Subgroups — C₁₃×#60828 #15747167

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3219	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3218	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#556	—	2	2	no	—
22	C₁₃×#551	—	2	4	no	—
23	D₄×Q₈×C₁₃	—	2	2	no	—
24	C₁₃×#547	—	2	4	no	—
25	C₁₃×#547	—	2	2	no	—
26	C₁₃×#542	C₂²	1	4	yes	—
27	C₁₃×#536	C₂²	1	2	yes	—
28	C₁₃×#536	C₂²	1	1	yes	characteristic
29	C₁₃×#536	C₂²	1	4	yes	complemented
30	C₁₃×#535	C₂²	1	1	yes	characteristic
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#532	C₂²	1	2	yes	complemented
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₃×#529	C₂²	1	4	yes	—
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
38	C₁₃×#519	C₂²	1	1	yes	characteristic
39	C₁₃×#518	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
41	C₁₃×#497	C₂²	1	4	yes	—
42	C₁₃×#497	C₂²	1	4	yes	—
43	C₁₃×#497	C₂²	1	2	yes	—
44	C₁₃×#496	C₂²	1	2	yes	—
45	C₁₃×#495	C₂²	1	4	yes	—
46	C₁₃×#491	C₂²	1	2	yes	complemented
47	C₁₃×#491	C₂²	1	4	yes	complemented
48	C₁₃×#490	C₂²	1	2	yes	complemented
49	C₁₃×#489	C₂²	1	4	yes	complemented
50	C₁₃×#487	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#463	C₂²	1	8	yes	—
53	C₁₃×#462	C₂²	1	8	yes	complemented
54	C₁₃×#461	C₂²	1	8	yes	—
55	C₁₃×#452	C₂²	1	8	yes	complemented
56	C₁₃×#451	C₂²	1	8	yes	complemented
57	C₁₃×#449	C₂²	1	8	yes	—
58	C₁₃×#448	C₂²	1	8	yes	—
59	C₁₃×#433	C₂²	1	4	yes	complemented
60	C₁₃×#432	C₂²	1	4	yes	complemented
61	C₁₃×#424	C₂²	1	2	yes	—
62	C₁₃×#419	C₂²	1	2	yes	—
63	C₁₃×#419	C₂²	1	2	yes	—
64	C₁₃×#416	C₂²	1	2	yes	—
65	C₁₃×#416	C₂²	1	2	yes	—
66	C₁₃×#408	C₂²	1	2	yes	—
67	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
69	C₁₃×2₋¹⁺⁴	—	4	4	no	—
70	C₁₃×2₋¹⁺⁴	—	4	4	no	—
71	C₂×C₁₃×#41	—	2	4	no	—
72	C₂×C₁₃×#41	—	2	2	no	—
73	C₂×C₁₃×#41	C₂³	1	2	yes	—
74	C₂×C₁₃×#41	C₂³	1	4	yes	—
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	—	2	2	no	—
77	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#137	—	4	4	no	—
82	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
83	C₂×C₁₃×Q₁₆	—	4	4	no	—
84	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
85	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
86	C₂×C₁₃×SD₁₆	—	4	4	no	—
87	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×D₈	C₂³	1	4	yes	—
91	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
93	C₁₃×C₄⋊Q₈	—	2	1	no	—
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	2	4	no	—
96	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₁₃×#127	—	2	1	no	—
102	C₁₃×#127	C₂³	1	1	yes	characteristic
103	C₁₃×#126	—	2	4	no	—
104	C₁₃×#126	—	2	4	no	—
105	C₁₃×#125	C₂³	1	2	yes	—
106	C₁₃×#124	—	2	1	no	—
107	C₁₃×#124	—	2	1	no	—
108	C₁₃×#124	—	2	4	no	—
109	C₁₃×#124	—	2	2	no	—
110	C₁₃×#124	C₂³	1	4	yes	—
111	C₁₃×#124	C₂³	1	2	yes	—
112	C₁₃×#124	C₂³	1	2	yes	—
113	C₁₃×#124	C₂³	1	2	yes	—
114	C₁₃×#123	—	2	2	no	—
115	C₁₃×#123	—	2	4	no	—
116	C₁₃×#123	—	2	4	no	—
117	C₁₃×#123	—	2	8	no	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	4	no	—
121	C₁₃×C₂²⋊Q₈	—	2	8	no	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₁₃×#121	—	2	2	no	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#121	C₂³	1	4	yes	—
127	C₁₃×#120	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	2	no	—
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	D₄	1	2	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
132	C₄×D₄×C₁₃	—	2	4	no	—
133	C₄×D₄×C₁₃	—	2	2	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	—	2	4	no	—
136	C₄×D₄×C₁₃	D₄	1	4	yes	—
137	C₄×D₄×C₁₃	D₄	1	2	yes	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₁₃×#117	—	2	2	no	—
140	C₁₃×#117	—	2	4	no	—
141	C₁₃×#117	C₂³	1	1	yes	characteristic
142	C₁₃×#117	C₂³	1	1	yes	characteristic
143	C₁₃×#117	C₂³	1	1	yes	characteristic
144	C₁₃×#117	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	4	yes	—
154	C₁₃×#103	C₂³	1	8	yes	—
155	C₁₃×#103	C₂³	1	8	yes	—
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
159	C₁₃×#97	C₂³	1	2	yes	—
160	C₁₃×#97	C₂³	1	2	yes	—
161	C₁₃×#97	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	2	yes	—
163	#60828	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₁₃×#41	—	2	4	no	—
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	2	4	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₁₃×#41	—	4	16	no	—
171	C₁₃×#41	—	4	8	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	4	no	—
174	C₂×Q₈×C₁₃	—	2	2	no	—
175	C₂×Q₈×C₁₃	—	2	2	no	—
176	C₂×Q₈×C₁₃	—	2	4	no	—
177	C₂×Q₈×C₁₃	—	2	4	no	—
178	C₂×Q₈×C₁₃	—	2	4	no	—
179	C₂×Q₈×C₁₃	—	4	4	no	—
180	C₂×Q₈×C₁₃	—	4	4	no	—
181	C₂×Q₈×C₁₃	—	4	8	no	—
182	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
184	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
185	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	2	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	2	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
193	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	4	no	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₁₃×Q₁₆	—	4	8	no	—
207	C₁₃×Q₁₆	—	4	4	no	—
208	C₁₃×SD₁₆	—	4	8	no	—
209	C₁₃×SD₁₆	—	4	4	no	—
210	C₁₃×SD₁₆	—	4	4	no	—
211	C₁₃×D₈	—	4	4	no	—
212	C₁₃×M₁₆	—	2	4	no	—
213	C₂×C₈×C₁₃	—	2	4	no	—
214	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
215	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	2	4	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	4	no	—
222	C₁₃×C₄⋊C₄	—	2	4	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
226	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
227	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
229	C₁₃×C₂²⋊C₄	—	2	1	no	—
230	C₁₃×C₂²⋊C₄	—	2	1	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	4	no	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	4	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	8	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
240	C₄²×C₁₃	—	2	4	no	—
241	C₄²×C₁₃	—	2	1	no	—
242	C₄²×C₁₃	—	2	1	no	—
243	C₄²×C₁₃	C₂×D₄	1	4	yes	—
244	C₄²×C₁₃	C₂×D₄	1	2	yes	—
245	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₄²×C₁₃	C₂⁴	1	2	yes	—
248	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#3225	C₂×C₁₃	1	8	yes	complemented
251	#3219	C₂×C₁₃	1	4	yes	complemented
252	#3218	C₂×C₁₃	1	4	yes	complemented
253	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3044	C₂×C₁₃	1	2	yes	complemented
258	#3042	C₂×C₁₃	1	2	yes	complemented
259	#3011	C₂×C₁₃	1	2	yes	complemented
260	#3010	C₂×C₁₃	1	2	yes	complemented
261	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	4	2	no	—
265	C₂³×C₁₃	—	8	2	no	—
266	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₁₃	—	2	2	no	—
269	Q₈×C₁₃	—	2	4	no	—
270	Q₈×C₁₃	—	2	2	no	—
271	Q₈×C₁₃	—	2	4	no	—
272	Q₈×C₁₃	—	2	4	no	—
273	Q₈×C₁₃	—	2	2	no	—
274	Q₈×C₁₃	—	4	8	no	—
275	Q₈×C₁₃	—	4	2	no	—
276	Q₈×C₁₃	—	4	4	no	—
277	Q₈×C₁₃	—	8	2	no	—
278	D₄×C₁₃	—	2	4	no	—
279	D₄×C₁₃	—	2	2	no	—
280	D₄×C₁₃	—	2	2	no	—
281	D₄×C₁₃	—	2	4	no	—
282	D₄×C₁₃	—	2	2	no	—
283	D₄×C₁₃	—	4	4	no	—
284	D₄×C₁₃	—	4	8	no	—
285	D₄×C₁₃	—	4	4	no	—
286	D₄×C₁₃	—	4	2	no	—
287	D₄×C₁₃	—	8	4	no	—
288	C₂×C₄×C₁₃	—	2	4	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	4	4	no	—
295	C₂×C₄×C₁₃	—	4	2	no	—
296	C₂×C₄×C₁₃	—	4	8	no	—
297	C₂×C₄×C₁₃	—	4	8	no	—
298	C₂×C₄×C₁₃	—	4	2	no	—
299	C₂×C₄×C₁₃	—	4	4	no	—
300	C₂×C₄×C₁₃	—	4	4	no	—
301	C₂×C₄×C₁₃	—	8	4	no	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
308	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
309	C₈×C₁₃	—	2	4	no	—
310	C₈×C₁₃	—	2	4	no	—
311	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
312	C₂×#137	C₂²×C₁₃	1	2	yes	—
313	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
314	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
315	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
316	#559	—	2	2	no	—
317	#556	—	2	2	no	—
318	#551	—	2	4	no	—
319	D₄×Q₈	—	2	2	no	—
320	#547	—	2	4	no	—
321	#547	—	2	2	no	—
322	#542	C₂²×C₁₃	1	4	yes	—
323	#536	C₂²×C₁₃	1	2	yes	—
324	#536	C₂²×C₁₃	1	1	yes	characteristic
325	#536	C₂²×C₁₃	1	4	yes	complemented
326	#535	C₂²×C₁₃	1	1	yes	characteristic
327	#533	C₂²×C₁₃	1	1	yes	characteristic
328	#532	C₂²×C₁₃	1	1	yes	characteristic
329	#532	C₂²×C₁₃	1	2	yes	complemented
330	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
332	#529	C₂²×C₁₃	1	4	yes	—
333	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
334	#519	C₂²×C₁₃	1	1	yes	characteristic
335	#518	C₂²×C₁₃	1	1	yes	characteristic
336	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
337	#497	C₂²×C₁₃	1	4	yes	—
338	#497	C₂²×C₁₃	1	4	yes	—
339	#497	C₂²×C₁₃	1	2	yes	—
340	#496	C₂²×C₁₃	1	2	yes	—
341	#495	C₂²×C₁₃	1	4	yes	—
342	#491	C₂²×C₁₃	1	2	yes	complemented
343	#491	C₂²×C₁₃	1	4	yes	complemented
344	#490	C₂²×C₁₃	1	2	yes	complemented
345	#489	C₂²×C₁₃	1	4	yes	complemented
346	#487	C₂²×C₁₃	1	4	yes	complemented
347	#464	C₂²×C₁₃	1	8	yes	complemented
348	#463	C₂²×C₁₃	1	8	yes	—
349	#462	C₂²×C₁₃	1	8	yes	complemented
350	#461	C₂²×C₁₃	1	8	yes	—
351	#452	C₂²×C₁₃	1	8	yes	complemented
352	#451	C₂²×C₁₃	1	8	yes	complemented
353	#449	C₂²×C₁₃	1	8	yes	—
354	#448	C₂²×C₁₃	1	8	yes	—
355	#433	C₂²×C₁₃	1	4	yes	complemented
356	#432	C₂²×C₁₃	1	4	yes	complemented
357	#424	C₂²×C₁₃	1	2	yes	—
358	#419	C₂²×C₁₃	1	2	yes	—
359	#419	C₂²×C₁₃	1	2	yes	—
360	#416	C₂²×C₁₃	1	2	yes	—
361	#416	C₂²×C₁₃	1	2	yes	—
362	#408	C₂²×C₁₃	1	2	yes	—
363	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
365	C₂²×C₁₃	—	2	2	no	—
366	C₂²×C₁₃	—	2	4	no	—
367	C₂²×C₁₃	—	2	2	no	—
368	C₂²×C₁₃	—	4	4	no	—
369	C₂²×C₁₃	—	4	4	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	4	2	no	—
372	C₂²×C₁₃	—	16	2	no	—
373	C₂²×C₁₃	#535	1	2	yes	—
374	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
375	C₄×C₁₃	—	2	2	no	—
376	C₄×C₁₃	—	2	4	no	—
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	4	2	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	—	4	4	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	—	4	2	no	—
384	C₄×C₁₃	#535	1	2	yes	—
385	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
386	2₋¹⁺⁴	—	4	4	no	—
387	2₋¹⁺⁴	—	4	4	no	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	C₂³×C₁₃	1	2	yes	—
391	C₂×#41	C₂³×C₁₃	1	4	yes	—
392	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×Q₈	—	2	2	no	—
394	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
396	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
397	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
398	#137	—	4	4	no	—
399	AGL(1,ℤ/8)	—	4	4	no	—
400	C₂×Q₁₆	—	4	4	no	—
401	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
402	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
403	C₂×SD₁₆	—	4	4	no	—
404	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
405	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
406	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
407	C₂×D₈	C₂³×C₁₃	1	4	yes	—
408	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
409	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
410	C₄⋊Q₈	—	2	1	no	—
411	C₄⋊Q₈	—	2	2	no	—
412	C₄⋊Q₈	—	2	4	no	—
413	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
414	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
415	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
417	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
418	#127	—	2	1	no	—
419	#127	C₂³×C₁₃	1	1	yes	characteristic
420	#126	—	2	4	no	—
421	#126	—	2	4	no	—
422	#125	C₂³×C₁₃	1	2	yes	—
423	#124	—	2	1	no	—
424	#124	—	2	1	no	—
425	#124	—	2	4	no	—
426	#124	—	2	2	no	—
427	#124	C₂³×C₁₃	1	2	yes	—
428	#124	C₂³×C₁₃	1	2	yes	—
429	#124	C₂³×C₁₃	1	2	yes	—
430	#124	C₂³×C₁₃	1	4	yes	—
431	#123	—	2	2	no	—
432	#123	—	2	4	no	—
433	#123	—	2	4	no	—
434	#123	—	2	8	no	—
435	#123	—	2	4	no	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	4	no	—
438	C₂²⋊Q₈	—	2	8	no	—
439	C₂²⋊Q₈	—	2	4	no	—
440	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
441	#121	—	2	2	no	—
442	#121	—	2	4	no	—
443	#121	C₂³×C₁₃	1	4	yes	—
444	#120	—	2	2	no	—
445	C₄×Q₈	—	2	2	no	—
446	C₄×Q₈	—	2	2	no	—
447	C₄×Q₈	D₄×C₁₃	1	2	yes	—
448	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
449	C₄×D₄	—	2	4	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	4	no	—
453	C₄×D₄	D₄×C₁₃	1	4	yes	—
454	C₄×D₄	D₄×C₁₃	1	2	yes	—
455	C₄×D₄	C₂³×C₁₃	1	4	yes	—
456	#117	—	2	2	no	—
457	#117	—	2	4	no	—
458	#117	C₂³×C₁₃	1	1	yes	characteristic
459	#117	C₂³×C₁₃	1	1	yes	characteristic
460	#117	C₂³×C₁₃	1	1	yes	characteristic
461	#117	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄⋊C₄	—	2	2	no	—
463	C₂×C₄⋊C₄	—	2	4	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	—	2	2	no	—
466	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
468	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
469	#103	C₂³×C₁₃	1	4	yes	—
470	#103	C₂³×C₁₃	1	4	yes	—
471	#103	C₂³×C₁₃	1	8	yes	—
472	#103	C₂³×C₁₃	1	8	yes	—
473	#102	C₂³×C₁₃	1	4	yes	—
474	#102	C₂³×C₁₃	1	4	yes	—
475	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
476	#97	C₂³×C₁₃	1	2	yes	—
477	#97	C₂³×C₁₃	1	2	yes	—
478	#97	C₂³×C₁₃	1	2	yes	—
479	C₄×C₈	C₂³×C₁₃	1	2	yes	—
480	C₂×C₁₃	—	2	2	no	—
481	C₂×C₁₃	—	4	2	no	—
482	C₂×C₁₃	—	8	2	no	—
483	C₂×C₁₃	—	8	2	no	—
484	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
485	C₂×C₁₃	#3586	1	2	yes	—
486	C₂⁴	—	2	1	no	—
487	#41	—	2	4	no	—
488	#41	—	2	4	no	—
489	#41	—	2	4	no	—
490	#41	—	4	4	no	—
491	#41	—	4	4	no	—
492	#41	—	4	16	no	—
493	#41	—	4	8	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	—	2	4	no	—
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	—	4	4	no	—
503	C₂×Q₈	—	4	8	no	—
504	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
506	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
507	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
515	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
517	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	Q₁₆	—	4	8	no	—
529	Q₁₆	—	4	4	no	—
530	SD₁₆	—	4	8	no	—
531	SD₁₆	—	4	4	no	—
532	SD₁₆	—	4	4	no	—
533	D₈	—	4	4	no	—
534	M₁₆	—	2	4	no	—
535	C₂×C₈	—	2	4	no	—
536	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
537	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	8	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
548	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
549	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
550	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
561	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	C₂×D₄×C₁₃	1	4	yes	—
566	C₄²	C₂×D₄×C₁₃	1	2	yes	—
567	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
568	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₄²	C₂⁴×C₁₃	1	2	yes	—
570	C₁₃	#60828	1	1	yes	characteristic, direct product factor, Sylow
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	8	2	no	—
575	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
576	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	2	4	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	4	no	—
581	Q₈	—	2	4	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	8	no	—
584	Q₈	—	4	4	no	—
585	Q₈	—	4	2	no	—
586	Q₈	—	8	2	no	—
587	D₄	—	2	4	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	8	no	—
594	D₄	—	4	4	no	—
595	D₄	—	4	2	no	—
596	D₄	—	8	4	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	8	no	—
606	C₂×C₄	—	4	8	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
612	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
613	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
614	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
616	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
617	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
618	C₈	—	2	4	no	—
619	C₈	—	2	4	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	4	4	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	16	2	no	—
628	C₂²	C₁₃×#535	1	2	yes	—
629	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	C₁₃×#535	1	2	yes	—
640	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
641	C₂	—	2	2	no	—
642	C₂	—	4	2	no	—
643	C₂	—	8	2	no	—
644	C₂	—	8	2	no	—
645	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
646	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3219	C₂	semidirect
5. C₁₃×#3218	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₂×C₁₃×#497	C₂	semidirect
8. C₁₃×#3139	C₂	semidirect
9. C₁₃×#3135	C₂	semidirect
10. C₁₃×#3044	C₂	semidirect
11. C₁₃×#3042	C₂	semidirect
12. C₁₃×#3011	C₂	semidirect
13. C₁₃×#3010	C₂	semidirect
14. C₁₃×#2923	C₂	semidirect
29. C₁₃×#536	C₂²	semidirect
33. C₁₃×#532	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
46. C₁₃×#491	C₂²	semidirect
47. C₁₃×#491	C₂²	semidirect
48. C₁₃×#490	C₂²	semidirect
49. C₁₃×#489	C₂²	semidirect
50. C₁₃×#487	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
53. C₁₃×#462	C₂²	semidirect
55. C₁₃×#452	C₂²	semidirect
56. C₁₃×#451	C₂²	semidirect
59. C₁₃×#433	C₂²	semidirect
60. C₁₃×#432	C₂²	semidirect
163. #60828	C₁₃	direct (N × H)
248. #3510	C₂×C₁₃	semidirect
249. #3499	C₂×C₁₃	semidirect
250. #3225	C₂×C₁₃	semidirect
251. #3219	C₂×C₁₃	semidirect
252. #3218	C₂×C₁₃	semidirect
253. #3153	C₂×C₁₃	semidirect
254. C₂×#497	C₂×C₁₃	semidirect
255. #3139	C₂×C₁₃	semidirect
256. #3135	C₂×C₁₃	semidirect
257. #3044	C₂×C₁₃	semidirect
258. #3042	C₂×C₁₃	semidirect
259. #3011	C₂×C₁₃	semidirect
260. #3010	C₂×C₁₃	semidirect
261. #2923	C₂×C₁₃	semidirect
325. #536	C₂²×C₁₃	semidirect
329. #532	C₂²×C₁₃	semidirect
331. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
342. #491	C₂²×C₁₃	semidirect
343. #491	C₂²×C₁₃	semidirect
344. #490	C₂²×C₁₃	semidirect
345. #489	C₂²×C₁₃	semidirect
346. #487	C₂²×C₁₃	semidirect
347. #464	C₂²×C₁₃	semidirect
349. #462	C₂²×C₁₃	semidirect
351. #452	C₂²×C₁₃	semidirect
352. #451	C₂²×C₁₃	semidirect
355. #433	C₂²×C₁₃	semidirect
356. #432	C₂²×C₁₃	semidirect
570. C₁₃	#60828	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×#3510	2
C₁₃×#3499	2
C₁₃×#3225	2
C₁₃×#3219	2
C₁₃×#3218	2
C₁₃×#3153	2
C₂×C₁₃×#497	2
C₁₃×#3139	2
C₁₃×#3135	2
C₁₃×#3044	2
C₁₃×#3042	2
C₁₃×#3011	2
C₁₃×#3010	2
C₁₃×#2923	2
#60828	13

Subgroups — C13×#60828 #15747167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60828 #15747167