Subgroups — C₁₃×#24834 #15711173

Order 3328.

852 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal
10	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1804	C₂	1	2	yes	maximal
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#476	—	2	4	no	—
18	C₁₃×#440	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₁₃×#400	—	2	1	no	—
29	C₁₃×#400	—	2	1	no	—
30	C₁₃×#391	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#385	—	2	2	no	—
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₁₃×#382	C₂²	1	2	yes	—
36	C₁₃×#380	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#95	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	4	2	no	—
61	C₄×D₄×C₁₃	D₄	1	4	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#106	—	2	4	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	4	2	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#103	—	4	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	D₄	1	1	yes	characteristic
92	C₁₃×#95	D₄	1	1	yes	characteristic
93	#24834	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	4	4	no	—
101	C₂×Q₈×C₁₃	—	4	2	no	—
102	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂×D₄×C₁₃	#41	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	8	2	no	—
118	C₂²×C₄×C₁₃	—	8	2	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₁₃×SD₁₆	—	2	8	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	8	2	no	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	4	2	no	—
151	C₄²×C₁₃	C₂×D₄	1	2	yes	—
152	C₄²×C₁₃	#41	1	2	yes	—
153	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
154	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
155	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2349	C₂×C₁₃	1	1	yes	characteristic
157	#2085	C₂×C₁₃	1	2	yes	complemented
158	#2066	C₂×C₁₃	1	2	yes	complemented
159	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1877	C₂×C₁₃	1	2	yes	—
162	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1804	C₂×C₁₃	1	2	yes	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	1	no	—
173	Q₈×C₁₃	—	4	1	no	—
174	Q₈×C₁₃	—	8	4	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	8	4	no	—
200	C₂×C₄×C₁₃	—	8	8	no	—
201	C₂×C₄×C₁₃	#121	1	2	yes	—
202	C₂×C₄×C₁₃	#121	1	2	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	#476	—	2	4	no	—
218	#440	—	2	4	no	—
219	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#106	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
223	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#103	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#102	C₂²×C₁₃	1	2	yes	—
227	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
228	#400	—	2	1	no	—
229	#400	—	2	1	no	—
230	#391	—	2	2	no	—
231	#391	C₂²×C₁₃	1	2	yes	—
232	#389	C₂²×C₁₃	1	2	yes	—
233	#385	—	2	2	no	—
234	#382	C₂²×C₁₃	1	2	yes	—
235	#382	C₂²×C₁₃	1	1	yes	characteristic
236	#380	—	2	1	no	—
237	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#95	—	2	1	no	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	2	yes	—
241	#340	C₂²×C₁₃	1	2	yes	—
242	#336	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
249	C₂²×C₁₃	#546	1	1	yes	characteristic
250	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
251	C₂²×C₁₃	#575	1	2	yes	—
252	C₂²×C₁₃	#577	1	2	yes	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	1	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
263	C₄×C₁₃	#537	1	1	yes	characteristic
264	C₄×C₁₃	#552	1	1	yes	characteristic
265	C₄×C₁₃	#554	1	1	yes	characteristic
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	4	2	no	—
284	C₄×D₄	D₄×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	#107	—	2	2	no	—
299	#106	—	2	4	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	4	2	no	—
302	#103	—	2	2	no	—
303	#103	—	4	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	4	no	—
306	#97	—	2	2	no	—
307	#95	—	2	1	no	—
308	#95	—	2	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	D₄×C₁₃	1	1	yes	characteristic
315	#95	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₁₃	—	4	4	no	—
317	C₂×C₁₃	#2417	1	1	yes	characteristic
318	C₂×C₁₃	#3040	1	1	yes	characteristic
319	C₂×C₁₃	#3042	1	1	yes	characteristic
320	C₂×C₁₃	#3311	1	2	yes	—
321	C₂×C₁₃	#3388	1	2	yes	—
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
336	C₂×D₄	C₁₃×#41	1	2	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	—	8	2	no	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
352	SD₁₆	—	2	8	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	8	2	no	—
373	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	2	no	—
379	C₄²	C₂×D₄×C₁₃	1	2	yes	—
380	C₄²	C₁₃×#41	1	2	yes	—
381	C₁₃	#24834	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	1	no	—
391	Q₈	—	4	1	no	—
392	Q₈	—	8	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₁₃×#121	1	2	yes	—
420	C₂×C₄	C₁₃×#121	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
436	C₂²	C₁₃×#546	1	1	yes	characteristic
437	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
438	C₂²	C₁₃×#575	1	2	yes	—
439	C₂²	C₁₃×#577	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	2	no	—
449	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
450	C₄	C₁₃×#537	1	1	yes	characteristic
451	C₄	C₁₃×#552	1	1	yes	characteristic
452	C₄	C₁₃×#554	1	1	yes	characteristic
453	C₂	—	4	4	no	—
454	C₂	C₁₃×#2417	1	1	yes	characteristic
455	C₂	C₁₃×#3040	1	1	yes	characteristic
456	C₂	C₁₃×#3042	1	1	yes	characteristic
457	C₂	C₁₃×#3311	1	2	yes	—
458	C₂	C₁₃×#3388	1	2	yes	—

	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2568	C₂	semidirect
5. C₁₃×#2085	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1805	C₂	semidirect
50. C₂×C₁₃×SD₁₆	Q₈	semidirect
93. #24834	C₁₃	direct (N × H)
155. #2568	C₂×C₁₃	semidirect
157. #2085	C₂×C₁₃	semidirect
158. #2066	C₂×C₁₃	semidirect
159. #1993	C₂×C₁₃	semidirect
160. #1940	C₂×C₁₃	semidirect
162. #1805	C₂×C₁₃	semidirect
273. C₂×SD₁₆	Q₈×C₁₃	semidirect
381. C₁₃	#24834	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×#476	2
C₂×C₁₃×#440	2
C₁₃×#2568	2
C₁₃×#2349	2
C₁₃×#2085	2
C₁₃×#2066	2
C₁₃×#1993	2
C₁₃×#1940	2
C₁₃×#1877	2
C₁₃×#1805	2
C₁₃×#1804	2
#24834	13

Subgroups — C13×#24834 #15711173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24834 #15711173