁₃	1	2	yes	—
230	#390	C₂²×C₁₃	1	2	yes	—
231	#387	—	2	2	no	—
232	#384	C₂²×C₁₃	1	2	yes	—
233	#383	—	2	1	no	—
234	#382	C₂²×C₁₃	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
236	C₄×C₄⋊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	—	4	4	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	1	no	—
246	C₂²×C₁₃	—	8	1	no	—
247	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
248	C₂²×C₁₃	#547	1	1	yes	characteristic
249	C₂²×C₁₃	#548	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
251	C₂²×C₁₃	#578	1	2	yes	—
252	C₄×C₁₃	—	2	4	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	—	8	1	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	#525	1	1	yes	characteristic
262	C₄×C₁₃	#536	1	1	yes	characteristic
263	C₄×C₁₃	#552	1	1	yes	characteristic
264	C₄×C₁₃	#556	1	1	yes	characteristic
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₂²⋊Q₈	—	4	8	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	D₄×C₁₃	1	4	yes	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	#107	—	2	2	no	—
299	#107	—	2	4	no	—
300	C₄⋊C₈	—	2	4	no	—
301	C₄⋊C₈	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	2	no	—
306	#97	—	2	2	no	—
307	#95	—	2	1	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	1	no	—
311	#95	—	2	2	no	—
312	#95	D₄×C₁₃	1	1	yes	characteristic
313	#95	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₁₃	—	8	2	no	—
315	C₂×C₁₃	#2415	1	1	yes	characteristic
316	C₂×C₁₃	#3038	1	1	yes	characteristic
317	C₂×C₁₃	#3044	1	1	yes	characteristic
318	C₂×C₁₃	#3343	1	2	yes	—
319	C₂×C₁₃	#3367	1	2	yes	—
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₁₃×#41	1	2	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
347	SD₁₆	—	2	8	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	C₁₃×#41	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	4	4	no	—
377	C₄²	C₂×D₄×C₁₃	1	2	yes	—
378	C₄²	C₁₃×#41	1	2	yes	—
379	C₁₃	#24694	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
386	Q₈	—	2	2	no	—
387	Q₈	—	2	2	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	8	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	C₁₃×#121	1	2	yes	—
417	C₂×C₄	C₁₃×#121	1	2	yes	—
418	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
424	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	2	no	—
427	C₈	—	4	1	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	2	no	—
433	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
434	C₂²	C₁₃×#547	1	1	yes	characteristic
435	C₂²	C₁₃×#548	1	1	yes	characteristic
436	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
437	C₂²	C₁₃×#578	1	2	yes	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₄	C₁₃×#525	1	1	yes	characteristic
448	C₄	C₁₃×#536	1	1	yes	characteristic
449	C₄	C₁₃×#552	1	1	yes	characteristic
450	C₄	C₁₃×#556	1	1	yes	characteristic
451	C₂	—	8	2	no	—
452	C₂	C₁₃×#2415	1	1	yes	characteristic
453	C₂	C₁₃×#3038	1	1	yes	characteristic
454	C₂	C₁₃×#3044	1	1	yes	characteristic
455	C₂	C₁₃×#3343	1	2	yes	—
456	C₂	C₁₃×#3367	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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×#477	C₂	semidirect
4. C₁₃×#2356	C₂	semidirect
5. C₁₃×#2072	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
92. #24694	C₁₃	direct (N × H)
152. C₂×#477	C₂×C₁₃	semidirect
155. #2356	C₂×C₁₃	semidirect
156. #2072	C₂×C₁₃	semidirect
158. #1993	C₂×C₁₃	semidirect
159. #1947	C₂×C₁₃	semidirect
160. #1940	C₂×C₁₃	semidirect
379. C₁₃	#24694	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×#477	2
C₂×C₁₃×#440	2
C₁₃×#2542	2
C₁₃×#2356	2
C₁₃×#2072	2
C₁₃×#2055	2
C₁₃×#1993	2
C₁₃×#1947	2
C₁₃×#1940	2
C₁₃×#1925	2
C₁₃×#1804	2
#24694	13

Subgroups — C13×#24694 #15711033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24694 #15711033