Subgroups — C₁₃×#18015 #15704354

Order 3328.

640 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1586	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₁₃×#482	C₄	1	2	yes	—
15	C₁₃×#477	C₄	1	1	yes	characteristic
16	C₁₃×#476	C₄	1	1	yes	characteristic
17	C₁₃×#460	C₄	1	1	yes	characteristic
18	C₁₃×#459	C₄	1	1	yes	characteristic
19	C₁₃×#449	C₄	1	2	yes	—
20	C₁₃×#446	C₂²	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×D₈	C₂²	1	2	yes	—
23	C₁₃×#436	—	2	1	no	—
24	C₁₃×#436	C₂²	1	2	yes	—
25	C₁₃×#435	—	2	2	no	—
26	C₈×D₄×C₁₃	—	2	1	no	—
27	C₈×D₄×C₁₃	C₂²	1	2	yes	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#432	—	2	1	no	—
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#431	C₂²	1	1	yes	characteristic
32	C₁₃×#431	C₂²	1	1	yes	characteristic
33	C₁₃×#423	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
35	C₁₃×#408	—	2	2	no	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#335	C₂²	1	2	yes	—
38	C₁₃×#334	C₂²	1	2	yes	—
39	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₃×#322	C₂²	1	2	yes	—
46	C₈²×C₁₃	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#124	—	2	1	no	—
59	C₁₃×#121	—	2	1	no	—
60	C₁₃×#121	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₁₃	C₂³	1	2	yes	—
69	C₁₃×#117	—	2	1	no	—
70	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#107	C₂×C₄	1	2	yes	—
74	C₁₃×#106	C₂×C₄	1	2	yes	—
75	C₁₃×C₄⋊C₈	—	2	2	no	—
76	C₁₃×C₄⋊C₈	—	2	1	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₃×#103	C₂×C₄	1	2	yes	—
85	C₁₃×#102	C₂×C₄	1	2	yes	—
86	C₁₃×#102	C₂×C₄	1	2	yes	—
87	C₁₃×#102	C₂×C₄	1	2	yes	—
88	C₁₃×C₂²⋊C₈	—	2	1	no	—
89	C₁₃×C₂²⋊C₈	—	2	2	no	—
90	C₁₃×C₂²⋊C₈	—	2	2	no	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
94	C₁₃×#97	—	2	2	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	C₄×C₈×C₁₃	—	2	1	no	—
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂³	1	2	yes	—
100	C₄×C₈×C₁₃	C₂³	1	2	yes	—
101	#18015	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	4	1	no	—
104	C₁₃×#41	—	8	1	no	—
105	C₁₃×#41	—	8	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×SD₁₆	—	4	2	no	—
122	C₁₃×D₈	—	2	4	no	—
123	C₁₃×M₁₆	—	8	2	no	—
124	C₁₃×M₁₆	—	8	1	no	—
125	C₂×C₈×C₁₃	—	2	4	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	1	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	8	2	no	—
132	C₂×C₈×C₁₃	—	8	2	no	—
133	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	2	no	—
146	C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₃	#41	1	1	yes	characteristic
154	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
155	#3106	C₂×C₁₃	1	1	yes	characteristic
156	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1590	C₂×C₁₃	1	2	yes	complemented
159	#1586	C₂×C₁₃	1	2	yes	complemented
160	#1585	C₂×C₁₃	1	2	yes	complemented
161	C₈×D₈	C₂×C₁₃	1	2	yes	complemented
162	#1574	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1450	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	2	1	no	—
170	Q₈×C₁₃	—	2	1	no	—
171	Q₈×C₁₃	—	8	1	no	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	2	1	no	—
174	D₄×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	8	1	no	—
178	D₄×C₁₃	—	8	2	no	—
179	D₄×C₁₃	#131	1	2	yes	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	2	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	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	2	no	—
209	C₈×C₁₃	—	4	1	no	—
210	#532	C₂²×C₁₃	1	1	yes	characteristic
211	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
212	#482	C₄×C₁₃	1	2	yes	—
213	#477	C₄×C₁₃	1	1	yes	characteristic
214	#476	C₄×C₁₃	1	1	yes	characteristic
215	#460	C₄×C₁₃	1	1	yes	characteristic
216	#459	C₄×C₁₃	1	1	yes	characteristic
217	#449	C₄×C₁₃	1	2	yes	—
218	#446	C₂²×C₁₃	1	2	yes	—
219	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
220	C₄×D₈	C₂²×C₁₃	1	2	yes	—
221	#436	—	2	1	no	—
222	#436	C₂²×C₁₃	1	2	yes	—
223	#435	—	2	2	no	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	C₂²×C₁₃	1	2	yes	—
226	C₈×D₄	C₂²×C₁₃	1	2	yes	—
227	#432	—	2	1	no	—
228	#431	C₂²×C₁₃	1	1	yes	characteristic
229	#431	C₂²×C₁₃	1	1	yes	characteristic
230	#431	C₂²×C₁₃	1	1	yes	characteristic
231	#423	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₈	—	2	1	no	—
233	#408	—	2	2	no	—
234	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
235	#335	C₂²×C₁₃	1	2	yes	—
236	#334	C₂²×C₁₃	1	2	yes	—
237	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
238	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
239	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
240	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
241	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
242	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
243	#322	C₂²×C₁₃	1	2	yes	—
244	C₈²	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	4	1	no	—
250	C₂²×C₁₃	—	4	1	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	4	1	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	1	no	—
262	C₄×C₁₃	#443	1	2	yes	—
263	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
264	C₄×C₁₃	#568	1	1	yes	characteristic
265	C₄×C₁₃	#576	1	1	yes	characteristic
266	C₄×C₁₃	#577	1	1	yes	characteristic
267	C₂×#41	—	2	1	no	—
268	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
270	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
277	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
278	#124	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	C₂×C₄×C₁₃	1	2	yes	—
281	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
282	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₄×D₄	C₂³×C₁₃	1	2	yes	—
289	#117	—	2	1	no	—
290	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	#107	C₂×C₄×C₁₃	1	2	yes	—
294	#106	C₂×C₄×C₁₃	1	2	yes	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
298	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
299	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
300	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
302	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
304	#103	C₂×C₄×C₁₃	1	2	yes	—
305	#102	C₂×C₄×C₁₃	1	2	yes	—
306	#102	C₂×C₄×C₁₃	1	2	yes	—
307	#102	C₂×C₄×C₁₃	1	2	yes	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
313	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
314	#97	—	2	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₁₃	1	2	yes	—
320	C₄×C₈	C₂³×C₁₃	1	2	yes	—
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	—	4	2	no	—
323	C₂×C₁₃	—	8	2	no	—
324	C₂×C₁₃	#2933	1	1	yes	characteristic
325	C₂×C₁₃	#2946	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
327	#41	—	2	2	no	—
328	#41	—	4	1	no	—
329	#41	—	8	1	no	—
330	#41	—	8	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
346	SD₁₆	—	4	2	no	—
347	D₈	—	2	4	no	—
348	M₁₆	—	8	2	no	—
349	M₁₆	—	8	1	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	8	2	no	—
357	C₂×C₈	—	8	2	no	—
358	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
359	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
366	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₄²	C₁₃×#41	1	1	yes	characteristic
379	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
380	C₁₃	#18015	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	8	1	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	D₄	C₁₃×#131	1	2	yes	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	1	no	—
442	C₄	C₁₃×#443	1	2	yes	—
443	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
444	C₄	C₁₃×#568	1	1	yes	characteristic
445	C₄	C₁₃×#576	1	1	yes	characteristic
446	C₄	C₁₃×#577	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	2	no	—
450	C₂	C₁₃×#2933	1	1	yes	characteristic
451	C₂	C₁₃×#2946	1	1	yes	characteristic
452	C₂	C₂×C₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2990	C₂	semidirect
3. C₁₃×#2979	C₂	semidirect
4. C₁₃×#1590	C₂	semidirect
5. C₁₃×#1586	C₂	semidirect
6. C₁₃×#1585	C₂	semidirect
7. C₈×C₁₃×D₈	C₂	semidirect
8. C₁₃×#1574	C₂	semidirect
9. C₁₃×#1492	C₂	semidirect
10. C₁₃×#1476	C₂	semidirect
11. C₁₃×#1450	C₂	semidirect
101. #18015	C₁₃	direct (N × H)
156. #2990	C₂×C₁₃	semidirect
157. #2979	C₂×C₁₃	semidirect
158. #1590	C₂×C₁₃	semidirect
159. #1586	C₂×C₁₃	semidirect
160. #1585	C₂×C₁₃	semidirect
161. C₈×D₈	C₂×C₁₃	semidirect
162. #1574	C₂×C₁₃	semidirect
163. #1492	C₂×C₁₃	semidirect
164. #1476	C₂×C₁₃	semidirect
165. #1450	C₂×C₁₃	semidirect
380. C₁₃	#18015	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3106	2
C₁₃×#2990	2
C₁₃×#2979	2
C₁₃×#1590	2
C₁₃×#1586	2
C₁₃×#1585	2
C₈×C₁₃×D₈	2
C₁₃×#1574	2
C₁₃×#1492	2
C₁₃×#1476	2
C₁₃×#1450	2
#18015	13

Subgroups — C13×#18015 #15704354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18015 #15704354