Subgroups — C₁₃×#18069 #15704408

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2969	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1582	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1482	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	C₂²	1	2	yes	—
13	C₁₃×#499	C₄	1	1	yes	characteristic
14	C₁₃×#495	C₄	1	1	yes	characteristic
15	C₁₃×#488	C₄	1	2	yes	—
16	C₁₃×#467	C₄	1	1	yes	characteristic
17	C₁₃×#466	C₄	1	1	yes	characteristic
18	C₁₃×#465	C₄	1	2	yes	—
19	C₁₃×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
24	C₁₃×#436	—	2	2	no	—
25	C₁₃×#436	C₂²	1	2	yes	—
26	C₁₃×#435	—	2	2	no	—
27	C₈×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#433	—	2	2	no	—
29	C₁₃×#431	C₂²	1	2	yes	—
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#405	—	2	2	no	—
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#335	C₂²	1	1	yes	characteristic
35	C₁₃×#335	C₂²	1	1	yes	characteristic
36	C₁₃×#334	C₂²	1	2	yes	—
37	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
40	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
41	C₁₃×#322	C₂²	1	1	yes	characteristic
42	C₁₃×#322	C₂²	1	1	yes	characteristic
43	C₈²×C₁₃	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#126	—	2	2	no	—
55	C₁₃×#125	C₂×C₄	1	2	yes	—
56	C₁₃×#124	C₂×C₄	1	2	yes	—
57	C₁₃×#123	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₁₃×#121	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#117	—	2	2	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
66	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
67	C₁₃×#106	C₂×C₄	1	2	yes	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	—	2	2	no	—
70	C₁₃×C₄⋊C₈	—	2	1	no	—
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×#103	C₂×C₄	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#102	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	—	2	2	no	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	—	2	2	no	—
81	C₁₃×#97	—	2	2	no	—
82	C₁₃×#97	D₄	1	1	yes	characteristic
83	C₁₃×#97	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	#18069	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
102	C₁₃×Q₁₆	—	2	2	no	—
103	C₁₃×SD₁₆	—	4	2	no	—
104	C₁₃×D₈	—	2	2	no	—
105	C₁₃×M₁₆	—	2	2	no	—
106	C₁₃×M₁₆	—	2	2	no	—
107	C₁₃×M₁₆	—	4	4	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	4	1	no	—
114	C₂×C₈×C₁₃	—	4	4	no	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	#41	1	1	yes	characteristic
138	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
139	#3168	C₂×C₁₃	1	1	yes	characteristic
140	#2969	C₂×C₁₃	1	2	yes	complemented
141	#1591	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#1589	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1583	C₂×C₁₃	1	2	yes	complemented
144	#1582	C₂×C₁₃	1	2	yes	complemented
145	C₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1564	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1482	C₂×C₁₃	1	2	yes	complemented
149	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
152	Q₈×C₁₃	—	2	2	no	—
153	Q₈×C₁₃	—	2	2	no	—
154	D₄×C₁₃	—	2	2	no	—
155	D₄×C₁₃	—	2	2	no	—
156	D₄×C₁₃	—	8	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₈×C₁₃	—	2	1	no	—
174	C₈×C₁₃	—	2	1	no	—
175	C₈×C₁₃	—	2	1	no	—
176	C₈×C₁₃	—	2	1	no	—
177	C₈×C₁₃	—	2	1	no	—
178	C₈×C₁₃	—	4	1	no	—
179	C₈×C₁₃	—	4	1	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	4	2	no	—
182	C₈×C₁₃	#131	1	2	yes	—
183	C₈×C₁₃	#135	1	2	yes	—
184	C₈×C₁₃	#135	1	2	yes	—
185	#529	C₂²×C₁₃	1	2	yes	—
186	#499	C₄×C₁₃	1	1	yes	characteristic
187	#495	C₄×C₁₃	1	1	yes	characteristic
188	#488	C₄×C₁₃	1	2	yes	—
189	#467	C₄×C₁₃	1	1	yes	characteristic
190	#466	C₄×C₁₃	1	1	yes	characteristic
191	#465	C₄×C₁₃	1	2	yes	—
192	#446	C₂²×C₁₃	1	2	yes	—
193	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
194	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
195	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
196	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
197	#436	—	2	2	no	—
198	#436	C₂²×C₁₃	1	2	yes	—
199	#435	—	2	2	no	—
200	C₈×D₄	C₂²×C₁₃	1	2	yes	—
201	#433	—	2	2	no	—
202	#431	C₂²×C₁₃	1	2	yes	—
203	#431	C₂²×C₁₃	1	1	yes	characteristic
204	#405	—	2	2	no	—
205	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
207	#335	C₂²×C₁₃	1	1	yes	characteristic
208	#335	C₂²×C₁₃	1	1	yes	characteristic
209	#334	C₂²×C₁₃	1	2	yes	—
210	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
211	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
212	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
213	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
214	#322	C₂²×C₁₃	1	1	yes	characteristic
215	#322	C₂²×C₁₃	1	1	yes	characteristic
216	C₈²	C₂²×C₁₃	1	1	yes	characteristic
217	C₈²	C₂²×C₁₃	1	1	yes	characteristic
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	—	4	2	no	—
223	C₂²×C₁₃	—	4	2	no	—
224	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
233	C₄×C₁₃	#568	1	1	yes	characteristic
234	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
235	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
236	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
237	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
238	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
241	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
245	#126	—	2	2	no	—
246	#125	C₂×C₄×C₁₃	1	2	yes	—
247	#124	C₂×C₄×C₁₃	1	2	yes	—
248	#123	—	2	2	no	—
249	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
250	#121	C₂×C₄×C₁₃	1	2	yes	—
251	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	C₂³×C₁₃	1	2	yes	—
254	#117	—	2	2	no	—
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
257	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
258	#106	C₂×C₄×C₁₃	1	2	yes	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
264	#103	C₂×C₄×C₁₃	1	2	yes	—
265	#103	C₂×C₄×C₁₃	1	2	yes	—
266	#102	C₂×C₄×C₁₃	1	2	yes	—
267	#102	C₂×C₄×C₁₃	1	2	yes	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	1	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	#97	—	2	2	no	—
273	#97	D₄×C₁₃	1	1	yes	characteristic
274	#97	D₄×C₁₃	1	1	yes	characteristic
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
278	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₁₃	—	4	1	no	—
286	C₂×C₁₃	—	8	2	no	—
287	C₂×C₁₃	#2935	1	1	yes	characteristic
288	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
289	C₂×C₁₃	#2957	1	1	yes	characteristic
290	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
297	Q₁₆	—	2	2	no	—
298	SD₁₆	—	4	2	no	—
299	D₈	—	2	2	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	4	no	—
310	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
313	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
323	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₄²	C₁₃×#41	1	1	yes	characteristic
333	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
334	C₁₃	#18069	1	1	yes	characteristic, direct product factor, Sylow
335	C₂³	—	2	2	no	—
336	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
337	Q₈	—	2	2	no	—
338	Q₈	—	2	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	8	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	4	1	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₈	C₁₃×#131	1	2	yes	—
368	C₈	C₁₃×#135	1	2	yes	—
369	C₈	C₁₃×#135	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
385	C₄	C₁₃×#568	1	1	yes	characteristic
386	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
387	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
388	C₂	—	4	1	no	—
389	C₂	—	8	2	no	—
390	C₂	C₁₃×#2935	1	1	yes	characteristic
391	C₂	C₄×C₁₃×#135	1	1	yes	characteristic
392	C₂	C₁₃×#2957	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×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2969	C₂	semidirect
3. C₁₃×#1591	C₂	semidirect
4. C₁₃×#1589	C₂	semidirect
5. C₁₃×#1583	C₂	semidirect
6. C₁₃×#1582	C₂	semidirect
7. C₈×C₁₃×Q₁₆	C₂	semidirect
8. C₈×C₁₃×D₈	C₂	semidirect
9. C₁₃×#1564	C₂	semidirect
10. C₁₃×#1482	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
94. #18069	C₁₃	direct (N × H)
140. #2969	C₂×C₁₃	semidirect
141. #1591	C₂×C₁₃	semidirect
142. #1589	C₂×C₁₃	semidirect
143. #1583	C₂×C₁₃	semidirect
144. #1582	C₂×C₁₃	semidirect
145. C₈×Q₁₆	C₂×C₁₃	semidirect
146. C₈×D₈	C₂×C₁₃	semidirect
147. #1564	C₂×C₁₃	semidirect
148. #1482	C₂×C₁₃	semidirect
149. C₈×M₁₆	C₂×C₁₃	semidirect
334. C₁₃	#18069	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×#3168	2
C₁₃×#2969	2
C₁₃×#1591	2
C₁₃×#1589	2
C₁₃×#1583	2
C₁₃×#1582	2
C₈×C₁₃×Q₁₆	2
C₈×C₁₃×D₈	2
C₁₃×#1564	2
C₁₃×#1482	2
C₈×C₁₃×M₁₆	2
#18069	13

Subgroups — C13×#18069 #15704408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18069 #15704408