Subgroups — C₁₃×#19877 #15706216

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 582 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×#3381	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1671	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1636	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×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#557	C₂²	1	1	yes	characteristic
17	C₁₃×#555	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×#499	—	2	1	no	—
22	C₁₃×#498	C₂²	1	1	yes	characteristic
23	C₁₃×#492	—	2	1	no	—
24	C₁₃×#492	C₂²	1	1	yes	characteristic
25	C₁₃×#492	C₂²	1	1	yes	characteristic
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#482	—	2	1	no	—
30	C₁₃×#480	—	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×#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×#466	—	2	1	no	—
40	C₁₃×#461	—	2	1	no	—
41	C₁₃×#461	C₂²	1	1	yes	characteristic
42	C₁₃×#460	—	2	1	no	—
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#449	—	2	1	no	—
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	—	2	1	no	—
50	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
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×#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×SD₁₆	—	2	1	no	—
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	—	4	1	no	—
73	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×D₈	—	2	1	no	—
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#125	—	2	1	no	—
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×#125	—	4	1	no	—
87	C₁₃×#124	—	4	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	4	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	#19877	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	—	4	1	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₁₃×SD₁₆	—	2	2	no	—
165	C₁₃×SD₁₆	—	2	2	no	—
166	C₁₃×SD₁₆	—	4	2	no	—
167	C₁₃×SD₁₆	—	8	1	no	—
168	C₁₃×SD₁₆	—	8	1	no	—
169	C₁₃×SD₁₆	—	8	1	no	—
170	C₁₃×SD₁₆	—	8	2	no	—
171	C₁₃×D₈	—	8	1	no	—
172	C₁₃×M₁₆	—	4	2	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	8	1	no	—
179	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	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	—	4	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	no	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	4	1	no	—
209	C₄²×C₁₃	—	4	1	no	—
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#3357	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3305	C₂×C₁₃	1	1	yes	characteristic
215	#1714	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1685	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1676	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1671	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1646	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1636	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1622	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
225	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	4	1	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	8	1	no	—
235	Q₈×C₁₃	—	8	1	no	—
236	Q₈×C₁₃	#137	1	2	yes	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	1	no	—
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	—	8	2	no	—
246	D₄×C₁₃	—	8	1	no	—
247	D₄×C₁₃	—	16	1	no	—
248	D₄×C₁₃	—	16	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	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	8	2	no	—
263	C₂×C₄×C₁₃	—	16	1	no	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	—	2	1	no	—
269	C₈×C₁₃	—	2	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	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	#135	1	2	yes	—
276	#557	C₂²×C₁₃	1	1	yes	characteristic
277	#555	C₂²×C₁₃	1	1	yes	characteristic
278	#554	C₂²×C₁₃	1	1	yes	characteristic
279	#550	C₂²×C₁₃	1	1	yes	characteristic
280	#500	C₂²×C₁₃	1	1	yes	characteristic
281	#499	—	2	1	no	—
282	#498	C₂²×C₁₃	1	1	yes	characteristic
283	#492	—	2	1	no	—
284	#492	C₂²×C₁₃	1	1	yes	characteristic
285	#492	C₂²×C₁₃	1	1	yes	characteristic
286	#487	C₂²×C₁₃	1	1	yes	characteristic
287	#486	C₂²×C₁₃	1	1	yes	characteristic
288	#485	—	2	1	no	—
289	#482	—	2	1	no	—
290	#480	—	2	1	no	—
291	#479	—	2	1	no	—
292	#478	—	2	1	no	—
293	#477	C₂²×C₁₃	1	1	yes	characteristic
294	#477	C₂²×C₁₃	1	1	yes	characteristic
295	#477	C₂²×C₁₃	1	1	yes	characteristic
296	#476	C₂²×C₁₃	1	1	yes	characteristic
297	#474	C₂²×C₁₃	1	1	yes	characteristic
298	#468	—	2	1	no	—
299	#466	—	2	1	no	—
300	#461	—	2	1	no	—
301	#461	C₂²×C₁₃	1	1	yes	characteristic
302	#460	—	2	1	no	—
303	#460	C₂²×C₁₃	1	1	yes	characteristic
304	#459	C₂²×C₁₃	1	1	yes	characteristic
305	#449	—	2	1	no	—
306	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×SD₁₆	—	2	1	no	—
309	C₄×SD₁₆	—	2	1	no	—
310	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
311	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
312	#436	C₂²×C₁₃	1	1	yes	characteristic
313	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
314	#428	—	2	1	no	—
315	#416	—	2	1	no	—
316	#335	C₂²×C₁₃	1	1	yes	characteristic
317	#334	C₂²×C₁₃	1	1	yes	characteristic
318	#333	C₂²×C₁₃	1	1	yes	characteristic
319	#333	C₂²×C₁₃	1	1	yes	characteristic
320	#332	C₂²×C₁₃	1	1	yes	characteristic
321	#331	C₂²×C₁₃	1	1	yes	characteristic
322	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	#322	C₂²×C₁₃	1	1	yes	characteristic
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	—	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	D₄²	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	—	8	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
348	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
349	C₄×C₁₃	#577	1	1	yes	characteristic
350	C₄×C₁₃	#577	1	1	yes	characteristic
351	C₂×#41	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	4	1	no	—
357	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
358	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
359	C₂×D₈	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
366	#127	—	2	1	no	—
367	#127	C₂³×C₁₃	1	1	yes	characteristic
368	#125	—	2	1	no	—
369	#125	—	2	1	no	—
370	#125	—	4	1	no	—
371	#124	—	4	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	4	1	no	—
374	#121	—	2	1	no	—
375	#121	—	2	1	no	—
376	#121	—	2	1	no	—
377	#121	—	4	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#107	—	2	1	no	—
394	#107	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	D₄×C₁₃	1	1	yes	characteristic
399	#106	D₄×C₁₃	1	1	yes	characteristic
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	—	2	1	no	—
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	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	4	1	no	—
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	D₄×C₁₃	1	1	yes	characteristic
420	#102	D₄×C₁₃	1	1	yes	characteristic
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₁₃	—	8	1	no	—
429	C₂×C₁₃	—	8	1	no	—
430	C₂×C₁₃	—	16	1	no	—
431	C₂×C₁₃	#3266	1	1	yes	characteristic
432	C₂×C₁₃	#3284	1	1	yes	characteristic
433	C₂×C₁₃	#3288	1	1	yes	characteristic
434	#41	—	4	2	no	—
435	#41	—	8	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	SD₁₆	—	2	2	no	—
454	SD₁₆	—	2	2	no	—
455	SD₁₆	—	4	2	no	—
456	SD₁₆	—	8	1	no	—
457	SD₁₆	—	8	1	no	—
458	SD₁₆	—	8	1	no	—
459	SD₁₆	—	8	2	no	—
460	D₈	—	8	1	no	—
461	M₁₆	—	4	2	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	8	1	no	—
468	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	4	1	no	—
498	C₄²	—	4	1	no	—
499	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₁₃	#19877	1	1	yes	characteristic, direct product factor, Sylow
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	4	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	8	1	no	—
510	Q₈	—	8	1	no	—
511	Q₈	C₁₃×#137	1	2	yes	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	8	2	no	—
521	D₄	—	8	1	no	—
522	D₄	—	16	1	no	—
523	D₄	—	16	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	—	16	1	no	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	C₁₃×#135	1	2	yes	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	D₄²×C₁₃	1	1	yes	characteristic
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
572	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
573	C₄	C₁₃×#577	1	1	yes	characteristic
574	C₄	C₁₃×#577	1	1	yes	characteristic
575	C₂	—	8	1	no	—
576	C₂	—	8	1	no	—
577	C₂	—	16	1	no	—
578	C₂	C₁₃×#3266	1	1	yes	characteristic
579	C₂	C₁₃×#3284	1	1	yes	characteristic
580	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3305	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×#3381	C₂	semidirect
3. C₁₃×#3357	C₂	semidirect
5. C₁₃×#1714	C₂	semidirect
6. C₁₃×#1685	C₂	semidirect
7. C₁₃×#1678	C₂	semidirect
8. C₁₃×#1676	C₂	semidirect
9. C₁₃×#1671	C₂	semidirect
10. C₁₃×#1646	C₂	semidirect
11. C₁₃×#1636	C₂	semidirect
12. C₁₃×#1631	C₂	semidirect
13. C₁₃×#1622	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19877	C₁₃	direct (N × H)
211. #3392	C₂×C₁₃	semidirect
212. #3381	C₂×C₁₃	semidirect
213. #3357	C₂×C₁₃	semidirect
215. #1714	C₂×C₁₃	semidirect
216. #1685	C₂×C₁₃	semidirect
217. #1678	C₂×C₁₃	semidirect
218. #1676	C₂×C₁₃	semidirect
219. #1671	C₂×C₁₃	semidirect
220. #1646	C₂×C₁₃	semidirect
221. #1636	C₂×C₁₃	semidirect
222. #1631	C₂×C₁₃	semidirect
223. #1622	C₂×C₁₃	semidirect
224. #1583	C₂×C₁₃	semidirect
225. SD₁₆⋊C₈	C₂×C₁₃	semidirect
500. C₁₃	#19877	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×#3381	2
C₁₃×#3357	2
C₁₃×#3305	2
C₁₃×#1714	2
C₁₃×#1685	2
C₁₃×#1678	2
C₁₃×#1676	2
C₁₃×#1671	2
C₁₃×#1646	2
C₁₃×#1636	2
C₁₃×#1631	2
C₁₃×#1622	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19877	13

Subgroups — C13×#19877 #15706216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19877 #15706216