Subgroups — C₁₃×#19825 #15706164

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1619	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#554	C₂²	1	1	yes	characteristic
19	D₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#495	—	2	1	no	—
21	C₁₃×#493	C₂²	1	1	yes	characteristic
22	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#488	—	2	1	no	—
24	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#486	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#482	—	2	1	no	—
29	C₁₃×#481	—	2	1	no	—
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#476	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#468	—	2	1	no	—
35	C₁₃×#465	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#463	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#460	C₂²	1	1	yes	characteristic
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#450	—	2	1	no	—
45	C₁₃×#450	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₁₃×SD₁₆	—	2	1	no	—
49	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×D₈	—	2	1	no	—
52	C₁₃×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₁₃×#418	—	2	1	no	—
55	C₂×C₁₃×#102	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#331	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
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, complemented
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×D₈	—	4	1	no	—
79	C₂×C₁₃×M₁₆	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×#127	C₂³	1	1	yes	characteristic
84	C₁₃×#127	C₂³	1	1	yes	characteristic
85	C₁₃×#126	—	4	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#124	—	2	1	no	—
88	C₁₃×#124	—	2	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	4	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#120	—	4	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#117	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	D₄	1	1	yes	characteristic
111	C₁₃×#106	D₄	1	1	yes	characteristic
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	—	4	1	no	—
121	C₁₃×#103	D₄	1	1	yes	characteristic
122	C₁₃×#103	D₄	1	1	yes	characteristic
123	C₁₃×#102	—	2	1	no	—
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
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	C₄×C₈×C₁₃	—	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	#19825	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	4	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
156	C₂×D₄×C₁₃	—	4	1	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	—	4	2	no	—
160	C₂×D₄×C₁₃	—	8	1	no	—
161	C₂×D₄×C₁₃	—	8	1	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	1	no	—
168	C₁₃×Q₁₆	—	8	1	no	—
169	C₁₃×SD₁₆	—	2	2	no	—
170	C₁₃×SD₁₆	—	4	1	no	—
171	C₁₃×SD₁₆	—	4	2	no	—
172	C₁₃×SD₁₆	—	8	1	no	—
173	C₁₃×SD₁₆	—	8	1	no	—
174	C₁₃×SD₁₆	—	8	1	no	—
175	C₁₃×D₈	—	4	2	no	—
176	C₁₃×D₈	—	8	1	no	—
177	C₁₃×D₈	—	8	2	no	—
178	C₁₃×M₁₆	—	8	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	8	1	no	—
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₁₃×C₂²⋊C₄	—	4	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	4	1	no	—
214	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
215	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1717	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1697	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1644	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1620	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1619	C₂×C₁₃	1	1	yes	characteristic
228	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
229	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	8	2	no	—
235	C₂³×C₁₃	—	8	2	no	—
236	C₂³×C₁₃	—	16	1	no	—
237	Q₈×C₁₃	—	2	1	no	—
238	Q₈×C₁₃	—	2	1	no	—
239	Q₈×C₁₃	—	2	1	no	—
240	Q₈×C₁₃	—	2	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	8	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	8	1	no	—
256	D₄×C₁₃	—	8	1	no	—
257	D₄×C₁₃	—	8	2	no	—
258	D₄×C₁₃	—	8	2	no	—
259	D₄×C₁₃	#135	1	2	yes	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	16	1	no	—
273	C₂×C₄×C₁₃	—	16	1	no	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	2	1	no	—
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	2	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	—	4	1	no	—
285	C₈×C₁₃	—	4	1	no	—
286	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	#556	C₂²×C₁₃	1	1	yes	characteristic
288	#554	C₂²×C₁₃	1	1	yes	characteristic
289	D₄²	C₂²×C₁₃	1	1	yes	characteristic
290	#495	—	2	1	no	—
291	#493	C₂²×C₁₃	1	1	yes	characteristic
292	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	#488	—	2	1	no	—
294	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	#486	C₂²×C₁₃	1	1	yes	characteristic
296	#486	C₂²×C₁₃	1	1	yes	characteristic
297	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	#482	—	2	1	no	—
299	#481	—	2	1	no	—
300	#478	—	2	1	no	—
301	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	#476	C₂²×C₁₃	1	1	yes	characteristic
303	#474	C₂²×C₁₃	1	1	yes	characteristic
304	#468	—	2	1	no	—
305	#465	—	2	1	no	—
306	#464	—	2	1	no	—
307	#463	—	2	1	no	—
308	#463	—	2	1	no	—
309	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#460	C₂²×C₁₃	1	1	yes	characteristic
311	#460	C₂²×C₁₃	1	1	yes	characteristic
312	#459	C₂²×C₁₃	1	1	yes	characteristic
313	#459	C₂²×C₁₃	1	1	yes	characteristic
314	#450	—	2	1	no	—
315	#450	—	2	1	no	—
316	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	C₄×SD₁₆	—	2	1	no	—
319	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
320	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
321	C₄×D₈	—	2	1	no	—
322	#436	C₂²×C₁₃	1	1	yes	characteristic
323	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
324	#418	—	2	1	no	—
325	C₂×#102	—	2	1	no	—
326	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	#333	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	#332	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	#331	C₂²×C₁₃	1	1	yes	characteristic
331	#331	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
333	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
334	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
336	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	—	16	4	no	—
350	C₂²×C₁₃	D₄²	1	1	yes	characteristic
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	8	1	no	—
359	C₄×C₁₃	—	8	1	no	—
360	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
361	C₄×C₁₃	#575	1	1	yes	characteristic
362	C₄×C₁₃	#576	1	1	yes	characteristic
363	C₄×C₁₃	#577	1	1	yes	characteristic
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
372	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
373	C₂×D₈	—	2	1	no	—
374	C₂×D₈	—	2	1	no	—
375	C₂×D₈	—	4	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
380	#127	C₂³×C₁₃	1	1	yes	characteristic
381	#127	C₂³×C₁₃	1	1	yes	characteristic
382	#126	—	4	1	no	—
383	#125	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	—	2	1	no	—
386	#124	—	2	1	no	—
387	#123	—	4	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	4	1	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#120	—	4	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
402	#117	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	#107	—	2	1	no	—
405	#107	—	2	1	no	—
406	#106	—	2	1	no	—
407	#106	D₄×C₁₃	1	1	yes	characteristic
408	#106	D₄×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	4	1	no	—
418	#103	D₄×C₁₃	1	1	yes	characteristic
419	#103	D₄×C₁₃	1	1	yes	characteristic
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	D₄×C₁₃	1	1	yes	characteristic
433	#102	D₄×C₁₃	1	1	yes	characteristic
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₁₃	—	4	2	no	—
442	C₂×C₁₃	—	8	1	no	—
443	C₂×C₁₃	—	16	1	no	—
444	C₂×C₁₃	—	16	1	no	—
445	C₂×C₁₃	#3268	1	1	yes	characteristic
446	C₂×C₁₃	#3282	1	1	yes	characteristic
447	C₂×C₁₃	#3288	1	1	yes	characteristic
448	C₂⁴	—	4	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	8	1	no	—
464	C₂×D₄	—	8	1	no	—
465	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	Q₁₆	—	8	1	no	—
472	SD₁₆	—	2	2	no	—
473	SD₁₆	—	4	1	no	—
474	SD₁₆	—	4	2	no	—
475	SD₁₆	—	8	1	no	—
476	SD₁₆	—	8	1	no	—
477	SD₁₆	—	8	1	no	—
478	D₈	—	4	2	no	—
479	D₈	—	8	1	no	—
480	D₈	—	8	2	no	—
481	M₁₆	—	8	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	8	1	no	—
488	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	4	1	no	—
517	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₁₃	#19825	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	8	2	no	—
524	C₂³	—	8	2	no	—
525	C₂³	—	16	1	no	—
526	Q₈	—	2	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	2	1	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	8	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	2	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	1	no	—
546	D₄	—	8	2	no	—
547	D₄	—	8	2	no	—
548	D₄	C₁₃×#135	1	2	yes	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	16	1	no	—
562	C₂×C₄	—	16	1	no	—
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
565	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	16	4	no	—
588	C₂²	D₄²×C₁₃	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	1	no	—
598	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
599	C₄	C₁₃×#575	1	1	yes	characteristic
600	C₄	C₁₃×#576	1	1	yes	characteristic
601	C₄	C₁₃×#577	1	1	yes	characteristic
602	C₂	—	4	2	no	—
603	C₂	—	8	1	no	—
604	C₂	—	16	1	no	—
605	C₂	—	16	1	no	—
606	C₂	C₁₃×#3268	1	1	yes	characteristic
607	C₂	C₁₃×#3282	1	1	yes	characteristic
608	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#1619	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
1. C₁₃×#3394	C₂	semidirect
2. C₁₃×#3361	C₂	semidirect
3. C₁₃×#3324	C₂	semidirect
4. C₁₃×#3295	C₂	semidirect
5. C₁₃×#1717	C₂	semidirect
6. C₁₃×#1697	C₂	semidirect
7. C₁₃×#1682	C₂	semidirect
8. C₁₃×#1678	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1644	C₂	semidirect
11. C₁₃×#1638	C₂	semidirect
12. C₁₃×#1620	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
16. C₁₃×#559	C₂²	semidirect
22. C₁₃×#492	C₂²	semidirect
24. C₁₃×#487	C₂²	semidirect
27. C₁₃×#486	C₂²	semidirect
31. C₁₃×#477	C₂²	semidirect
39. C₁₃×#462	C₂²	semidirect
46. C₈×Q₈×C₁₃	C₂²	semidirect
47. C₈×Q₈×C₁₃	C₂²	semidirect
56. C₁₃×#335	C₂²	semidirect
57. C₁₃×#334	C₂²	semidirect
58. C₁₃×#333	C₂²	semidirect
59. C₁₃×#332	C₂²	semidirect
61. C₁₃×#331	C₂²	semidirect
62. C₁₃×Q₈⋊C₈	C₂²	semidirect
63. C₁₃×Q₈⋊C₈	C₂²	semidirect
66. C₁₃×#322	C₂²	semidirect
144. #19825	C₁₃	direct (N × H)
215. #3394	C₂×C₁₃	semidirect
216. #3361	C₂×C₁₃	semidirect
217. #3324	C₂×C₁₃	semidirect
218. #3295	C₂×C₁₃	semidirect
219. #1717	C₂×C₁₃	semidirect
220. #1697	C₂×C₁₃	semidirect
221. #1682	C₂×C₁₃	semidirect
222. #1678	C₂×C₁₃	semidirect
223. #1665	C₂×C₁₃	semidirect
224. #1644	C₂×C₁₃	semidirect
225. #1638	C₂×C₁₃	semidirect
226. #1620	C₂×C₁₃	semidirect
228. #1583	C₂×C₁₃	semidirect
229. SD₁₆⋊C₈	C₂×C₁₃	semidirect
286. #559	C₂²×C₁₃	semidirect
292. #492	C₂²×C₁₃	semidirect
294. #487	C₂²×C₁₃	semidirect
297. #486	C₂²×C₁₃	semidirect
301. #477	C₂²×C₁₃	semidirect
309. #462	C₂²×C₁₃	semidirect
316. C₈×Q₈	C₂²×C₁₃	semidirect
317. C₈×Q₈	C₂²×C₁₃	semidirect
326. #335	C₂²×C₁₃	semidirect
327. #334	C₂²×C₁₃	semidirect
328. #333	C₂²×C₁₃	semidirect
329. #332	C₂²×C₁₃	semidirect
331. #331	C₂²×C₁₃	semidirect
332. Q₈⋊C₈	C₂²×C₁₃	semidirect
333. Q₈⋊C₈	C₂²×C₁₃	semidirect
336. #322	C₂²×C₁₃	semidirect
518. C₁₃	#19825	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×#3394	2
C₁₃×#3361	2
C₁₃×#3324	2
C₁₃×#3295	2
C₁₃×#1717	2
C₁₃×#1697	2
C₁₃×#1682	2
C₁₃×#1678	2
C₁₃×#1665	2
C₁₃×#1644	2
C₁₃×#1638	2
C₁₃×#1620	2
C₁₃×#1619	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19825	13

Subgroups — C13×#19825 #15706164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19825 #15706164