Subgroups — C₁₃×#25841 #15712180

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2057	C₂	1	4	yes	maximal
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1863	C₂	1	4	yes	maximal
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₁₃	—	2	4	no	—
11	Q₈²×C₁₃	—	2	4	no	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#500	—	2	4	no	—
22	C₁₃×#477	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	2	yes	—
24	C₂×C₁₃×#107	C₂²	1	4	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#391	—	2	1	no	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#384	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₁₃×C₄⋊Q₈	—	2	16	no	—
45	C₁₃×C₄⋊Q₈	—	2	8	no	—
46	C₁₃×C₄⋊Q₈	—	2	4	no	—
47	C₁₃×C₄⋊Q₈	—	2	4	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
52	C₄×Q₈×C₁₃	—	2	8	no	—
53	C₄×Q₈×C₁₃	—	2	4	no	—
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	D₄	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	4	no	—
77	C₁₃×#107	—	2	8	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	Q₈	1	8	yes	complemented
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	4	no	—
84	#25841	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂×Q₈×C₁₃	—	2	8	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	8	2	no	—
93	C₂×Q₈×C₁₃	—	8	2	no	—
94	C₂×Q₈×C₁₃	—	8	4	no	—
95	C₂×Q₈×C₁₃	Q₁₆	1	4	yes	—
96	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
112	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
113	C₁₃×C₄⋊C₄	—	2	8	no	—
114	C₁₃×C₄⋊C₄	—	2	8	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	8	4	no	—
126	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
129	C₄²×C₁₃	—	2	8	no	—
130	C₄²×C₁₃	—	2	4	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	4	2	no	—
134	C₄²×C₁₃	C₂×D₄	1	2	yes	—
135	C₄²×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic
137	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
138	C₂×#477	C₂×C₁₃	1	1	yes	characteristic
139	#2567	C₂×C₁₃	1	1	yes	characteristic
140	#2057	C₂×C₁₃	1	4	yes	—
141	#1987	C₂×C₁₃	1	1	yes	characteristic
142	#1984	C₂×C₁₃	1	1	yes	characteristic
143	#1863	C₂×C₁₃	1	4	yes	—
144	C₄×#103	C₂×C₁₃	1	1	yes	characteristic
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	2	no	—
147	Q₈×C₁₃	—	2	4	no	—
148	Q₈×C₁₃	—	2	8	no	—
149	Q₈×C₁₃	—	8	4	no	—
150	Q₈×C₁₃	—	8	4	no	—
151	Q₈×C₁₃	—	8	8	no	—
152	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	4	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	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	#120	1	2	yes	—
170	C₂×C₄×C₁₃	#120	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
172	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
173	C₂×C₄×C₁₃	#137	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
178	C₈×C₁₃	—	2	4	no	—
179	C₈×C₁₃	—	4	2	no	—
180	Q₈²	—	2	4	no	—
181	Q₈²	—	2	4	no	—
182	C₂×C₄⋊Q₈	—	2	1	no	—
183	C₂×C₄⋊Q₈	—	2	2	no	—
184	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×C₄×Q₈	—	2	1	no	—
188	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
189	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
191	#500	—	2	4	no	—
192	#477	—	2	4	no	—
193	C₂×#107	C₂²×C₁₃	1	2	yes	—
194	C₂×#107	C₂²×C₁₃	1	4	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#103	C₂²×C₁₃	1	2	yes	—
197	C₂×#103	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	#395	—	2	2	no	—
200	#391	—	2	1	no	—
201	#389	C₂²×C₁₃	1	4	yes	—
202	#384	—	2	1	no	—
203	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
204	#340	C₂²×C₁₃	1	2	yes	—
205	#340	C₂²×C₁₃	1	4	yes	—
206	#336	C₂²×C₁₃	1	4	yes	—
207	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
208	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
209	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
210	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
211	C₂²×C₁₃	#576	1	2	yes	—
212	C₄×C₁₃	—	2	4	no	—
213	C₄×C₁₃	—	2	4	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	4	4	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	4	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	#451	1	4	yes	—
221	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
222	C₄×C₁₃	#536	1	1	yes	characteristic
223	C₄×C₁₃	D₄×Q₈	1	2	yes	—
224	C₂²×Q₈	—	2	2	no	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
231	C₄⋊Q₈	—	2	16	no	—
232	C₄⋊Q₈	—	2	8	no	—
233	C₄⋊Q₈	—	2	4	no	—
234	C₄⋊Q₈	—	2	4	no	—
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
239	C₄×Q₈	—	2	8	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	C₄×Q₈	—	2	2	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	D₄×C₁₃	1	4	yes	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	#107	—	2	8	no	—
265	C₄⋊C₈	—	2	2	no	—
266	#103	—	2	4	no	—
267	#103	Q₈×C₁₃	1	8	yes	complemented
268	C₄×C₈	—	2	2	no	—
269	#95	—	2	1	no	—
270	#95	—	2	4	no	—
271	C₂×C₁₃	#2434	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
273	C₂×C₁₃	#3008	1	1	yes	characteristic
274	C₂×C₁₃	Q₈×Q₁₆	1	2	yes	—
275	C₂×C₁₃	#3385	1	2	yes	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	8	2	no	—
284	C₂×Q₈	—	8	2	no	—
285	C₂×Q₈	—	8	4	no	—
286	C₂×Q₈	C₁₃×Q₁₆	1	4	yes	—
287	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
288	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	8	4	no	—
317	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
318	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
319	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
320	C₄²	—	2	8	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	C₂×D₄×C₁₃	1	2	yes	—
326	C₄²	C₂×D₄×C₁₃	1	2	yes	—
327	C₁₃	#25841	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	Q₈	—	2	8	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	2	4	no	—
332	Q₈	—	8	4	no	—
333	Q₈	—	8	4	no	—
334	Q₈	—	8	8	no	—
335	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	C₁₃×#120	1	2	yes	—
353	C₂×C₄	C₁₃×#120	1	2	yes	—
354	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
355	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
356	C₂×C₄	C₁₃×#137	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
360	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
364	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
365	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
366	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
367	C₂²	C₁₃×#576	1	2	yes	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	4	no	—
375	C₄	—	8	2	no	—
376	C₄	C₁₃×#451	1	4	yes	—
377	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
378	C₄	C₁₃×#536	1	1	yes	characteristic
379	C₄	D₄×Q₈×C₁₃	1	2	yes	—
380	C₂	C₁₃×#2434	1	1	yes	characteristic
381	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
382	C₂	C₁₃×#3008	1	1	yes	characteristic
383	C₂	Q₈×C₁₃×Q₁₆	1	2	yes	—
384	C₂	C₁₃×#3385	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
80. C₁₃×#103	Q₈	semidirect
84. #25841	C₁₃	direct (N × H)
267. #103	Q₈×C₁₃	semidirect
327. C₁₃	#25841	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×Q₈²×C₁₃	2
C₂×C₁₃×#500	2
C₂×C₁₃×#477	2
C₁₃×#2567	2
C₁₃×#2057	2
C₁₃×#1987	2
C₁₃×#1984	2
C₁₃×#1863	2
C₄×C₁₃×#103	2
#25841	13

Subgroups — C13×#25841 #15712180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25841 #15712180