Subgroups — C₁₃×#18757 #15705096

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1654	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1635	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₁₃×#547	—	2	2	no	—
12	C₁₃×#547	—	2	2	no	—
13	C₁₃×#547	—	2	2	no	—
14	C₁₃×#547	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#123	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×#121	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₁₃×#498	C₂²	1	2	yes	complemented
24	C₁₃×#487	C₂²	1	2	yes	complemented
25	C₁₃×#483	—	2	1	no	—
26	C₁₃×#483	—	2	2	no	—
27	C₁₃×#478	—	2	2	no	—
28	C₁₃×#476	C₂²	1	2	yes	complemented
29	C₁₃×#476	C₂²	1	2	yes	complemented
30	C₁₃×#475	—	2	2	no	—
31	C₁₃×#474	C₂²	1	2	yes	complemented
32	C₁₃×#461	C₂²	1	2	yes	complemented
33	C₁₃×#450	—	2	1	no	—
34	C₄×C₁₃×SD₁₆	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₁₃×#428	—	2	1	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#418	—	2	1	no	—
40	C₁₃×#332	C₂²	1	4	yes	complemented
41	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	—	4	4	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₃×#125	—	2	1	no	—
63	C₁₃×#123	—	2	8	no	—
64	C₁₃×#123	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	4	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	—	2	1	no	—
69	C₁₃×#121	—	2	4	no	—
70	C₁₃×#121	—	2	4	no	—
71	C₄×Q₈×C₁₃	—	2	1	no	—
72	C₄×Q₈×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	—	2	1	no	—
75	C₄×D₄×C₁₃	—	2	1	no	—
76	C₄×D₄×C₁₃	—	2	1	no	—
77	C₄×D₄×C₁₃	D₄	1	2	yes	—
78	C₄×D₄×C₁₃	D₄	1	2	yes	—
79	C₄×D₄×C₁₃	C₂³	1	2	yes	—
80	C₄×D₄×C₁₃	C₂³	1	2	yes	—
81	C₁₃×#117	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#107	—	2	2	no	—
94	C₁₃×#106	—	2	2	no	—
95	C₁₃×#106	—	2	2	no	—
96	C₁₃×#106	—	2	4	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
100	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
101	C₁₃×#103	—	2	2	no	—
102	C₁₃×#103	—	2	4	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×C₂²⋊C₈	—	2	1	no	—
107	C₁₃×C₂²⋊C₈	—	2	1	no	—
108	C₄×C₈×C₁₃	—	2	1	no	—
109	C₄×C₈×C₁₃	C₂³	1	2	yes	—
110	#18757	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	1	no	—
112	C₂⁴×C₁₃	—	2	1	no	—
113	C₁₃×#41	—	4	8	no	—
114	C₁₃×#41	—	4	16	no	—
115	C₁₃×#41	—	4	8	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	4	2	no	—
121	C₂×Q₈×C₁₃	—	4	2	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	4	8	no	—
128	C₂×D₄×C₁₃	SD₁₆	1	4	yes	complemented
129	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	—	2	8	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	4	4	no	—
140	C₂²×C₄×C₁₃	—	4	8	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×SD₁₆	—	4	4	no	—
147	C₁₃×M₁₆	—	4	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	4	1	no	—
162	C₁₃×C₄⋊C₄	—	4	1	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	1	no	—
172	C₄²×C₁₃	—	4	1	no	—
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
178	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1654	C₂×C₁₃	1	4	yes	complemented
182	#1635	C₂×C₁₃	1	4	yes	complemented
183	#1546	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1486	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1478	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	4	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	#120	1	1	yes	characteristic
195	Q₈×C₁₃	—	4	2	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	Q₈×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	2	2	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	4	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	4	16	no	—
206	D₄×C₁₃	C₂×SD₁₆	1	4	yes	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	16	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
227	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₁₃	—	4	2	no	—
232	C₈×C₁₃	—	4	2	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₂²×#41	—	2	1	no	—
235	#547	—	2	2	no	—
236	#547	—	2	2	no	—
237	#547	—	2	2	no	—
238	#547	C₂²×C₁₃	1	4	yes	—
239	#533	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#123	—	2	2	no	—
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	C₂×#121	—	2	1	no	—
244	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	—	2	1	no	—
247	#498	C₂²×C₁₃	1	2	yes	complemented
248	#487	C₂²×C₁₃	1	2	yes	complemented
249	#483	—	2	1	no	—
250	#483	—	2	2	no	—
251	#478	—	2	2	no	—
252	#476	C₂²×C₁₃	1	2	yes	complemented
253	#476	C₂²×C₁₃	1	2	yes	complemented
254	#475	—	2	2	no	—
255	#474	C₂²×C₁₃	1	2	yes	complemented
256	#461	C₂²×C₁₃	1	2	yes	complemented
257	#450	—	2	1	no	—
258	C₄×SD₁₆	—	2	2	no	—
259	#431	C₂²×C₁₃	1	1	yes	characteristic
260	#431	C₂²×C₁₃	1	1	yes	characteristic
261	#428	—	2	1	no	—
262	#423	C₂²×C₁₃	1	1	yes	characteristic
263	#418	—	2	1	no	—
264	#332	C₂²×C₁₃	1	4	yes	complemented
265	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
266	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	4	no	—
270	C₂²×C₁₃	—	4	8	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	8	4	no	—
277	C₂²×C₁₃	#450	1	2	yes	—
278	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	4	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	8	1	no	—
286	C₄×C₁₃	—	8	1	no	—
287	C₄×C₁₃	#450	1	2	yes	—
288	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
289	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₄×C₁₃	#575	1	2	yes	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	4	4	no	—
294	C₂×#41	—	4	4	no	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
310	#125	—	2	1	no	—
311	#123	—	2	8	no	—
312	#123	—	2	8	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	#121	—	2	4	no	—
318	#121	—	2	4	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	D₄×C₁₃	1	2	yes	—
326	C₄×D₄	D₄×C₁₃	1	2	yes	—
327	C₄×D₄	C₂³×C₁₃	1	2	yes	—
328	C₄×D₄	C₂³×C₁₃	1	2	yes	—
329	#117	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	#106	—	2	2	no	—
343	#106	—	2	2	no	—
344	#106	—	2	4	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
348	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
349	#103	—	2	2	no	—
350	#103	—	2	4	no	—
351	#102	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	C₂²⋊C₈	—	2	1	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	C₂³×C₁₃	1	2	yes	—
358	C₂×C₁₃	—	2	2	no	—
359	C₂×C₁₃	—	4	4	no	—
360	C₂×C₁₃	—	8	2	no	—
361	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
362	C₂×C₁₃	#3005	1	1	yes	characteristic
363	C₂×C₁₃	#3020	1	1	yes	characteristic
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	2	1	no	—
366	#41	—	4	16	no	—
367	#41	—	4	8	no	—
368	#41	—	4	8	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	4	2	no	—
374	C₂×Q₈	—	4	2	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	C₁₃×SD₁₆	1	4	yes	complemented
382	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	SD₁₆	—	4	4	no	—
400	M₁₆	—	4	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
417	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
418	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	4	1	no	—
425	C₄²	—	4	1	no	—
426	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₁₃	#18757	1	1	yes	characteristic, direct product factor, Sylow
431	C₂³	—	2	4	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	C₁₃×#120	1	1	yes	characteristic
440	Q₈	—	4	2	no	—
441	Q₈	—	4	4	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	16	no	—
451	D₄	C₂×C₁₃×SD₁₆	1	4	yes	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	16	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
470	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
472	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	4	8	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	8	4	no	—
489	C₂²	C₁₃×#450	1	2	yes	—
490	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	C₁₃×#450	1	2	yes	—
500	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
501	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
502	C₄	C₁₃×#575	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	4	4	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
507	C₂	C₁₃×#3005	1	1	yes	characteristic
508	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#547	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×#3229	C₂	semidirect
3. C₁₃×#3101	C₂	semidirect
4. C₁₃×#3077	C₂	semidirect
5. C₁₃×#1654	C₂	semidirect
6. C₁₃×#1635	C₂	semidirect
7. C₁₃×#1546	C₂	semidirect
8. C₁₃×#1486	C₂	semidirect
9. C₁₃×#1478	C₂	semidirect
23. C₁₃×#498	C₂²	semidirect
24. C₁₃×#487	C₂²	semidirect
28. C₁₃×#476	C₂²	semidirect
29. C₁₃×#476	C₂²	semidirect
31. C₁₃×#474	C₂²	semidirect
32. C₁₃×#461	C₂²	semidirect
40. C₁₃×#332	C₂²	semidirect
41. C₁₃×D₄⋊C₈	C₂²	semidirect
42. C₁₃×D₄⋊C₈	C₂²	semidirect
110. #18757	C₁₃	direct (N × H)
128. C₂×D₄×C₁₃	SD₁₆	semidirect
178. #3229	C₂×C₁₃	semidirect
179. #3101	C₂×C₁₃	semidirect
180. #3077	C₂×C₁₃	semidirect
181. #1654	C₂×C₁₃	semidirect
182. #1635	C₂×C₁₃	semidirect
183. #1546	C₂×C₁₃	semidirect
184. #1486	C₂×C₁₃	semidirect
185. #1478	C₂×C₁₃	semidirect
247. #498	C₂²×C₁₃	semidirect
248. #487	C₂²×C₁₃	semidirect
252. #476	C₂²×C₁₃	semidirect
253. #476	C₂²×C₁₃	semidirect
255. #474	C₂²×C₁₃	semidirect
256. #461	C₂²×C₁₃	semidirect
264. #332	C₂²×C₁₃	semidirect
265. D₄⋊C₈	C₂²×C₁₃	semidirect
266. D₄⋊C₈	C₂²×C₁₃	semidirect
381. C₂×D₄	C₁₃×SD₁₆	semidirect
430. C₁₃	#18757	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#547	2
C₁₃×#3229	2
C₁₃×#3101	2
C₁₃×#3077	2
C₁₃×#1654	2
C₁₃×#1635	2
C₁₃×#1546	2
C₁₃×#1486	2
C₁₃×#1478	2
#18757	13

Subgroups — C13×#18757 #15705096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18757 #15705096