Subgroups — C₁₃×#17979 #15704318

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 384 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×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1588	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1585	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#131	—	2	1	no	—
11	C₁₃×#533	C₂²	1	1	yes	characteristic
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₁₃×#498	C₄	1	1	yes	characteristic
14	C₁₃×#492	C₄	1	1	yes	characteristic
15	C₁₃×#487	C₄	1	1	yes	characteristic
16	C₁₃×#486	C₄	1	1	yes	characteristic
17	C₁₃×#465	C₄	1	4	yes	—
18	C₁₃×#446	—	2	1	no	—
19	C₁₃×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₃	—	2	1	no	—
21	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
23	C₁₃×#436	—	2	1	no	—
24	C₁₃×#436	C₂²	1	2	yes	—
25	C₈×D₄×C₁₃	—	2	1	no	—
26	C₈×D₄×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#424	—	2	1	no	—
28	C₁₃×#423	C₂²	1	1	yes	characteristic
29	C₁₃×#423	C₂²	1	1	yes	characteristic
30	C₁₃×#408	—	2	1	no	—
31	C₁₃×#405	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#335	C₂²	1	4	yes	—
36	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
37	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
38	C₁₃×#322	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	2	yes	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
42	C₁₃×#131	—	4	4	no	—
43	C₂×C₁₃×M₁₆	—	2	1	no	—
44	C₂×C₁₃×M₁₆	—	2	1	no	—
45	C₂×C₁₃×M₁₆	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	1	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	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×#127	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#125	—	2	1	no	—
56	C₁₃×#124	—	2	1	no	—
57	C₁₃×C₂²⋊Q₈	—	2	1	no	—
58	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₁₃×#121	—	2	1	no	—
60	C₁₃×#121	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₁₃	—	2	1	no	—
62	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	C₂³	1	2	yes	—
65	C₁₃×#117	—	2	1	no	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#106	C₂×C₄	1	4	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	—	2	1	no	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	4	yes	—
75	C₁₃×#102	C₂×C₄	1	4	yes	—
76	C₁₃×C₂²⋊C₈	—	2	2	no	—
77	C₁₃×C₂²⋊C₈	—	2	2	no	—
78	C₁₃×#97	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	1	no	—
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	2	yes	—
86	C₄×C₈×C₁₃	C₂³	1	2	yes	—
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#17979	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	4	2	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
103	C₁₃×SD₁₆	—	4	4	no	—
104	C₁₃×M₁₆	—	4	4	no	—
105	C₁₃×M₁₆	—	4	2	no	—
106	C₁₃×M₁₆	—	4	2	no	—
107	C₂×C₈×C₁₃	—	2	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	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	4	2	no	—
114	C₂×C₈×C₁₃	—	4	4	no	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	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	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	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	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	#41	1	1	yes	characteristic
136	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
137	#3167	C₂×C₁₃	1	1	yes	characteristic
138	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2931	C₂×C₁₃	1	1	yes	characteristic
140	#1588	C₂×C₁₃	1	4	yes	complemented
141	#1585	C₂×C₁₃	1	4	yes	complemented
142	#1567	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1492	C₂×C₁₃	1	1	yes	characteristic
145	C₂×#322	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	2	4	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	2	4	no	—
152	D₄×C₁₃	—	4	4	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₁₃	#137	1	2	yes	—
167	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₈×C₁₃	—	2	4	no	—
171	C₈×C₁₃	—	2	2	no	—
172	C₈×C₁₃	—	2	2	no	—
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	—	4	2	no	—
178	C₈×C₁₃	—	4	2	no	—
179	C₂×#131	—	2	1	no	—
180	#533	C₂²×C₁₃	1	1	yes	characteristic
181	#532	C₂²×C₁₃	1	1	yes	characteristic
182	#498	C₄×C₁₃	1	1	yes	characteristic
183	#492	C₄×C₁₃	1	1	yes	characteristic
184	#487	C₄×C₁₃	1	1	yes	characteristic
185	#486	C₄×C₁₃	1	1	yes	characteristic
186	#465	C₄×C₁₃	1	4	yes	—
187	#446	—	2	1	no	—
188	#446	C₂²×C₁₃	1	2	yes	—
189	C₈×Q₈	—	2	1	no	—
190	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
191	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
192	#436	—	2	1	no	—
193	#436	C₂²×C₁₃	1	2	yes	—
194	C₈×D₄	—	2	1	no	—
195	C₈×D₄	C₂²×C₁₃	1	2	yes	—
196	#424	—	2	1	no	—
197	#423	C₂²×C₁₃	1	1	yes	characteristic
198	#423	C₂²×C₁₃	1	1	yes	characteristic
199	#408	—	2	1	no	—
200	#405	—	2	1	no	—
201	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
204	#335	C₂²×C₁₃	1	4	yes	—
205	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
206	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
207	#322	C₂²×C₁₃	1	2	yes	—
208	#322	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	#440	1	2	yes	—
215	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	—	4	2	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	#440	1	2	yes	—
222	C₄×C₁₃	#443	1	2	yes	—
223	C₄×C₁₃	#568	1	2	yes	—
224	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
226	C₂×#41	—	2	1	no	—
227	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
228	#131	—	4	4	no	—
229	C₂×M₁₆	—	2	1	no	—
230	C₂×M₁₆	—	2	1	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
235	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
236	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
237	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
240	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
241	#125	—	2	1	no	—
242	#124	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
245	#121	—	2	1	no	—
246	#121	C₂×C₄×C₁₃	1	2	yes	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	C₂³×C₁₃	1	2	yes	—
251	#117	—	2	1	no	—
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	#106	C₂×C₄×C₁₃	1	4	yes	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
259	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
260	#103	C₂×C₄×C₁₃	1	4	yes	—
261	#102	C₂×C₄×C₁₃	1	4	yes	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	2	2	no	—
264	#97	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
268	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
270	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₃	1	2	yes	—
272	C₄×C₈	C₂³×C₁₃	1	2	yes	—
273	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₁₃	—	2	2	no	—
276	C₂×C₁₃	—	8	2	no	—
277	C₂×C₁₃	#2932	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
279	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
293	SD₁₆	—	4	4	no	—
294	M₁₆	—	4	4	no	—
295	M₁₆	—	4	2	no	—
296	M₁₆	—	4	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
306	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
307	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
318	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₄²	C₁₃×#41	1	1	yes	characteristic
326	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
327	C₁₃	#17979	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	2	2	no	—
329	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
346	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
348	C₂×C₄	C₁₃×#137	1	2	yes	—
349	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₁₃×#440	1	2	yes	—
367	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	C₁₃×#440	1	2	yes	—
374	C₄	C₁₃×#443	1	2	yes	—
375	C₄	C₁₃×#568	1	2	yes	—
376	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	8	2	no	—
380	C₂	C₁₃×#2932	1	1	yes	characteristic
381	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
382	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×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2960	C₂	semidirect
4. C₁₃×#1588	C₂	semidirect
5. C₁₃×#1585	C₂	semidirect
6. C₁₃×#1567	C₂	semidirect
7. C₁₃×#1493	C₂	semidirect
9. C₂×C₁₃×#322	C₂	semidirect
89. #17979	C₁₃	direct (N × H)
138. #2960	C₂×C₁₃	semidirect
140. #1588	C₂×C₁₃	semidirect
141. #1585	C₂×C₁₃	semidirect
142. #1567	C₂×C₁₃	semidirect
143. #1493	C₂×C₁₃	semidirect
145. C₂×#322	C₂×C₁₃	semidirect
327. C₁₃	#17979	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×#2960	2
C₁₃×#2931	2
C₁₃×#1588	2
C₁₃×#1585	2
C₁₃×#1567	2
C₁₃×#1493	2
C₁₃×#1492	2
C₂×C₁₃×#322	2
#17979	13

Subgroups — C13×#17979 #15704318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17979 #15704318