Subgroups — C₁₃×#60645 #15746984

Order 3328.

3158 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×#137	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3156	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3154	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3153	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3152	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#575	—	2	16	no	—
14	C₂×C₁₃×#137	—	2	16	no	—
15	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
16	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
17	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	8	yes	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
24	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
25	C₁₃×#537	—	2	2	no	—
26	C₁₃×#536	—	2	4	no	—
27	C₁₃×#536	C₂²	1	8	yes	complemented
28	C₁₃×#536	C₂²	1	4	yes	complemented
29	C₁₃×#535	C₂²	1	4	yes	complemented
30	C₁₃×#534	—	2	2	no	—
31	C₁₃×#532	C₂²	1	4	yes	—
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
34	C₁₃×#525	—	2	4	no	—
35	C₂×C₁₃×#123	—	2	2	no	—
36	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₁₃×#497	C₂²	1	16	yes	complemented
39	C₁₃×#497	C₂²	1	8	yes	complemented
40	C₁₃×#496	C₂²	1	8	yes	complemented
41	C₁₃×#495	C₂²	1	16	yes	complemented
42	C₁₃×#494	C₂²	1	8	yes	complemented
43	C₁₃×#492	C₂²	1	8	yes	complemented
44	C₁₃×#405	C₂²	1	8	yes	complemented
45	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	8	no	—
50	C₂×C₁₃×#41	—	2	8	no	—
51	C₂×C₁₃×#41	—	2	8	no	—
52	C₂×C₁₃×#41	C₂³	1	4	yes	—
53	C₂×C₁₃×#41	C₂³	1	4	yes	—
54	C₂×C₁₃×#41	C₂³	1	4	yes	—
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	—	2	2	no	—
57	C₂²×Q₈×C₁₃	—	2	8	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
61	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	—	2	2	no	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#137	—	2	32	no	—
71	C₁₃×#137	—	2	32	no	—
72	C₁₃×#137	—	2	16	no	—
73	C₁₃×#137	—	2	16	no	—
74	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
75	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
76	C₁₃×#135	—	2	32	no	—
77	C₂×C₁₃×Q₁₆	—	2	16	no	—
78	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
79	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
80	C₂×C₁₃×SD₁₆	—	2	16	no	—
81	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
84	C₂×C₁₃×D₈	C₂³	1	8	yes	—
85	C₂×C₁₃×M₁₆	D₄	1	16	yes	complemented
86	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
88	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
89	C₁₃×C₄⋊Q₈	—	2	4	no	—
90	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
92	C₁₃×#127	C₂³	1	4	yes	—
93	C₁₃×#124	—	2	4	no	—
94	C₁₃×#124	C₂³	1	8	yes	—
95	C₁₃×#124	C₂³	1	8	yes	—
96	C₁₃×#123	—	2	16	no	—
97	C₁₃×#123	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	16	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₁₃×#121	—	2	8	no	—
101	C₁₃×#121	—	2	8	no	—
102	C₁₃×#120	—	2	8	no	—
103	C₄×D₄×C₁₃	—	2	8	no	—
104	C₁₃×#117	D₄	1	4	yes	—
105	C₁₃×#117	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₁₃×#97	C₂³	1	8	yes	—
112	C₄×C₈×C₁₃	C₂³	1	8	yes	—
113	#60645	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	1	no	—
115	C₂⁴×C₁₃	—	2	2	no	—
116	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₁₃×#41	—	2	8	no	—
118	C₁₃×#41	—	2	8	no	—
119	C₁₃×#41	—	2	8	no	—
120	C₁₃×#41	—	2	8	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₁₃×#41	—	2	8	no	—
123	C₁₃×#41	—	4	8	no	—
124	C₁₃×#41	—	4	8	no	—
125	C₁₃×#41	—	4	8	no	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	8	no	—
133	C₂×Q₈×C₁₃	—	2	8	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₃	—	4	8	no	—
138	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	8	no	—
150	C₂×D₄×C₁₃	—	4	4	no	—
151	C₂×D₄×C₁₃	—	4	8	no	—
152	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	4	4	no	—
162	C₂²×C₄×C₁₃	—	4	4	no	—
163	C₂²×C₄×C₁₃	—	4	8	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₁₃×Q₁₆	—	2	32	no	—
171	C₁₃×Q₁₆	—	2	16	no	—
172	C₁₃×SD₁₆	—	2	32	no	—
173	C₁₃×SD₁₆	—	2	16	no	—
174	C₁₃×SD₁₆	—	2	16	no	—
175	C₁₃×D₈	—	2	16	no	—
176	C₁₃×M₁₆	C₂×D₄	1	16	yes	—
177	C₁₃×M₁₆	C₂×D₄	1	16	yes	—
178	C₂×C₈×C₁₃	C₂×D₄	1	16	yes	—
179	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
180	C₁₃×C₄⋊C₄	—	2	16	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
183	C₁₃×C₂²⋊C₄	—	2	16	no	—
184	C₁₃×C₂²⋊C₄	—	2	16	no	—
185	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
186	C₄²×C₁₃	C₂×D₄	1	4	yes	—
187	C₄²×C₁₃	C₂⁴	1	4	yes	—
188	C₂×#575	C₂×C₁₃	1	2	yes	complemented
189	C₂²×#137	C₂×C₁₃	1	2	yes	complemented
190	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#3156	C₂×C₁₃	1	8	yes	complemented
193	#3154	C₂×C₁₃	1	8	yes	complemented
194	#3153	C₂×C₁₃	1	4	yes	complemented
195	#3152	C₂×C₁₃	1	4	yes	complemented
196	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	4	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	4	4	no	—
203	C₂³×C₁₃	—	8	4	no	—
204	C₂³×C₁₃	#127	1	4	yes	—
205	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₃	—	2	8	no	—
208	Q₈×C₁₃	—	2	4	no	—
209	Q₈×C₁₃	—	2	4	no	—
210	Q₈×C₁₃	—	2	4	no	—
211	Q₈×C₁₃	—	4	8	no	—
212	Q₈×C₁₃	—	4	4	no	—
213	Q₈×C₁₃	—	4	4	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	D₄×C₁₃	—	2	4	no	—
216	D₄×C₁₃	—	2	4	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	4	8	no	—
219	D₄×C₁₃	—	4	8	no	—
220	D₄×C₁₃	—	4	8	no	—
221	D₄×C₁₃	—	4	4	no	—
222	D₄×C₁₃	—	4	2	no	—
223	D₄×C₁₃	—	8	8	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	8	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	#127	1	4	yes	—
236	C₂×C₄×C₁₃	#127	1	8	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
244	C₈×C₁₃	C₂²×D₄	1	16	yes	—
245	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×#41	C₂²×C₁₃	1	2	yes	—
247	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	#575	—	2	16	no	—
249	C₂×#137	—	2	16	no	—
250	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
251	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
252	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
253	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
254	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
255	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
256	C₂×#135	C₂²×C₁₃	1	8	yes	—
257	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
258	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
259	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
260	#537	—	2	2	no	—
261	#536	—	2	4	no	—
262	#536	C₂²×C₁₃	1	8	yes	complemented
263	#536	C₂²×C₁₃	1	4	yes	complemented
264	#535	C₂²×C₁₃	1	4	yes	complemented
265	#534	—	2	2	no	—
266	#532	C₂²×C₁₃	1	4	yes	—
267	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
268	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
269	#525	—	2	4	no	—
270	C₂×#123	—	2	2	no	—
271	C₂×C₂²⋊Q₈	—	2	2	no	—
272	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
273	#497	C₂²×C₁₃	1	16	yes	complemented
274	#497	C₂²×C₁₃	1	8	yes	complemented
275	#496	C₂²×C₁₃	1	8	yes	complemented
276	#495	C₂²×C₁₃	1	16	yes	complemented
277	#494	C₂²×C₁₃	1	8	yes	complemented
278	#492	C₂²×C₁₃	1	8	yes	complemented
279	#405	C₂²×C₁₃	1	8	yes	complemented
280	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	4	8	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	8	4	no	—
289	C₂²×C₁₃	—	8	8	no	—
290	C₂²×C₁₃	C₂×#127	1	4	yes	—
291	C₂²×C₁₃	C₂×#127	1	2	yes	—
292	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
293	C₄×C₁₃	—	2	8	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	C₂×#127	1	2	yes	—
298	C₄×C₁₃	C₂×#127	1	4	yes	—
299	C₄×C₁₃	C₂³×D₄	1	2	yes	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	8	no	—
304	C₂×#41	—	2	8	no	—
305	C₂×#41	—	2	8	no	—
306	C₂×#41	C₂³×C₁₃	1	4	yes	—
307	C₂×#41	C₂³×C₁₃	1	4	yes	—
308	C₂×#41	C₂³×C₁₃	1	4	yes	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	8	no	—
312	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
313	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
315	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	#137	—	2	32	no	—
325	#137	—	2	32	no	—
326	#137	—	2	16	no	—
327	#137	—	2	16	no	—
328	AGL(1,ℤ/8)	—	2	16	no	—
329	AGL(1,ℤ/8)	—	2	16	no	—
330	#135	—	2	32	no	—
331	C₂×Q₁₆	—	2	16	no	—
332	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
333	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
334	C₂×SD₁₆	—	2	16	no	—
335	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
336	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
337	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
338	C₂×D₈	C₂³×C₁₃	1	8	yes	—
339	C₂×M₁₆	D₄×C₁₃	1	16	yes	complemented
340	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
341	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
342	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
343	C₄⋊Q₈	—	2	4	no	—
344	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
345	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
346	#127	C₂³×C₁₃	1	4	yes	—
347	#124	—	2	4	no	—
348	#124	C₂³×C₁₃	1	8	yes	—
349	#124	C₂³×C₁₃	1	8	yes	—
350	#123	—	2	16	no	—
351	#123	—	2	8	no	—
352	C₂²⋊Q₈	—	2	16	no	—
353	C₂²⋊Q₈	—	2	8	no	—
354	#121	—	2	8	no	—
355	#121	—	2	8	no	—
356	#120	—	2	8	no	—
357	C₄×D₄	—	2	8	no	—
358	#117	D₄×C₁₃	1	4	yes	—
359	#117	C₂³×C₁₃	1	4	yes	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
365	#97	C₂³×C₁₃	1	8	yes	—
366	C₄×C₈	C₂³×C₁₃	1	8	yes	—
367	C₂×C₁₃	—	2	2	no	—
368	C₂×C₁₃	—	2	4	no	—
369	C₂×C₁₃	—	8	4	no	—
370	C₂×C₁₃	—	8	2	no	—
371	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
372	C₂×C₁₃	#3586	1	2	yes	—
373	C₂⁴	—	2	1	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
376	#41	—	2	8	no	—
377	#41	—	2	8	no	—
378	#41	—	2	8	no	—
379	#41	—	2	8	no	—
380	#41	—	2	8	no	—
381	#41	—	2	8	no	—
382	#41	—	4	8	no	—
383	#41	—	4	8	no	—
384	#41	—	4	8	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	8	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	8	no	—
397	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
398	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
399	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	8	no	—
411	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
412	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	8	no	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
429	Q₁₆	—	2	32	no	—
430	Q₁₆	—	2	16	no	—
431	SD₁₆	—	2	32	no	—
432	SD₁₆	—	2	16	no	—
433	SD₁₆	—	2	16	no	—
434	D₈	—	2	16	no	—
435	M₁₆	C₂×D₄×C₁₃	1	16	yes	—
436	M₁₆	C₂×D₄×C₁₃	1	16	yes	—
437	C₂×C₈	C₂×D₄×C₁₃	1	16	yes	—
438	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
439	C₄⋊C₄	—	2	16	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
442	C₂²⋊C₄	—	2	16	no	—
443	C₂²⋊C₄	—	2	16	no	—
444	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
445	C₄²	C₂×D₄×C₁₃	1	4	yes	—
446	C₄²	C₂⁴×C₁₃	1	4	yes	—
447	C₁₃	#60645	1	1	yes	characteristic, direct product factor, Sylow
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	8	4	no	—
455	C₂³	C₁₃×#127	1	4	yes	—
456	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
457	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
458	Q₈	—	2	8	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	2	4	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	4	8	no	—
463	Q₈	—	4	4	no	—
464	Q₈	—	4	4	no	—
465	Q₈	—	4	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	8	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	8	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	C₁₃×#127	1	4	yes	—
487	C₂×C₄	C₁₃×#127	1	8	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
492	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
494	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
495	C₈	C₂²×D₄×C₁₃	1	16	yes	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	8	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	4	no	—
504	C₂²	—	8	8	no	—
505	C₂²	C₂×C₁₃×#127	1	4	yes	—
506	C₂²	C₂×C₁₃×#127	1	2	yes	—
507	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
508	C₄	—	2	8	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	4	no	—
512	C₄	C₂×C₁₃×#127	1	2	yes	—
513	C₄	C₂×C₁₃×#127	1	4	yes	—
514	C₄	C₂³×D₄×C₁₃	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	4	no	—
517	C₂	—	8	4	no	—
518	C₂	—	8	2	no	—
519	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
520	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#575	C₂	semidirect
2. C₂²×C₁₃×#137	C₂	semidirect
3. C₁₃×#3449	C₂	semidirect
4. C₂×C₁₃×#536	C₂	semidirect
5. C₁₃×#3156	C₂	semidirect
6. C₁₃×#3154	C₂	semidirect
7. C₁₃×#3153	C₂	semidirect
8. C₁₃×#3152	C₂	semidirect
9. C₁₃×#2873	C₂	semidirect
15. C₂×C₁₃×#137	C₂²	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂²×C₁₃×Q₁₆	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
27. C₁₃×#536	C₂²	semidirect
28. C₁₃×#536	C₂²	semidirect
29. C₁₃×#535	C₂²	semidirect
32. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#124	C₂²	semidirect
38. C₁₃×#497	C₂²	semidirect
39. C₁₃×#497	C₂²	semidirect
40. C₁₃×#496	C₂²	semidirect
41. C₁₃×#495	C₂²	semidirect
42. C₁₃×#494	C₂²	semidirect
43. C₁₃×#492	C₂²	semidirect
44. C₁₃×#405	C₂²	semidirect
45. C₄×C₁₃×M₁₆	C₂²	semidirect
85. C₂×C₁₃×M₁₆	D₄	semidirect
113. #60645	C₁₃	direct (N × H)
188. C₂×#575	C₂×C₁₃	semidirect
189. C₂²×#137	C₂×C₁₃	semidirect
190. #3449	C₂×C₁₃	semidirect
191. C₂×#536	C₂×C₁₃	semidirect
192. #3156	C₂×C₁₃	semidirect
193. #3154	C₂×C₁₃	semidirect
194. #3153	C₂×C₁₃	semidirect
195. #3152	C₂×C₁₃	semidirect
196. #2873	C₂×C₁₃	semidirect
250. C₂×#137	C₂²×C₁₃	semidirect
251. C₂×#137	C₂²×C₁₃	semidirect
252. C₂×#137	C₂²×C₁₃	semidirect
253. C₂×#137	C₂²×C₁₃	semidirect
254. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
255. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
257. C₂²×Q₁₆	C₂²×C₁₃	semidirect
258. C₂²×SD₁₆	C₂²×C₁₃	semidirect
262. #536	C₂²×C₁₃	semidirect
263. #536	C₂²×C₁₃	semidirect
264. #535	C₂²×C₁₃	semidirect
267. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
268. C₂×#124	C₂²×C₁₃	semidirect
273. #497	C₂²×C₁₃	semidirect
274. #497	C₂²×C₁₃	semidirect
275. #496	C₂²×C₁₃	semidirect
276. #495	C₂²×C₁₃	semidirect
277. #494	C₂²×C₁₃	semidirect
278. #492	C₂²×C₁₃	semidirect
279. #405	C₂²×C₁₃	semidirect
280. C₄×M₁₆	C₂²×C₁₃	semidirect
339. C₂×M₁₆	D₄×C₁₃	semidirect
447. C₁₃	#60645	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#575	2
C₂²×C₁₃×#137	2
C₁₃×#3449	2
C₂×C₁₃×#536	2
C₁₃×#3156	2
C₁₃×#3154	2
C₁₃×#3153	2
C₁₃×#3152	2
C₁₃×#2873	2
#60645	13

Subgroups — C13×#60645 #15746984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60645 #15746984