Subgroups — C₁₃×#32974 #15719313

Order 3328.

1186 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1860	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1859	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1806	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₁₃×#520	—	2	2	no	—
15	C₁₃×#520	—	2	2	no	—
16	C₁₃×#520	C₂²	1	2	yes	—
17	C₁₃×#519	—	2	2	no	—
18	C₁₃×#519	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×#41	—	2	2	no	—
20	C₄×C₁₃×#41	—	2	2	no	—
21	C₄×C₁₃×#41	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#479	—	2	2	no	—
25	C₁₃×#479	—	2	2	no	—
26	C₁₃×#478	—	2	2	no	—
27	C₁₃×#478	—	2	2	no	—
28	C₁₃×#428	C₂²	1	2	yes	—
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#423	C₂²	1	2	yes	—
31	C₂×C₁₃×#104	C₂²	1	2	yes	—
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#417	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
37	C₁₃×#398	—	2	2	no	—
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#387	—	2	2	no	—
41	C₁₃×#384	C₂²	1	1	yes	characteristic
42	C₁₃×#382	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₁₃×#343	C₂²	1	2	yes	—
45	C₁₃×#339	C₂²	1	2	yes	—
46	C₁₃×#339	C₂²	1	2	yes	—
47	C₁₃×2₋¹⁺⁴	—	2	4	no	—
48	C₁₃×2₋¹⁺⁴	—	2	2	no	—
49	C₁₃×2₋¹⁺⁴	Q₈	1	4	yes	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₁₃×#125	—	2	2	no	—
58	C₁₃×#125	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	4	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	D₄	1	2	yes	—
68	C₄×Q₈×C₁₃	D₄	1	2	yes	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	4	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	4	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	D₄	1	2	yes	—
77	C₄×D₄×C₁₃	D₄	1	2	yes	—
78	C₁₃×#117	—	2	4	no	—
79	C₁₃×#117	—	2	4	no	—
80	C₁₃×#117	—	2	2	no	—
81	C₁₃×#117	—	2	2	no	—
82	C₁₃×#117	—	2	2	no	—
83	C₁₃×#117	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	—	2	4	no	—
95	C₂×C₄²×C₁₃	—	2	2	no	—
96	C₂×C₄²×C₁₃	D₄	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	2	no	—
101	C₁₃×#107	—	2	2	no	—
102	C₁₃×#106	—	2	2	no	—
103	C₁₃×#106	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×#104	—	2	4	no	—
107	C₁₃×#104	—	2	4	no	—
108	C₁₃×#103	—	2	2	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#101	—	2	2	no	—
113	C₁₃×#101	—	2	2	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	2	no	—
116	C₁₃×#95	—	2	2	no	—
117	C₁₃×#95	—	2	2	no	—
118	#32974	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₁₃×#41	—	2	8	no	—
120	C₁₃×#41	—	2	8	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₁₃×#41	—	2	8	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	C₂×Q₈	1	4	yes	—
126	C₁₃×#41	#41	1	4	yes	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	8	no	—
129	C₂×Q₈×C₁₃	—	2	8	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
134	C₂×Q₈×C₁₃	#41	1	2	yes	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	2	2	no	—
155	C₁₃×M₁₆	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	—	4	4	no	—
169	C₁₃×C₄⋊C₄	—	4	1	no	—
170	C₁₃×C₄⋊C₄	—	4	1	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₄²×C₁₃	—	2	4	no	—
179	C₄²×C₁₃	—	2	4	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	2	2	no	—
185	C₄²×C₁₃	—	2	2	no	—
186	C₄²×C₁₃	—	2	2	no	—
187	C₄²×C₁₃	C₂×D₄	1	2	yes	—
188	C₄²×C₁₃	C₂×D₄	1	2	yes	—
189	C₄×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic
190	#3080	C₂×C₁₃	1	2	yes	complemented
191	#2565	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1860	C₂×C₁₃	1	2	yes	complemented
193	#1859	C₂×C₁₃	1	2	yes	complemented
194	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#1806	C₂×C₁₃	1	2	yes	complemented
197	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1793	C₂×C₁₃	1	1	yes	characteristic
199	#1793	C₂×C₁₃	1	1	yes	characteristic
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₁₃	—	2	8	no	—
203	Q₈×C₁₃	—	2	4	no	—
204	Q₈×C₁₃	—	2	2	no	—
205	Q₈×C₁₃	—	2	4	no	—
206	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
207	D₄×C₁₃	—	2	8	no	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	2	4	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
212	C₂×C₄×C₁₃	—	2	16	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	8	2	no	—
236	C₂×C₄×C₁₃	—	8	4	no	—
237	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#120	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
245	C₈×C₁₃	—	4	2	no	—
246	C₈×C₁₃	—	4	2	no	—
247	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
249	#520	—	2	2	no	—
250	#520	—	2	2	no	—
251	#520	C₂²×C₁₃	1	2	yes	—
252	#519	—	2	2	no	—
253	#519	C₂²×C₁₃	1	1	yes	characteristic
254	C₄×#41	—	2	2	no	—
255	C₄×#41	—	2	2	no	—
256	C₄×#41	C₂²×C₁₃	1	2	yes	—
257	C₂×C₄×Q₈	—	2	2	no	—
258	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
259	#479	—	2	2	no	—
260	#479	—	2	2	no	—
261	#478	—	2	2	no	—
262	#478	—	2	2	no	—
263	#428	C₂²×C₁₃	1	2	yes	—
264	#428	C₂²×C₁₃	1	2	yes	—
265	#423	C₂²×C₁₃	1	2	yes	—
266	C₂×#104	C₂²×C₁₃	1	2	yes	—
267	C₂×#104	C₂²×C₁₃	1	2	yes	—
268	#417	C₂²×C₁₃	1	2	yes	—
269	#417	C₂²×C₁₃	1	2	yes	—
270	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
272	#398	—	2	2	no	—
273	#391	C₂²×C₁₃	1	1	yes	characteristic
274	#391	C₂²×C₁₃	1	1	yes	characteristic
275	#387	—	2	2	no	—
276	#384	C₂²×C₁₃	1	1	yes	characteristic
277	#382	C₂²×C₁₃	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
279	#343	C₂²×C₁₃	1	2	yes	—
280	#339	C₂²×C₁₃	1	2	yes	—
281	#339	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
288	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
289	C₂²×C₁₃	#525	1	1	yes	characteristic
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	2	4	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	4	2	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	—	8	1	no	—
301	C₄×C₁₃	—	8	1	no	—
302	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
303	C₄×C₁₃	#525	1	2	yes	—
304	2₋¹⁺⁴	—	2	4	no	—
305	2₋¹⁺⁴	—	2	2	no	—
306	2₋¹⁺⁴	Q₈×C₁₃	1	4	yes	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	C₂³×C₁₃	1	2	yes	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
313	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
314	#125	—	2	2	no	—
315	#125	—	2	2	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	D₄×C₁₃	1	2	yes	—
325	C₄×Q₈	D₄×C₁₃	1	2	yes	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	D₄×C₁₃	1	2	yes	—
334	C₄×D₄	D₄×C₁₃	1	2	yes	—
335	#117	—	2	4	no	—
336	#117	—	2	4	no	—
337	#117	—	2	2	no	—
338	#117	—	2	2	no	—
339	#117	—	2	2	no	—
340	#117	C₂³×C₁₃	1	2	yes	—
341	C₂×C₄⋊C₄	—	2	4	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₄²	—	2	4	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	D₄×C₁₃	1	2	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	#107	—	2	2	no	—
358	#107	—	2	2	no	—
359	#106	—	2	2	no	—
360	#106	—	2	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	—	2	2	no	—
363	#104	—	2	4	no	—
364	#104	—	2	4	no	—
365	#103	—	2	2	no	—
366	#103	—	2	2	no	—
367	#102	—	2	2	no	—
368	#102	—	2	2	no	—
369	#101	—	2	2	no	—
370	#101	—	2	2	no	—
371	#95	—	2	1	no	—
372	#95	—	2	2	no	—
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₂×C₁₃	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	—	4	4	no	—
378	C₂×C₁₃	#2848	1	1	yes	characteristic
379	C₂×C₁₃	#3018	1	1	yes	characteristic
380	C₂×C₁₃	#3020	1	1	yes	characteristic
381	#41	—	2	8	no	—
382	#41	—	2	8	no	—
383	#41	—	2	8	no	—
384	#41	—	2	8	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	C₂×Q₈×C₁₃	1	4	yes	—
388	#41	C₁₃×#41	1	4	yes	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	8	no	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
395	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
396	C₂×Q₈	C₁₃×#41	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	4	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	C₂×D₄×C₁₃	1	2	yes	—
450	C₄²	C₂×D₄×C₁₃	1	2	yes	—
451	C₁₃	#32974	1	1	yes	characteristic, direct product factor, Sylow
452	C₂³	—	2	2	no	—
453	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	Q₈	—	2	8	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	4	no	—
458	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
459	D₄	—	2	8	no	—
460	D₄	—	2	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	2	no	—
463	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
464	C₂×C₄	—	2	16	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	—	8	4	no	—
489	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
490	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
491	C₂×C₄	C₁₃×#120	1	2	yes	—
492	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
496	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
497	C₈	—	4	2	no	—
498	C₈	—	4	2	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
505	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
506	C₂²	C₁₃×#525	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	4	no	—
511	C₄	—	2	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
520	C₄	C₁₃×#525	1	2	yes	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	4	no	—
524	C₂	C₁₃×#2848	1	1	yes	characteristic
525	C₂	C₁₃×#3018	1	1	yes	characteristic
526	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3080	C₂	semidirect
3. C₁₃×#2565	C₂	semidirect
4. C₁₃×#1860	C₂	semidirect
5. C₁₃×#1859	C₂	semidirect
6. C₁₃×#1857	C₂	semidirect
7. C₁₃×#1857	C₂	semidirect
8. C₁₃×#1806	C₂	semidirect
9. C₁₃×#1801	C₂	semidirect
118. #32974	C₁₃	direct (N × H)
190. #3080	C₂×C₁₃	semidirect
191. #2565	C₂×C₁₃	semidirect
192. #1860	C₂×C₁₃	semidirect
193. #1859	C₂×C₁₃	semidirect
194. #1857	C₂×C₁₃	semidirect
195. #1857	C₂×C₁₃	semidirect
196. #1806	C₂×C₁₃	semidirect
197. #1801	C₂×C₁₃	semidirect
451. C₁₃	#32974	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×2₋¹⁺⁴	2
C₁₃×#3080	2
C₁₃×#2565	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1857	2
C₁₃×#1806	2
C₁₃×#1801	2
C₁₃×#1793	2
#32974	13

Subgroups — C13×#32974 #15719313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32974 #15719313