Subgroups — C₁₃×#60945 #15747284

Order 3328.

1866 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3250	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3232	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3187	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3186	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#3168	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3108	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3105	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	—	2	2	no	—
13	C₁₃×#529	—	2	2	no	—
14	C₁₃×#529	—	2	2	no	—
15	C₁₃×#529	—	2	2	no	—
16	C₁₃×#529	C₂²	1	4	yes	—
17	C₁₃×#529	C₂²	1	4	yes	—
18	C₁₃×#529	C₂²	1	4	yes	complemented
19	C₁₃×#529	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#126	—	2	2	no	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₂×C₄×D₄×C₁₃	—	2	2	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#117	—	2	2	no	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#499	C₂²	1	4	yes	complemented
32	C₁₃×#495	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#484	C₂²	1	4	yes	complemented
35	C₁₃×#483	C₂²	1	4	yes	complemented
36	C₁₃×#481	C₂²	1	4	yes	—
37	C₁₃×#480	C₂²	1	4	yes	—
38	C₁₃×#479	C₂²	1	8	yes	complemented
39	C₁₃×#478	C₂²	1	8	yes	complemented
40	C₁₃×#467	C₂²	1	4	yes	complemented
41	C₁₃×#466	C₂²	1	4	yes	—
42	C₁₃×#465	C₂²	1	8	yes	complemented
43	C₁₃×#464	C₂²	1	8	yes	complemented
44	C₁₃×#463	C₂²	1	8	yes	complemented
45	C₁₃×#451	C₂²	1	4	yes	complemented
46	C₁₃×#450	C₂²	1	4	yes	complemented
47	C₁₃×#448	C₂²	1	4	yes	—
48	C₁₃×#447	C₂²	1	4	yes	—
49	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
50	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
52	C₁₃×#431	C₂²	1	4	yes	complemented
53	C₁₃×#431	C₂²	1	4	yes	complemented
54	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	—	2	2	no	—
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
67	C₂×C₁₃×D₈	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
70	C₁₃×#126	—	2	4	no	—
71	C₁₃×#126	—	2	4	no	—
72	C₁₃×#126	—	2	4	no	—
73	C₁₃×#126	—	2	4	no	—
74	C₁₃×#125	—	2	2	no	—
75	C₁₃×#125	—	2	2	no	—
76	C₁₃×#125	C₂³	1	4	yes	—
77	C₁₃×#125	C₂³	1	4	yes	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#124	C₂³	1	4	yes	—
81	C₁₃×#124	C₂³	1	4	yes	—
82	C₁₃×#123	—	2	4	no	—
83	C₁₃×#123	—	2	4	no	—
84	C₁₃×#123	—	2	4	no	—
85	C₁₃×#123	—	2	4	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	C₂³	1	4	yes	—
93	C₁₃×#121	C₂³	1	4	yes	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
98	C₄×D₄×C₁₃	—	2	4	no	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	4	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	C₂³	1	4	yes	—
106	C₁₃×#117	—	2	4	no	—
107	C₁₃×#117	—	2	4	no	—
108	C₁₃×#117	—	2	4	no	—
109	C₁₃×#117	—	2	4	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₄²×C₁₃	—	2	2	no	—
122	C₂×C₄²×C₁₃	D₄	1	2	yes	—
123	C₂×C₄²×C₁₃	D₄	1	2	yes	—
124	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₁₃×#107	C₂³	1	4	yes	—
131	C₁₃×#107	C₂³	1	4	yes	—
132	C₁₃×#106	C₂³	1	8	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
134	C₁₃×#103	C₂³	1	8	yes	—
135	C₁₃×#103	C₂³	1	8	yes	—
136	C₁₃×#102	C₂³	1	8	yes	—
137	C₁₃×#102	C₂³	1	8	yes	—
138	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
139	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
140	C₄×C₈×C₁₃	C₂³	1	4	yes	—
141	C₄×C₈×C₁₃	C₂³	1	4	yes	—
142	#60945	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	2	no	—
144	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	4	4	no	—
147	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	4	4	no	—
152	C₂×D₄×C₁₃	—	4	8	no	—
153	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	8	no	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×Q₁₆	—	4	4	no	—
176	C₁₃×SD₁₆	—	4	8	no	—
177	C₁₃×D₈	—	4	4	no	—
178	C₂×C₈×C₁₃	—	4	2	no	—
179	C₂×C₈×C₁₃	—	4	2	no	—
180	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
181	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₄²×C₁₃	—	2	4	no	—
205	C₄²×C₁₃	—	2	4	no	—
206	C₄²×C₁₃	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	C₂×D₄	1	2	yes	—
208	C₄²×C₁₃	C₂×D₄	1	2	yes	—
209	C₄²×C₁₃	C₂×D₄	1	2	yes	—
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂×D₄	1	2	yes	—
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₄²×C₁₃	C₂⁴	1	2	yes	—
215	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂×#529	C₂×C₁₃	1	2	yes	complemented
217	#3250	C₂×C₁₃	1	4	yes	complemented
218	#3232	C₂×C₁₃	1	4	yes	complemented
219	#3211	C₂×C₁₃	1	4	yes	complemented
220	#3189	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3187	C₂×C₁₃	1	2	yes	complemented
222	#3186	C₂×C₁₃	1	1	yes	characteristic
223	#3168	C₂×C₁₃	1	4	yes	complemented
224	#3108	C₂×C₁₃	1	4	yes	complemented
225	#3105	C₂×C₁₃	1	4	yes	complemented
226	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	4	no	—
231	C₂³×C₁₃	—	4	4	no	—
232	C₂³×C₁₃	—	4	4	no	—
233	C₂³×C₁₃	#135	1	4	yes	—
234	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
236	Q₈×C₁₃	—	2	8	no	—
237	Q₈×C₁₃	—	4	4	no	—
238	D₄×C₁₃	—	2	8	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	8	no	—
241	D₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	4	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
271	C₈×C₁₃	—	2	4	no	—
272	C₈×C₁₃	—	2	4	no	—
273	#529	—	2	2	no	—
274	#529	—	2	2	no	—
275	#529	—	2	2	no	—
276	#529	—	2	2	no	—
277	#529	C₂²×C₁₃	1	4	yes	—
278	#529	C₂²×C₁₃	1	4	yes	—
279	#529	C₂²×C₁₃	1	4	yes	complemented
280	#529	C₂²×C₁₃	1	4	yes	complemented
281	C₂×#126	—	2	2	no	—
282	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
283	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
284	C₂×#123	—	2	2	no	—
285	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
286	C₂×#121	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
288	C₂×C₄×D₄	—	2	2	no	—
289	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
290	C₂×#117	—	2	2	no	—
291	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
292	#499	C₂²×C₁₃	1	4	yes	complemented
293	#495	C₂²×C₁₃	1	4	yes	complemented
294	#488	C₂²×C₁₃	1	8	yes	complemented
295	#484	C₂²×C₁₃	1	4	yes	complemented
296	#483	C₂²×C₁₃	1	4	yes	complemented
297	#481	C₂²×C₁₃	1	4	yes	—
298	#480	C₂²×C₁₃	1	4	yes	—
299	#479	C₂²×C₁₃	1	8	yes	complemented
300	#478	C₂²×C₁₃	1	8	yes	complemented
301	#467	C₂²×C₁₃	1	4	yes	complemented
302	#466	C₂²×C₁₃	1	4	yes	—
303	#465	C₂²×C₁₃	1	8	yes	complemented
304	#464	C₂²×C₁₃	1	8	yes	complemented
305	#463	C₂²×C₁₃	1	8	yes	complemented
306	#451	C₂²×C₁₃	1	4	yes	complemented
307	#450	C₂²×C₁₃	1	4	yes	complemented
308	#448	C₂²×C₁₃	1	4	yes	—
309	#447	C₂²×C₁₃	1	4	yes	—
310	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
311	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
312	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
313	#431	C₂²×C₁₃	1	4	yes	complemented
314	#431	C₂²×C₁₃	1	4	yes	complemented
315	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
316	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	8	8	no	—
328	C₂²×C₁₃	C₂×#135	1	4	yes	—
329	C₂²×C₁₃	C₂×#135	1	2	yes	—
330	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	4	4	no	—
339	C₄×C₁₃	—	4	4	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	#575	1	2	yes	—
342	C₄×C₁₃	#585	1	2	yes	—
343	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
348	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
351	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
352	C₂×D₈	C₂³×C₁₃	1	4	yes	—
353	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
354	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
355	#126	—	2	4	no	—
356	#126	—	2	4	no	—
357	#126	—	2	4	no	—
358	#126	—	2	4	no	—
359	#125	—	2	2	no	—
360	#125	—	2	2	no	—
361	#125	C₂³×C₁₃	1	4	yes	—
362	#125	C₂³×C₁₃	1	4	yes	—
363	#124	—	2	2	no	—
364	#124	—	2	2	no	—
365	#124	C₂³×C₁₃	1	4	yes	—
366	#124	C₂³×C₁₃	1	4	yes	—
367	#123	—	2	4	no	—
368	#123	—	2	4	no	—
369	#123	—	2	4	no	—
370	#123	—	2	4	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
374	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
375	#121	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	C₂³×C₁₃	1	4	yes	—
378	#121	C₂³×C₁₃	1	4	yes	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
382	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	—	2	4	no	—
385	C₄×D₄	—	2	4	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	C₂³×C₁₃	1	4	yes	—
390	C₄×D₄	C₂³×C₁₃	1	4	yes	—
391	#117	—	2	4	no	—
392	#117	—	2	4	no	—
393	#117	—	2	4	no	—
394	#117	—	2	4	no	—
395	C₂×C₄⋊C₄	—	2	2	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	—	2	2	no	—
406	C₂×C₄²	—	2	2	no	—
407	C₂×C₄²	D₄×C₁₃	1	2	yes	—
408	C₂×C₄²	D₄×C₁₃	1	2	yes	—
409	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	#107	C₂³×C₁₃	1	4	yes	—
416	#107	C₂³×C₁₃	1	4	yes	—
417	#106	C₂³×C₁₃	1	8	yes	—
418	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
419	#103	C₂³×C₁₃	1	8	yes	—
420	#103	C₂³×C₁₃	1	8	yes	—
421	#102	C₂³×C₁₃	1	8	yes	—
422	#102	C₂³×C₁₃	1	8	yes	—
423	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
424	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
425	C₄×C₈	C₂³×C₁₃	1	4	yes	—
426	C₄×C₈	C₂³×C₁₃	1	4	yes	—
427	C₂×C₁₃	—	2	4	no	—
428	C₂×C₁₃	—	2	2	no	—
429	C₂×C₁₃	—	8	4	no	—
430	C₂×C₁₃	#3449	1	1	yes	characteristic
431	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
432	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
433	C₂⁴	—	2	2	no	—
434	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	4	4	no	—
437	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	8	no	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
465	Q₁₆	—	4	4	no	—
466	SD₁₆	—	4	8	no	—
467	D₈	—	4	4	no	—
468	C₂×C₈	—	4	2	no	—
469	C₂×C₈	—	4	2	no	—
470	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
471	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
483	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	4	no	—
496	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₃	1	2	yes	—
498	C₄²	C₂×D₄×C₁₃	1	2	yes	—
499	C₄²	C₂×D₄×C₁₃	1	2	yes	—
500	C₄²	C₂×D₄×C₁₃	1	2	yes	—
501	C₄²	C₂×D₄×C₁₃	1	2	yes	—
502	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
505	C₄²	C₂⁴×C₁₃	1	2	yes	—
506	C₁₃	#60945	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	4	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	4	no	—
513	C₂³	C₁₃×#135	1	4	yes	—
514	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
516	Q₈	—	2	8	no	—
517	Q₈	—	4	4	no	—
518	D₄	—	2	8	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	8	no	—
521	D₄	—	4	8	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	8	no	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
551	C₈	—	2	4	no	—
552	C₈	—	2	4	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	8	8	no	—
562	C₂²	C₂×C₁₃×#135	1	4	yes	—
563	C₂²	C₂×C₁₃×#135	1	2	yes	—
564	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	C₁₃×#575	1	2	yes	—
576	C₄	C₁₃×#585	1	2	yes	—
577	C₂	—	2	4	no	—
578	C₂	—	2	2	no	—
579	C₂	—	8	4	no	—
580	C₂	C₁₃×#3449	1	1	yes	characteristic
581	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
582	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₁₃×#3186	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₁₃×#3250	C₂	semidirect
3. C₁₃×#3232	C₂	semidirect
4. C₁₃×#3211	C₂	semidirect
5. C₁₃×#3189	C₂	semidirect
6. C₁₃×#3187	C₂	semidirect
8. C₁₃×#3168	C₂	semidirect
9. C₁₃×#3108	C₂	semidirect
10. C₁₃×#3105	C₂	semidirect
11. C₂×C₁₃×#431	C₂	semidirect
18. C₁₃×#529	C₂²	semidirect
19. C₁₃×#529	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#495	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#484	C₂²	semidirect
35. C₁₃×#483	C₂²	semidirect
38. C₁₃×#479	C₂²	semidirect
39. C₁₃×#478	C₂²	semidirect
40. C₁₃×#467	C₂²	semidirect
42. C₁₃×#465	C₂²	semidirect
43. C₁₃×#464	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#451	C₂²	semidirect
46. C₁₃×#450	C₂²	semidirect
49. C₄×C₁₃×Q₁₆	C₂²	semidirect
50. C₄×C₁₃×SD₁₆	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
52. C₁₃×#431	C₂²	semidirect
53. C₁₃×#431	C₂²	semidirect
54. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
57. C₂×C₄×C₈×C₁₃	C₂²	semidirect
142. #60945	C₁₃	direct (N × H)
216. C₂×#529	C₂×C₁₃	semidirect
217. #3250	C₂×C₁₃	semidirect
218. #3232	C₂×C₁₃	semidirect
219. #3211	C₂×C₁₃	semidirect
220. #3189	C₂×C₁₃	semidirect
221. #3187	C₂×C₁₃	semidirect
223. #3168	C₂×C₁₃	semidirect
224. #3108	C₂×C₁₃	semidirect
225. #3105	C₂×C₁₃	semidirect
226. C₂×#431	C₂×C₁₃	semidirect
279. #529	C₂²×C₁₃	semidirect
280. #529	C₂²×C₁₃	semidirect
282. C₂×#125	C₂²×C₁₃	semidirect
283. C₂×#124	C₂²×C₁₃	semidirect
287. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
289. C₂×C₄×D₄	C₂²×C₁₃	semidirect
292. #499	C₂²×C₁₃	semidirect
293. #495	C₂²×C₁₃	semidirect
294. #488	C₂²×C₁₃	semidirect
295. #484	C₂²×C₁₃	semidirect
296. #483	C₂²×C₁₃	semidirect
299. #479	C₂²×C₁₃	semidirect
300. #478	C₂²×C₁₃	semidirect
301. #467	C₂²×C₁₃	semidirect
303. #465	C₂²×C₁₃	semidirect
304. #464	C₂²×C₁₃	semidirect
305. #463	C₂²×C₁₃	semidirect
306. #451	C₂²×C₁₃	semidirect
307. #450	C₂²×C₁₃	semidirect
310. C₄×Q₁₆	C₂²×C₁₃	semidirect
311. C₄×SD₁₆	C₂²×C₁₃	semidirect
312. C₄×D₈	C₂²×C₁₃	semidirect
313. #431	C₂²×C₁₃	semidirect
314. #431	C₂²×C₁₃	semidirect
315. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
318. C₂×C₄×C₈	C₂²×C₁₃	semidirect
506. C₁₃	#60945	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×#529	2
C₁₃×#3250	2
C₁₃×#3232	2
C₁₃×#3211	2
C₁₃×#3189	2
C₁₃×#3187	2
C₁₃×#3186	2
C₁₃×#3168	2
C₁₃×#3108	2
C₁₃×#3105	2
C₂×C₁₃×#431	2
#60945	13

Subgroups — C13×#60945 #15747284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60945 #15747284