Subgroups — C₂×C₁₃×#1683 #15705448

Order 3328.

726 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	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1683	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₁₃	—	2	1	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#487	—	2	2	no	—
14	C₁₃×#487	C₂²	1	4	yes	complemented
15	C₁₃×#476	—	2	2	no	—
16	C₁₃×#476	C₂²	1	4	yes	—
17	C₁₃×#474	—	2	2	no	—
18	C₁₃×#474	C₂²	1	4	yes	—
19	C₈×D₄×C₁₃	—	2	2	no	—
20	C₈×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂×C₁₃×#107	—	2	1	no	—
22	C₂×C₁₃×#106	—	2	1	no	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	—	2	1	no	—
27	C₂×C₁₃×#103	—	2	1	no	—
28	C₂×C₁₃×#102	—	2	1	no	—
29	C₂×C₁₃×#102	—	2	1	no	—
30	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#335	C₂²	1	4	yes	complemented
33	C₁₃×#333	C₂²	1	4	yes	complemented
34	C₁₃×#332	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₃	—	2	1	no	—
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	—	4	4	no	—
44	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	D₄	1	2	yes	—
57	C₄×D₄×C₁₃	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#107	—	2	4	no	—
66	C₁₃×#106	—	2	4	no	—
67	C₁₃×C₄⋊C₈	—	2	1	no	—
68	C₁₃×C₄⋊C₈	—	2	1	no	—
69	C₁₃×C₄⋊C₈	—	2	1	no	—
70	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×#103	—	2	4	no	—
74	C₁₃×#103	—	2	4	no	—
75	C₁₃×#102	—	2	4	no	—
76	C₁₃×#102	—	2	4	no	—
77	C₁₃×C₂²⋊C₈	—	2	4	no	—
78	C₄×C₈×C₁₃	D₄	1	2	yes	—
79	C₄×C₈×C₁₃	C₂³	1	2	yes	—
80	C₂×#1683	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	1	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	4	1	no	—
85	C₂×Q₈×C₁₃	—	4	1	no	—
86	C₂×Q₈×C₁₃	—	4	2	no	—
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	8	2	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	Q₁₆	1	4	yes	—
92	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	4	8	no	—
109	C₂×C₈×C₁₃	—	4	2	no	—
110	C₂×C₈×C₁₃	—	4	2	no	—
111	C₂×C₈×C₁₃	—	4	2	no	—
112	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₁₃×C₂²⋊C₄	—	2	2	no	—
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃	#41	1	1	yes	characteristic
129	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
132	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
133	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
134	#1683	C₂×C₁₃	1	8	yes	direct product factor
135	C₂×#335	C₂×C₁₃	1	1	yes	characteristic, complemented
136	C₂×#333	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂×#332	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	—	2	4	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	#121	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	2	no	—
144	Q₈×C₁₃	—	4	2	no	—
145	Q₈×C₁₃	—	8	2	no	—
146	Q₈×C₁₃	—	8	2	no	—
147	Q₈×C₁₃	—	8	2	no	—
148	D₄×C₁₃	—	2	2	no	—
149	D₄×C₁₃	—	2	4	no	—
150	D₄×C₁₃	C₂×Q₁₆	1	4	yes	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	8	2	no	—
160	C₂×C₄×C₁₃	—	8	2	no	—
161	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
165	C₂×C₄×C₁₃	#135	1	2	yes	—
166	C₂×C₄×C₁₃	#135	1	2	yes	—
167	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
171	C₈×C₁₃	—	2	2	no	—
172	C₈×C₁₃	—	2	2	no	—
173	C₈×C₁₃	—	4	2	no	—
174	C₈×C₁₃	—	4	2	no	—
175	C₈×C₁₃	—	4	2	no	—
176	C₂³×C₈	—	2	1	no	—
177	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
180	#487	—	2	2	no	—
181	#487	C₂²×C₁₃	1	4	yes	complemented
182	#476	—	2	2	no	—
183	#476	C₂²×C₁₃	1	4	yes	—
184	#474	—	2	2	no	—
185	#474	C₂²×C₁₃	1	4	yes	—
186	C₈×D₄	—	2	2	no	—
187	C₈×D₄	C₂²×C₁₃	1	4	yes	—
188	C₂×#107	—	2	1	no	—
189	C₂×#106	—	2	1	no	—
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#103	—	2	1	no	—
194	C₂×#103	—	2	1	no	—
195	C₂×#102	—	2	1	no	—
196	C₂×#102	—	2	1	no	—
197	C₂×C₂²⋊C₈	—	2	1	no	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	#335	C₂²×C₁₃	1	4	yes	complemented
200	#333	C₂²×C₁₃	1	4	yes	complemented
201	#332	C₂²×C₁₃	1	4	yes	complemented
202	C₂²×C₁₃	—	2	4	no	—
203	C₂²×C₁₃	—	4	8	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	4	2	no	—
206	C₂²×C₁₃	#463	1	2	yes	—
207	C₂²×C₁₃	#467	1	2	yes	—
208	C₂²×C₁₃	#471	1	2	yes	—
209	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	4	2	no	—
213	C₄×C₁₃	—	8	2	no	—
214	C₄×C₁₃	—	8	2	no	—
215	C₄×C₁₃	#463	1	2	yes	—
216	C₄×C₁₃	#467	1	2	yes	—
217	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
218	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
219	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
220	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	4	4	no	—
230	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
231	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
239	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	D₄×C₁₃	1	2	yes	—
243	C₄×D₄	C₂³×C₁₃	1	2	yes	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
251	#107	—	2	4	no	—
252	#106	—	2	4	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
257	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
258	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
259	#103	—	2	4	no	—
260	#103	—	2	4	no	—
261	#102	—	2	4	no	—
262	#102	—	2	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	C₄×C₈	D₄×C₁₃	1	2	yes	—
265	C₄×C₈	C₂³×C₁₃	1	2	yes	—
266	C₂×C₁₃	—	4	4	no	—
267	C₂×C₁₃	#1683	1	4	yes	direct product factor
268	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
269	C₂×C₁₃	C₂×#467	1	1	yes	characteristic
270	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
271	C₂⁴	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	8	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₁₃×Q₁₆	1	4	yes	—
282	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	C₂×D₄×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	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	8	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₄²	C₁₃×#41	1	1	yes	characteristic
319	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₁₃	C₂×#1683	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	2	4	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	C₁₃×#121	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	—	8	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	2	2	no	—
333	D₄	C₂×C₁₃×Q₁₆	1	4	yes	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
345	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
346	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
347	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
348	C₂×C₄	C₁₃×#135	1	2	yes	—
349	C₂×C₄	C₁₃×#135	1	2	yes	—
350	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	8	no	—
363	C₂²	C₁₃×#463	1	2	yes	—
364	C₂²	C₁₃×#467	1	2	yes	—
365	C₂²	C₁₃×#471	1	2	yes	—
366	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	C₁₃×#463	1	2	yes	—
373	C₄	C₁₃×#467	1	2	yes	—
374	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
375	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
376	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
377	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂	—	4	4	no	—
379	C₂	C₁₃×#1683	1	4	yes	direct product factor
380	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
381	C₂	C₂×C₁₃×#467	1	1	yes	characteristic
382	C₂	C₂×C₁₃×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#487	C₂	semidirect
5. C₁₃×#1683	C₂	direct (N × H)
6. C₂×C₁₃×#335	C₂	semidirect
7. C₂×C₁₃×#333	C₂	semidirect
8. C₂×C₁₃×#332	C₂	semidirect
14. C₁₃×#487	C₂²	semidirect
32. C₁₃×#335	C₂²	semidirect
33. C₁₃×#333	C₂²	semidirect
34. C₁₃×#332	C₂²	semidirect
80. C₂×#1683	C₁₃	direct (N × H)
130. C₂×#487	C₂×C₁₃	semidirect
134. #1683	C₂×C₁₃	direct (N × H)
135. C₂×#335	C₂×C₁₃	semidirect
136. C₂×#333	C₂×C₁₃	semidirect
137. C₂×#332	C₂×C₁₃	semidirect
181. #487	C₂²×C₁₃	semidirect
199. #335	C₂²×C₁₃	semidirect
200. #333	C₂²×C₁₃	semidirect
201. #332	C₂²×C₁₃	semidirect
267. C₂×C₁₃	#1683	direct (N × H)
320. C₁₃	C₂×#1683	direct (N × H)
379. C₂	C₁₃×#1683	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#487	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₂×C₈×D₄×C₁₃	2
C₁₃×#1683	2
C₂×C₁₃×#335	2
C₂×C₁₃×#333	2
C₂×C₁₃×#332	2
C₂×#1683	13

Subgroups — C2×C13×#1683 #15705448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1683 #15705448