Subgroups — C₁₃×#19808 #15706147

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3335	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1716	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1679	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1654	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	—	2	1	no	—
17	C₁₃×#557	C₂²	1	1	yes	characteristic
18	C₁₃×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#547	C₂²	1	1	yes	characteristic
21	C₁₃×#499	—	2	1	no	—
22	C₁₃×#498	C₂²	1	1	yes	characteristic
23	C₁₃×#498	C₂²	1	1	yes	characteristic
24	C₁₃×#498	C₂²	1	1	yes	characteristic
25	C₁₃×#494	C₂²	1	1	yes	characteristic
26	C₁₃×#487	—	2	1	no	—
27	C₁₃×#487	C₂²	1	1	yes	characteristic
28	C₁₃×#487	C₂²	1	1	yes	characteristic
29	C₁₃×#483	—	2	1	no	—
30	C₁₃×#481	—	2	1	no	—
31	C₁₃×#479	—	2	1	no	—
32	C₁₃×#478	—	2	1	no	—
33	C₁₃×#477	C₂²	1	1	yes	characteristic
34	C₁₃×#476	C₂²	1	1	yes	characteristic
35	C₁₃×#475	—	2	1	no	—
36	C₁₃×#475	C₂²	1	1	yes	characteristic
37	C₁₃×#475	C₂²	1	1	yes	characteristic
38	C₁₃×#474	C₂²	1	1	yes	characteristic
39	C₁₃×#470	—	2	1	no	—
40	C₁₃×#465	—	2	1	no	—
41	C₁₃×#462	C₂²	1	1	yes	characteristic
42	C₁₃×#461	—	2	1	no	—
43	C₁₃×#461	C₂²	1	1	yes	characteristic
44	C₁₃×#461	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₁₃×#451	—	2	1	no	—
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×SD₁₆	—	2	1	no	—
50	C₄×C₁₃×SD₁₆	—	2	1	no	—
51	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
53	C₁₃×#436	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#106	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#332	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	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₁₃×#137	—	4	4	no	—
70	C₂×C₁₃×Q₁₆	—	2	1	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	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×M₁₆	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	—	4	1	no	—
88	C₁₃×#123	—	4	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	4	1	no	—
93	C₁₃×C₂²⋊Q₈	—	4	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×#106	—	2	1	no	—
110	C₁₃×#106	—	2	1	no	—
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	2	1	no	—
114	C₁₃×#106	—	4	1	no	—
115	C₁₃×#106	D₄	1	1	yes	characteristic
116	C₁₃×#106	D₄	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	4	1	no	—
132	C₁₃×#103	D₄	1	1	yes	characteristic
133	C₁₃×#103	D₄	1	1	yes	characteristic
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×#102	D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	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	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	#19808	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	4	1	no	—
153	C₂×Q₈×C₁₃	—	4	2	no	—
154	C₂×Q₈×C₁₃	—	8	1	no	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₁₃×Q₁₆	—	4	2	no	—
166	C₁₃×Q₁₆	—	4	2	no	—
167	C₁₃×Q₁₆	—	8	1	no	—
168	C₁₃×SD₁₆	—	4	1	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	4	2	no	—
171	C₁₃×SD₁₆	SD₁₆	1	4	yes	complemented
172	C₁₃×M₁₆	—	4	2	no	—
173	C₂×C₈×C₁₃	—	2	1	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	—	4	2	no	—
179	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	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	—	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	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	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	C₂⁴	1	1	yes	characteristic
213	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3335	C₂×C₁₃	1	1	yes	characteristic
216	#3276	C₂×C₁₃	1	1	yes	characteristic
217	#1716	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1691	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1679	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1672	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1670	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1654	C₂×C₁₃	1	1	yes	characteristic
223	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1643	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1637	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
227	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	8	2	no	—
240	Q₈×C₁₃	—	8	1	no	—
241	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	C₂×SD₁₆	1	2	yes	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	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	—	8	2	no	—
262	C₂×C₄×C₁₃	—	8	2	no	—
263	C₂×C₄×C₁₃	—	16	1	no	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	—	2	1	no	—
269	C₈×C₁₃	—	2	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
276	C₂×#137	—	2	1	no	—
277	#557	C₂²×C₁₃	1	1	yes	characteristic
278	#554	C₂²×C₁₃	1	1	yes	characteristic
279	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	#547	C₂²×C₁₃	1	1	yes	characteristic
281	#499	—	2	1	no	—
282	#498	C₂²×C₁₃	1	1	yes	characteristic
283	#498	C₂²×C₁₃	1	1	yes	characteristic
284	#498	C₂²×C₁₃	1	1	yes	characteristic
285	#494	C₂²×C₁₃	1	1	yes	characteristic
286	#487	—	2	1	no	—
287	#487	C₂²×C₁₃	1	1	yes	characteristic
288	#487	C₂²×C₁₃	1	1	yes	characteristic
289	#483	—	2	1	no	—
290	#481	—	2	1	no	—
291	#479	—	2	1	no	—
292	#478	—	2	1	no	—
293	#477	C₂²×C₁₃	1	1	yes	characteristic
294	#476	C₂²×C₁₃	1	1	yes	characteristic
295	#475	—	2	1	no	—
296	#475	C₂²×C₁₃	1	1	yes	characteristic
297	#475	C₂²×C₁₃	1	1	yes	characteristic
298	#474	C₂²×C₁₃	1	1	yes	characteristic
299	#470	—	2	1	no	—
300	#465	—	2	1	no	—
301	#462	C₂²×C₁₃	1	1	yes	characteristic
302	#461	—	2	1	no	—
303	#461	C₂²×C₁₃	1	1	yes	characteristic
304	#461	C₂²×C₁₃	1	1	yes	characteristic
305	#452	—	2	1	no	—
306	#451	—	2	1	no	—
307	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₄×SD₁₆	—	2	1	no	—
310	C₄×SD₁₆	—	2	1	no	—
311	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
312	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
313	#436	C₂²×C₁₃	1	1	yes	characteristic
314	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#106	—	2	1	no	—
316	#335	C₂²×C₁₃	1	1	yes	characteristic
317	#334	C₂²×C₁₃	1	1	yes	characteristic
318	#333	C₂²×C₁₃	1	1	yes	characteristic
319	#332	C₂²×C₁₃	1	1	yes	characteristic
320	#332	C₂²×C₁₃	1	1	yes	characteristic
321	#332	C₂²×C₁₃	1	1	yes	characteristic
322	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	#322	C₂²×C₁₃	1	1	yes	characteristic
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	D₄²	1	1	yes	characteristic
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
346	C₄×C₁₃	#575	1	1	yes	characteristic
347	C₄×C₁₃	#577	1	1	yes	characteristic
348	C₄×C₁₃	#578	1	1	yes	characteristic
349	C₂×#41	—	2	1	no	—
350	C₂²×Q₈	—	2	1	no	—
351	#137	—	4	4	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
358	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
359	C₂×M₁₆	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	#125	—	2	1	no	—
368	#125	—	2	1	no	—
369	#125	—	4	1	no	—
370	#123	—	4	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	4	1	no	—
375	C₂²⋊Q₈	—	4	1	no	—
376	#121	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	4	1	no	—
397	#106	D₄×C₁₃	1	1	yes	characteristic
398	#106	D₄×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	4	1	no	—
414	#103	D₄×C₁₃	1	1	yes	characteristic
415	#103	D₄×C₁₃	1	1	yes	characteristic
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	D₄×C₁₃	1	1	yes	characteristic
419	#102	D₄×C₁₃	1	1	yes	characteristic
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₁₃	—	4	2	no	—
428	C₂×C₁₃	—	8	1	no	—
429	C₂×C₁₃	#3269	1	1	yes	characteristic
430	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
431	C₂×C₁₃	#3289	1	1	yes	characteristic
432	#41	—	4	2	no	—
433	#41	—	8	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	—	4	2	no	—
440	C₂×Q₈	—	8	1	no	—
441	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	Q₁₆	—	4	2	no	—
452	Q₁₆	—	4	2	no	—
453	Q₁₆	—	8	1	no	—
454	SD₁₆	—	4	1	no	—
455	SD₁₆	—	4	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	C₁₃×SD₁₆	1	4	yes	complemented
458	M₁₆	—	4	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₄⋊C₄	—	2	1	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	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	4	1	no	—
498	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₁₃	#19808	1	1	yes	characteristic, direct product factor, Sylow
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	8	2	no	—
512	Q₈	—	8	1	no	—
513	Q₈	C₂×C₁₃×SD₁₆	1	2	yes	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	8	2	no	—
518	D₄	C₂×C₁₃×SD₁₆	1	2	yes	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	16	1	no	—
536	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	C₂×C₁₃×SD₁₆	1	2	yes	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	D₄²×C₁₃	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
567	C₄	C₁₃×#575	1	1	yes	characteristic
568	C₄	C₁₃×#577	1	1	yes	characteristic
569	C₄	C₁₃×#578	1	1	yes	characteristic
570	C₂	—	4	2	no	—
571	C₂	—	8	1	no	—
572	C₂	C₁₃×#3269	1	1	yes	characteristic
573	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
574	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#547	C₂²
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×#3381	C₂	semidirect
2. C₁₃×#3359	C₂	semidirect
5. C₁₃×#1716	C₂	semidirect
6. C₁₃×#1691	C₂	semidirect
7. C₁₃×#1679	C₂	semidirect
8. C₁₃×#1672	C₂	semidirect
9. C₁₃×#1670	C₂	semidirect
11. C₁₃×#1653	C₂	semidirect
12. C₁₃×#1643	C₂	semidirect
13. C₁₃×#1637	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
145. #19808	C₁₃	direct (N × H)
171. C₁₃×SD₁₆	SD₁₆	semidirect
213. #3381	C₂×C₁₃	semidirect
214. #3359	C₂×C₁₃	semidirect
217. #1716	C₂×C₁₃	semidirect
218. #1691	C₂×C₁₃	semidirect
219. #1679	C₂×C₁₃	semidirect
220. #1672	C₂×C₁₃	semidirect
221. #1670	C₂×C₁₃	semidirect
223. #1653	C₂×C₁₃	semidirect
224. #1643	C₂×C₁₃	semidirect
225. #1637	C₂×C₁₃	semidirect
226. #1583	C₂×C₁₃	semidirect
227. SD₁₆⋊C₈	C₂×C₁₃	semidirect
457. SD₁₆	C₁₃×SD₁₆	semidirect
499. C₁₃	#19808	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×#3381	2
C₁₃×#3359	2
C₁₃×#3335	2
C₁₃×#3276	2
C₁₃×#1716	2
C₁₃×#1691	2
C₁₃×#1679	2
C₁₃×#1672	2
C₁₃×#1670	2
C₁₃×#1654	2
C₁₃×#1653	2
C₁₃×#1643	2
C₁₃×#1637	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19808	13

Subgroups — C13×#19808 #15706147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19808 #15706147