Subgroups — C₁₃×#19840 #15706179

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1675	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#556	C₂²	1	1	yes	characteristic
17	C₁₃×#554	C₂²	1	1	yes	characteristic
18	C₁₃×#554	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#492	C₂²	1	1	yes	characteristic
22	C₁₃×#490	—	2	1	no	—
23	C₁₃×#488	—	2	1	no	—
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#484	—	2	1	no	—
29	C₁₃×#484	—	2	1	no	—
30	C₁₃×#482	—	2	1	no	—
31	C₁₃×#479	—	2	1	no	—
32	C₁₃×#478	—	2	1	no	—
33	C₁₃×#477	C₂²	1	1	yes	characteristic
34	C₁₃×#477	C₂²	1	1	yes	characteristic
35	C₁₃×#476	C₂²	1	1	yes	characteristic
36	C₁₃×#476	C₂²	1	1	yes	characteristic
37	C₁₃×#475	C₂²	1	1	yes	characteristic
38	C₁₃×#467	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#463	—	2	1	no	—
41	C₁₃×#461	C₂²	1	1	yes	characteristic
42	C₁₃×#460	C₂²	1	1	yes	characteristic
43	C₁₃×#459	—	2	1	no	—
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₁₃×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#442	—	2	1	no	—
49	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×SD₁₆	—	2	1	no	—
51	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#107	—	2	1	no	—
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
69	C₂×C₁₃×SD₁₆	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	4	1	no	—
72	C₂×C₁₃×D₈	—	2	1	no	—
73	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×#127	—	2	1	no	—
80	C₁₃×#127	C₂³	1	1	yes	characteristic
81	C₁₃×#126	—	4	1	no	—
82	C₁₃×#125	—	2	1	no	—
83	C₁₃×#125	—	2	1	no	—
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	4	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	4	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#117	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₁₃×#107	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	D₄	1	1	yes	characteristic
108	C₁₃×#107	D₄	1	1	yes	characteristic
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	—	2	1	no	—
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	4	1	no	—
125	C₁₃×#103	D₄	1	1	yes	characteristic
126	C₁₃×#103	D₄	1	1	yes	characteristic
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×#97	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19840	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
146	C₁₃×#41	—	8	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	—	4	1	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₁₃×Q₁₆	—	4	1	no	—
165	C₁₃×SD₁₆	—	4	2	no	—
166	C₁₃×SD₁₆	—	8	1	no	—
167	C₁₃×SD₁₆	—	8	2	no	—
168	C₁₃×D₈	—	2	2	no	—
169	C₁₃×D₈	—	4	2	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	4	2	no	—
176	C₂×C₈×C₁₃	—	8	1	no	—
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	4	1	no	—
208	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
209	#3366	C₂×C₁₃	1	1	yes	characteristic
210	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1719	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1704	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1681	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1675	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1643	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1622	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	2	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	Q₈×C₁₃	—	4	1	no	—
233	Q₈×C₁₃	—	8	1	no	—
234	Q₈×C₁₃	—	8	1	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	8	1	no	—
243	D₄×C₁₃	—	8	2	no	—
244	D₄×C₁₃	—	16	1	no	—
245	D₄×C₁₃	#135	1	2	yes	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	8	2	no	—
260	C₂×C₄×C₁₃	—	16	1	no	—
261	C₂×C₄×C₁₃	—	16	1	no	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	—	2	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	#556	C₂²×C₁₃	1	1	yes	characteristic
275	#554	C₂²×C₁₃	1	1	yes	characteristic
276	#554	C₂²×C₁₃	1	1	yes	characteristic
277	#550	C₂²×C₁₃	1	1	yes	characteristic
278	#500	C₂²×C₁₃	1	1	yes	characteristic
279	#492	C₂²×C₁₃	1	1	yes	characteristic
280	#490	—	2	1	no	—
281	#488	—	2	1	no	—
282	#487	C₂²×C₁₃	1	1	yes	characteristic
283	#487	C₂²×C₁₃	1	1	yes	characteristic
284	#486	C₂²×C₁₃	1	1	yes	characteristic
285	#486	C₂²×C₁₃	1	1	yes	characteristic
286	#484	—	2	1	no	—
287	#484	—	2	1	no	—
288	#482	—	2	1	no	—
289	#479	—	2	1	no	—
290	#478	—	2	1	no	—
291	#477	C₂²×C₁₃	1	1	yes	characteristic
292	#477	C₂²×C₁₃	1	1	yes	characteristic
293	#476	C₂²×C₁₃	1	1	yes	characteristic
294	#476	C₂²×C₁₃	1	1	yes	characteristic
295	#475	C₂²×C₁₃	1	1	yes	characteristic
296	#467	—	2	1	no	—
297	#465	—	2	1	no	—
298	#463	—	2	1	no	—
299	#461	C₂²×C₁₃	1	1	yes	characteristic
300	#460	C₂²×C₁₃	1	1	yes	characteristic
301	#459	—	2	1	no	—
302	#459	C₂²×C₁₃	1	1	yes	characteristic
303	#452	—	2	1	no	—
304	#446	C₂²×C₁₃	1	1	yes	characteristic
305	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	#442	—	2	1	no	—
307	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×SD₁₆	—	2	1	no	—
309	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
311	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#107	—	2	1	no	—
313	#416	—	2	1	no	—
314	#335	C₂²×C₁₃	1	1	yes	characteristic
315	#334	C₂²×C₁₃	1	1	yes	characteristic
316	#333	C₂²×C₁₃	1	1	yes	characteristic
317	#333	C₂²×C₁₃	1	1	yes	characteristic
318	#332	C₂²×C₁₃	1	1	yes	characteristic
319	#331	C₂²×C₁₃	1	1	yes	characteristic
320	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	#322	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	—	4	1	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	8	1	no	—
332	C₂²×C₁₃	—	8	1	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	D₄²	1	1	yes	characteristic
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
346	C₄×C₁₃	#575	1	1	yes	characteristic
347	C₄×C₁₃	#577	1	1	yes	characteristic
348	C₄×C₁₃	#578	1	1	yes	characteristic
349	C₂×#41	—	2	1	no	—
350	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	4	1	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
361	#127	—	2	1	no	—
362	#127	C₂³×C₁₃	1	1	yes	characteristic
363	#126	—	4	1	no	—
364	#125	—	2	1	no	—
365	#125	—	2	1	no	—
366	#124	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	4	1	no	—
371	C₂²⋊Q₈	—	4	1	no	—
372	#121	—	2	1	no	—
373	#121	—	4	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
382	#117	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	D₄×C₁₃	1	1	yes	characteristic
390	#107	D₄×C₁₃	1	1	yes	characteristic
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	4	1	no	—
407	#103	D₄×C₁₃	1	1	yes	characteristic
408	#103	D₄×C₁₃	1	1	yes	characteristic
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	D₄×C₁₃	1	1	yes	characteristic
418	#102	D₄×C₁₃	1	1	yes	characteristic
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	#97	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₁₃	—	4	2	no	—
427	C₂×C₁₃	—	8	1	no	—
428	C₂×C₁₃	—	16	1	no	—
429	C₂×C₁₃	#3267	1	1	yes	characteristic
430	C₂×C₁₃	#3285	1	1	yes	characteristic
431	C₂×C₁₃	#3288	1	1	yes	characteristic
432	#41	—	4	2	no	—
433	#41	—	8	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	Q₁₆	—	4	1	no	—
452	SD₁₆	—	4	2	no	—
453	SD₁₆	—	8	1	no	—
454	SD₁₆	—	8	2	no	—
455	D₈	—	2	2	no	—
456	D₈	—	4	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	4	2	no	—
463	C₂×C₈	—	8	1	no	—
464	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	4	1	no	—
495	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
496	C₁₃	#19840	1	1	yes	characteristic, direct product factor, Sylow
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	4	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	8	1	no	—
507	Q₈	—	8	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	8	1	no	—
516	D₄	—	8	2	no	—
517	D₄	—	16	1	no	—
518	D₄	C₁₃×#135	1	2	yes	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	16	1	no	—
534	C₂×C₄	—	16	1	no	—
535	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	D₄²×C₁₃	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
568	C₄	C₁₃×#575	1	1	yes	characteristic
569	C₄	C₁₃×#577	1	1	yes	characteristic
570	C₄	C₁₃×#578	1	1	yes	characteristic
571	C₂	—	4	2	no	—
572	C₂	—	8	1	no	—
573	C₂	—	16	1	no	—
574	C₂	C₁₃×#3267	1	1	yes	characteristic
575	C₂	C₁₃×#3285	1	1	yes	characteristic
576	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3366	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3360	C₂	semidirect
3. C₁₃×#3338	C₂	semidirect
4. C₁₃×#3304	C₂	semidirect
5. C₁₃×#1719	C₂	semidirect
6. C₁₃×#1704	C₂	semidirect
7. C₁₃×#1681	C₂	semidirect
8. C₁₃×#1678	C₂	semidirect
9. C₁₃×#1675	C₂	semidirect
10. C₁₃×#1643	C₂	semidirect
11. C₁₃×#1638	C₂	semidirect
12. C₁₃×#1631	C₂	semidirect
13. C₁₃×#1622	C₂	semidirect
14. C₁₃×#1584	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
144. #19840	C₁₃	direct (N × H)
210. #3360	C₂×C₁₃	semidirect
211. #3338	C₂×C₁₃	semidirect
212. #3304	C₂×C₁₃	semidirect
213. #1719	C₂×C₁₃	semidirect
214. #1704	C₂×C₁₃	semidirect
215. #1681	C₂×C₁₃	semidirect
216. #1678	C₂×C₁₃	semidirect
217. #1675	C₂×C₁₃	semidirect
218. #1643	C₂×C₁₃	semidirect
219. #1638	C₂×C₁₃	semidirect
220. #1631	C₂×C₁₃	semidirect
221. #1622	C₂×C₁₃	semidirect
222. #1584	C₂×C₁₃	semidirect
223. #1580	C₂×C₁₃	semidirect
496. C₁₃	#19840	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×#3366	2
C₁₃×#3360	2
C₁₃×#3338	2
C₁₃×#3304	2
C₁₃×#1719	2
C₁₃×#1704	2
C₁₃×#1681	2
C₁₃×#1678	2
C₁₃×#1675	2
C₁₃×#1643	2
C₁₃×#1638	2
C₁₃×#1631	2
C₁₃×#1622	2
C₁₃×#1584	2
C₁₃×#1580	2
#19840	13

Subgroups — C13×#19840 #15706179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19840 #15706179