Subgroups — C₁₃×#17974 #15704313

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2993	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1590	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1495	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	C₂²	1	2	yes	—
13	C₁₃×#499	C₄	1	1	yes	characteristic
14	C₁₃×#495	C₄	1	1	yes	characteristic
15	C₁₃×#488	C₄	1	2	yes	—
16	C₁₃×#467	C₄	1	1	yes	characteristic
17	C₁₃×#466	C₄	1	1	yes	characteristic
18	C₁₃×#465	C₄	1	2	yes	—
19	C₁₃×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
24	C₁₃×#436	—	2	2	no	—
25	C₁₃×#436	C₂²	1	2	yes	—
26	C₁₃×#435	—	2	2	no	—
27	C₈×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#433	—	2	2	no	—
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#424	—	2	2	no	—
32	C₁₃×#423	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#334	C₂²	1	2	yes	—
35	C₁₃×#334	C₂²	1	1	yes	characteristic
36	C₁₃×#334	C₂²	1	1	yes	characteristic
37	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
40	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
41	C₁₃×#322	C₂²	1	1	yes	characteristic
42	C₁₃×#322	C₂²	1	1	yes	characteristic
43	C₈²×C₁₃	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#126	—	2	2	no	—
54	C₁₃×#125	C₂×C₄	1	2	yes	—
55	C₁₃×#124	C₂×C₄	1	2	yes	—
56	C₁₃×#123	—	2	2	no	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₁₃×#121	C₂×C₄	1	2	yes	—
59	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	C₂³	1	2	yes	—
62	C₁₃×#117	—	2	2	no	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
66	C₁₃×#106	C₂×C₄	1	2	yes	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
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	D₄	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#103	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₁₃×#102	C₂×C₄	1	2	yes	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	—	2	2	no	—
81	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
82	C₁₃×#97	—	2	2	no	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	#17974	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
100	C₁₃×Q₁₆	—	2	2	no	—
101	C₁₃×SD₁₆	—	2	4	no	—
102	C₁₃×D₈	—	2	2	no	—
103	C₁₃×M₁₆	—	8	2	no	—
104	C₁₃×M₁₆	—	8	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	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	8	2	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₁₃×C₂²⋊C₄	—	2	2	no	—
126	C₁₃×C₂²⋊C₄	—	2	2	no	—
127	C₁₃×C₂²⋊C₄	—	2	2	no	—
128	C₁₃×C₂²⋊C₄	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	#41	1	1	yes	characteristic
133	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
134	#3168	C₂×C₁₃	1	1	yes	characteristic
135	#2993	C₂×C₁₃	1	2	yes	complemented
136	#1594	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1593	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1590	C₂×C₁₃	1	2	yes	complemented
139	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
142	#1566	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1495	C₂×C₁₃	1	2	yes	complemented
144	#1450	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
147	Q₈×C₁₃	—	2	2	no	—
148	Q₈×C₁₃	—	2	2	no	—
149	D₄×C₁₃	—	2	2	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	—	8	2	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
167	C₈×C₁₃	—	2	1	no	—
168	C₈×C₁₃	—	2	1	no	—
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	—	2	2	no	—
171	C₈×C₁₃	—	4	1	no	—
172	C₈×C₁₃	—	4	1	no	—
173	C₈×C₁₃	—	4	2	no	—
174	C₈×C₁₃	—	4	2	no	—
175	C₈×C₁₃	#131	1	2	yes	—
176	C₈×C₁₃	#131	1	2	yes	—
177	#529	C₂²×C₁₃	1	2	yes	—
178	#499	C₄×C₁₃	1	1	yes	characteristic
179	#495	C₄×C₁₃	1	1	yes	characteristic
180	#488	C₄×C₁₃	1	2	yes	—
181	#467	C₄×C₁₃	1	1	yes	characteristic
182	#466	C₄×C₁₃	1	1	yes	characteristic
183	#465	C₄×C₁₃	1	2	yes	—
184	#446	C₂²×C₁₃	1	2	yes	—
185	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
186	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
187	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
188	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
189	#436	—	2	2	no	—
190	#436	C₂²×C₁₃	1	2	yes	—
191	#435	—	2	2	no	—
192	C₈×D₄	C₂²×C₁₃	1	2	yes	—
193	#433	—	2	2	no	—
194	#431	C₂²×C₁₃	1	1	yes	characteristic
195	#431	C₂²×C₁₃	1	1	yes	characteristic
196	#424	—	2	2	no	—
197	#423	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	#334	C₂²×C₁₃	1	2	yes	—
200	#334	C₂²×C₁₃	1	1	yes	characteristic
201	#334	C₂²×C₁₃	1	1	yes	characteristic
202	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
203	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
204	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
205	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
206	#322	C₂²×C₁₃	1	1	yes	characteristic
207	#322	C₂²×C₁₃	1	1	yes	characteristic
208	C₈²	C₂²×C₁₃	1	1	yes	characteristic
209	C₈²	C₂²×C₁₃	1	1	yes	characteristic
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	1	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
225	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
226	C₄×C₁₃	#577	1	2	yes	—
227	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
229	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
235	#126	—	2	2	no	—
236	#125	C₂×C₄×C₁₃	1	2	yes	—
237	#124	C₂×C₄×C₁₃	1	2	yes	—
238	#123	—	2	2	no	—
239	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
240	#121	C₂×C₄×C₁₃	1	2	yes	—
241	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	C₂³×C₁₃	1	2	yes	—
244	#117	—	2	2	no	—
245	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
246	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
247	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
248	#106	C₂×C₄×C₁₃	1	2	yes	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
254	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
255	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
256	#103	C₂×C₄×C₁₃	1	2	yes	—
257	#103	C₂×C₄×C₁₃	1	2	yes	—
258	#102	C₂×C₄×C₁₃	1	2	yes	—
259	#102	C₂×C₄×C₁₃	1	2	yes	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
264	#97	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
267	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₁₃	—	4	1	no	—
275	C₂×C₁₃	—	8	2	no	—
276	C₂×C₁₃	#2931	1	1	yes	characteristic
277	C₂×C₁₃	#2952	1	1	yes	characteristic
278	C₂×C₁₃	#2957	1	1	yes	characteristic
279	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
286	Q₁₆	—	2	2	no	—
287	SD₁₆	—	2	4	no	—
288	D₈	—	2	2	no	—
289	M₁₆	—	8	2	no	—
290	M₁₆	—	8	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	8	2	no	—
298	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
309	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	C₂²×C₄×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	#17974	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	2	2	no	—
322	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	8	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	—	2	2	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	C₁₃×#131	1	2	yes	—
352	C₈	C₁₃×#131	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
368	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
369	C₄	C₁₃×#577	1	2	yes	—
370	C₂	—	4	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₁₃×#2931	1	1	yes	characteristic
373	C₂	C₁₃×#2952	1	1	yes	characteristic
374	C₂	C₁₃×#2957	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×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2993	C₂	semidirect
3. C₁₃×#1594	C₂	semidirect
4. C₁₃×#1593	C₂	semidirect
5. C₁₃×#1590	C₂	semidirect
6. C₁₃×#1580	C₂	semidirect
7. C₁₃×#1579	C₂	semidirect
8. C₈×C₁₃×SD₁₆	C₂	semidirect
9. C₁₃×#1566	C₂	semidirect
10. C₁₃×#1495	C₂	semidirect
11. C₁₃×#1450	C₂	semidirect
92. #17974	C₁₃	direct (N × H)
135. #2993	C₂×C₁₃	semidirect
136. #1594	C₂×C₁₃	semidirect
137. #1593	C₂×C₁₃	semidirect
138. #1590	C₂×C₁₃	semidirect
139. #1580	C₂×C₁₃	semidirect
140. #1579	C₂×C₁₃	semidirect
141. C₈×SD₁₆	C₂×C₁₃	semidirect
142. #1566	C₂×C₁₃	semidirect
143. #1495	C₂×C₁₃	semidirect
144. #1450	C₂×C₁₃	semidirect
320. C₁₃	#17974	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×#3168	2
C₁₃×#2993	2
C₁₃×#1594	2
C₁₃×#1593	2
C₁₃×#1590	2
C₁₃×#1580	2
C₁₃×#1579	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1566	2
C₁₃×#1495	2
C₁₃×#1450	2
#17974	13

Subgroups — C13×#17974 #15704313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17974 #15704313