Subgroups — C₁₃×#19833 #15706172

Order 3328.

608 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1621	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1620	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	1	yes	characteristic
17	C₁₃×#557	C₂²	1	1	yes	characteristic
18	C₁₃×#554	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#493	C₂²	1	1	yes	characteristic
21	C₁₃×#492	—	2	1	no	—
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#488	—	2	1	no	—
24	C₁₃×#488	—	2	1	no	—
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×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#480	—	2	1	no	—
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#478	—	2	1	no	—
32	C₁₃×#477	C₂²	1	1	yes	characteristic
33	C₁₃×#477	C₂²	1	1	yes	characteristic
34	C₁₃×#475	C₂²	1	1	yes	characteristic
35	C₁₃×#468	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#463	—	2	1	no	—
38	C₁₃×#461	—	2	1	no	—
39	C₁₃×#461	C₂²	1	1	yes	characteristic
40	C₁₃×#460	—	2	1	no	—
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#460	C₂²	1	1	yes	characteristic
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×SD₁₆	—	2	1	no	—
51	C₄×C₁₃×SD₁₆	—	2	1	no	—
52	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×D₈	—	2	1	no	—
54	C₁₃×#436	C₂²	1	1	yes	characteristic
55	C₁₃×#417	—	2	1	no	—
56	C₁₃×#334	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#331	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×Q₈⋊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	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	4	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×#127	—	2	1	no	—
83	C₁₃×#127	C₂³	1	1	yes	characteristic
84	C₁₃×#127	C₂³	1	1	yes	characteristic
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	—	4	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	—	4	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	4	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	D₄	1	1	yes	characteristic
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	—	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	—	4	1	no	—
123	C₁₃×#103	D₄	1	1	yes	characteristic
124	C₁₃×#103	D₄	1	1	yes	characteristic
125	C₁₃×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₄×C₈×C₁₃	—	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	#19833	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	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	4	1	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₁₃×Q₁₆	—	2	2	no	—
166	C₁₃×SD₁₆	—	4	1	no	—
167	C₁₃×SD₁₆	—	4	2	no	—
168	C₁₃×SD₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	8	1	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×SD₁₆	—	8	1	no	—
172	C₁₃×SD₁₆	—	8	1	no	—
173	C₁₃×D₈	—	4	2	no	—
174	C₁₃×D₈	—	8	2	no	—
175	C₁₃×M₁₆	—	8	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	4	1	no	—
211	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
212	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1717	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1701	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1666	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1643	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1636	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1621	C₂×C₁₃	1	1	yes	characteristic
224	#1620	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	8	1	no	—
238	Q₈×C₁₃	#135	1	2	yes	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	8	2	no	—
250	D₄×C₁₃	—	8	1	no	—
251	D₄×C₁₃	—	8	1	no	—
252	D₄×C₁₃	—	16	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	8	2	no	—
265	C₂×C₄×C₁₃	—	16	1	no	—
266	C₂×C₄×C₁₃	—	16	1	no	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	#559	C₂²×C₁₃	1	1	yes	characteristic
280	#557	C₂²×C₁₃	1	1	yes	characteristic
281	#554	C₂²×C₁₃	1	1	yes	characteristic
282	#550	C₂²×C₁₃	1	1	yes	characteristic
283	#493	C₂²×C₁₃	1	1	yes	characteristic
284	#492	—	2	1	no	—
285	#492	C₂²×C₁₃	1	1	yes	characteristic
286	#488	—	2	1	no	—
287	#488	—	2	1	no	—
288	#487	C₂²×C₁₃	1	1	yes	characteristic
289	#486	C₂²×C₁₃	1	1	yes	characteristic
290	#486	C₂²×C₁₃	1	1	yes	characteristic
291	#486	C₂²×C₁₃	1	1	yes	characteristic
292	#480	—	2	1	no	—
293	#478	—	2	1	no	—
294	#478	—	2	1	no	—
295	#477	C₂²×C₁₃	1	1	yes	characteristic
296	#477	C₂²×C₁₃	1	1	yes	characteristic
297	#475	C₂²×C₁₃	1	1	yes	characteristic
298	#468	—	2	1	no	—
299	#464	—	2	1	no	—
300	#463	—	2	1	no	—
301	#461	—	2	1	no	—
302	#461	C₂²×C₁₃	1	1	yes	characteristic
303	#460	—	2	1	no	—
304	#460	C₂²×C₁₃	1	1	yes	characteristic
305	#460	C₂²×C₁₃	1	1	yes	characteristic
306	#460	C₂²×C₁₃	1	1	yes	characteristic
307	#459	C₂²×C₁₃	1	1	yes	characteristic
308	#452	—	2	1	no	—
309	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
313	C₄×SD₁₆	—	2	1	no	—
314	C₄×SD₁₆	—	2	1	no	—
315	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
316	C₄×D₈	—	2	1	no	—
317	#436	C₂²×C₁₃	1	1	yes	characteristic
318	#417	—	2	1	no	—
319	#334	C₂²×C₁₃	1	1	yes	characteristic
320	#334	C₂²×C₁₃	1	1	yes	characteristic
321	#333	C₂²×C₁₃	1	1	yes	characteristic
322	#332	C₂²×C₁₃	1	1	yes	characteristic
323	#331	C₂²×C₁₃	1	1	yes	characteristic
324	#331	C₂²×C₁₃	1	1	yes	characteristic
325	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
327	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	#322	C₂²×C₁₃	1	1	yes	characteristic
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	—	8	1	no	—
335	C₂²×C₁₃	—	8	1	no	—
336	C₂²×C₁₃	—	8	1	no	—
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	D₄²	1	1	yes	characteristic
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
351	C₄×C₁₃	#575	1	1	yes	characteristic
352	C₄×C₁₃	#577	1	1	yes	characteristic
353	C₄×C₁₃	#577	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
363	C₂×D₈	—	2	1	no	—
364	C₂×D₈	—	4	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
369	#127	—	2	1	no	—
370	#127	C₂³×C₁₃	1	1	yes	characteristic
371	#127	C₂³×C₁₃	1	1	yes	characteristic
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#125	—	4	1	no	—
375	#124	—	2	1	no	—
376	#124	—	2	1	no	—
377	#123	—	4	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	4	1	no	—
380	#121	—	2	1	no	—
381	#121	—	4	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	—	2	1	no	—
393	#107	—	2	1	no	—
394	#107	—	2	1	no	—
395	#107	D₄×C₁₃	1	1	yes	characteristic
396	#106	—	2	1	no	—
397	#106	D₄×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	4	1	no	—
410	#103	D₄×C₁₃	1	1	yes	characteristic
411	#103	D₄×C₁₃	1	1	yes	characteristic
412	#103	D₄×C₁₃	1	1	yes	characteristic
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	D₄×C₁₃	1	1	yes	characteristic
424	C₂²⋊C₈	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₁₃	—	8	1	no	—
432	C₂×C₁₃	—	16	1	no	—
433	C₂×C₁₃	—	16	1	no	—
434	C₂×C₁₃	#3271	1	1	yes	characteristic
435	C₂×C₁₃	#3282	1	1	yes	characteristic
436	C₂×C₁₃	#3288	1	1	yes	characteristic
437	#41	—	4	2	no	—
438	#41	—	8	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	Q₁₆	—	2	2	no	—
458	SD₁₆	—	4	1	no	—
459	SD₁₆	—	4	2	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	8	1	no	—
462	SD₁₆	—	8	1	no	—
463	SD₁₆	—	8	1	no	—
464	SD₁₆	—	8	1	no	—
465	D₈	—	4	2	no	—
466	D₈	—	8	2	no	—
467	M₁₆	—	8	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₁₃	#19833	1	1	yes	characteristic, direct product factor, Sylow
505	C₂³	—	2	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	8	1	no	—
516	Q₈	C₁₃×#135	1	2	yes	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	16	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	16	1	no	—
544	C₂×C₄	—	16	1	no	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	D₄²×C₁₃	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
578	C₄	C₁₃×#575	1	1	yes	characteristic
579	C₄	C₁₃×#577	1	1	yes	characteristic
580	C₄	C₁₃×#577	1	1	yes	characteristic
581	C₂	—	8	1	no	—
582	C₂	—	16	1	no	—
583	C₂	—	16	1	no	—
584	C₂	C₁₃×#3271	1	1	yes	characteristic
585	C₂	C₁₃×#3282	1	1	yes	characteristic
586	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#1621	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×#3392	C₂	semidirect
2. C₁₃×#3365	C₂	semidirect
3. C₁₃×#3361	C₂	semidirect
4. C₁₃×#3333	C₂	semidirect
5. C₁₃×#1717	C₂	semidirect
6. C₁₃×#1701	C₂	semidirect
7. C₁₃×#1678	C₂	semidirect
8. C₁₃×#1678	C₂	semidirect
9. C₁₃×#1666	C₂	semidirect
10. C₁₃×#1643	C₂	semidirect
11. C₁₃×#1636	C₂	semidirect
13. C₁₃×#1620	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×#1579	C₂	semidirect
144. #19833	C₁₃	direct (N × H)
212. #3392	C₂×C₁₃	semidirect
213. #3365	C₂×C₁₃	semidirect
214. #3361	C₂×C₁₃	semidirect
215. #3333	C₂×C₁₃	semidirect
216. #1717	C₂×C₁₃	semidirect
217. #1701	C₂×C₁₃	semidirect
218. #1678	C₂×C₁₃	semidirect
219. #1678	C₂×C₁₃	semidirect
220. #1666	C₂×C₁₃	semidirect
221. #1643	C₂×C₁₃	semidirect
222. #1636	C₂×C₁₃	semidirect
224. #1620	C₂×C₁₃	semidirect
225. #1583	C₂×C₁₃	semidirect
226. #1579	C₂×C₁₃	semidirect
504. C₁₃	#19833	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×#3392	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3333	2
C₁₃×#1717	2
C₁₃×#1701	2
C₁₃×#1678	2
C₁₃×#1666	2
C₁₃×#1643	2
C₁₃×#1636	2
C₁₃×#1621	2
C₁₃×#1620	2
C₁₃×#1583	2
C₁₃×#1579	2
#19833	13

Subgroups — C13×#19833 #15706172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19833 #15706172