Subgroups — C₁₃×#18016 #15704355

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1591	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₁₃×#485	C₄	1	2	yes	—
15	C₁₃×#475	C₄	1	1	yes	characteristic
16	C₁₃×#474	C₄	1	1	yes	characteristic
17	C₁₃×#462	C₄	1	1	yes	characteristic
18	C₁₃×#461	C₄	1	1	yes	characteristic
19	C₁₃×#452	C₄	1	2	yes	—
20	C₁₃×#446	—	2	1	no	—
21	C₁₃×#446	C₂²	1	2	yes	—
22	C₁₃×#446	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₃	—	2	1	no	—
24	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
26	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
27	C₁₃×#435	—	2	2	no	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#433	—	2	2	no	—
30	C₁₃×#432	—	2	1	no	—
31	C₁₃×#431	C₂²	1	1	yes	characteristic
32	C₁₃×#431	C₂²	1	1	yes	characteristic
33	C₁₃×#431	C₂²	1	1	yes	characteristic
34	C₁₃×#423	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊C₈	—	2	1	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×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#322	C₂²	1	2	yes	—
46	C₈²×C₁₃	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#125	—	2	1	no	—
56	C₁₃×C₂²⋊Q₈	—	2	1	no	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₁₃	—	2	1	no	—
59	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
61	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	C₂×C₄	1	2	yes	—
72	C₁₃×#106	C₂×C₄	1	2	yes	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
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	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₃×#103	C₂×C₄	1	2	yes	—
85	C₁₃×#103	C₂×C₄	1	2	yes	—
86	C₁₃×#103	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	C₂×C₄	1	2	yes	—
91	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
92	C₁₃×#97	—	2	2	no	—
93	C₁₃×#97	—	2	2	no	—
94	C₄×C₈×C₁₃	—	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	#18016	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	4	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	4	2	no	—
116	C₁₃×SD₁₆	—	2	4	no	—
117	C₁₃×M₁₆	—	8	1	no	—
118	C₂×C₈×C₁₃	—	2	4	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	8	2	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃	#41	1	1	yes	characteristic
150	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
151	#3107	C₂×C₁₃	1	1	yes	characteristic
152	#2990	C₂×C₁₃	1	1	yes	characteristic
153	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1591	C₂×C₁₃	1	2	yes	complemented
155	#1587	C₂×C₁₃	1	2	yes	complemented
156	#1585	C₂×C₁₃	1	2	yes	complemented
157	C₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
158	#1574	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1476	C₂×C₁₃	1	1	yes	characteristic
161	#1450	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	2	no	—
165	Q₈×C₁₃	—	2	1	no	—
166	Q₈×C₁₃	—	2	1	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	2	1	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	#131	1	2	yes	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	2	2	no	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	—	4	2	no	—
200	C₈×C₁₃	—	4	1	no	—
201	#533	C₂²×C₁₃	1	1	yes	characteristic
202	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
203	#485	C₄×C₁₃	1	2	yes	—
204	#475	C₄×C₁₃	1	1	yes	characteristic
205	#474	C₄×C₁₃	1	1	yes	characteristic
206	#462	C₄×C₁₃	1	1	yes	characteristic
207	#461	C₄×C₁₃	1	1	yes	characteristic
208	#452	C₄×C₁₃	1	2	yes	—
209	#446	—	2	1	no	—
210	#446	C₂²×C₁₃	1	2	yes	—
211	#446	C₂²×C₁₃	1	2	yes	—
212	C₈×Q₈	—	2	1	no	—
213	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
214	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
215	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
216	#435	—	2	2	no	—
217	C₈×D₄	C₂²×C₁₃	1	2	yes	—
218	#433	—	2	2	no	—
219	#432	—	2	1	no	—
220	#431	C₂²×C₁₃	1	1	yes	characteristic
221	#431	C₂²×C₁₃	1	1	yes	characteristic
222	#431	C₂²×C₁₃	1	1	yes	characteristic
223	#423	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
226	#335	C₂²×C₁₃	1	2	yes	—
227	#334	C₂²×C₁₃	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
229	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
231	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
233	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
234	#322	C₂²×C₁₃	1	2	yes	—
235	C₈²	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	4	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	1	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	#443	1	2	yes	—
252	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
253	C₄×C₁₃	#568	1	1	yes	characteristic
254	C₄×C₁₃	#577	1	1	yes	characteristic
255	C₄×C₁₃	#578	1	1	yes	characteristic
256	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
258	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
263	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
264	#125	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
274	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	#107	C₂×C₄×C₁₃	1	2	yes	—
281	#106	C₂×C₄×C₁₃	1	2	yes	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
288	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
289	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
293	#103	C₂×C₄×C₁₃	1	2	yes	—
294	#103	C₂×C₄×C₁₃	1	2	yes	—
295	#103	C₂×C₄×C₁₃	1	2	yes	—
296	#102	C₂×C₄×C₁₃	1	2	yes	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	2	2	no	—
299	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
300	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
301	#97	—	2	2	no	—
302	#97	—	2	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₁₃	1	2	yes	—
309	C₄×C₈	C₂³×C₁₃	1	2	yes	—
310	C₂×C₁₃	—	4	1	no	—
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	#2933	1	1	yes	characteristic
313	C₂×C₁₃	#2947	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
315	#41	—	2	2	no	—
316	#41	—	4	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
319	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
328	Q₁₆	—	4	2	no	—
329	SD₁₆	—	2	4	no	—
330	M₁₆	—	8	1	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	8	2	no	—
338	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
339	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
350	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₄²	C₁₃×#41	1	1	yes	characteristic
363	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
364	C₁₃	#18016	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	1	no	—
366	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	1	no	—
373	D₄	—	4	2	no	—
374	D₄	C₁₃×#131	1	2	yes	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
390	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
391	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	2	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	C₁₃×#443	1	2	yes	—
420	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
421	C₄	C₁₃×#568	1	1	yes	characteristic
422	C₄	C₁₃×#577	1	1	yes	characteristic
423	C₄	C₁₃×#578	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	C₁₃×#2933	1	1	yes	characteristic
427	C₂	C₁₃×#2947	1	1	yes	characteristic
428	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	C₂×C₁₃×#41	C₂×C₄
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
3. C₁₃×#2986	C₂	semidirect
4. C₁₃×#1591	C₂	semidirect
5. C₁₃×#1587	C₂	semidirect
6. C₁₃×#1585	C₂	semidirect
7. C₈×C₁₃×SD₁₆	C₂	semidirect
8. C₁₃×#1574	C₂	semidirect
9. C₁₃×#1493	C₂	semidirect
11. C₁₃×#1450	C₂	semidirect
101. #18016	C₁₃	direct (N × H)
153. #2986	C₂×C₁₃	semidirect
154. #1591	C₂×C₁₃	semidirect
155. #1587	C₂×C₁₃	semidirect
156. #1585	C₂×C₁₃	semidirect
157. C₈×SD₁₆	C₂×C₁₃	semidirect
158. #1574	C₂×C₁₃	semidirect
159. #1493	C₂×C₁₃	semidirect
161. #1450	C₂×C₁₃	semidirect
364. C₁₃	#18016	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×#3107	2
C₁₃×#2990	2
C₁₃×#2986	2
C₁₃×#1591	2
C₁₃×#1587	2
C₁₃×#1585	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1574	2
C₁₃×#1493	2
C₁₃×#1476	2
C₁₃×#1450	2
#18016	13

Subgroups — C13×#18016 #15704355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18016 #15704355