Subgroups — C₁₃×#19863 #15706202

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1673	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#556	C₂²	1	1	yes	characteristic
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#555	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#500	C₂²	1	1	yes	characteristic
22	C₁₃×#498	C₂²	1	1	yes	characteristic
23	C₁₃×#495	—	2	1	no	—
24	C₁₃×#494	C₂²	1	1	yes	characteristic
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#484	—	2	1	no	—
30	C₁₃×#482	—	2	1	no	—
31	C₁₃×#482	—	2	1	no	—
32	C₁₃×#477	C₂²	1	1	yes	characteristic
33	C₁₃×#476	C₂²	1	1	yes	characteristic
34	C₁₃×#475	C₂²	1	1	yes	characteristic
35	C₁₃×#474	C₂²	1	1	yes	characteristic
36	C₁₃×#474	C₂²	1	1	yes	characteristic
37	C₁₃×#468	—	2	1	no	—
38	C₁₃×#465	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#464	—	2	1	no	—
41	C₁₃×#464	—	2	1	no	—
42	C₁₃×#461	C₂²	1	1	yes	characteristic
43	C₁₃×#461	C₂²	1	1	yes	characteristic
44	C₁₃×#461	C₂²	1	1	yes	characteristic
45	C₁₃×#449	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×Q₁₆	—	2	1	no	—
48	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
50	C₁₃×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₁₃×#428	—	2	1	no	—
54	C₁₃×#427	—	2	1	no	—
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#335	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×D₄⋊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×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×#126	—	4	1	no	—
83	C₁₃×#126	—	4	1	no	—
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×#124	—	4	1	no	—
87	C₁₃×#123	—	4	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#117	—	2	1	no	—
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#117	—	2	1	no	—
103	C₁₃×#117	—	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×#107	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	4	1	no	—
111	C₁₃×#107	D₄	1	1	yes	characteristic
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	2	1	no	—
114	C₁₃×#106	—	2	1	no	—
115	C₁₃×#106	—	2	1	no	—
116	C₁₃×#106	D₄	1	1	yes	characteristic
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	—	2	1	no	—
129	C₁₃×#103	—	4	1	no	—
130	C₁₃×#103	D₄	1	1	yes	characteristic
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	D₄	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₈	—	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	#19863	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	—	2	1	no	—
151	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	4	1	no	—
153	C₂×D₄×C₁₃	—	4	1	no	—
154	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₁₃×Q₁₆	—	4	2	no	—
162	C₁₃×Q₁₆	—	8	1	no	—
163	C₁₃×SD₁₆	—	2	2	no	—
164	C₁₃×SD₁₆	—	8	1	no	—
165	C₁₃×SD₁₆	—	8	1	no	—
166	C₁₃×SD₁₆	—	8	1	no	—
167	C₁₃×D₈	—	4	1	no	—
168	C₁₃×M₁₆	—	4	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	4	2	no	—
175	C₂×C₈×C₁₃	—	8	1	no	—
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	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	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	4	1	no	—
208	C₄²×C₁₃	—	4	1	no	—
209	C₄²×C₁₃	—	4	1	no	—
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3353	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3303	C₂×C₁₃	1	1	yes	characteristic
215	#1723	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1691	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1684	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1673	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1669	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1650	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1647	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1646	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
225	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	Q₈×C₁₃	—	4	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	—	8	1	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	8	2	no	—
245	D₄×C₁₃	—	16	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
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	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	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	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	#135	1	2	yes	—
274	#556	C₂²×C₁₃	1	1	yes	characteristic
275	#556	C₂²×C₁₃	1	1	yes	characteristic
276	#555	C₂²×C₁₃	1	1	yes	characteristic
277	#547	C₂²×C₁₃	1	1	yes	characteristic
278	#500	C₂²×C₁₃	1	1	yes	characteristic
279	#500	C₂²×C₁₃	1	1	yes	characteristic
280	#498	C₂²×C₁₃	1	1	yes	characteristic
281	#495	—	2	1	no	—
282	#494	C₂²×C₁₃	1	1	yes	characteristic
283	#487	C₂²×C₁₃	1	1	yes	characteristic
284	#487	C₂²×C₁₃	1	1	yes	characteristic
285	#485	—	2	1	no	—
286	#485	—	2	1	no	—
287	#484	—	2	1	no	—
288	#482	—	2	1	no	—
289	#482	—	2	1	no	—
290	#477	C₂²×C₁₃	1	1	yes	characteristic
291	#476	C₂²×C₁₃	1	1	yes	characteristic
292	#475	C₂²×C₁₃	1	1	yes	characteristic
293	#474	C₂²×C₁₃	1	1	yes	characteristic
294	#474	C₂²×C₁₃	1	1	yes	characteristic
295	#468	—	2	1	no	—
296	#465	—	2	1	no	—
297	#465	—	2	1	no	—
298	#464	—	2	1	no	—
299	#464	—	2	1	no	—
300	#461	C₂²×C₁₃	1	1	yes	characteristic
301	#461	C₂²×C₁₃	1	1	yes	characteristic
302	#461	C₂²×C₁₃	1	1	yes	characteristic
303	#449	—	2	1	no	—
304	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₄×Q₁₆	—	2	1	no	—
306	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
308	#436	C₂²×C₁₃	1	1	yes	characteristic
309	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
311	#428	—	2	1	no	—
312	#427	—	2	1	no	—
313	#416	—	2	1	no	—
314	#335	C₂²×C₁₃	1	1	yes	characteristic
315	#335	C₂²×C₁₃	1	1	yes	characteristic
316	#333	C₂²×C₁₃	1	1	yes	characteristic
317	#332	C₂²×C₁₃	1	1	yes	characteristic
318	#332	C₂²×C₁₃	1	1	yes	characteristic
319	#332	C₂²×C₁₃	1	1	yes	characteristic
320	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	#322	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	—	4	1	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	—	4	1	no	—
334	C₂²×C₁₃	D₄²	1	1	yes	characteristic
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	C₂×#135	1	1	yes	characteristic
346	C₄×C₁₃	#575	1	1	yes	characteristic
347	C₄×C₁₃	#576	1	1	yes	characteristic
348	C₄×C₁₃	#578	1	1	yes	characteristic
349	C₂×#41	—	2	1	no	—
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
356	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
357	C₂×M₁₆	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
364	#126	—	4	1	no	—
365	#126	—	4	1	no	—
366	#124	—	2	1	no	—
367	#124	—	2	1	no	—
368	#124	—	4	1	no	—
369	#123	—	4	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	—	2	1	no	—
375	#121	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	4	1	no	—
393	#107	D₄×C₁₃	1	1	yes	characteristic
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	D₄×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
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	#103	—	2	1	no	—
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	—	4	1	no	—
412	#103	D₄×C₁₃	1	1	yes	characteristic
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	D₄×C₁₃	1	1	yes	characteristic
417	#102	D₄×C₁₃	1	1	yes	characteristic
418	#102	D₄×C₁₃	1	1	yes	characteristic
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₁₃	—	8	1	no	—
427	C₂×C₁₃	—	8	1	no	—
428	C₂×C₁₃	—	8	1	no	—
429	C₂×C₁₃	#3268	1	1	yes	characteristic
430	C₂×C₁₃	#3283	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	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	Q₁₆	—	4	2	no	—
449	Q₁₆	—	8	1	no	—
450	SD₁₆	—	2	2	no	—
451	SD₁₆	—	8	1	no	—
452	SD₁₆	—	8	1	no	—
453	SD₁₆	—	8	1	no	—
454	D₈	—	4	1	no	—
455	M₁₆	—	4	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	8	1	no	—
463	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	4	1	no	—
495	C₄²	—	4	1	no	—
496	C₄²	—	4	1	no	—
497	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₁₃	#19863	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	4	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	—	8	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	8	2	no	—
518	D₄	—	16	1	no	—
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	—	4	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	—	4	1	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	C₁₃×#135	1	2	yes	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	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	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	D₄²×C₁₃	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
568	C₄	C₁₃×#575	1	1	yes	characteristic
569	C₄	C₁₃×#576	1	1	yes	characteristic
570	C₄	C₁₃×#578	1	1	yes	characteristic
571	C₂	—	8	1	no	—
572	C₂	—	8	1	no	—
573	C₂	—	8	1	no	—
574	C₂	C₁₃×#3268	1	1	yes	characteristic
575	C₂	C₁₃×#3283	1	1	yes	characteristic
576	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3303	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×#3393	C₂	semidirect
2. C₁₃×#3353	C₂	semidirect
3. C₁₃×#3340	C₂	semidirect
5. C₁₃×#1723	C₂	semidirect
6. C₁₃×#1691	C₂	semidirect
7. C₁₃×#1684	C₂	semidirect
8. C₁₃×#1673	C₂	semidirect
9. C₁₃×#1669	C₂	semidirect
10. C₁₃×#1650	C₂	semidirect
11. C₁₃×#1647	C₂	semidirect
12. C₁₃×#1646	C₂	semidirect
13. C₁₃×#1638	C₂	semidirect
14. C₁₃×#1581	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19863	C₁₃	direct (N × H)
211. #3393	C₂×C₁₃	semidirect
212. #3353	C₂×C₁₃	semidirect
213. #3340	C₂×C₁₃	semidirect
215. #1723	C₂×C₁₃	semidirect
216. #1691	C₂×C₁₃	semidirect
217. #1684	C₂×C₁₃	semidirect
218. #1673	C₂×C₁₃	semidirect
219. #1669	C₂×C₁₃	semidirect
220. #1650	C₂×C₁₃	semidirect
221. #1647	C₂×C₁₃	semidirect
222. #1646	C₂×C₁₃	semidirect
223. #1638	C₂×C₁₃	semidirect
224. #1581	C₂×C₁₃	semidirect
225. SD₁₆⋊C₈	C₂×C₁₃	semidirect
498. C₁₃	#19863	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×#3393	2
C₁₃×#3353	2
C₁₃×#3340	2
C₁₃×#3303	2
C₁₃×#1723	2
C₁₃×#1691	2
C₁₃×#1684	2
C₁₃×#1673	2
C₁₃×#1669	2
C₁₃×#1650	2
C₁₃×#1647	2
C₁₃×#1646	2
C₁₃×#1638	2
C₁₃×#1581	2
C₁₃×SD₁₆⋊C₈	2
#19863	13

Subgroups — C13×#19863 #15706202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19863 #15706202