Subgroups — C₁₃×#25902 #15712241

Order 3328.

1306 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2024	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1990	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1872	C₂	1	4	yes	maximal
7	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₃	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#487	—	2	8	no	—
20	C₂×C₁₃×#103	C₂²	1	8	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#391	C₂²	1	2	yes	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#384	C₂²	1	1	yes	characteristic
27	C₁₃×#380	—	2	1	no	—
28	C₁₃×#380	—	2	1	no	—
29	C₁₃×#340	C₂²	1	8	yes	—
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₂²×Q₈×C₁₃	—	2	8	no	—
32	C₂²×Q₈×C₁₃	—	2	2	no	—
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂²×Q₈×C₁₃	—	4	4	no	—
35	C₂²×Q₈×C₁₃	—	4	4	no	—
36	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃	—	2	2	no	—
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
42	C₁₃×C₄⋊Q₈	—	2	8	no	—
43	C₁₃×C₄⋊Q₈	—	2	8	no	—
44	C₁₃×C₄⋊Q₈	—	2	8	no	—
45	C₁₃×C₄⋊Q₈	—	2	4	no	—
46	C₁₃×C₄⋊Q₈	—	2	4	no	—
47	C₁₃×C₄⋊Q₈	D₄	1	8	yes	—
48	C₁₃×C₂²⋊Q₈	—	2	8	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₄²×C₁₃	—	2	4	no	—
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#103	—	2	16	no	—
68	C₁₃×C₂²⋊C₈	—	2	4	no	—
69	C₄×C₈×C₁₃	—	2	4	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	#25902	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂×Q₈×C₁₃	—	2	8	no	—
75	C₂×Q₈×C₁₃	—	2	8	no	—
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	—	2	4	no	—
79	C₂×Q₈×C₁₃	—	4	4	no	—
80	C₂×Q₈×C₁₃	—	4	32	no	—
81	C₂×Q₈×C₁₃	—	4	4	no	—
82	C₂×Q₈×C₁₃	—	4	4	no	—
83	C₂×Q₈×C₁₃	—	4	4	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	8	no	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	4	4	no	—
95	C₂²×C₄×C₁₃	—	4	4	no	—
96	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
97	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	#41	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃	—	2	4	no	—
106	C₂×C₈×C₁₃	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₁₃×C₄⋊C₄	—	2	8	no	—
109	C₁₃×C₄⋊C₄	—	2	8	no	—
110	C₁₃×C₄⋊C₄	—	2	8	no	—
111	C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	4	2	no	—
114	C₁₃×C₄⋊C₄	—	4	2	no	—
115	C₁₃×C₄⋊C₄	—	4	4	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	C₂×D₄	1	4	yes	—
124	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
125	C₂×#487	C₂×C₁₃	1	2	yes	complemented
126	#2857	C₂×C₁₃	1	1	yes	characteristic
127	#2024	C₂×C₁₃	1	4	yes	complemented
128	#1990	C₂×C₁₃	1	2	yes	complemented
129	#1872	C₂×C₁₃	1	4	yes	—
130	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	#124	1	2	yes	—
136	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
137	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
138	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₁₃	—	4	16	no	—
140	Q₈×C₁₃	—	4	16	no	—
141	Q₈×C₁₃	—	4	8	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	8	no	—
149	C₂×C₄×C₁₃	—	2	8	no	—
150	C₂×C₄×C₁₃	—	2	8	no	—
151	C₂×C₄×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	4	16	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	#120	1	2	yes	—
162	C₂×C₄×C₁₃	#120	1	2	yes	—
163	C₂×C₄×C₁₃	#124	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
168	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₁₃	#137	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₁₃	—	4	4	no	—
174	C₂³×Q₈	—	2	1	no	—
175	C₂×C₄⋊Q₈	—	2	8	no	—
176	C₂×C₄⋊Q₈	—	2	1	no	—
177	C₂×C₄⋊Q₈	—	2	1	no	—
178	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
181	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₄⋊C₄	—	2	1	no	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
184	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
185	#487	—	2	8	no	—
186	C₂×#103	C₂²×C₁₃	1	8	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
189	#391	C₂²×C₁₃	1	2	yes	—
190	#389	—	2	1	no	—
191	#389	—	2	1	no	—
192	#384	C₂²×C₁₃	1	1	yes	characteristic
193	#380	—	2	1	no	—
194	#380	—	2	1	no	—
195	#340	C₂²×C₁₃	1	8	yes	—
196	#336	C₂²×C₁₃	1	2	yes	—
197	C₂²×C₁₃	—	2	2	no	—
198	C₂²×C₁₃	—	2	2	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	#487	1	4	yes	complemented
204	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
205	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
206	C₂²×C₁₃	#536	1	1	yes	characteristic
207	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
208	C₂²×C₁₃	C₂²×Q₁₆	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	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	4	8	no	—
215	C₄×C₁₃	—	8	2	no	—
216	C₄×C₁₃	—	8	2	no	—
217	C₄×C₁₃	#450	1	4	yes	—
218	C₄×C₁₃	#451	1	4	yes	—
219	C₄×C₁₃	#548	1	4	yes	—
220	C₂²×Q₈	—	2	8	no	—
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	—	4	4	no	—
224	C₂²×Q₈	—	4	4	no	—
225	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
231	C₄⋊Q₈	—	2	8	no	—
232	C₄⋊Q₈	—	2	8	no	—
233	C₄⋊Q₈	—	2	8	no	—
234	C₄⋊Q₈	—	2	4	no	—
235	C₄⋊Q₈	—	2	4	no	—
236	C₄⋊Q₈	D₄×C₁₃	1	8	yes	—
237	C₂²⋊Q₈	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	8	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	8	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
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	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	4	no	—
252	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	#103	—	2	16	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	C₂×C₁₃	—	2	4	no	—
262	C₂×C₁₃	#2436	1	1	yes	characteristic
263	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
264	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
265	C₂×C₁₃	C₂×#487	1	1	yes	characteristic
266	C₂×C₁₃	#3141	1	1	yes	characteristic
267	C₂×C₁₃	#3229	1	1	yes	characteristic
268	C₂×C₁₃	#3230	1	1	yes	characteristic
269	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
270	C₂×Q₈	—	2	8	no	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×Q₈	—	4	32	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
293	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₁₃×#41	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	C₂×D₄×C₁₃	1	4	yes	—
320	C₁₃	#25902	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₁₃×#124	1	2	yes	—
326	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
327	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
328	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	Q₈	—	4	16	no	—
330	Q₈	—	4	16	no	—
331	Q₈	—	4	8	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	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	C₁₃×#120	1	2	yes	—
352	C₂×C₄	C₁₃×#120	1	2	yes	—
353	C₂×C₄	C₁₃×#124	1	2	yes	—
354	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
355	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
356	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
357	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
358	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
359	C₂×C₄	C₁₃×#137	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
361	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
362	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
363	C₈	—	4	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	C₁₃×#487	1	4	yes	complemented
371	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
372	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
373	C₂²	C₁₃×#536	1	1	yes	characteristic
374	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
375	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
376	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	8	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	C₁₃×#450	1	4	yes	—
385	C₄	C₁₃×#451	1	4	yes	—
386	C₄	C₁₃×#548	1	4	yes	—
387	C₂	—	2	4	no	—
388	C₂	C₁₃×#2436	1	1	yes	characteristic
389	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
390	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
391	C₂	C₂×C₁₃×#487	1	1	yes	characteristic
392	C₂	C₁₃×#3141	1	1	yes	characteristic
393	C₂	C₁₃×#3229	1	1	yes	characteristic
394	C₂	C₁₃×#3230	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#487	C₂	semidirect
4. C₁₃×#2024	C₂	semidirect
5. C₁₃×#1990	C₂	semidirect
72. #25902	C₁₃	direct (N × H)
125. C₂×#487	C₂×C₁₃	semidirect
127. #2024	C₂×C₁₃	semidirect
128. #1990	C₂×C₁₃	semidirect
203. C₂²×C₁₃	#487	semidirect
320. C₁₃	#25902	direct (N × H)
370. C₂²	C₁₃×#487	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#487	2
C₁₃×#2857	2
C₁₃×#2024	2
C₁₃×#1990	2
C₁₃×#1872	2
C₄×C₁₃×C₂²⋊C₈	2
#25902	13

Subgroups — C13×#25902 #15712241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25902 #15712241