Subgroups — C₁₃×#60699 #15747038

Order 3328.

1842 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3461	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3185	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3183	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3181	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3178	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3177	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3173	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₁₃×#544	C₂²	1	2	yes	—
24	C₁₃×#542	—	2	2	no	—
25	C₁₃×#542	C₂²	1	4	yes	—
26	C₁₃×#541	—	2	2	no	—
27	C₁₃×#541	C₂²	1	4	yes	—
28	C₁₃×#539	—	2	4	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#536	C₂²	1	2	yes	—
31	C₁₃×#536	C₂²	1	2	yes	—
32	C₁₃×#533	—	2	2	no	—
33	C₁₃×#533	C₂²	1	4	yes	—
34	C₁₃×#529	—	2	4	no	—
35	C₁₃×#529	—	2	2	no	—
36	C₁₃×#529	C₂²	1	4	yes	—
37	C₄×C₁₃×#41	C₂²	1	2	yes	—
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#501	C₂²	1	4	yes	—
41	C₁₃×#499	C₂²	1	2	yes	—
42	C₁₃×#498	C₂²	1	2	yes	—
43	C₁₃×#497	C₂²	1	4	yes	—
44	C₁₃×#495	C₂²	1	2	yes	—
45	C₁₃×#494	C₂²	1	2	yes	—
46	C₁₃×#491	C₂²	1	4	yes	—
47	C₁₃×#489	C₂²	1	4	yes	—
48	C₁₃×#488	C₂²	1	4	yes	—
49	C₁₃×#487	C₂²	1	4	yes	—
50	C₁₃×#470	C₂²	1	2	yes	—
51	C₁₃×#470	C₂²	1	2	yes	—
52	C₁₃×#470	C₂²	1	2	yes	—
53	C₁₃×#470	C₂²	1	4	yes	—
54	C₁₃×#469	C₂²	1	2	yes	—
55	C₁₃×#468	C₂²	1	4	yes	—
56	C₁₃×#467	C₂²	1	4	yes	—
57	C₁₃×#467	C₂²	1	4	yes	—
58	C₁₃×#465	C₂²	1	4	yes	—
59	C₁₃×#465	C₂²	1	4	yes	—
60	C₁₃×#442	C₂²	1	1	yes	characteristic
61	C₁₃×#442	C₂²	1	1	yes	characteristic
62	C₁₃×#441	C₂²	1	2	yes	—
63	C₁₃×#441	C₂²	1	1	yes	characteristic
64	C₁₃×#441	C₂²	1	2	yes	—
65	C₁₃×#441	C₂²	1	2	yes	—
66	C₁₃×#441	C₂²	1	4	yes	—
67	C₁₃×#441	C₂²	1	2	yes	—
68	C₁₃×#441	C₂²	1	1	yes	characteristic
69	C₁₃×#440	C₂²	1	2	yes	—
70	C₁₃×#440	C₂²	1	2	yes	—
71	C₁₃×#440	C₂²	1	4	yes	—
72	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
73	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
74	C₁₃×#428	C₂²	1	2	yes	—
75	C₁₃×#427	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
77	C₁₃×#419	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₂×C₁₃×#103	C₂²	1	2	yes	—
81	C₁₃×#405	C₂²	1	1	yes	characteristic
82	C₁₃×#405	C₂²	1	1	yes	characteristic
83	C₁₃×#405	C₂²	1	2	yes	—
84	C₁₃×#405	C₂²	1	2	yes	—
85	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
86	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×#97	C₂²	1	2	yes	—
88	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#41	C₂³	1	2	yes	—
90	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
92	C₁₃×#137	—	2	8	no	—
93	C₁₃×#135	—	2	4	no	—
94	C₂×C₁₃×Q₁₆	—	2	4	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
102	C₁₃×#131	—	2	4	no	—
103	C₁₃×#131	—	2	4	no	—
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	—	2	2	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×#126	—	2	4	no	—
117	C₁₃×#126	—	2	4	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#125	—	2	4	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	4	no	—
127	C₁₃×#124	C₂³	1	4	yes	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×#123	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	C₂³	1	4	yes	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	2	no	—
146	C₄×Q₈×C₁₃	—	2	4	no	—
147	C₄×Q₈×C₁₃	D₄	1	2	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	4	no	—
155	C₄×D₄×C₁₃	D₄	1	4	yes	—
156	C₄×D₄×C₁₃	D₄	1	2	yes	—
157	C₄×D₄×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	C₂³	1	2	yes	—
159	C₁₃×#117	—	2	4	no	—
160	C₁₃×#117	—	2	2	no	—
161	C₁₃×#117	—	2	4	no	—
162	C₁₃×#117	C₂³	1	2	yes	—
163	C₁₃×#117	C₂³	1	1	yes	characteristic
164	C₁₃×#117	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	—	2	2	no	—
168	C₂×C₄²×C₁₃	—	2	2	no	—
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#107	C₂³	1	4	yes	—
173	C₁₃×#106	C₂³	1	2	yes	—
174	C₁₃×#106	C₂³	1	2	yes	—
175	C₁₃×#106	C₂³	1	1	yes	characteristic
176	C₁₃×#106	C₂³	1	1	yes	characteristic
177	C₁₃×#106	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#103	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	2	yes	—
181	C₁₃×#103	C₂³	1	2	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	2	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×#97	C₂³	1	1	yes	characteristic
189	C₁₃×#97	C₂³	1	2	yes	—
190	C₁₃×#97	C₂³	1	1	yes	characteristic
191	C₁₃×#97	C₂³	1	1	yes	characteristic
192	C₁₃×#97	C₂³	1	1	yes	characteristic
193	C₁₃×#97	C₂³	1	2	yes	—
194	C₁₃×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₁₃	C₂³	1	2	yes	—
196	C₄×C₈×C₁₃	C₂³	1	2	yes	—
197	C₄×C₈×C₁₃	C₂³	1	2	yes	—
198	#60699	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃×#41	—	2	2	no	—
200	C₁₃×#41	—	2	2	no	—
201	C₁₃×#41	—	2	4	no	—
202	C₁₃×#41	—	2	4	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	4	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₁₃×Q₁₆	—	2	4	no	—
225	C₁₃×Q₁₆	—	2	4	no	—
226	C₁₃×Q₁₆	—	2	2	no	—
227	C₁₃×Q₁₆	—	2	8	no	—
228	C₁₃×SD₁₆	—	2	4	no	—
229	C₁₃×SD₁₆	—	2	8	no	—
230	C₁₃×D₈	—	2	2	no	—
231	C₁₃×M₁₆	—	2	2	no	—
232	C₁₃×M₁₆	—	2	4	no	—
233	C₁₃×M₁₆	—	2	4	no	—
234	C₁₃×M₁₆	#41	1	4	yes	—
235	C₂×C₈×C₁₃	—	2	2	no	—
236	C₂×C₈×C₁₃	—	2	4	no	—
237	C₂×C₈×C₁₃	—	2	4	no	—
238	C₂×C₈×C₁₃	#41	1	4	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	—	2	2	no	—
278	C₄²×C₁₃	—	2	4	no	—
279	C₄²×C₁₃	C₂×D₄	1	2	yes	—
280	C₄²×C₁₃	C₂×D₄	1	4	yes	—
281	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₁₃	C₂⁴	1	2	yes	—
283	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
284	#3461	C₂×C₁₃	1	2	yes	complemented
285	#3185	C₂×C₁₃	1	2	yes	complemented
286	#3183	C₂×C₁₃	1	2	yes	complemented
287	#3181	C₂×C₁₃	1	4	yes	complemented
288	#3178	C₂×C₁₃	1	4	yes	complemented
289	#3177	C₂×C₁₃	1	2	yes	complemented
290	#3173	C₂×C₁₃	1	2	yes	complemented
291	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3137	C₂×C₁₃	1	2	yes	complemented
294	#3063	C₂×C₁₃	1	2	yes	complemented
295	#3060	C₂×C₁₃	1	1	yes	characteristic
296	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₄×#137	C₂×C₁₃	1	2	yes	complemented
298	#2943	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
303	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₁₃	—	2	2	no	—
305	Q₈×C₁₃	—	2	4	no	—
306	Q₈×C₁₃	—	2	2	no	—
307	Q₈×C₁₃	—	2	4	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	4	4	no	—
310	Q₈×C₁₃	—	8	4	no	—
311	D₄×C₁₃	—	2	4	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	2	2	no	—
314	D₄×C₁₃	—	2	2	no	—
315	D₄×C₁₃	—	4	4	no	—
316	D₄×C₁₃	—	8	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	4	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	4	no	—
324	C₂×C₄×C₁₃	—	4	2	no	—
325	C₂×C₄×C₁₃	—	4	4	no	—
326	C₂×C₄×C₁₃	—	4	4	no	—
327	C₂×C₄×C₁₃	—	4	4	no	—
328	C₂×C₄×C₁₃	—	4	4	no	—
329	C₂×C₄×C₁₃	—	8	2	no	—
330	C₂×C₄×C₁₃	—	8	2	no	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
337	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
339	C₈×C₁₃	—	2	1	no	—
340	C₈×C₁₃	—	2	1	no	—
341	C₈×C₁₃	—	2	2	no	—
342	C₈×C₁₃	C₂×#41	1	2	yes	—
343	C₈×C₁₃	C₂×#41	1	4	yes	—
344	C₈×C₁₃	C₂×#41	1	2	yes	—
345	C₂×#137	C₂²×C₁₃	1	2	yes	—
346	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
350	#544	C₂²×C₁₃	1	2	yes	—
351	#542	—	2	2	no	—
352	#542	C₂²×C₁₃	1	4	yes	—
353	#541	—	2	2	no	—
354	#541	C₂²×C₁₃	1	4	yes	—
355	#539	—	2	4	no	—
356	#537	C₂²×C₁₃	1	2	yes	—
357	#536	C₂²×C₁₃	1	2	yes	—
358	#536	C₂²×C₁₃	1	2	yes	—
359	#533	—	2	2	no	—
360	#533	C₂²×C₁₃	1	4	yes	—
361	#529	—	2	4	no	—
362	#529	—	2	2	no	—
363	#529	C₂²×C₁₃	1	4	yes	—
364	C₄×#41	C₂²×C₁₃	1	2	yes	—
365	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
367	#501	C₂²×C₁₃	1	4	yes	—
368	#499	C₂²×C₁₃	1	2	yes	—
369	#498	C₂²×C₁₃	1	2	yes	—
370	#497	C₂²×C₁₃	1	4	yes	—
371	#495	C₂²×C₁₃	1	2	yes	—
372	#494	C₂²×C₁₃	1	2	yes	—
373	#491	C₂²×C₁₃	1	4	yes	—
374	#489	C₂²×C₁₃	1	4	yes	—
375	#488	C₂²×C₁₃	1	4	yes	—
376	#487	C₂²×C₁₃	1	4	yes	—
377	#470	C₂²×C₁₃	1	2	yes	—
378	#470	C₂²×C₁₃	1	2	yes	—
379	#470	C₂²×C₁₃	1	2	yes	—
380	#470	C₂²×C₁₃	1	4	yes	—
381	#469	C₂²×C₁₃	1	2	yes	—
382	#468	C₂²×C₁₃	1	4	yes	—
383	#467	C₂²×C₁₃	1	4	yes	—
384	#467	C₂²×C₁₃	1	4	yes	—
385	#465	C₂²×C₁₃	1	4	yes	—
386	#465	C₂²×C₁₃	1	4	yes	—
387	#442	C₂²×C₁₃	1	1	yes	characteristic
388	#442	C₂²×C₁₃	1	1	yes	characteristic
389	#441	C₂²×C₁₃	1	2	yes	—
390	#441	C₂²×C₁₃	1	1	yes	characteristic
391	#441	C₂²×C₁₃	1	2	yes	—
392	#441	C₂²×C₁₃	1	2	yes	—
393	#441	C₂²×C₁₃	1	4	yes	—
394	#441	C₂²×C₁₃	1	2	yes	—
395	#441	C₂²×C₁₃	1	1	yes	characteristic
396	#440	C₂²×C₁₃	1	2	yes	—
397	#440	C₂²×C₁₃	1	2	yes	—
398	#440	C₂²×C₁₃	1	4	yes	—
399	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
400	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
401	#428	C₂²×C₁₃	1	2	yes	—
402	#427	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
404	#419	C₂²×C₁₃	1	2	yes	—
405	#417	C₂²×C₁₃	1	2	yes	—
406	#416	C₂²×C₁₃	1	2	yes	—
407	C₂×#103	C₂²×C₁₃	1	2	yes	—
408	#405	C₂²×C₁₃	1	1	yes	characteristic
409	#405	C₂²×C₁₃	1	1	yes	characteristic
410	#405	C₂²×C₁₃	1	2	yes	—
411	#405	C₂²×C₁₃	1	2	yes	—
412	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
413	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#97	C₂²×C₁₃	1	2	yes	—
415	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	4	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	4	2	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	#532	1	2	yes	—
423	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₁₃	—	2	2	no	—
425	C₄×C₁₃	—	2	2	no	—
426	C₄×C₁₃	—	2	4	no	—
427	C₄×C₁₃	—	2	2	no	—
428	C₄×C₁₃	—	4	2	no	—
429	C₄×C₁₃	—	4	4	no	—
430	C₄×C₁₃	—	4	2	no	—
431	C₄×C₁₃	—	4	2	no	—
432	C₄×C₁₃	—	4	4	no	—
433	C₄×C₁₃	#532	1	2	yes	—
434	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
435	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
436	C₂×#41	C₂³×C₁₃	1	2	yes	—
437	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
439	#137	—	2	8	no	—
440	#135	—	2	4	no	—
441	C₂×Q₁₆	—	2	4	no	—
442	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
443	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
444	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
446	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
447	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
448	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
449	#131	—	2	4	no	—
450	#131	—	2	4	no	—
451	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
453	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
454	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
457	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
458	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₄⋊Q₈	—	2	2	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
462	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
463	#126	—	2	4	no	—
464	#126	—	2	4	no	—
465	#126	—	2	4	no	—
466	#126	—	2	4	no	—
467	#125	—	2	4	no	—
468	#125	—	2	2	no	—
469	#125	—	2	4	no	—
470	#125	—	2	4	no	—
471	#125	C₂³×C₁₃	1	4	yes	—
472	#124	—	2	2	no	—
473	#124	—	2	4	no	—
474	#124	C₂³×C₁₃	1	4	yes	—
475	#123	—	2	4	no	—
476	#123	—	2	4	no	—
477	#123	—	2	4	no	—
478	#123	—	2	4	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
486	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
487	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
488	#121	—	2	4	no	—
489	#121	—	2	2	no	—
490	#121	C₂³×C₁₃	1	4	yes	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	D₄×C₁₃	1	2	yes	—
495	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
496	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
497	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
498	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	D₄×C₁₃	1	4	yes	—
503	C₄×D₄	D₄×C₁₃	1	2	yes	—
504	C₄×D₄	C₂³×C₁₃	1	2	yes	—
505	C₄×D₄	C₂³×C₁₃	1	2	yes	—
506	#117	—	2	4	no	—
507	#117	—	2	2	no	—
508	#117	—	2	4	no	—
509	#117	C₂³×C₁₃	1	2	yes	—
510	#117	C₂³×C₁₃	1	1	yes	characteristic
511	#117	C₂³×C₁₃	1	2	yes	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄²	—	2	2	no	—
515	C₂×C₄²	—	2	2	no	—
516	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
518	#107	C₂³×C₁₃	1	2	yes	—
519	#107	C₂³×C₁₃	1	4	yes	—
520	#106	C₂³×C₁₃	1	2	yes	—
521	#106	C₂³×C₁₃	1	2	yes	—
522	#106	C₂³×C₁₃	1	1	yes	characteristic
523	#106	C₂³×C₁₃	1	1	yes	characteristic
524	#106	C₂³×C₁₃	1	4	yes	—
525	#103	C₂³×C₁₃	1	4	yes	—
526	#103	C₂³×C₁₃	1	4	yes	—
527	#103	C₂³×C₁₃	1	2	yes	—
528	#103	C₂³×C₁₃	1	2	yes	—
529	#103	C₂³×C₁₃	1	4	yes	—
530	#103	C₂³×C₁₃	1	4	yes	—
531	#103	C₂³×C₁₃	1	4	yes	—
532	#102	C₂³×C₁₃	1	2	yes	—
533	#102	C₂³×C₁₃	1	2	yes	—
534	#102	C₂³×C₁₃	1	4	yes	—
535	#97	C₂³×C₁₃	1	1	yes	characteristic
536	#97	C₂³×C₁₃	1	2	yes	—
537	#97	C₂³×C₁₃	1	1	yes	characteristic
538	#97	C₂³×C₁₃	1	1	yes	characteristic
539	#97	C₂³×C₁₃	1	1	yes	characteristic
540	#97	C₂³×C₁₃	1	2	yes	—
541	#97	C₂³×C₁₃	1	2	yes	—
542	C₄×C₈	C₂³×C₁₃	1	2	yes	—
543	C₄×C₈	C₂³×C₁₃	1	2	yes	—
544	C₄×C₈	C₂³×C₁₃	1	2	yes	—
545	C₂×C₁₃	—	2	2	no	—
546	C₂×C₁₃	—	4	2	no	—
547	C₂×C₁₃	—	8	2	no	—
548	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
549	C₂×C₁₃	#3586	1	2	yes	—
550	#41	—	2	2	no	—
551	#41	—	2	2	no	—
552	#41	—	2	4	no	—
553	#41	—	2	4	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	4	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
559	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
560	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
564	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
572	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
575	Q₁₆	—	2	4	no	—
576	Q₁₆	—	2	4	no	—
577	Q₁₆	—	2	2	no	—
578	Q₁₆	—	2	8	no	—
579	SD₁₆	—	2	4	no	—
580	SD₁₆	—	2	8	no	—
581	D₈	—	2	2	no	—
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	4	no	—
584	M₁₆	—	2	4	no	—
585	M₁₆	C₁₃×#41	1	4	yes	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	4	no	—
588	C₂×C₈	—	2	4	no	—
589	C₂×C₈	C₁₃×#41	1	4	yes	—
590	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
592	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
593	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
594	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
595	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
610	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
611	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
612	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
624	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	2	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	4	no	—
630	C₄²	C₂×D₄×C₁₃	1	2	yes	—
631	C₄²	C₂×D₄×C₁₃	1	4	yes	—
632	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
633	C₄²	C₂⁴×C₁₃	1	2	yes	—
634	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₁₃	#60699	1	1	yes	characteristic, direct product factor, Sylow
636	C₂³	—	2	2	no	—
637	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
638	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
639	Q₈	—	2	2	no	—
640	Q₈	—	2	4	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	4	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	8	4	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	4	4	no	—
651	D₄	—	8	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	—	8	2	no	—
666	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
672	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
673	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
674	C₈	—	2	1	no	—
675	C₈	—	2	1	no	—
676	C₈	—	2	2	no	—
677	C₈	C₂×C₁₃×#41	1	2	yes	—
678	C₈	C₂×C₁₃×#41	1	4	yes	—
679	C₈	C₂×C₁₃×#41	1	2	yes	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	C₁₃×#532	1	2	yes	—
687	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	4	no	—
697	C₄	C₁₃×#532	1	2	yes	—
698	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
699	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	8	2	no	—
703	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
704	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3060	C₂
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×#3461	C₂	semidirect
2. C₁₃×#3185	C₂	semidirect
3. C₁₃×#3183	C₂	semidirect
4. C₁₃×#3181	C₂	semidirect
5. C₁₃×#3178	C₂	semidirect
6. C₁₃×#3177	C₂	semidirect
7. C₁₃×#3173	C₂	semidirect
8. C₁₃×#3163	C₂	semidirect
9. C₁₃×#3156	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3063	C₂	semidirect
13. C₁₃×#3059	C₂	semidirect
14. C₄×C₁₃×#137	C₂	semidirect
15. C₁₃×#2943	C₂	semidirect
16. C₂×C₁₃×#441	C₂	semidirect
17. C₁₃×#2875	C₂	semidirect
198. #60699	C₁₃	direct (N × H)
284. #3461	C₂×C₁₃	semidirect
285. #3185	C₂×C₁₃	semidirect
286. #3183	C₂×C₁₃	semidirect
287. #3181	C₂×C₁₃	semidirect
288. #3178	C₂×C₁₃	semidirect
289. #3177	C₂×C₁₃	semidirect
290. #3173	C₂×C₁₃	semidirect
291. #3163	C₂×C₁₃	semidirect
292. #3156	C₂×C₁₃	semidirect
293. #3137	C₂×C₁₃	semidirect
294. #3063	C₂×C₁₃	semidirect
296. #3059	C₂×C₁₃	semidirect
297. C₄×#137	C₂×C₁₃	semidirect
298. #2943	C₂×C₁₃	semidirect
299. C₂×#441	C₂×C₁₃	semidirect
300. #2875	C₂×C₁₃	semidirect
635. C₁₃	#60699	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×#3461	2
C₁₃×#3185	2
C₁₃×#3183	2
C₁₃×#3181	2
C₁₃×#3178	2
C₁₃×#3177	2
C₁₃×#3173	2
C₁₃×#3163	2
C₁₃×#3156	2
C₁₃×#3137	2
C₁₃×#3063	2
C₁₃×#3060	2
C₁₃×#3059	2
C₄×C₁₃×#137	2
C₁₃×#2943	2
C₂×C₁₃×#441	2
C₁₃×#2875	2
#60699	13

Subgroups — C13×#60699 #15747038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60699 #15747038