Subgroups — C₁₃×#19847 #15706186

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1720	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1626	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#557	C₂²	1	1	yes	characteristic
17	C₁₃×#557	C₂²	1	1	yes	characteristic
18	C₁₃×#556	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#498	C₂²	1	1	yes	characteristic
21	C₁₃×#494	—	2	1	no	—
22	C₁₃×#494	C₂²	1	1	yes	characteristic
23	C₁₃×#490	—	2	1	no	—
24	C₁₃×#488	—	2	1	no	—
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#482	—	2	1	no	—
30	C₁₃×#479	—	2	1	no	—
31	C₁₃×#478	—	2	1	no	—
32	C₁₃×#475	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#474	C₂²	1	1	yes	characteristic
35	C₁₃×#465	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#462	—	2	1	no	—
38	C₁₃×#462	—	2	1	no	—
39	C₁₃×#462	C₂²	1	1	yes	characteristic
40	C₁₃×#462	C₂²	1	1	yes	characteristic
41	C₁₃×#462	C₂²	1	1	yes	characteristic
42	C₁₃×#460	—	2	1	no	—
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#460	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₁₃×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#440	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	—	2	1	no	—
51	C₄×C₁₃×Q₁₆	—	2	1	no	—
52	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#335	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×Q₈⋊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×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×#127	—	2	1	no	—
84	C₁₃×#127	C₂³	1	1	yes	characteristic
85	C₁₃×#126	—	4	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	—	2	1	no	—
88	C₁₃×#125	—	4	1	no	—
89	C₁₃×#125	—	4	1	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	4	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	D₄	1	1	yes	characteristic
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	4	1	no	—
110	C₁₃×#106	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
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×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
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×#103	D₄	1	1	yes	characteristic
125	C₁₃×#103	D₄	1	1	yes	characteristic
126	C₁₃×#103	D₄	1	1	yes	characteristic
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×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	4	1	no	—
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×#97	—	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	#19847	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×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	—	4	1	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₁₃×Q₁₆	—	4	1	no	—
162	C₁₃×Q₁₆	—	4	2	no	—
163	C₁₃×Q₁₆	—	4	2	no	—
164	C₁₃×Q₁₆	—	8	1	no	—
165	C₁₃×Q₁₆	—	8	1	no	—
166	C₁₃×Q₁₆	—	8	1	no	—
167	C₁₃×SD₁₆	—	2	2	no	—
168	C₁₃×SD₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	8	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	—	2	1	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	—	4	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	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×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	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	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3368	C₂×C₁₃	1	1	yes	characteristic
213	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3304	C₂×C₁₃	1	1	yes	characteristic
215	#1720	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1700	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1669	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1641	C₂×C₁₃	1	1	yes	characteristic
223	#1626	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1584	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	—	4	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×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	#135	1	2	yes	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	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	—	8	1	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	16	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	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	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	—	2	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	—	4	1	no	—
274	#557	C₂²×C₁₃	1	1	yes	characteristic
275	#557	C₂²×C₁₃	1	1	yes	characteristic
276	#556	C₂²×C₁₃	1	1	yes	characteristic
277	#550	C₂²×C₁₃	1	1	yes	characteristic
278	#498	C₂²×C₁₃	1	1	yes	characteristic
279	#494	—	2	1	no	—
280	#494	C₂²×C₁₃	1	1	yes	characteristic
281	#490	—	2	1	no	—
282	#488	—	2	1	no	—
283	#487	C₂²×C₁₃	1	1	yes	characteristic
284	#486	C₂²×C₁₃	1	1	yes	characteristic
285	#486	C₂²×C₁₃	1	1	yes	characteristic
286	#486	C₂²×C₁₃	1	1	yes	characteristic
287	#482	—	2	1	no	—
288	#479	—	2	1	no	—
289	#478	—	2	1	no	—
290	#475	C₂²×C₁₃	1	1	yes	characteristic
291	#474	C₂²×C₁₃	1	1	yes	characteristic
292	#474	C₂²×C₁₃	1	1	yes	characteristic
293	#465	—	2	1	no	—
294	#464	—	2	1	no	—
295	#462	—	2	1	no	—
296	#462	—	2	1	no	—
297	#462	C₂²×C₁₃	1	1	yes	characteristic
298	#462	C₂²×C₁₃	1	1	yes	characteristic
299	#462	C₂²×C₁₃	1	1	yes	characteristic
300	#460	—	2	1	no	—
301	#460	C₂²×C₁₃	1	1	yes	characteristic
302	#460	C₂²×C₁₃	1	1	yes	characteristic
303	#452	—	2	1	no	—
304	#446	C₂²×C₁₃	1	1	yes	characteristic
305	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	#440	—	2	1	no	—
308	C₄×Q₁₆	—	2	1	no	—
309	C₄×Q₁₆	—	2	1	no	—
310	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
311	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
312	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
313	#416	—	2	1	no	—
314	#335	C₂²×C₁₃	1	1	yes	characteristic
315	#335	C₂²×C₁₃	1	1	yes	characteristic
316	#332	C₂²×C₁₃	1	1	yes	characteristic
317	#332	C₂²×C₁₃	1	1	yes	characteristic
318	#332	C₂²×C₁₃	1	1	yes	characteristic
319	#331	C₂²×C₁₃	1	1	yes	characteristic
320	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	Q₈⋊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	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	D₄²	1	1	yes	characteristic
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	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	—	8	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
344	C₄×C₁₃	#575	1	1	yes	characteristic
345	C₄×C₁₃	#576	1	1	yes	characteristic
346	C₄×C₁₃	#578	1	1	yes	characteristic
347	C₂×#41	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×Q₁₆	—	2	1	no	—
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	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	#127	—	2	1	no	—
364	#127	C₂³×C₁₃	1	1	yes	characteristic
365	#126	—	4	1	no	—
366	#125	—	2	1	no	—
367	#125	—	2	1	no	—
368	#125	—	4	1	no	—
369	#125	—	4	1	no	—
370	#124	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	4	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	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×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	D₄×C₁₃	1	1	yes	characteristic
388	#106	—	2	1	no	—
389	#106	—	4	1	no	—
390	#106	D₄×C₁₃	1	1	yes	characteristic
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	D₄×C₁₃	1	1	yes	characteristic
405	#103	D₄×C₁₃	1	1	yes	characteristic
406	#103	D₄×C₁₃	1	1	yes	characteristic
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	4	1	no	—
416	#102	D₄×C₁₃	1	1	yes	characteristic
417	C₂²⋊C₈	—	2	1	no	—
418	#97	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₁₃	—	8	1	no	—
425	C₂×C₁₃	—	16	1	no	—
426	C₂×C₁₃	#3268	1	1	yes	characteristic
427	C₂×C₁₃	#3285	1	1	yes	characteristic
428	C₂×C₁₃	#3289	1	1	yes	characteristic
429	#41	—	4	2	no	—
430	#41	—	8	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	Q₁₆	—	4	1	no	—
446	Q₁₆	—	4	2	no	—
447	Q₁₆	—	4	2	no	—
448	Q₁₆	—	8	1	no	—
449	Q₁₆	—	8	1	no	—
450	Q₁₆	—	8	1	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	4	2	no	—
453	SD₁₆	—	8	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	8	1	no	—
460	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
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	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	—	4	1	no	—
494	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
495	C₁₃	#19847	1	1	yes	characteristic, direct product factor, Sylow
496	C₂³	—	2	1	no	—
497	C₂³	—	4	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	4	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	C₁₃×#135	1	2	yes	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	8	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	—	2	1	no	—
525	C₂×C₄	—	2	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	—	8	2	no	—
532	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	D₄²×C₁₃	1	1	yes	characteristic
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	8	1	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
563	C₄	C₁₃×#575	1	1	yes	characteristic
564	C₄	C₁₃×#576	1	1	yes	characteristic
565	C₄	C₁₃×#578	1	1	yes	characteristic
566	C₂	—	8	1	no	—
567	C₂	—	16	1	no	—
568	C₂	C₁₃×#3268	1	1	yes	characteristic
569	C₂	C₁₃×#3285	1	1	yes	characteristic
570	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#550	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×#3395	C₂	semidirect
3. C₁₃×#3364	C₂	semidirect
5. C₁₃×#1720	C₂	semidirect
6. C₁₃×#1700	C₂	semidirect
7. C₁₃×#1682	C₂	semidirect
8. C₁₃×#1682	C₂	semidirect
9. C₁₃×#1669	C₂	semidirect
10. C₁₃×#1653	C₂	semidirect
11. C₁₃×#1652	C₂	semidirect
13. C₁₃×#1626	C₂	semidirect
14. C₁₃×#1584	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19847	C₁₃	direct (N × H)
211. #3395	C₂×C₁₃	semidirect
213. #3364	C₂×C₁₃	semidirect
215. #1720	C₂×C₁₃	semidirect
216. #1700	C₂×C₁₃	semidirect
217. #1682	C₂×C₁₃	semidirect
218. #1682	C₂×C₁₃	semidirect
219. #1669	C₂×C₁₃	semidirect
220. #1653	C₂×C₁₃	semidirect
221. #1652	C₂×C₁₃	semidirect
223. #1626	C₂×C₁₃	semidirect
224. #1584	C₂×C₁₃	semidirect
225. SD₁₆⋊C₈	C₂×C₁₃	semidirect
495. C₁₃	#19847	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×#3395	2
C₁₃×#3368	2
C₁₃×#3364	2
C₁₃×#3304	2
C₁₃×#1720	2
C₁₃×#1700	2
C₁₃×#1682	2
C₁₃×#1669	2
C₁₃×#1653	2
C₁₃×#1652	2
C₁₃×#1641	2
C₁₃×#1626	2
C₁₃×#1584	2
C₁₃×SD₁₆⋊C₈	2
#19847	13

Subgroups — C13×#19847 #15706186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19847 #15706186