Subgroups — C₁₃×#19879 #15706218

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1640	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1625	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	1	yes	characteristic
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#556	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#498	C₂²	1	1	yes	characteristic
22	C₁₃×#495	—	2	1	no	—
23	C₁₃×#495	—	2	1	no	—
24	C₁₃×#492	C₂²	1	1	yes	characteristic
25	C₁₃×#492	C₂²	1	1	yes	characteristic
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#484	—	2	1	no	—
30	C₁₃×#482	—	2	1	no	—
31	C₁₃×#475	C₂²	1	1	yes	characteristic
32	C₁₃×#474	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#468	—	2	1	no	—
35	C₁₃×#467	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#464	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#463	—	2	1	no	—
40	C₁₃×#462	C₂²	1	1	yes	characteristic
41	C₁₃×#462	C₂²	1	1	yes	characteristic
42	C₁₃×#462	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×SD₁₆	—	2	1	no	—
49	C₄×C₁₃×SD₁₆	—	2	1	no	—
50	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
52	C₁₃×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₁₃×#428	—	2	1	no	—
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#332	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	—	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×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×M₁₆	—	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×#127	C₂³	1	1	yes	characteristic
85	C₁₃×#126	—	4	1	no	—
86	C₁₃×#126	—	4	1	no	—
87	C₁₃×#124	—	2	1	no	—
88	C₁₃×#124	—	2	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×#123	—	4	1	no	—
92	C₁₃×#123	—	4	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×C₂²⋊Q₈	—	2	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	4	1	no	—
114	C₁₃×#106	D₄	1	1	yes	characteristic
115	C₁₃×#106	D₄	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	—	2	1	no	—
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	D₄	1	1	yes	characteristic
129	C₁₃×#103	D₄	1	1	yes	characteristic
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	4	1	no	—
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19879	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
146	C₁₃×#41	—	8	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₁₃×Q₁₆	—	8	1	no	—
163	C₁₃×Q₁₆	—	8	1	no	—
164	C₁₃×Q₁₆	—	8	1	no	—
165	C₁₃×SD₁₆	—	2	2	no	—
166	C₁₃×SD₁₆	—	4	1	no	—
167	C₁₃×SD₁₆	—	4	2	no	—
168	C₁₃×SD₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	8	1	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×D₈	—	8	1	no	—
172	C₁₃×D₈	—	8	1	no	—
173	C₁₃×M₁₆	—	4	2	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	8	1	no	—
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	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	C₁₃×C₂²⋊C₄	—	4	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	4	1	no	—
212	C₄²×C₁₃	—	4	1	no	—
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3353	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1714	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1685	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1674	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1640	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1625	C₂×C₁₃	1	1	yes	characteristic
227	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
228	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	8	1	no	—
251	D₄×C₁₃	—	8	2	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	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	—	8	2	no	—
266	C₂×C₄×C₁₃	—	16	1	no	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	#135	1	2	yes	—
279	#559	C₂²×C₁₃	1	1	yes	characteristic
280	#556	C₂²×C₁₃	1	1	yes	characteristic
281	#556	C₂²×C₁₃	1	1	yes	characteristic
282	#547	C₂²×C₁₃	1	1	yes	characteristic
283	#500	C₂²×C₁₃	1	1	yes	characteristic
284	#498	C₂²×C₁₃	1	1	yes	characteristic
285	#495	—	2	1	no	—
286	#495	—	2	1	no	—
287	#492	C₂²×C₁₃	1	1	yes	characteristic
288	#492	C₂²×C₁₃	1	1	yes	characteristic
289	#487	C₂²×C₁₃	1	1	yes	characteristic
290	#486	C₂²×C₁₃	1	1	yes	characteristic
291	#485	—	2	1	no	—
292	#484	—	2	1	no	—
293	#482	—	2	1	no	—
294	#475	C₂²×C₁₃	1	1	yes	characteristic
295	#474	C₂²×C₁₃	1	1	yes	characteristic
296	#474	C₂²×C₁₃	1	1	yes	characteristic
297	#468	—	2	1	no	—
298	#467	—	2	1	no	—
299	#464	—	2	1	no	—
300	#464	—	2	1	no	—
301	#463	—	2	1	no	—
302	#463	—	2	1	no	—
303	#462	C₂²×C₁₃	1	1	yes	characteristic
304	#462	C₂²×C₁₃	1	1	yes	characteristic
305	#462	C₂²×C₁₃	1	1	yes	characteristic
306	#459	C₂²×C₁₃	1	1	yes	characteristic
307	#459	C₂²×C₁₃	1	1	yes	characteristic
308	#452	—	2	1	no	—
309	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₄×SD₁₆	—	2	1	no	—
312	C₄×SD₁₆	—	2	1	no	—
313	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
315	#436	C₂²×C₁₃	1	1	yes	characteristic
316	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	#428	—	2	1	no	—
318	#416	—	2	1	no	—
319	#335	C₂²×C₁₃	1	1	yes	characteristic
320	#334	C₂²×C₁₃	1	1	yes	characteristic
321	#332	C₂²×C₁₃	1	1	yes	characteristic
322	#332	C₂²×C₁₃	1	1	yes	characteristic
323	#332	C₂²×C₁₃	1	1	yes	characteristic
324	#331	C₂²×C₁₃	1	1	yes	characteristic
325	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
327	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	#322	C₂²×C₁₃	1	1	yes	characteristic
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	8	1	no	—
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	D₄²	1	1	yes	characteristic
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
351	C₄×C₁₃	#575	1	1	yes	characteristic
352	C₄×C₁₃	#576	1	1	yes	characteristic
353	C₄×C₁₃	#577	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂×Q₁₆	—	2	1	no	—
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
363	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
364	C₂×D₈	—	2	1	no	—
365	C₂×D₈	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	#127	C₂³×C₁₃	1	1	yes	characteristic
372	#126	—	4	1	no	—
373	#126	—	4	1	no	—
374	#124	—	2	1	no	—
375	#124	—	2	1	no	—
376	#124	—	2	1	no	—
377	#124	—	2	1	no	—
378	#123	—	4	1	no	—
379	#123	—	4	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	#121	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	C₂³×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	C₂³×C₁₃	1	1	yes	characteristic
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	#107	—	2	1	no	—
396	#107	—	2	1	no	—
397	#107	—	2	1	no	—
398	#107	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	4	1	no	—
401	#106	D₄×C₁₃	1	1	yes	characteristic
402	#106	D₄×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	D₄×C₁₃	1	1	yes	characteristic
416	#103	D₄×C₁₃	1	1	yes	characteristic
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	4	1	no	—
422	#102	D₄×C₁₃	1	1	yes	characteristic
423	#102	D₄×C₁₃	1	1	yes	characteristic
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₁₃	—	8	1	no	—
432	C₂×C₁₃	—	8	1	no	—
433	C₂×C₁₃	—	16	1	no	—
434	C₂×C₁₃	#3268	1	1	yes	characteristic
435	C₂×C₁₃	#3284	1	1	yes	characteristic
436	C₂×C₁₃	#3289	1	1	yes	characteristic
437	#41	—	4	2	no	—
438	#41	—	8	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	Q₁₆	—	8	1	no	—
455	Q₁₆	—	8	1	no	—
456	Q₁₆	—	8	1	no	—
457	SD₁₆	—	2	2	no	—
458	SD₁₆	—	4	1	no	—
459	SD₁₆	—	4	2	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	8	1	no	—
462	SD₁₆	—	8	1	no	—
463	D₈	—	8	1	no	—
464	D₈	—	8	1	no	—
465	M₁₆	—	4	2	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	8	1	no	—
472	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₁₃	#19879	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	4	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	16	1	no	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	C₁₃×#135	1	2	yes	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	D₄²×C₁₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
578	C₄	C₁₃×#575	1	1	yes	characteristic
579	C₄	C₁₃×#576	1	1	yes	characteristic
580	C₄	C₁₃×#577	1	1	yes	characteristic
581	C₂	—	8	1	no	—
582	C₂	—	8	1	no	—
583	C₂	—	16	1	no	—
584	C₂	C₁₃×#3268	1	1	yes	characteristic
585	C₂	C₁₃×#3284	1	1	yes	characteristic
586	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#1625	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3394	C₂	semidirect
2. C₁₃×#3394	C₂	semidirect
3. C₁₃×#3353	C₂	semidirect
4. C₁₃×#3302	C₂	semidirect
5. C₁₃×#1714	C₂	semidirect
6. C₁₃×#1685	C₂	semidirect
7. C₁₃×#1680	C₂	semidirect
8. C₁₃×#1674	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1652	C₂	semidirect
11. C₁₃×#1652	C₂	semidirect
12. C₁₃×#1640	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19879	C₁₃	direct (N × H)
214. #3394	C₂×C₁₃	semidirect
215. #3394	C₂×C₁₃	semidirect
216. #3353	C₂×C₁₃	semidirect
217. #3302	C₂×C₁₃	semidirect
218. #1714	C₂×C₁₃	semidirect
219. #1685	C₂×C₁₃	semidirect
220. #1680	C₂×C₁₃	semidirect
221. #1674	C₂×C₁₃	semidirect
222. #1665	C₂×C₁₃	semidirect
223. #1652	C₂×C₁₃	semidirect
224. #1652	C₂×C₁₃	semidirect
225. #1640	C₂×C₁₃	semidirect
227. #1583	C₂×C₁₃	semidirect
228. SD₁₆⋊C₈	C₂×C₁₃	semidirect
506. C₁₃	#19879	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×#3394	2
C₁₃×#3353	2
C₁₃×#3302	2
C₁₃×#1714	2
C₁₃×#1685	2
C₁₃×#1680	2
C₁₃×#1674	2
C₁₃×#1665	2
C₁₃×#1652	2
C₁₃×#1640	2
C₁₃×#1625	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19879	13

Subgroups — C13×#19879 #15706218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19879 #15706218