Subgroups — C₁₃×#18675 #15705014

Order 3328.

1122 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1651	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1642	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1637	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1631	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
13	C₁₃×#550	—	2	1	no	—
14	C₁₃×#550	C₂²	1	2	yes	—
15	D₄×Q₈×C₁₃	—	2	1	no	—
16	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#548	—	2	2	no	—
18	C₁₃×#548	—	2	2	no	—
19	C₁₃×#537	—	2	2	no	—
20	C₁₃×#537	—	2	1	no	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	—	2	2	no	—
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#498	C₂²	1	1	yes	characteristic
27	C₁₃×#492	C₂²	1	1	yes	characteristic
28	C₁₃×#487	C₂²	1	1	yes	characteristic
29	C₁₃×#486	C₂²	1	1	yes	characteristic
30	C₁₃×#479	—	2	2	no	—
31	C₁₃×#477	C₂²	1	2	yes	—
32	C₁₃×#476	C₂²	1	2	yes	—
33	C₁₃×#475	—	2	1	no	—
34	C₁₃×#475	C₂²	1	2	yes	—
35	C₁₃×#465	—	2	2	no	—
36	C₁₃×#465	—	2	2	no	—
37	C₁₃×#461	C₂²	1	2	yes	—
38	C₁₃×#460	—	2	1	no	—
39	C₄×C₁₃×SD₁₆	—	2	2	no	—
40	C₁₃×#428	—	2	1	no	—
41	C₁₃×#423	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×#419	—	2	1	no	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#332	C₂²	1	2	yes	—
46	C₁₃×#331	C₂²	1	2	yes	—
47	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
50	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
51	C₁₃×2₋¹⁺⁴	—	4	4	no	—
52	C₁₃×2₋¹⁺⁴	—	4	4	no	—
53	C₂×C₁₃×#41	—	2	4	no	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂×C₁₃×#41	—	2	1	no	—
57	C₂×C₁₃×#41	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	2	no	—
59	C₂²×Q₈×C₁₃	—	2	2	no	—
60	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂²×C₈×C₁₃	—	2	1	no	—
65	C₂²×C₈×C₁₃	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₃×#127	—	2	2	no	—
72	C₁₃×#127	D₄	1	1	yes	characteristic
73	C₁₃×#127	C₂³	1	1	yes	characteristic
74	C₁₃×#125	—	2	1	no	—
75	C₁₃×#124	—	2	4	no	—
76	C₁₃×#124	—	2	1	no	—
77	C₁₃×#124	—	2	1	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×#121	—	2	4	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	4	no	—
87	C₁₃×#121	—	2	4	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	D₄	1	2	yes	—
92	C₁₃×#121	D₄	1	2	yes	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	D₄	1	2	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	D₄	1	2	yes	—
105	C₄×D₄×C₁₃	C₂³	1	2	yes	—
106	C₁₃×#117	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	—	2	1	no	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#107	—	2	2	no	—
112	C₁₃×#106	—	2	2	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×C₄⋊C₈	—	2	1	no	—
116	C₁₃×C₄⋊C₈	—	2	1	no	—
117	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#103	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	—	2	2	no	—
125	C₄×C₈×C₁₃	—	2	1	no	—
126	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
128	#18675	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₁₃×#41	—	4	16	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	4	8	no	—
132	C₁₃×#41	—	4	4	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₁₃×#41	—	4	2	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	4	4	no	—
145	C₂×Q₈×C₁₃	—	4	8	no	—
146	C₂×Q₈×C₁₃	—	4	4	no	—
147	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
148	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	4	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	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₁₃×SD₁₆	—	4	4	no	—
169	C₁₃×SD₁₆	—	8	2	no	—
170	C₁₃×M₁₆	—	4	2	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	4	2	no	—
176	C₂×C₈×C₁₃	—	8	1	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	2	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₄²×C₁₃	—	2	2	no	—
200	C₄²×C₁₃	—	2	2	no	—
201	C₄²×C₁₃	—	4	1	no	—
202	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
206	#3497	C₂×C₁₃	1	1	yes	characteristic
207	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1651	C₂×C₁₃	1	2	yes	complemented
211	#1642	C₂×C₁₃	1	2	yes	complemented
212	#1637	C₂×C₁₃	1	2	yes	complemented
213	#1631	C₂×C₁₃	1	2	yes	complemented
214	#1547	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	#120	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	2	no	—
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	4	8	no	—
223	Q₈×C₁₃	—	4	2	no	—
224	Q₈×C₁₃	—	4	1	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	—	4	2	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	—
230	D₄×C₁₃	—	2	2	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	4	8	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	4	4	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	8	1	no	—
242	D₄×C₁₃	—	8	4	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	8	no	—
252	C₂×C₄×C₁₃	—	4	8	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	8	1	no	—
259	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
263	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₈×C₁₃	—	2	2	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	2	no	—
270	C₈×C₁₃	—	4	2	no	—
271	C₂×2₋¹⁺⁴	—	2	1	no	—
272	#550	—	2	1	no	—
273	#550	C₂²×C₁₃	1	2	yes	—
274	D₄×Q₈	—	2	1	no	—
275	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
276	#548	—	2	2	no	—
277	#548	—	2	2	no	—
278	#537	—	2	2	no	—
279	#537	—	2	1	no	—
280	#533	C₂²×C₁₃	1	1	yes	characteristic
281	#532	—	2	2	no	—
282	#532	C₂²×C₁₃	1	1	yes	characteristic
283	#532	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
285	#498	C₂²×C₁₃	1	1	yes	characteristic
286	#492	C₂²×C₁₃	1	1	yes	characteristic
287	#487	C₂²×C₁₃	1	1	yes	characteristic
288	#486	C₂²×C₁₃	1	1	yes	characteristic
289	#479	—	2	2	no	—
290	#477	C₂²×C₁₃	1	2	yes	—
291	#476	C₂²×C₁₃	1	2	yes	—
292	#475	—	2	1	no	—
293	#475	C₂²×C₁₃	1	2	yes	—
294	#465	—	2	2	no	—
295	#465	—	2	2	no	—
296	#461	C₂²×C₁₃	1	2	yes	—
297	#460	—	2	1	no	—
298	C₄×SD₁₆	—	2	2	no	—
299	#428	—	2	1	no	—
300	#423	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
302	#419	—	2	1	no	—
303	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
304	#332	C₂²×C₁₃	1	2	yes	—
305	#331	C₂²×C₁₃	1	2	yes	—
306	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
307	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
308	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
309	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	#450	1	2	yes	—
319	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	2	no	—
326	C₄×C₁₃	—	4	2	no	—
327	C₄×C₁₃	—	8	1	no	—
328	C₄×C₁₃	—	8	1	no	—
329	C₄×C₁₃	#450	1	2	yes	—
330	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
331	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₄×C₁₃	#577	1	1	yes	characteristic
333	C₄×C₁₃	#578	1	1	yes	characteristic
334	2₋¹⁺⁴	—	4	4	no	—
335	2₋¹⁺⁴	—	4	4	no	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂²×Q₈	—	2	2	no	—
342	C₂²×Q₈	—	2	2	no	—
343	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	2	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
354	#127	—	2	2	no	—
355	#127	D₄×C₁₃	1	1	yes	characteristic
356	#127	C₂³×C₁₃	1	1	yes	characteristic
357	#125	—	2	1	no	—
358	#124	—	2	4	no	—
359	#124	—	2	1	no	—
360	#124	—	2	1	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	#121	—	2	4	no	—
368	#121	—	2	2	no	—
369	#121	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	2	no	—
374	#121	D₄×C₁₃	1	2	yes	—
375	#121	D₄×C₁₃	1	2	yes	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	D₄×C₁₃	1	2	yes	—
381	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	D₄×C₁₃	1	2	yes	—
388	C₄×D₄	C₂³×C₁₃	1	2	yes	—
389	#117	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	#107	—	2	2	no	—
395	#106	—	2	2	no	—
396	#106	—	2	2	no	—
397	#106	—	2	2	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
401	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
402	#103	—	2	2	no	—
403	#103	—	2	2	no	—
404	#103	—	2	2	no	—
405	#103	—	2	2	no	—
406	#102	—	2	2	no	—
407	#102	—	2	2	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₁₃	—	2	2	no	—
412	C₂×C₁₃	—	8	2	no	—
413	C₂×C₁₃	—	8	2	no	—
414	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
415	C₂×C₁₃	#3013	1	1	yes	characteristic
416	C₂×C₁₃	#3018	1	1	yes	characteristic
417	#41	—	4	16	no	—
418	#41	—	4	8	no	—
419	#41	—	4	4	no	—
420	#41	—	4	4	no	—
421	#41	—	4	2	no	—
422	#41	—	4	2	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	4	8	no	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×Q₈	—	4	4	no	—
435	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	complemented
436	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	SD₁₆	—	4	4	no	—
457	SD₁₆	—	8	2	no	—
458	M₁₆	—	4	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	4	2	no	—
464	C₂×C₈	—	8	1	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
479	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	4	1	no	—
490	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
494	C₁₃	#18675	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	C₁₃×#120	1	1	yes	characteristic
498	Q₈	—	2	4	no	—
499	Q₈	—	2	2	no	—
500	Q₈	—	4	8	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	C₂×C₁₃×SD₁₆	1	4	yes	—
508	D₄	—	2	2	no	—
509	D₄	—	2	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	8	1	no	—
520	D₄	—	8	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	8	1	no	—
537	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
538	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
539	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
540	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
541	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
545	C₈	—	2	2	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	2	no	—
548	C₈	—	4	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	C₁₃×#450	1	2	yes	—
558	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	4	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	C₁₃×#450	1	2	yes	—
569	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
570	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
571	C₄	C₁₃×#577	1	1	yes	characteristic
572	C₄	C₁₃×#578	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	2	no	—
576	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
577	C₂	C₁₃×#3013	1	1	yes	characteristic
578	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3497	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×#3246	C₂	semidirect
3. C₁₃×#3167	C₂	semidirect
4. C₁₃×#3078	C₂	semidirect
5. C₁₃×#1651	C₂	semidirect
6. C₁₃×#1642	C₂	semidirect
7. C₁₃×#1637	C₂	semidirect
8. C₁₃×#1631	C₂	semidirect
9. C₁₃×#1547	C₂	semidirect
10. C₁₃×#1492	C₂	semidirect
11. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
128. #18675	C₁₃	direct (N × H)
147. C₂×Q₈×C₁₃	SD₁₆	semidirect
207. #3246	C₂×C₁₃	semidirect
208. #3167	C₂×C₁₃	semidirect
209. #3078	C₂×C₁₃	semidirect
210. #1651	C₂×C₁₃	semidirect
211. #1642	C₂×C₁₃	semidirect
212. #1637	C₂×C₁₃	semidirect
213. #1631	C₂×C₁₃	semidirect
214. #1547	C₂×C₁₃	semidirect
215. #1492	C₂×C₁₃	semidirect
216. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
435. C₂×Q₈	C₁₃×SD₁₆	semidirect
494. C₁₃	#18675	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×#3497	2
C₁₃×#3246	2
C₁₃×#3167	2
C₁₃×#3078	2
C₁₃×#1651	2
C₁₃×#1642	2
C₁₃×#1637	2
C₁₃×#1631	2
C₁₃×#1547	2
C₁₃×#1492	2
C₂×C₁₃×Q₈⋊C₈	2
#18675	13

Subgroups — C13×#18675 #15705014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18675 #15705014