Subgroups — C₁₃×#19810 #15706149

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 586 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
2	C₁₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1693	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1642	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1626	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	C₂×C₁₃×#137	—	2	1	no	—
17	C₁₃×#557	C₂²	1	1	yes	characteristic
18	C₁₃×#557	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#500	C₂²	1	1	yes	characteristic
22	C₁₃×#499	—	2	1	no	—
23	C₁₃×#498	C₂²	1	1	yes	characteristic
24	C₁₃×#492	—	2	1	no	—
25	C₁₃×#492	C₂²	1	1	yes	characteristic
26	C₁₃×#492	C₂²	1	1	yes	characteristic
27	C₁₃×#487	—	2	1	no	—
28	C₁₃×#487	C₂²	1	1	yes	characteristic
29	C₁₃×#486	C₂²	1	1	yes	characteristic
30	C₁₃×#479	—	2	1	no	—
31	C₁₃×#479	—	2	1	no	—
32	C₁₃×#475	—	2	1	no	—
33	C₁₃×#475	C₂²	1	1	yes	characteristic
34	C₁₃×#475	C₂²	1	1	yes	characteristic
35	C₁₃×#475	C₂²	1	1	yes	characteristic
36	C₁₃×#468	—	2	1	no	—
37	C₁₃×#462	C₂²	1	1	yes	characteristic
38	C₁₃×#461	—	2	1	no	—
39	C₁₃×#461	—	2	1	no	—
40	C₁₃×#461	C₂²	1	1	yes	characteristic
41	C₁₃×#461	C₂²	1	1	yes	characteristic
42	C₁₃×#460	—	2	1	no	—
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#460	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₁₃×#448	—	2	1	no	—
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×Q₁₆	—	2	1	no	—
51	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×SD₁₆	—	2	1	no	—
53	C₄×C₁₃×SD₁₆	—	2	1	no	—
54	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
55	C₁₃×#436	C₂²	1	1	yes	characteristic
56	C₁₃×#334	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#332	C₂²	1	1	yes	characteristic
59	C₁₃×#332	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×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	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₁₃×#137	—	4	4	no	—
70	C₂×C₁₃×Q₁₆	—	2	1	no	—
71	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
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	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₃×#127	—	2	1	no	—
89	C₁₃×#127	C₂³	1	1	yes	characteristic
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	—	4	1	no	—
93	C₁₃×#125	—	4	1	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×C₂²⋊Q₈	—	4	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	4	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×Q₈×C₁₃	—	2	1	no	—
101	C₄×Q₈×C₁₃	—	2	1	no	—
102	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₃	—	2	1	no	—
106	C₄×D₄×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	D₄	1	1	yes	characteristic
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	2	1	no	—
114	C₁₃×#106	—	4	1	no	—
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	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	D₄	1	1	yes	characteristic
132	C₁₃×#103	D₄	1	1	yes	characteristic
133	C₁₃×#103	D₄	1	1	yes	characteristic
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	—	4	1	no	—
137	C₁₃×#102	D₄	1	1	yes	characteristic
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	—	2	1	no	—
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	#19810	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	4	1	no	—
152	C₂×Q₈×C₁₃	—	4	2	no	—
153	C₂×Q₈×C₁₃	—	8	1	no	—
154	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	4	1	no	—
161	C₂×D₄×C₁₃	—	4	1	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₁₃×Q₁₆	—	4	2	no	—
167	C₁₃×Q₁₆	SD₁₆	1	4	yes	complemented
168	C₁₃×SD₁₆	—	4	1	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	4	2	no	—
171	C₁₃×SD₁₆	—	4	2	no	—
172	C₁₃×SD₁₆	—	4	2	no	—
173	C₁₃×SD₁₆	—	8	1	no	—
174	C₁₃×SD₁₆	—	8	1	no	—
175	C₁₃×SD₁₆	—	8	1	no	—
176	C₁₃×SD₁₆	—	8	1	no	—
177	C₁₃×M₁₆	—	4	2	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	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₄⋊C₄	—	4	1	no	—
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	4	1	no	—
214	C₄²×C₁₃	—	4	1	no	—
215	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
216	#3392	C₂×C₁₃	1	1	yes	characteristic
217	#3383	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#3278	C₂×C₁₃	1	1	yes	characteristic
220	#1714	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1693	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1666	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1666	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1642	C₂×C₁₃	1	1	yes	characteristic
228	#1626	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	2	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	8	2	no	—
244	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	—
245	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	2	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	—	8	2	no	—
253	D₄×C₁₃	—	8	1	no	—
254	D₄×C₁₃	—	16	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	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	8	2	no	—
268	C₂×C₄×C₁₃	—	8	2	no	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	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	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
281	C₂×#137	—	2	1	no	—
282	#557	C₂²×C₁₃	1	1	yes	characteristic
283	#557	C₂²×C₁₃	1	1	yes	characteristic
284	#550	C₂²×C₁₃	1	1	yes	characteristic
285	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	#500	C₂²×C₁₃	1	1	yes	characteristic
287	#499	—	2	1	no	—
288	#498	C₂²×C₁₃	1	1	yes	characteristic
289	#492	—	2	1	no	—
290	#492	C₂²×C₁₃	1	1	yes	characteristic
291	#492	C₂²×C₁₃	1	1	yes	characteristic
292	#487	—	2	1	no	—
293	#487	C₂²×C₁₃	1	1	yes	characteristic
294	#486	C₂²×C₁₃	1	1	yes	characteristic
295	#479	—	2	1	no	—
296	#479	—	2	1	no	—
297	#475	—	2	1	no	—
298	#475	C₂²×C₁₃	1	1	yes	characteristic
299	#475	C₂²×C₁₃	1	1	yes	characteristic
300	#475	C₂²×C₁₃	1	1	yes	characteristic
301	#468	—	2	1	no	—
302	#462	C₂²×C₁₃	1	1	yes	characteristic
303	#461	—	2	1	no	—
304	#461	—	2	1	no	—
305	#461	C₂²×C₁₃	1	1	yes	characteristic
306	#461	C₂²×C₁₃	1	1	yes	characteristic
307	#460	—	2	1	no	—
308	#460	C₂²×C₁₃	1	1	yes	characteristic
309	#460	C₂²×C₁₃	1	1	yes	characteristic
310	#452	—	2	1	no	—
311	#448	—	2	1	no	—
312	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
313	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
314	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
315	C₄×Q₁₆	—	2	1	no	—
316	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×SD₁₆	—	2	1	no	—
318	C₄×SD₁₆	—	2	1	no	—
319	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
320	#436	C₂²×C₁₃	1	1	yes	characteristic
321	#334	C₂²×C₁₃	1	1	yes	characteristic
322	#334	C₂²×C₁₃	1	1	yes	characteristic
323	#332	C₂²×C₁₃	1	1	yes	characteristic
324	#332	C₂²×C₁₃	1	1	yes	characteristic
325	#332	C₂²×C₁₃	1	1	yes	characteristic
326	#331	C₂²×C₁₃	1	1	yes	characteristic
327	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	#322	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	8	1	no	—
336	C₂²×C₁₃	—	8	1	no	—
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	D₄²	1	1	yes	characteristic
339	C₄×C₁₃	—	2	2	no	—
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	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	C₂²×SD₁₆	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	C₂²×Q₈	—	2	1	no	—
356	#137	—	4	4	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
368	C₂×M₁₆	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	#127	—	2	1	no	—
376	#127	C₂³×C₁₃	1	1	yes	characteristic
377	#125	—	2	1	no	—
378	#125	—	2	1	no	—
379	#125	—	4	1	no	—
380	#125	—	4	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	4	1	no	—
383	#121	—	2	1	no	—
384	#121	—	4	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
395	#107	—	2	1	no	—
396	#107	—	2	1	no	—
397	#107	D₄×C₁₃	1	1	yes	characteristic
398	#106	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	4	1	no	—
402	#106	D₄×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	D₄×C₁₃	1	1	yes	characteristic
419	#103	D₄×C₁₃	1	1	yes	characteristic
420	#103	D₄×C₁₃	1	1	yes	characteristic
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	4	1	no	—
424	#102	D₄×C₁₃	1	1	yes	characteristic
425	C₂²⋊C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₁₃	—	8	1	no	—
433	C₂×C₁₃	—	16	1	no	—
434	C₂×C₁₃	#3271	1	1	yes	characteristic
435	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
436	C₂×C₁₃	#3289	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	—	2	1	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	—	4	2	no	—
444	C₂×Q₈	—	8	1	no	—
445	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	Q₁₆	—	4	2	no	—
458	Q₁₆	C₁₃×SD₁₆	1	4	yes	complemented
459	SD₁₆	—	4	1	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	4	2	no	—
464	SD₁₆	—	8	1	no	—
465	SD₁₆	—	8	1	no	—
466	SD₁₆	—	8	1	no	—
467	SD₁₆	—	8	1	no	—
468	M₁₆	—	4	2	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	—	2	1	no	—
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	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
507	C₁₃	#19810	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	—	2	1	no	—
509	C₂³	—	4	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	8	2	no	—
521	Q₈	C₂×C₁₃×SD₁₆	1	2	yes	—
522	Q₈	C₂×C₁₃×SD₁₆	1	2	yes	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	8	2	no	—
530	D₄	—	8	1	no	—
531	D₄	—	16	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	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
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	C₈	C₂×C₁₃×SD₁₆	1	2	yes	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	D₄²×C₁₃	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
577	C₄	C₁₃×#575	1	1	yes	characteristic
578	C₄	C₁₃×#577	1	1	yes	characteristic
579	C₄	C₁₃×#577	1	1	yes	characteristic
580	C₂	—	8	1	no	—
581	C₂	—	16	1	no	—
582	C₂	C₁₃×#3271	1	1	yes	characteristic
583	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
584	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#550	C₂²
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×#3383	C₂	semidirect
3. C₁₃×#3359	C₂	semidirect
5. C₁₃×#1714	C₂	semidirect
6. C₁₃×#1693	C₂	semidirect
7. C₁₃×#1680	C₂	semidirect
8. C₁₃×#1666	C₂	semidirect
9. C₁₃×#1666	C₂	semidirect
10. C₁₃×#1653	C₂	semidirect
11. C₁₃×#1651	C₂	semidirect
13. C₁₃×#1626	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×#1579	C₂	semidirect
145. #19810	C₁₃	direct (N × H)
167. C₁₃×Q₁₆	SD₁₆	semidirect
217. #3383	C₂×C₁₃	semidirect
218. #3359	C₂×C₁₃	semidirect
220. #1714	C₂×C₁₃	semidirect
221. #1693	C₂×C₁₃	semidirect
222. #1680	C₂×C₁₃	semidirect
223. #1666	C₂×C₁₃	semidirect
224. #1666	C₂×C₁₃	semidirect
225. #1653	C₂×C₁₃	semidirect
226. #1651	C₂×C₁₃	semidirect
228. #1626	C₂×C₁₃	semidirect
229. #1583	C₂×C₁₃	semidirect
230. #1579	C₂×C₁₃	semidirect
458. Q₁₆	C₁₃×SD₁₆	semidirect
507. C₁₃	#19810	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×#3383	2
C₁₃×#3359	2
C₁₃×#3278	2
C₁₃×#1714	2
C₁₃×#1693	2
C₁₃×#1680	2
C₁₃×#1666	2
C₁₃×#1653	2
C₁₃×#1651	2
C₁₃×#1642	2
C₁₃×#1626	2
C₁₃×#1583	2
C₁₃×#1579	2
#19810	13

Subgroups — C13×#19810 #15706149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19810 #15706149