Subgroups — C₁₃×#19837 #15706176

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3359	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×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1681	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1640	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	—	2	1	no	—
17	C₁₃×#559	C₂²	1	1	yes	characteristic
18	C₁₃×#557	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×#488	—	2	1	no	—
25	C₁₃×#487	—	2	1	no	—
26	C₁₃×#487	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#486	C₂²	1	1	yes	characteristic
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#476	—	2	1	no	—
32	C₁₃×#475	—	2	1	no	—
33	C₁₃×#475	C₂²	1	1	yes	characteristic
34	C₁₃×#475	C₂²	1	1	yes	characteristic
35	C₁₃×#475	C₂²	1	1	yes	characteristic
36	C₁₃×#467	—	2	1	no	—
37	C₁₃×#464	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#462	C₂²	1	1	yes	characteristic
40	C₁₃×#462	C₂²	1	1	yes	characteristic
41	C₁₃×#461	—	2	1	no	—
42	C₁₃×#461	C₂²	1	1	yes	characteristic
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
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	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#442	—	2	1	no	—
51	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×SD₁₆	—	2	1	no	—
53	C₄×C₁₃×SD₁₆	—	2	1	no	—
54	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₁₃	—	2	1	no	—
68	C₂²×Q₈×C₁₃	—	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	—	4	4	no	—
74	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×#127	C₂³	1	1	yes	characteristic
87	C₁₃×#125	—	2	1	no	—
88	C₁₃×#125	—	4	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×#123	—	4	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	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
105	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#107	D₄	1	1	yes	characteristic
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	—	4	1	no	—
111	C₁₃×#106	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	—	2	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	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	—	4	1	no	—
137	C₁₃×#102	D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×#97	—	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	#19837	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	4	1	no	—
150	C₂×Q₈×C₁₃	—	4	1	no	—
151	C₂×Q₈×C₁₃	—	4	2	no	—
152	C₂×Q₈×C₁₃	—	4	2	no	—
153	C₂×Q₈×C₁₃	—	8	1	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×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₁₃×Q₁₆	—	2	2	no	—
167	C₁₃×Q₁₆	—	4	2	no	—
168	C₁₃×Q₁₆	—	4	2	no	—
169	C₁₃×Q₁₆	—	4	2	no	—
170	C₁₃×Q₁₆	—	8	1	no	—
171	C₁₃×SD₁₆	—	2	2	no	—
172	C₁₃×SD₁₆	—	4	2	no	—
173	C₁₃×SD₁₆	—	4	2	no	—
174	C₁₃×D₈	—	4	2	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	—	2	1	no	—
180	C₂×C₈×C₁₃	—	4	2	no	—
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	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	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	C₂×D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	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	—	2	1	no	—
212	C₄²×C₁₃	—	4	1	no	—
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3373	C₂×C₁₃	1	1	yes	characteristic
215	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
217	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1720	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1700	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1681	C₂×C₁₃	1	1	yes	characteristic
222	#1670	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1640	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1627	C₂×C₁₃	1	1	yes	characteristic
227	#1584	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	—	4	1	no	—
231	Q₈×C₁₃	—	2	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	Q₈×C₁₃	—	8	2	no	—
243	Q₈×C₁₃	—	8	2	no	—
244	Q₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
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	#135	1	2	yes	—
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	—	2	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	—	8	2	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	—	2	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	—	4	1	no	—
279	C₂²×Q₁₆	—	2	1	no	—
280	#559	C₂²×C₁₃	1	1	yes	characteristic
281	#557	C₂²×C₁₃	1	1	yes	characteristic
282	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
283	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
284	#498	C₂²×C₁₃	1	1	yes	characteristic
285	#494	C₂²×C₁₃	1	1	yes	characteristic
286	#489	—	2	1	no	—
287	#488	—	2	1	no	—
288	#487	—	2	1	no	—
289	#487	C₂²×C₁₃	1	1	yes	characteristic
290	#486	C₂²×C₁₃	1	1	yes	characteristic
291	#486	C₂²×C₁₃	1	1	yes	characteristic
292	#486	C₂²×C₁₃	1	1	yes	characteristic
293	#478	—	2	1	no	—
294	#476	—	2	1	no	—
295	#475	—	2	1	no	—
296	#475	C₂²×C₁₃	1	1	yes	characteristic
297	#475	C₂²×C₁₃	1	1	yes	characteristic
298	#475	C₂²×C₁₃	1	1	yes	characteristic
299	#467	—	2	1	no	—
300	#464	—	2	1	no	—
301	#463	—	2	1	no	—
302	#462	C₂²×C₁₃	1	1	yes	characteristic
303	#462	C₂²×C₁₃	1	1	yes	characteristic
304	#461	—	2	1	no	—
305	#461	C₂²×C₁₃	1	1	yes	characteristic
306	#460	C₂²×C₁₃	1	1	yes	characteristic
307	#459	C₂²×C₁₃	1	1	yes	characteristic
308	#451	—	2	1	no	—
309	#451	—	2	1	no	—
310	#446	C₂²×C₁₃	1	1	yes	characteristic
311	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
313	#442	—	2	1	no	—
314	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
315	C₄×SD₁₆	—	2	1	no	—
316	C₄×SD₁₆	—	2	1	no	—
317	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
318	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
319	#335	C₂²×C₁₃	1	1	yes	characteristic
320	#335	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	Q₈⋊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	—	2	2	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	—	8	1	no	—
335	C₂²×C₁₃	—	8	1	no	—
336	C₂²×C₁₃	D₄²	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	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	—	8	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
349	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₄×C₁₃	#577	1	1	yes	characteristic
351	C₄×C₁₃	#578	1	1	yes	characteristic
352	C₂²×Q₈	—	2	1	no	—
353	C₂²×Q₈	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×Q₁₆	—	2	1	no	—
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×Q₁₆	—	4	4	no	—
359	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
363	C₂×D₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	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	#125	—	2	1	no	—
373	#125	—	4	1	no	—
374	#124	—	2	1	no	—
375	#124	—	2	1	no	—
376	#123	—	4	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	4	1	no	—
380	C₂²⋊Q₈	—	4	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
391	#107	D₄×C₁₃	1	1	yes	characteristic
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	4	1	no	—
396	#106	D₄×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
412	#103	D₄×C₁₃	1	1	yes	characteristic
413	#103	D₄×C₁₃	1	1	yes	characteristic
414	#103	D₄×C₁₃	1	1	yes	characteristic
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
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	C₂²⋊C₈	—	2	1	no	—
424	#97	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₁₃	—	4	2	no	—
431	C₂×C₁₃	—	16	1	no	—
432	C₂×C₁₃	#3265	1	1	yes	characteristic
433	C₂×C₁₃	#3285	1	1	yes	characteristic
434	C₂×C₁₃	#3289	1	1	yes	characteristic
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	1	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	4	2	no	—
442	C₂×Q₈	—	8	1	no	—
443	C₂×Q₈	—	8	1	no	—
444	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	Q₁₆	—	2	2	no	—
456	Q₁₆	—	4	2	no	—
457	Q₁₆	—	4	2	no	—
458	Q₁₆	—	4	2	no	—
459	Q₁₆	—	8	1	no	—
460	SD₁₆	—	2	2	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	D₈	—	4	2	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	4	2	no	—
470	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
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	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₁₃	#19837	1	1	yes	characteristic, direct product factor, Sylow
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	8	2	no	—
518	Q₈	—	8	2	no	—
519	Q₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
520	D₄	—	2	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	8	1	no	—
526	D₄	C₁₃×#135	1	2	yes	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	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	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	16	1	no	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	D₄²×C₁₃	1	1	yes	characteristic
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
573	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
574	C₄	C₁₃×#577	1	1	yes	characteristic
575	C₄	C₁₃×#578	1	1	yes	characteristic
576	C₂	—	4	2	no	—
577	C₂	—	16	1	no	—
578	C₂	C₁₃×#3265	1	1	yes	characteristic
579	C₂	C₁₃×#3285	1	1	yes	characteristic
580	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#459	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
2. C₁₃×#3365	C₂	semidirect
3. C₁₃×#3359	C₂	semidirect
4. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#1720	C₂	semidirect
6. C₁₃×#1700	C₂	semidirect
7. C₁₃×#1682	C₂	semidirect
9. C₁₃×#1670	C₂	semidirect
10. C₁₃×#1653	C₂	semidirect
11. C₁₃×#1651	C₂	semidirect
12. C₁₃×#1640	C₂	semidirect
14. C₁₃×#1584	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
145. #19837	C₁₃	direct (N × H)
215. #3365	C₂×C₁₃	semidirect
216. #3359	C₂×C₁₃	semidirect
217. D₄×Q₁₆	C₂×C₁₃	semidirect
218. #1720	C₂×C₁₃	semidirect
219. #1700	C₂×C₁₃	semidirect
220. #1682	C₂×C₁₃	semidirect
222. #1670	C₂×C₁₃	semidirect
223. #1653	C₂×C₁₃	semidirect
224. #1651	C₂×C₁₃	semidirect
225. #1640	C₂×C₁₃	semidirect
227. #1584	C₂×C₁₃	semidirect
228. SD₁₆⋊C₈	C₂×C₁₃	semidirect
503. C₁₃	#19837	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×#3373	2
C₁₃×#3365	2
C₁₃×#3359	2
D₄×C₁₃×Q₁₆	2
C₁₃×#1720	2
C₁₃×#1700	2
C₁₃×#1682	2
C₁₃×#1681	2
C₁₃×#1670	2
C₁₃×#1653	2
C₁₃×#1651	2
C₁₃×#1640	2
C₁₃×#1627	2
C₁₃×#1584	2
C₁₃×SD₁₆⋊C₈	2
#19837	13

Subgroups — C13×#19837 #15706176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19837 #15706176