Subgroups — C₁₃×#19412 #15705751

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1667	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1666	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1551	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#532	C₂²	1	1	yes	characteristic
17	C₁₃×#532	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₁₃×#493	C₂²	1	1	yes	characteristic
20	C₁₃×#492	C₂²	1	1	yes	characteristic
21	C₁₃×#487	C₂²	1	1	yes	characteristic
22	C₁₃×#486	C₂²	1	1	yes	characteristic
23	C₁₃×#482	—	2	1	no	—
24	C₁₃×#482	—	2	1	no	—
25	C₁₃×#477	C₂²	1	1	yes	characteristic
26	C₁₃×#476	C₂²	1	1	yes	characteristic
27	C₁₃×#475	C₂²	1	1	yes	characteristic
28	C₁₃×#474	C₂²	1	1	yes	characteristic
29	C₁₃×#463	—	2	1	no	—
30	C₁₃×#463	—	2	1	no	—
31	C₁₃×#460	C₂²	1	1	yes	characteristic
32	C₁₃×#460	C₂²	1	1	yes	characteristic
33	C₁₃×#459	C₂²	1	1	yes	characteristic
34	C₁₃×#459	C₂²	1	1	yes	characteristic
35	C₁₃×#449	—	2	1	no	—
36	C₁₃×#449	—	2	1	no	—
37	C₁₃×#449	—	2	1	no	—
38	C₁₃×#449	—	2	1	no	—
39	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#442	—	2	1	no	—
42	C₁₃×#440	—	2	1	no	—
43	C₄×C₁₃×SD₁₆	—	2	1	no	—
44	C₄×C₁₃×D₈	—	2	1	no	—
45	C₈×D₄×C₁₃	—	2	1	no	—
46	C₈×D₄×C₁₃	—	2	1	no	—
47	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#432	C₂²	1	1	yes	characteristic
50	C₁₃×#431	—	2	1	no	—
51	C₁₃×#431	C₂²	1	1	yes	characteristic
52	C₁₃×#431	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₃×#335	C₂²	1	1	yes	characteristic
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#334	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#333	C₂²	1	1	yes	characteristic
61	C₁₃×#332	C₂²	1	1	yes	characteristic
62	C₁₃×#332	C₂²	1	1	yes	characteristic
63	C₁₃×#331	C₂²	1	1	yes	characteristic
64	C₁₃×#331	C₂²	1	1	yes	characteristic
65	C₁₃×#331	C₂²	1	1	yes	characteristic
66	C₁₃×#331	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×#41	—	2	1	no	—
69	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×D₈	—	2	1	no	—
75	C₂×C₁₃×D₈	—	2	1	no	—
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×#127	C₂³	1	1	yes	characteristic
84	C₁₃×#127	C₂³	1	1	yes	characteristic
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×#124	—	2	1	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#117	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×C₄⋊C₈	—	2	1	no	—
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×C₂²⋊C₈	—	2	1	no	—
133	C₁₃×C₂²⋊C₈	—	2	1	no	—
134	C₁₃×C₂²⋊C₈	—	2	1	no	—
135	C₁₃×C₂²⋊C₈	—	2	1	no	—
136	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₃×#97	—	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	#19412	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	2	2	no	—
146	C₁₃×#41	—	2	2	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₁₃×#41	—	8	1	no	—
149	C₁₃×#41	—	8	2	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	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	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	1	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
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×D₈	—	4	2	no	—
176	C₁₃×D₈	—	4	2	no	—
177	C₁₃×D₈	—	8	1	no	—
178	C₁₃×D₈	—	8	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	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	8	1	no	—
186	C₂×C₈×C₁₃	—	8	1	no	—
187	C₂×C₈×C₁₃	—	8	1	no	—
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	#41	1	1	yes	characteristic
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1684	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1683	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1677	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1668	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1667	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1666	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1572	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1551	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1540	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	#121	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	8	1	no	—
237	Q₈×C₁₃	#135	1	2	yes	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	8	1	no	—
249	D₄×C₁₃	—	8	1	no	—
250	D₄×C₁₃	—	8	2	no	—
251	D₄×C₁₃	—	8	2	no	—
252	D₄×C₁₃	#135	1	2	yes	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	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	—	4	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	—	8	1	no	—
267	C₂×C₄×C₁₃	—	8	2	no	—
268	C₂×C₄×C₁₃	—	8	2	no	—
269	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
270	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
271	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	2	1	no	—
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	2	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	—	4	1	no	—
285	#532	C₂²×C₁₃	1	1	yes	characteristic
286	#532	C₂²×C₁₃	1	1	yes	characteristic
287	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
288	#493	C₂²×C₁₃	1	1	yes	characteristic
289	#492	C₂²×C₁₃	1	1	yes	characteristic
290	#487	C₂²×C₁₃	1	1	yes	characteristic
291	#486	C₂²×C₁₃	1	1	yes	characteristic
292	#482	—	2	1	no	—
293	#482	—	2	1	no	—
294	#477	C₂²×C₁₃	1	1	yes	characteristic
295	#476	C₂²×C₁₃	1	1	yes	characteristic
296	#475	C₂²×C₁₃	1	1	yes	characteristic
297	#474	C₂²×C₁₃	1	1	yes	characteristic
298	#463	—	2	1	no	—
299	#463	—	2	1	no	—
300	#460	C₂²×C₁₃	1	1	yes	characteristic
301	#460	C₂²×C₁₃	1	1	yes	characteristic
302	#459	C₂²×C₁₃	1	1	yes	characteristic
303	#459	C₂²×C₁₃	1	1	yes	characteristic
304	#449	—	2	1	no	—
305	#449	—	2	1	no	—
306	#449	—	2	1	no	—
307	#449	—	2	1	no	—
308	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	#442	—	2	1	no	—
311	#440	—	2	1	no	—
312	C₄×SD₁₆	—	2	1	no	—
313	C₄×D₈	—	2	1	no	—
314	C₈×D₄	—	2	1	no	—
315	C₈×D₄	—	2	1	no	—
316	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
318	#432	C₂²×C₁₃	1	1	yes	characteristic
319	#431	—	2	1	no	—
320	#431	C₂²×C₁₃	1	1	yes	characteristic
321	#431	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₈	—	2	1	no	—
323	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	#335	C₂²×C₁₃	1	1	yes	characteristic
325	#335	C₂²×C₁₃	1	1	yes	characteristic
326	#334	C₂²×C₁₃	1	1	yes	characteristic
327	#334	C₂²×C₁₃	1	1	yes	characteristic
328	#333	C₂²×C₁₃	1	1	yes	characteristic
329	#333	C₂²×C₁₃	1	1	yes	characteristic
330	#332	C₂²×C₁₃	1	1	yes	characteristic
331	#332	C₂²×C₁₃	1	1	yes	characteristic
332	#331	C₂²×C₁₃	1	1	yes	characteristic
333	#331	C₂²×C₁₃	1	1	yes	characteristic
334	#331	C₂²×C₁₃	1	1	yes	characteristic
335	#331	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×C₁₃	—	2	1	no	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
359	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
360	C₄×C₁₃	#576	1	1	yes	characteristic
361	C₄×C₁₃	#577	1	1	yes	characteristic
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×D₈	—	2	1	no	—
370	C₂×D₈	—	2	1	no	—
371	C₂×D₈	—	2	1	no	—
372	C₂×D₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	#127	C₂³×C₁₃	1	1	yes	characteristic
379	#127	C₂³×C₁₃	1	1	yes	characteristic
380	#124	—	2	1	no	—
381	#124	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
387	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	#117	—	2	1	no	—
397	#117	D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	#107	—	2	1	no	—
401	#107	—	2	1	no	—
402	#106	—	2	1	no	—
403	#106	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
432	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
433	#97	—	2	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₁₃	—	4	1	no	—
440	C₂×C₁₃	—	4	2	no	—
441	C₂×C₁₃	—	16	1	no	—
442	C₂×C₁₃	—	16	1	no	—
443	C₂×C₁₃	#3045	1	1	yes	characteristic
444	C₂×C₁₃	#3050	1	1	yes	characteristic
445	C₂×C₁₃	#3068	1	1	yes	characteristic
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	8	1	no	—
449	#41	—	8	1	no	—
450	#41	—	8	2	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
472	SD₁₆	—	4	2	no	—
473	SD₁₆	—	4	2	no	—
474	SD₁₆	—	8	1	no	—
475	SD₁₆	—	8	1	no	—
476	D₈	—	4	2	no	—
477	D₈	—	4	2	no	—
478	D₈	—	8	1	no	—
479	D₈	—	8	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	8	1	no	—
487	C₂×C₈	—	8	1	no	—
488	C₂×C₈	—	8	1	no	—
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄²	C₁₃×#41	1	1	yes	characteristic
514	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
515	C₁₃	#19412	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	C₁₃×#121	1	1	yes	characteristic
520	Q₈	—	2	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	8	1	no	—
524	Q₈	C₁₃×#135	1	2	yes	—
525	D₄	—	2	4	no	—
526	D₄	—	2	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	2	no	—
539	D₄	C₁₃×#135	1	2	yes	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	8	2	no	—
556	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
557	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
558	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
595	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
596	C₄	C₁₃×#576	1	1	yes	characteristic
597	C₄	C₁₃×#577	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	16	1	no	—
601	C₂	—	16	1	no	—
602	C₂	C₁₃×#3045	1	1	yes	characteristic
603	C₂	C₁₃×#3050	1	1	yes	characteristic
604	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
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
1. C₁₃×#3207	C₂	semidirect
2. C₁₃×#3115	C₂	semidirect
3. C₁₃×#3106	C₂	semidirect
4. C₁₃×#2988	C₂	semidirect
5. C₁₃×#1684	C₂	semidirect
6. C₁₃×#1683	C₂	semidirect
7. C₁₃×#1678	C₂	semidirect
8. C₁₃×#1677	C₂	semidirect
9. C₁₃×#1668	C₂	semidirect
10. C₁₃×#1667	C₂	semidirect
11. C₁₃×#1666	C₂	semidirect
12. C₁₃×#1665	C₂	semidirect
13. C₁₃×#1572	C₂	semidirect
14. C₁₃×#1551	C₂	semidirect
15. C₁₃×#1540	C₂	semidirect
144. #19412	C₁₃	direct (N × H)
214. #3207	C₂×C₁₃	semidirect
215. #3115	C₂×C₁₃	semidirect
216. #3106	C₂×C₁₃	semidirect
217. #2988	C₂×C₁₃	semidirect
218. #1684	C₂×C₁₃	semidirect
219. #1683	C₂×C₁₃	semidirect
220. #1678	C₂×C₁₃	semidirect
221. #1677	C₂×C₁₃	semidirect
222. #1668	C₂×C₁₃	semidirect
223. #1667	C₂×C₁₃	semidirect
224. #1666	C₂×C₁₃	semidirect
225. #1665	C₂×C₁₃	semidirect
226. #1572	C₂×C₁₃	semidirect
227. #1551	C₂×C₁₃	semidirect
228. #1540	C₂×C₁₃	semidirect
515. C₁₃	#19412	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×#3207	2
C₁₃×#3115	2
C₁₃×#3106	2
C₁₃×#2988	2
C₁₃×#1684	2
C₁₃×#1683	2
C₁₃×#1678	2
C₁₃×#1677	2
C₁₃×#1668	2
C₁₃×#1667	2
C₁₃×#1666	2
C₁₃×#1665	2
C₁₃×#1572	2
C₁₃×#1551	2
C₁₃×#1540	2
#19412	13

Subgroups — C13×#19412 #15705751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19412 #15705751