Subgroups — C₁₃×#19835 #15706174

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1720	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1702	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	—	2	1	no	—
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#498	C₂²	1	1	yes	characteristic
22	C₁₃×#494	C₂²	1	1	yes	characteristic
23	C₁₃×#489	—	2	1	no	—
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#486	—	2	1	no	—
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×#477	—	2	1	no	—
31	C₁₃×#475	C₂²	1	1	yes	characteristic
32	C₁₃×#474	—	2	1	no	—
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#474	C₂²	1	1	yes	characteristic
35	C₁₃×#467	—	2	1	no	—
36	C₁₃×#465	—	2	1	no	—
37	C₁₃×#463	—	2	1	no	—
38	C₁₃×#462	C₂²	1	1	yes	characteristic
39	C₁₃×#462	C₂²	1	1	yes	characteristic
40	C₁₃×#461	C₂²	1	1	yes	characteristic
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#459	—	2	1	no	—
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#451	—	2	1	no	—
46	C₁₃×#451	—	2	1	no	—
47	C₁₃×#446	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#440	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×D₈	—	2	1	no	—
52	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	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×#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	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₂²×Q₈×C₁₃	—	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	—	2	1	no	—
74	C₂×C₁₃×Q₁₆	—	4	4	no	—
75	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×#127	—	2	1	no	—
88	C₁₃×#127	C₂³	1	1	yes	characteristic
89	C₁₃×#126	—	4	1	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	4	1	no	—
95	C₁₃×C₂²⋊Q₈	—	4	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	4	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	—	2	1	no	—
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	D₄	1	1	yes	characteristic
110	C₁₃×#107	D₄	1	1	yes	characteristic
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	4	1	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	—	2	1	no	—
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×#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	—	2	1	no	—
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×#102	D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×#97	—	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	#19835	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	—	4	1	no	—
152	C₂×Q₈×C₁₃	—	4	1	no	—
153	C₂×Q₈×C₁₃	—	4	2	no	—
154	C₂×Q₈×C₁₃	—	4	2	no	—
155	C₂×Q₈×C₁₃	—	8	1	no	—
156	C₂×Q₈×C₁₃	—	8	1	no	—
157	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	4	1	no	—
163	C₂×D₄×C₁₃	—	4	1	no	—
164	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	4	1	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₂²×C₄×C₁₃	—	4	1	no	—
171	C₁₃×Q₁₆	—	2	2	no	—
172	C₁₃×Q₁₆	—	4	2	no	—
173	C₁₃×Q₁₆	—	4	2	no	—
174	C₁₃×Q₁₆	—	4	2	no	—
175	C₁₃×Q₁₆	—	8	1	no	—
176	C₁₃×SD₁₆	—	4	2	no	—
177	C₁₃×SD₁₆	—	8	1	no	—
178	C₁₃×D₈	—	2	2	no	—
179	C₁₃×D₈	—	4	2	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	—	4	2	no	—
186	C₂×C₈×C₁₃	—	8	1	no	—
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₁₃×C₂²⋊C₄	—	4	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	4	1	no	—
216	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
217	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3358	C₂×C₁₃	1	1	yes	characteristic
219	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
220	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1720	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1702	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1681	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1669	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1627	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	2	1	no	—
237	Q₈×C₁₃	—	2	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	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	8	2	no	—
245	Q₈×C₁₃	—	8	2	no	—
246	Q₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
247	D₄×C₁₃	—	2	1	no	—
248	D₄×C₁₃	—	2	1	no	—
249	D₄×C₁₃	—	2	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	8	2	no	—
255	D₄×C₁₃	—	8	1	no	—
256	D₄×C₁₃	—	16	1	no	—
257	D₄×C₁₃	#135	1	2	yes	—
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	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	8	2	no	—
272	C₂×C₄×C₁₃	—	8	2	no	—
273	C₂×C₄×C₁₃	—	8	2	no	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	2	1	no	—
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	2	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	C₈×C₁₃	—	4	1	no	—
286	C₂²×Q₁₆	—	2	1	no	—
287	#556	C₂²×C₁₃	1	1	yes	characteristic
288	#550	C₂²×C₁₃	1	1	yes	characteristic
289	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
290	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	#498	C₂²×C₁₃	1	1	yes	characteristic
292	#494	C₂²×C₁₃	1	1	yes	characteristic
293	#489	—	2	1	no	—
294	#487	C₂²×C₁₃	1	1	yes	characteristic
295	#486	—	2	1	no	—
296	#486	C₂²×C₁₃	1	1	yes	characteristic
297	#486	C₂²×C₁₃	1	1	yes	characteristic
298	#486	C₂²×C₁₃	1	1	yes	characteristic
299	#482	—	2	1	no	—
300	#477	—	2	1	no	—
301	#475	C₂²×C₁₃	1	1	yes	characteristic
302	#474	—	2	1	no	—
303	#474	C₂²×C₁₃	1	1	yes	characteristic
304	#474	C₂²×C₁₃	1	1	yes	characteristic
305	#467	—	2	1	no	—
306	#465	—	2	1	no	—
307	#463	—	2	1	no	—
308	#462	C₂²×C₁₃	1	1	yes	characteristic
309	#462	C₂²×C₁₃	1	1	yes	characteristic
310	#461	C₂²×C₁₃	1	1	yes	characteristic
311	#460	C₂²×C₁₃	1	1	yes	characteristic
312	#459	—	2	1	no	—
313	#459	C₂²×C₁₃	1	1	yes	characteristic
314	#452	—	2	1	no	—
315	#451	—	2	1	no	—
316	#451	—	2	1	no	—
317	#446	C₂²×C₁₃	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	#440	—	2	1	no	—
320	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
321	C₄×D₈	—	2	1	no	—
322	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	#416	—	2	1	no	—
326	#335	C₂²×C₁₃	1	1	yes	characteristic
327	#334	C₂²×C₁₃	1	1	yes	characteristic
328	#332	C₂²×C₁₃	1	1	yes	characteristic
329	#332	C₂²×C₁₃	1	1	yes	characteristic
330	#332	C₂²×C₁₃	1	1	yes	characteristic
331	#331	C₂²×C₁₃	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
336	#322	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	D₄²	1	1	yes	characteristic
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
358	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
359	C₄×C₁₃	#576	1	1	yes	characteristic
360	C₄×C₁₃	#578	1	1	yes	characteristic
361	C₂×#41	—	2	1	no	—
362	C₂²×Q₈	—	2	1	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×Q₁₆	—	2	1	no	—
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×Q₁₆	—	2	1	no	—
368	C₂×Q₁₆	—	4	4	no	—
369	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×D₈	—	2	1	no	—
373	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	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⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
381	#127	—	2	1	no	—
382	#127	C₂³×C₁₃	1	1	yes	characteristic
383	#126	—	4	1	no	—
384	#124	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	4	1	no	—
389	C₂²⋊Q₈	—	4	1	no	—
390	#121	—	2	1	no	—
391	#121	—	4	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
400	#117	—	2	1	no	—
401	#107	—	2	1	no	—
402	#107	—	2	1	no	—
403	#107	D₄×C₁₃	1	1	yes	characteristic
404	#107	D₄×C₁₃	1	1	yes	characteristic
405	#106	—	2	1	no	—
406	#106	—	4	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
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	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	D₄×C₁₃	1	1	yes	characteristic
420	#103	D₄×C₁₃	1	1	yes	characteristic
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	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	4	1	no	—
430	#102	D₄×C₁₃	1	1	yes	characteristic
431	#102	D₄×C₁₃	1	1	yes	characteristic
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	#97	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₁₃	—	4	2	no	—
440	C₂×C₁₃	—	8	1	no	—
441	C₂×C₁₃	—	16	1	no	—
442	C₂×C₁₃	#3264	1	1	yes	characteristic
443	C₂×C₁₃	#3285	1	1	yes	characteristic
444	C₂×C₁₃	#3289	1	1	yes	characteristic
445	#41	—	4	2	no	—
446	#41	—	8	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	4	1	no	—
451	C₂×Q₈	—	4	1	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	—	8	1	no	—
455	C₂×Q₈	—	8	1	no	—
456	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	4	1	no	—
470	Q₁₆	—	2	2	no	—
471	Q₁₆	—	4	2	no	—
472	Q₁₆	—	4	2	no	—
473	Q₁₆	—	4	2	no	—
474	Q₁₆	—	8	1	no	—
475	SD₁₆	—	4	2	no	—
476	SD₁₆	—	8	1	no	—
477	D₈	—	2	2	no	—
478	D₈	—	4	2	no	—
479	C₂×C₈	—	2	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	—	4	2	no	—
485	C₂×C₈	—	8	1	no	—
486	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₁₃	#19835	1	1	yes	characteristic, direct product factor, Sylow
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	4	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	8	2	no	—
530	Q₈	—	8	2	no	—
531	Q₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	1	no	—
541	D₄	—	16	1	no	—
542	D₄	C₁₃×#135	1	2	yes	—
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	—	2	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	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₁₃×H(5,𝔽₂)	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	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	D₄²×C₁₃	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
592	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
593	C₄	C₁₃×#576	1	1	yes	characteristic
594	C₄	C₁₃×#578	1	1	yes	characteristic
595	C₂	—	4	2	no	—
596	C₂	—	8	1	no	—
597	C₂	—	16	1	no	—
598	C₂	C₁₃×#3264	1	1	yes	characteristic
599	C₂	C₁₃×#3285	1	1	yes	characteristic
600	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3358	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×#3367	C₂	semidirect
3. C₁₃×#3304	C₂	semidirect
4. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#1720	C₂	semidirect
6. C₁₃×#1702	C₂	semidirect
7. C₁₃×#1681	C₂	semidirect
8. C₁₃×#1680	C₂	semidirect
9. C₁₃×#1669	C₂	semidirect
10. C₁₃×#1652	C₂	semidirect
11. C₁₃×#1651	C₂	semidirect
12. C₁₃×#1641	C₂	semidirect
13. C₁₃×#1627	C₂	semidirect
14. C₁₃×#1584	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
145. #19835	C₁₃	direct (N × H)
217. #3367	C₂×C₁₃	semidirect
219. #3304	C₂×C₁₃	semidirect
220. D₄×Q₁₆	C₂×C₁₃	semidirect
221. #1720	C₂×C₁₃	semidirect
222. #1702	C₂×C₁₃	semidirect
223. #1681	C₂×C₁₃	semidirect
224. #1680	C₂×C₁₃	semidirect
225. #1669	C₂×C₁₃	semidirect
226. #1652	C₂×C₁₃	semidirect
227. #1651	C₂×C₁₃	semidirect
228. #1641	C₂×C₁₃	semidirect
229. #1627	C₂×C₁₃	semidirect
230. #1584	C₂×C₁₃	semidirect
231. #1580	C₂×C₁₃	semidirect
516. C₁₃	#19835	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×#3367	2
C₁₃×#3358	2
C₁₃×#3304	2
D₄×C₁₃×Q₁₆	2
C₁₃×#1720	2
C₁₃×#1702	2
C₁₃×#1681	2
C₁₃×#1680	2
C₁₃×#1669	2
C₁₃×#1652	2
C₁₃×#1651	2
C₁₃×#1641	2
C₁₃×#1627	2
C₁₃×#1584	2
C₁₃×#1580	2
#19835	13

Subgroups — C13×#19835 #15706174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19835 #15706174