Subgroups — C₁₃×#18651 #15704990

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1654	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1651	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
11	D₄×Q₈×C₁₃	—	2	1	no	—
12	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₁₃×#547	—	2	2	no	—
14	C₁₃×#547	—	2	1	no	—
15	C₁₃×#547	—	2	2	no	—
16	C₁₃×#547	C₂²	1	2	yes	—
17	C₁₃×#536	—	2	2	no	—
18	C₁₃×#536	—	2	1	no	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#498	—	2	2	no	—
26	C₁₃×#498	C₂²	1	4	yes	—
27	C₁₃×#492	—	2	1	no	—
28	C₁₃×#487	—	2	1	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#475	C₂²	1	2	yes	—
32	C₁₃×#474	C₂²	1	2	yes	—
33	C₁₃×#461	C₂²	1	4	yes	—
34	C₁₃×#448	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#428	—	2	1	no	—
37	C₂×C₁₃×#106	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#417	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
45	C₁₃×2₋¹⁺⁴	—	4	4	no	—
46	C₁₃×2₋¹⁺⁴	—	4	4	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	—	2	2	no	—
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂²×Q₈×C₁₃	—	2	1	no	—
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂×C₁₃×SD₁₆	—	2	4	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×#127	D₄	1	1	yes	characteristic
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	—	2	1	no	—
74	C₁₃×#123	—	2	4	no	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×#123	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	—	2	1	no	—
84	C₁₃×#121	D₄	1	2	yes	—
85	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
93	C₄×D₄×C₁₃	C₂³	1	2	yes	—
94	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	2	no	—
106	C₁₃×#106	—	2	8	no	—
107	C₁₃×#106	—	2	2	no	—
108	C₁₃×C₄⋊C₈	—	2	1	no	—
109	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
110	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	4	no	—
113	C₁₃×#102	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	1	no	—
115	C₄×C₈×C₁₃	—	2	1	no	—
116	C₄×C₈×C₁₃	—	2	1	no	—
117	C₄×C₈×C₁₃	C₂³	1	2	yes	—
118	#18651	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	4	8	no	—
121	C₁₃×#41	—	4	16	no	—
122	C₁₃×#41	—	4	4	no	—
123	C₁₃×#41	—	4	4	no	—
124	C₁₃×#41	—	4	2	no	—
125	C₁₃×#41	—	4	2	no	—
126	C₁₃×#41	SD₁₆	1	4	yes	complemented
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	4	8	no	—
133	C₂×Q₈×C₁₃	—	4	4	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	—	4	1	no	—
136	C₂×Q₈×C₁₃	—	4	2	no	—
137	C₂×Q₈×C₁₃	—	4	2	no	—
138	C₂×Q₈×C₁₃	—	8	2	no	—
139	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	4	1	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₁₃×SD₁₆	—	8	4	no	—
159	C₁₃×M₁₆	—	4	2	no	—
160	C₂×C₈×C₁₃	—	2	4	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	4	1	no	—
175	C₁₃×C₄⋊C₄	—	4	1	no	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
194	#3499	C₂×C₁₃	1	1	yes	characteristic
195	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1654	C₂×C₁₃	1	4	yes	complemented
199	#1651	C₂×C₁₃	1	4	yes	complemented
200	#1546	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	#120	1	1	yes	characteristic
206	Q₈×C₁₃	—	2	1	no	—
207	Q₈×C₁₃	—	4	8	no	—
208	Q₈×C₁₃	—	4	2	no	—
209	Q₈×C₁₃	—	4	2	no	—
210	Q₈×C₁₃	—	4	2	no	—
211	Q₈×C₁₃	—	4	4	no	—
212	Q₈×C₁₃	—	4	4	no	—
213	Q₈×C₁₃	—	8	2	no	—
214	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	—
215	D₄×C₁₃	—	2	4	no	—
216	D₄×C₁₃	—	2	1	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	4	8	no	—
219	D₄×C₁₃	—	4	4	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	4	8	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	8	2	no	—
240	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
244	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₁₃	—	2	4	no	—
249	C₈×C₁₃	—	4	2	no	—
250	C₈×C₁₃	—	4	2	no	—
251	C₂×2₋¹⁺⁴	—	2	1	no	—
252	D₄×Q₈	—	2	1	no	—
253	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
254	#547	—	2	2	no	—
255	#547	—	2	1	no	—
256	#547	—	2	2	no	—
257	#547	C₂²×C₁₃	1	2	yes	—
258	#536	—	2	2	no	—
259	#536	—	2	1	no	—
260	#532	—	2	1	no	—
261	#532	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	—	2	1	no	—
263	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
266	#498	—	2	2	no	—
267	#498	C₂²×C₁₃	1	4	yes	—
268	#492	—	2	1	no	—
269	#487	—	2	1	no	—
270	#477	—	2	1	no	—
271	#476	—	2	1	no	—
272	#475	C₂²×C₁₃	1	2	yes	—
273	#474	C₂²×C₁₃	1	2	yes	—
274	#461	C₂²×C₁₃	1	4	yes	—
275	#448	—	2	2	no	—
276	#431	C₂²×C₁₃	1	1	yes	characteristic
277	#428	—	2	1	no	—
278	C₂×#106	—	2	2	no	—
279	#423	C₂²×C₁₃	1	1	yes	characteristic
280	#417	—	2	1	no	—
281	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
282	#332	C₂²×C₁₃	1	4	yes	—
283	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
284	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
285	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	#450	1	2	yes	—
295	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	4	4	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	1	no	—
302	C₄×C₁₃	—	4	1	no	—
303	C₄×C₁₃	—	8	2	no	—
304	C₄×C₁₃	#450	1	2	yes	—
305	C₄×C₁₃	#456	1	2	yes	—
306	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
307	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
308	C₄×C₁₃	#577	1	2	yes	—
309	2₋¹⁺⁴	—	4	4	no	—
310	2₋¹⁺⁴	—	4	4	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	4	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
316	C₂²×Q₈	—	2	2	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	—	2	1	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
333	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
334	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
335	#127	D₄×C₁₃	1	1	yes	characteristic
336	#124	—	2	2	no	—
337	#124	—	2	1	no	—
338	#123	—	2	4	no	—
339	#123	—	2	4	no	—
340	#123	—	2	4	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	—	2	1	no	—
348	#121	D₄×C₁₃	1	2	yes	—
349	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
350	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
357	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₄×D₄	C₂³×C₁₃	1	2	yes	—
359	#117	—	2	1	no	—
360	#117	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
369	#107	—	2	2	no	—
370	#106	—	2	8	no	—
371	#106	—	2	2	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
374	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
375	#103	—	2	2	no	—
376	#103	—	2	4	no	—
377	#102	—	2	2	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	C₂³×C₁₃	1	2	yes	—
382	C₂×C₁₃	—	2	2	no	—
383	C₂×C₁₃	—	4	2	no	—
384	C₂×C₁₃	—	8	2	no	—
385	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
386	C₂×C₁₃	#3010	1	1	yes	characteristic
387	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
388	#41	—	2	2	no	—
389	#41	—	4	8	no	—
390	#41	—	4	16	no	—
391	#41	—	4	4	no	—
392	#41	—	4	4	no	—
393	#41	—	4	2	no	—
394	#41	—	4	2	no	—
395	#41	C₁₃×SD₁₆	1	4	yes	complemented
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	8	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	1	no	—
405	C₂×Q₈	—	4	2	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	8	2	no	—
408	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	SD₁₆	—	8	4	no	—
428	M₁₆	—	4	2	no	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
447	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₁₃	#18651	1	1	yes	characteristic, direct product factor, Sylow
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	C₁₃×#120	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	4	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	4	no	—
474	Q₈	—	8	2	no	—
475	Q₈	C₂×C₁₃×SD₁₆	1	2	yes	—
476	D₄	—	2	4	no	—
477	D₄	—	2	1	no	—
478	D₄	—	2	4	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	C₂×C₁₃×SD₁₆	1	2	yes	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
502	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
503	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
504	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
505	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
509	C₈	—	2	4	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	C₁₃×#450	1	2	yes	—
521	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	2	no	—
529	C₄	—	8	2	no	—
530	C₄	C₁₃×#450	1	2	yes	—
531	C₄	C₁₃×#456	1	2	yes	—
532	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
533	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
534	C₄	C₁₃×#577	1	2	yes	—
535	C₂	—	2	2	no	—
536	C₂	—	4	2	no	—
537	C₂	—	8	2	no	—
538	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
539	C₂	C₁₃×#3010	1	1	yes	characteristic
540	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3499	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#3206	C₂	semidirect
3. C₂×C₁₃×#498	C₂	semidirect
4. C₁₃×#3079	C₂	semidirect
5. C₁₃×#1654	C₂	semidirect
6. C₁₃×#1651	C₂	semidirect
7. C₁₃×#1546	C₂	semidirect
8. C₁₃×#1492	C₂	semidirect
9. C₁₃×#1476	C₂	semidirect
118. #18651	C₁₃	direct (N × H)
126. C₁₃×#41	SD₁₆	semidirect
195. #3206	C₂×C₁₃	semidirect
196. C₂×#498	C₂×C₁₃	semidirect
197. #3079	C₂×C₁₃	semidirect
198. #1654	C₂×C₁₃	semidirect
199. #1651	C₂×C₁₃	semidirect
200. #1546	C₂×C₁₃	semidirect
201. #1492	C₂×C₁₃	semidirect
202. #1476	C₂×C₁₃	semidirect
395. #41	C₁₃×SD₁₆	semidirect
463. C₁₃	#18651	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×#3499	2
C₁₃×#3206	2
C₂×C₁₃×#498	2
C₁₃×#3079	2
C₁₃×#1654	2
C₁₃×#1651	2
C₁₃×#1546	2
C₁₃×#1492	2
C₁₃×#1476	2
#18651	13

Subgroups — C13×#18651 #15704990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18651 #15704990