Subgroups — C₁₃×#19880 #15706219

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 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×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1672	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×#1630	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1624	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
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#555	C₂²	1	1	yes	characteristic
19	C₁₃×#554	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#498	C₂²	1	1	yes	characteristic
22	C₁₃×#495	—	2	1	no	—
23	C₁₃×#492	C₂²	1	1	yes	characteristic
24	C₁₃×#492	C₂²	1	1	yes	characteristic
25	C₁₃×#488	—	2	1	no	—
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#485	—	2	1	no	—
30	C₁₃×#482	—	2	1	no	—
31	C₁₃×#480	—	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×#477	C₂²	1	1	yes	characteristic
36	C₁₃×#476	C₂²	1	1	yes	characteristic
37	C₁₃×#474	C₂²	1	1	yes	characteristic
38	C₁₃×#468	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#464	—	2	1	no	—
41	C₁₃×#463	—	2	1	no	—
42	C₁₃×#463	—	2	1	no	—
43	C₁₃×#462	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#459	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
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×#428	—	2	1	no	—
55	C₁₃×#427	—	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×Q₁₆	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	4	1	no	—
71	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
72	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₂×C₁₃×D₈	—	2	1	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×#127	C₂³	1	1	yes	characteristic
81	C₁₃×#126	—	4	1	no	—
82	C₁₃×#125	—	2	1	no	—
83	C₁₃×#124	—	2	1	no	—
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×#124	—	4	1	no	—
87	C₁₃×#123	—	4	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	4	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#117	—	2	1	no	—
103	C₁₃×#117	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	2	1	no	—
114	C₁₃×#106	D₄	1	1	yes	characteristic
115	C₁₃×#106	D₄	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	—	2	1	no	—
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	4	1	no	—
127	C₁₃×#103	D₄	1	1	yes	characteristic
128	C₁₃×#103	D₄	1	1	yes	characteristic
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	#19880	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×Q₈×C₁₃	—	2	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	—	4	1	no	—
154	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₂²×C₄×C₁₃	—	4	1	no	—
160	C₁₃×Q₁₆	—	8	1	no	—
161	C₁₃×SD₁₆	—	2	2	no	—
162	C₁₃×SD₁₆	—	4	1	no	—
163	C₁₃×SD₁₆	—	4	2	no	—
164	C₁₃×SD₁₆	—	8	1	no	—
165	C₁₃×SD₁₆	—	8	2	no	—
166	C₁₃×D₈	—	4	2	no	—
167	C₁₃×D₈	—	8	1	no	—
168	C₁₃×M₁₆	—	4	2	no	—
169	C₂×C₈×C₁₃	—	2	1	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	—	4	2	no	—
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	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	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	4	1	no	—
207	C₄²×C₁₃	—	4	1	no	—
208	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
209	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3357	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1714	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1685	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1677	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1676	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1672	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1644	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1630	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1624	C₂×C₁₃	1	1	yes	characteristic
222	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
223	SD₁₆⋊C₈	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	—	2	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	8	1	no	—
244	D₄×C₁₃	—	16	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
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	—	4	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	—	16	1	no	—
259	C₂×C₄×C₁₃	—	16	1	no	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	#135	1	2	yes	—
272	#559	C₂²×C₁₃	1	1	yes	characteristic
273	#556	C₂²×C₁₃	1	1	yes	characteristic
274	#555	C₂²×C₁₃	1	1	yes	characteristic
275	#554	C₂²×C₁₃	1	1	yes	characteristic
276	#500	C₂²×C₁₃	1	1	yes	characteristic
277	#498	C₂²×C₁₃	1	1	yes	characteristic
278	#495	—	2	1	no	—
279	#492	C₂²×C₁₃	1	1	yes	characteristic
280	#492	C₂²×C₁₃	1	1	yes	characteristic
281	#488	—	2	1	no	—
282	#487	C₂²×C₁₃	1	1	yes	characteristic
283	#486	C₂²×C₁₃	1	1	yes	characteristic
284	#485	—	2	1	no	—
285	#485	—	2	1	no	—
286	#482	—	2	1	no	—
287	#480	—	2	1	no	—
288	#478	—	2	1	no	—
289	#477	C₂²×C₁₃	1	1	yes	characteristic
290	#477	C₂²×C₁₃	1	1	yes	characteristic
291	#477	C₂²×C₁₃	1	1	yes	characteristic
292	#476	C₂²×C₁₃	1	1	yes	characteristic
293	#474	C₂²×C₁₃	1	1	yes	characteristic
294	#468	—	2	1	no	—
295	#465	—	2	1	no	—
296	#464	—	2	1	no	—
297	#463	—	2	1	no	—
298	#463	—	2	1	no	—
299	#462	C₂²×C₁₃	1	1	yes	characteristic
300	#459	C₂²×C₁₃	1	1	yes	characteristic
301	#459	C₂²×C₁₃	1	1	yes	characteristic
302	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₄×SD₁₆	—	2	1	no	—
305	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×D₈	—	2	1	no	—
308	#436	C₂²×C₁₃	1	1	yes	characteristic
309	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	#428	—	2	1	no	—
311	#427	—	2	1	no	—
312	#335	C₂²×C₁₃	1	1	yes	characteristic
313	#334	C₂²×C₁₃	1	1	yes	characteristic
314	#333	C₂²×C₁₃	1	1	yes	characteristic
315	#333	C₂²×C₁₃	1	1	yes	characteristic
316	#332	C₂²×C₁₃	1	1	yes	characteristic
317	#331	C₂²×C₁₃	1	1	yes	characteristic
318	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	#322	C₂²×C₁₃	1	1	yes	characteristic
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	—	4	1	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	—	8	1	no	—
332	C₂²×C₁₃	D₄²	1	1	yes	characteristic
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	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	—	8	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
344	C₄×C₁₃	#575	1	1	yes	characteristic
345	C₄×C₁₃	#577	1	1	yes	characteristic
346	C₄×C₁₃	#578	1	1	yes	characteristic
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	4	1	no	—
351	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
352	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
353	C₂×D₈	—	2	1	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
360	#127	C₂³×C₁₃	1	1	yes	characteristic
361	#126	—	4	1	no	—
362	#125	—	2	1	no	—
363	#124	—	2	1	no	—
364	#124	—	2	1	no	—
365	#124	—	2	1	no	—
366	#124	—	4	1	no	—
367	#123	—	4	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	4	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	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	—	2	1	no	—
390	#107	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	D₄×C₁₃	1	1	yes	characteristic
395	#106	D₄×C₁₃	1	1	yes	characteristic
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
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	D₄×C₁₃	1	1	yes	characteristic
416	#102	D₄×C₁₃	1	1	yes	characteristic
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₁₃	—	8	1	no	—
425	C₂×C₁₃	—	8	1	no	—
426	C₂×C₁₃	—	16	1	no	—
427	C₂×C₁₃	#3269	1	1	yes	characteristic
428	C₂×C₁₃	#3284	1	1	yes	characteristic
429	C₂×C₁₃	#3288	1	1	yes	characteristic
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	Q₁₆	—	8	1	no	—
446	SD₁₆	—	2	2	no	—
447	SD₁₆	—	4	1	no	—
448	SD₁₆	—	4	2	no	—
449	SD₁₆	—	8	1	no	—
450	SD₁₆	—	8	2	no	—
451	D₈	—	4	2	no	—
452	D₈	—	8	1	no	—
453	M₁₆	—	4	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	4	2	no	—
460	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
494	C₁₃	#19880	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	4	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	8	1	no	—
505	Q₈	—	8	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	8	1	no	—
515	D₄	—	16	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	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	—	16	1	no	—
530	C₂×C₄	—	16	1	no	—
531	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	C₁₃×#135	1	2	yes	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	D₄²×C₁₃	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
564	C₄	C₁₃×#575	1	1	yes	characteristic
565	C₄	C₁₃×#577	1	1	yes	characteristic
566	C₄	C₁₃×#578	1	1	yes	characteristic
567	C₂	—	8	1	no	—
568	C₂	—	8	1	no	—
569	C₂	—	16	1	no	—
570	C₂	C₁₃×#3269	1	1	yes	characteristic
571	C₂	C₁₃×#3284	1	1	yes	characteristic
572	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#1624	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×#3357	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#1714	C₂	semidirect
6. C₁₃×#1685	C₂	semidirect
7. C₁₃×#1677	C₂	semidirect
8. C₁₃×#1676	C₂	semidirect
9. C₁₃×#1672	C₂	semidirect
10. C₁₃×#1644	C₂	semidirect
11. C₁₃×#1638	C₂	semidirect
12. C₁₃×#1630	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19880	C₁₃	direct (N × H)
209. #3394	C₂×C₁₃	semidirect
210. #3361	C₂×C₁₃	semidirect
211. #3357	C₂×C₁₃	semidirect
212. #3340	C₂×C₁₃	semidirect
213. #1714	C₂×C₁₃	semidirect
214. #1685	C₂×C₁₃	semidirect
215. #1677	C₂×C₁₃	semidirect
216. #1676	C₂×C₁₃	semidirect
217. #1672	C₂×C₁₃	semidirect
218. #1644	C₂×C₁₃	semidirect
219. #1638	C₂×C₁₃	semidirect
220. #1630	C₂×C₁₃	semidirect
222. #1583	C₂×C₁₃	semidirect
223. SD₁₆⋊C₈	C₂×C₁₃	semidirect
494. C₁₃	#19880	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×#3357	2
C₁₃×#3340	2
C₁₃×#1714	2
C₁₃×#1685	2
C₁₃×#1677	2
C₁₃×#1676	2
C₁₃×#1672	2
C₁₃×#1644	2
C₁₃×#1638	2
C₁₃×#1630	2
C₁₃×#1624	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19880	13

Subgroups — C13×#19880 #15706219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19880 #15706219