Subgroups — C₁₃×#17990 #15704329

Order 3328.

584 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1588	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1582	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1496	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₁₃×#498	C₄	1	1	yes	characteristic
15	C₁₃×#492	C₄	1	1	yes	characteristic
16	C₁₃×#487	C₄	1	1	yes	characteristic
17	C₁₃×#486	C₄	1	1	yes	characteristic
18	C₁₃×#465	C₄	1	2	yes	—
19	C₁₃×#465	C₄	1	2	yes	—
20	C₁₃×#446	—	2	2	no	—
21	C₁₃×#446	C₂²	1	2	yes	—
22	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
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×#432	C₂²	1	1	yes	characteristic
30	C₁₃×#432	C₂²	1	1	yes	characteristic
31	C₁₃×#431	C₂²	1	1	yes	characteristic
32	C₁₃×#431	C₂²	1	1	yes	characteristic
33	C₁₃×#408	—	2	2	no	—
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#335	C₂²	1	2	yes	—
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	C₁₃×#322	C₂²	1	1	yes	characteristic
44	C₁₃×#322	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
56	C₁₃×#125	—	2	1	no	—
57	C₁₃×#124	—	2	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
60	C₁₃×#121	—	2	1	no	—
61	C₁₃×#121	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#106	C₂×C₄	1	2	yes	—
69	C₁₃×#106	C₂×C₄	1	2	yes	—
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
74	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
76	C₁₃×#103	C₂×C₄	1	2	yes	—
77	C₁₃×#103	C₂×C₄	1	2	yes	—
78	C₁₃×#102	C₂×C₄	1	2	yes	—
79	C₁₃×#102	C₂×C₄	1	2	yes	—
80	C₁₃×C₂²⋊C₈	—	2	1	no	—
81	C₁₃×C₂²⋊C₈	—	2	1	no	—
82	C₁₃×C₂²⋊C₈	—	2	1	no	—
83	C₁₃×C₂²⋊C₈	—	2	2	no	—
84	C₁₃×C₂²⋊C₈	—	2	2	no	—
85	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
86	C₁₃×#97	—	2	2	no	—
87	C₁₃×#97	—	2	1	no	—
88	C₁₃×#97	—	2	1	no	—
89	C₄×C₈×C₁₃	—	2	2	no	—
90	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	#17990	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₁₃×#41	—	8	2	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
111	C₁₃×SD₁₆	—	4	2	no	—
112	C₁₃×SD₁₆	—	4	2	no	—
113	C₁₃×M₁₆	—	8	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	4	1	no	—
119	C₂×C₈×C₁₃	—	4	1	no	—
120	C₂×C₈×C₁₃	—	8	2	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₁₃×C₂²⋊C₄	—	2	2	no	—
137	C₁₃×C₂²⋊C₄	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	#41	1	1	yes	characteristic
142	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
143	#3167	C₂×C₁₃	1	1	yes	characteristic
144	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2981	C₂×C₁₃	1	1	yes	characteristic
146	#1588	C₂×C₁₃	1	2	yes	complemented
147	#1585	C₂×C₁₃	1	2	yes	complemented
148	#1583	C₂×C₁₃	1	2	yes	complemented
149	#1582	C₂×C₁₃	1	2	yes	complemented
150	#1568	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1497	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1496	C₂×C₁₃	1	1	yes	characteristic
153	#1452	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	2	no	—
157	Q₈×C₁₃	—	2	2	no	—
158	Q₈×C₁₃	—	8	1	no	—
159	Q₈×C₁₃	—	8	1	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	8	1	no	—
163	D₄×C₁₃	—	8	1	no	—
164	D₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₈×C₁₃	—	2	1	no	—
181	C₈×C₁₃	—	2	1	no	—
182	C₈×C₁₃	—	2	1	no	—
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	4	1	no	—
187	C₈×C₁₃	—	4	1	no	—
188	C₈×C₁₃	—	4	2	no	—
189	C₈×C₁₃	—	4	2	no	—
190	#533	C₂²×C₁₃	1	1	yes	characteristic
191	#532	C₂²×C₁₃	1	1	yes	characteristic
192	#498	C₄×C₁₃	1	1	yes	characteristic
193	#492	C₄×C₁₃	1	1	yes	characteristic
194	#487	C₄×C₁₃	1	1	yes	characteristic
195	#486	C₄×C₁₃	1	1	yes	characteristic
196	#465	C₄×C₁₃	1	2	yes	—
197	#465	C₄×C₁₃	1	2	yes	—
198	#446	—	2	2	no	—
199	#446	C₂²×C₁₃	1	2	yes	—
200	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
201	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
202	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
203	#436	C₂²×C₁₃	1	2	yes	—
204	#435	—	2	2	no	—
205	C₈×D₄	C₂²×C₁₃	1	2	yes	—
206	#433	—	2	2	no	—
207	#432	C₂²×C₁₃	1	1	yes	characteristic
208	#432	C₂²×C₁₃	1	1	yes	characteristic
209	#431	C₂²×C₁₃	1	1	yes	characteristic
210	#431	C₂²×C₁₃	1	1	yes	characteristic
211	#408	—	2	2	no	—
212	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
213	#335	C₂²×C₁₃	1	2	yes	—
214	#334	C₂²×C₁₃	1	2	yes	—
215	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
216	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
217	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
218	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
219	#322	C₂²×C₁₃	1	1	yes	characteristic
220	#322	C₂²×C₁₃	1	1	yes	characteristic
221	#322	C₂²×C₁₃	1	1	yes	characteristic
222	#322	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	#568	1	1	yes	characteristic
238	C₄×C₁₃	#568	1	1	yes	characteristic
239	C₄×C₁₃	#577	1	2	yes	—
240	C₂×#41	—	2	1	no	—
241	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
242	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
247	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
248	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
249	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
250	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
251	#125	—	2	1	no	—
252	#124	—	2	1	no	—
253	C₂²⋊Q₈	—	2	1	no	—
254	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
255	#121	—	2	1	no	—
256	#121	C₂×C₄×C₁₃	1	2	yes	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	C₂³×C₁₃	1	2	yes	—
261	#117	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	#106	C₂×C₄×C₁₃	1	2	yes	—
264	#106	C₂×C₄×C₁₃	1	2	yes	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
270	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
271	#103	C₂×C₄×C₁₃	1	2	yes	—
272	#103	C₂×C₄×C₁₃	1	2	yes	—
273	#102	C₂×C₄×C₁₃	1	2	yes	—
274	#102	C₂×C₄×C₁₃	1	2	yes	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
281	#97	—	2	2	no	—
282	#97	—	2	1	no	—
283	#97	—	2	1	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
286	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×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	1	yes	characteristic
293	C₂×C₁₃	—	4	1	no	—
294	C₂×C₁₃	—	8	2	no	—
295	C₂×C₁₃	#2932	1	1	yes	characteristic
296	C₂×C₁₃	#2949	1	1	yes	characteristic
297	C₂×C₁₃	#2957	1	1	yes	characteristic
298	#41	—	8	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
310	SD₁₆	—	4	2	no	—
311	SD₁₆	—	4	2	no	—
312	M₁₆	—	8	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	8	2	no	—
320	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
321	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
322	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
323	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
333	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₄²	C₁₃×#41	1	1	yes	characteristic
341	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₁₃	#17990	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	2	2	no	—
344	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	2	no	—
374	C₈	—	2	2	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	2	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₁₃×#568	1	1	yes	characteristic
394	C₄	C₁₃×#568	1	1	yes	characteristic
395	C₄	C₁₃×#577	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	C₁₃×#2932	1	1	yes	characteristic
399	C₂	C₁₃×#2949	1	1	yes	characteristic
400	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×#532	C₂²
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×#2985	C₂	semidirect
4. C₁₃×#1588	C₂	semidirect
5. C₁₃×#1585	C₂	semidirect
6. C₁₃×#1583	C₂	semidirect
7. C₁₃×#1582	C₂	semidirect
8. C₁₃×#1568	C₂	semidirect
9. C₁₃×#1497	C₂	semidirect
11. C₁₃×#1452	C₂	semidirect
98. #17990	C₁₃	direct (N × H)
144. #2985	C₂×C₁₃	semidirect
146. #1588	C₂×C₁₃	semidirect
147. #1585	C₂×C₁₃	semidirect
148. #1583	C₂×C₁₃	semidirect
149. #1582	C₂×C₁₃	semidirect
150. #1568	C₂×C₁₃	semidirect
151. #1497	C₂×C₁₃	semidirect
153. #1452	C₂×C₁₃	semidirect
342. C₁₃	#17990	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×#3167	2
C₁₃×#2985	2
C₁₃×#2981	2
C₁₃×#1588	2
C₁₃×#1585	2
C₁₃×#1583	2
C₁₃×#1582	2
C₁₃×#1568	2
C₁₃×#1497	2
C₁₃×#1496	2
C₁₃×#1452	2
#17990	13

Subgroups — C13×#17990 #15704329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17990 #15704329