Subgroups — C₁₃×#32834 #15719173

Order 3328.

720 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×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2860	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2093	C₂	1	2	yes	maximal
5	C₁₃×#2083	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2071	C₂	1	2	yes	maximal
7	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2023	C₂	1	2	yes	maximal
9	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₃×#126	—	2	1	no	—
14	C₂×C₁₃×#107	C₂²	1	4	yes	—
15	C₂×C₁₃×#102	C₂²	1	4	yes	—
16	C₁₃×#390	C₂²	1	1	yes	characteristic
17	C₁₃×#390	C₂²	1	1	yes	characteristic
18	C₁₃×#390	C₂²	1	1	yes	characteristic
19	C₁₃×#389	C₂²	1	1	yes	characteristic
20	C₁₃×#389	C₂²	1	1	yes	characteristic
21	C₁₃×#389	C₂²	1	1	yes	characteristic
22	C₁₃×#388	—	2	1	no	—
23	C₁₃×#388	—	2	1	no	—
24	C₁₃×#388	—	2	1	no	—
25	C₁₃×#384	—	2	1	no	—
26	C₁₃×#384	—	2	1	no	—
27	C₁₃×#384	C₂²	1	2	yes	—
28	C₁₃×#384	C₂²	1	2	yes	—
29	C₄³×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#340	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₁₃×C₄⋊Q₈	—	4	4	no	—
39	C₁₃×C₄⋊Q₈	—	4	4	no	—
40	C₁₃×C₄⋊Q₈	—	4	4	no	—
41	C₁₃×#126	—	4	4	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#107	—	4	4	no	—
68	C₁₃×#102	—	4	4	no	—
69	C₁₃×#95	—	2	1	no	—
70	C₁₃×#95	—	2	1	no	—
71	C₁₃×#95	—	2	1	no	—
72	#32834	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	1	no	—
74	C₂×Q₈×C₁₃	—	4	4	no	—
75	C₂×Q₈×C₁₃	—	4	4	no	—
76	C₂×Q₈×C₁₃	—	4	4	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	1	no	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₂×C₈×C₁₃	—	2	4	no	—
92	C₂×C₈×C₁₃	—	2	4	no	—
93	C₂×C₈×C₁₃	—	2	4	no	—
94	C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	4	4	no	—
100	C₁₃×C₄⋊C₄	—	4	4	no	—
101	C₁₃×C₄⋊C₄	—	4	2	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	4	2	no	—
104	C₁₃×C₄⋊C₄	—	4	4	no	—
105	C₁₃×C₄⋊C₄	—	4	4	no	—
106	C₁₃×C₄⋊C₄	—	4	4	no	—
107	C₁₃×C₂²⋊C₄	—	4	2	no	—
108	C₁₃×C₂²⋊C₄	—	4	2	no	—
109	C₁₃×C₂²⋊C₄	—	4	2	no	—
110	C₁₃×C₂²⋊C₄	—	4	2	no	—
111	C₁₃×C₂²⋊C₄	—	4	2	no	—
112	C₁₃×C₂²⋊C₄	—	4	2	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	D₈	1	4	yes	—
120	#2868	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#2860	C₂×C₁₃	1	1	yes	characteristic
122	#2099	C₂×C₁₃	1	2	yes	complemented
123	#2093	C₂×C₁₃	1	2	yes	—
124	#2083	C₂×C₁₃	1	2	yes	complemented
125	#2071	C₂×C₁₃	1	2	yes	—
126	#2057	C₂×C₁₃	1	2	yes	complemented
127	#2023	C₂×C₁₃	1	2	yes	—
128	#1839	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	—	4	1	no	—
131	C₂³×C₁₃	—	4	1	no	—
132	C₂³×C₁₃	—	4	1	no	—
133	C₂³×C₁₃	—	4	1	no	—
134	C₂³×C₁₃	—	4	1	no	—
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₃	—	8	8	no	—
138	D₄×C₁₃	—	4	4	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	4	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₁₃	#137	1	2	yes	—
168	C₂×C₄×C₁₃	#137	1	2	yes	—
169	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
171	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
172	C₈×C₁₃	—	4	4	no	—
173	C₂×C₄⋊Q₈	—	2	1	no	—
174	C₂×C₄⋊Q₈	—	2	1	no	—
175	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
176	C₂×#126	—	2	1	no	—
177	C₂×#107	C₂²×C₁₃	1	4	yes	—
178	C₂×#102	C₂²×C₁₃	1	4	yes	—
179	#390	C₂²×C₁₃	1	1	yes	characteristic
180	#390	C₂²×C₁₃	1	1	yes	characteristic
181	#390	C₂²×C₁₃	1	1	yes	characteristic
182	#389	C₂²×C₁₃	1	1	yes	characteristic
183	#389	C₂²×C₁₃	1	1	yes	characteristic
184	#389	C₂²×C₁₃	1	1	yes	characteristic
185	#388	—	2	1	no	—
186	#388	—	2	1	no	—
187	#388	—	2	1	no	—
188	#384	—	2	1	no	—
189	#384	—	2	1	no	—
190	#384	C₂²×C₁₃	1	2	yes	—
191	#384	C₂²×C₁₃	1	2	yes	—
192	C₄³	C₂²×C₁₃	1	1	yes	characteristic
193	#340	C₂²×C₁₃	1	4	yes	—
194	#340	C₂²×C₁₃	1	4	yes	—
195	#336	C₂²×C₁₃	1	2	yes	—
196	#336	C₂²×C₁₃	1	2	yes	—
197	#336	C₂²×C₁₃	1	2	yes	—
198	C₂²×C₁₃	—	8	1	no	—
199	C₂²×C₁₃	—	8	1	no	—
200	C₂²×C₁₃	—	8	1	no	—
201	C₂²×C₁₃	—	8	1	no	—
202	C₂²×C₁₃	—	8	1	no	—
203	C₂²×C₁₃	—	8	1	no	—
204	C₂²×C₁₃	—	8	1	no	—
205	C₂²×C₁₃	#535	1	1	yes	characteristic
206	C₂²×C₁₃	#536	1	1	yes	characteristic
207	C₂²×C₁₃	#536	1	1	yes	characteristic
208	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
209	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
211	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	—	8	1	no	—
219	C₄×C₁₃	—	8	4	no	—
220	C₄×C₁₃	—	8	1	no	—
221	C₄×C₁₃	—	8	1	no	—
222	C₄×C₁₃	#563	1	4	yes	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
226	C₄⋊Q₈	—	4	4	no	—
227	C₄⋊Q₈	—	4	4	no	—
228	C₄⋊Q₈	—	4	4	no	—
229	#126	—	4	4	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	C₂×C₂²⋊C₄	—	2	1	no	—
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
255	#107	—	4	4	no	—
256	#102	—	4	4	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	C₂×C₁₃	—	16	1	no	—
261	C₂×C₁₃	#2821	1	1	yes	characteristic
262	C₂×C₁₃	#3205	1	1	yes	characteristic
263	C₂×C₁₃	#3218	1	1	yes	characteristic
264	C₂×C₁₃	#3226	1	1	yes	characteristic
265	C₂×C₁₃	#3226	1	1	yes	characteristic
266	C₂×C₁₃	#3238	1	1	yes	characteristic
267	C₂×C₁₃	#3239	1	1	yes	characteristic
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	4	4	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	C₁₃×D₈	1	4	yes	—
315	C₁₃	#32834	1	1	yes	characteristic, direct product factor, Sylow
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
324	Q₈	—	8	8	no	—
325	D₄	—	4	4	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
351	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
352	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
353	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
354	C₂×C₄	C₁₃×#137	1	2	yes	—
355	C₂×C₄	C₁₃×#137	1	2	yes	—
356	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
357	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
358	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
359	C₈	—	4	4	no	—
360	C₂²	—	8	1	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	C₁₃×#535	1	1	yes	characteristic
368	C₂²	C₁₃×#536	1	1	yes	characteristic
369	C₂²	C₁₃×#536	1	1	yes	characteristic
370	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
371	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
373	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	4	no	—
382	C₄	—	8	1	no	—
383	C₄	—	8	1	no	—
384	C₄	C₁₃×#563	1	4	yes	—
385	C₂	—	16	1	no	—
386	C₂	C₁₃×#2821	1	1	yes	characteristic
387	C₂	C₁₃×#3205	1	1	yes	characteristic
388	C₂	C₁₃×#3218	1	1	yes	characteristic
389	C₂	C₁₃×#3226	1	1	yes	characteristic
390	C₂	C₁₃×#3226	1	1	yes	characteristic
391	C₂	C₁₃×#3238	1	1	yes	characteristic
392	C₂	C₁₃×#3239	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2868	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
5. C₁₃×#2083	C₂	semidirect
7. C₁₃×#2057	C₂	semidirect
9. C₁₃×#1839	C₂	semidirect
72. #32834	C₁₃	direct (N × H)
120. #2868	C₂×C₁₃	semidirect
122. #2099	C₂×C₁₃	semidirect
124. #2083	C₂×C₁₃	semidirect
126. #2057	C₂×C₁₃	semidirect
128. #1839	C₂×C₁₃	semidirect
315. C₁₃	#32834	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×#2868	2
C₁₃×#2860	2
C₁₃×#2099	2
C₁₃×#2093	2
C₁₃×#2083	2
C₁₃×#2071	2
C₁₃×#2057	2
C₁₃×#2023	2
C₁₃×#1839	2
#32834	13

Subgroups — C13×#32834 #15719173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32834 #15719173