Subgroups — C₁₃×#60882 #15747221

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3242	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3241	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3233	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3232	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3098	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#557	—	2	2	no	—
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	—	2	2	no	—
19	C₁₃×#553	—	2	4	no	—
20	C₁₃×#553	—	2	2	no	—
21	C₁₃×#552	—	2	2	no	—
22	C₁₃×#544	C₂²	1	2	yes	—
23	C₁₃×#544	C₂²	1	4	yes	—
24	C₁₃×#541	C₂²	1	2	yes	—
25	C₁₃×#540	C₂²	1	2	yes	—
26	C₁₃×#537	C₂²	1	2	yes	—
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#533	C₂²	1	2	yes	—
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#529	C₂²	1	4	yes	—
31	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#125	C₂²	1	2	yes	—
34	C₁₃×#520	C₂²	1	2	yes	—
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₁₃×#501	C₂²	1	4	yes	—
38	C₁₃×#499	C₂²	1	4	yes	—
39	C₁₃×#499	C₂²	1	4	yes	—
40	C₁₃×#499	C₂²	1	2	yes	—
41	C₁₃×#499	C₂²	1	2	yes	—
42	C₁₃×#491	C₂²	1	2	yes	—
43	C₁₃×#490	C₂²	1	2	yes	—
44	C₁₃×#488	C₂²	1	2	yes	—
45	C₁₃×#488	C₂²	1	2	yes	—
46	C₁₃×#488	C₂²	1	4	yes	—
47	C₁₃×#487	C₂²	1	2	yes	—
48	C₁₃×#486	C₂²	1	2	yes	—
49	C₁₃×#485	C₂²	1	4	yes	—
50	C₁₃×#485	C₂²	1	4	yes	—
51	C₁₃×#484	C₂²	1	4	yes	—
52	C₁₃×#483	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	4	yes	—
54	C₁₃×#482	C₂²	1	4	yes	—
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#480	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#479	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#478	C₂²	1	4	yes	—
61	C₁₃×#477	C₂²	1	4	yes	—
62	C₁₃×#476	C₂²	1	4	yes	—
63	C₁₃×#475	C₂²	1	4	yes	—
64	C₁₃×#474	C₂²	1	4	yes	—
65	C₁₃×#433	C₂²	1	4	yes	—
66	C₁₃×#431	C₂²	1	4	yes	—
67	C₁₃×#428	C₂²	1	2	yes	—
68	C₁₃×#428	C₂²	1	2	yes	—
69	C₂×C₁₃×#107	C₂²	1	2	yes	—
70	C₂×C₁₃×#106	C₂²	1	2	yes	—
71	C₁₃×#424	C₂²	1	1	yes	characteristic
72	C₁₃×#424	C₂²	1	1	yes	characteristic
73	C₁₃×#417	C₂²	1	2	yes	—
74	C₁₃×#417	C₂²	1	2	yes	—
75	C₁₃×#416	C₂²	1	2	yes	—
76	C₁₃×#416	C₂²	1	2	yes	—
77	C₁₃×#408	C₂²	1	1	yes	characteristic
78	C₁₃×#408	C₂²	1	1	yes	characteristic
79	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	2	yes	—
82	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	—	2	2	no	—
88	C₁₃×C₄⋊Q₈	—	2	4	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×#127	C₂³	1	1	yes	characteristic
93	C₁₃×#126	—	2	4	no	—
94	C₁₃×#126	—	2	4	no	—
95	C₁₃×#125	—	2	4	no	—
96	C₁₃×#125	—	2	2	no	—
97	C₁₃×#125	—	2	4	no	—
98	C₁₃×#125	—	2	2	no	—
99	C₁₃×#125	—	2	4	no	—
100	C₁₃×#125	—	2	2	no	—
101	C₁₃×#125	C₂³	1	4	yes	—
102	C₁₃×#125	C₂³	1	1	yes	characteristic
103	C₁₃×#125	C₂³	1	2	yes	—
104	C₁₃×#125	C₂³	1	1	yes	characteristic
105	C₁₃×#125	C₂³	1	2	yes	—
106	C₁₃×#125	C₂³	1	2	yes	—
107	C₁₃×#125	C₂³	1	2	yes	—
108	C₁₃×#124	C₂³	1	2	yes	—
109	C₁₃×#123	—	2	4	no	—
110	C₁₃×#123	—	2	4	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	4	no	—
114	C₁₃×C₂²⋊Q₈	—	2	4	no	—
115	C₁₃×C₂²⋊Q₈	—	2	4	no	—
116	C₁₃×C₂²⋊Q₈	—	2	4	no	—
117	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
118	C₁₃×#121	—	2	2	no	—
119	C₁₃×#121	—	2	4	no	—
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	4	no	—
122	C₁₃×#121	C₂³	1	4	yes	—
123	C₄×Q₈×C₁₃	—	2	2	no	—
124	C₄×Q₈×C₁₃	—	2	4	no	—
125	C₄×Q₈×C₁₃	—	2	2	no	—
126	C₄×Q₈×C₁₃	D₄	1	2	yes	—
127	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	2	no	—
130	C₄×D₄×C₁₃	—	2	4	no	—
131	C₄×D₄×C₁₃	—	2	4	no	—
132	C₄×D₄×C₁₃	—	2	2	no	—
133	C₄×D₄×C₁₃	D₄	1	4	yes	—
134	C₄×D₄×C₁₃	D₄	1	2	yes	—
135	C₄×D₄×C₁₃	C₂³	1	4	yes	—
136	C₁₃×#117	—	2	2	no	—
137	C₁₃×#117	—	2	4	no	—
138	C₁₃×#117	C₂³	1	2	yes	—
139	C₁₃×#117	C₂³	1	4	yes	—
140	C₁₃×#117	C₂³	1	1	yes	characteristic
141	C₁₃×#117	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₁₃×#107	C₂³	1	4	yes	—
152	C₁₃×#107	C₂³	1	4	yes	—
153	C₁₃×#107	C₂³	1	4	yes	—
154	C₁₃×#107	C₂³	1	4	yes	—
155	C₁₃×#106	C₂³	1	4	yes	—
156	C₁₃×#106	C₂³	1	4	yes	—
157	C₁₃×#106	C₂³	1	4	yes	—
158	C₁₃×#106	C₂³	1	4	yes	—
159	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
160	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
161	C₁₃×#103	C₂³	1	2	yes	—
162	C₁₃×#103	C₂³	1	2	yes	—
163	C₁₃×#103	C₂³	1	2	yes	—
164	C₁₃×#103	C₂³	1	2	yes	—
165	C₁₃×#103	C₂³	1	4	yes	—
166	C₁₃×#103	C₂³	1	4	yes	—
167	C₁₃×#102	C₂³	1	2	yes	—
168	C₁₃×#102	C₂³	1	2	yes	—
169	C₁₃×#102	C₂³	1	2	yes	—
170	C₁₃×#102	C₂³	1	2	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
175	C₁₃×#97	C₂³	1	2	yes	—
176	C₄×C₈×C₁₃	C₂³	1	2	yes	—
177	C₄×C₈×C₁₃	C₂³	1	2	yes	—
178	C₄×C₈×C₁₃	C₂³	1	2	yes	—
179	#60882	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₁₃×#41	—	2	2	no	—
181	C₁₃×#41	—	2	2	no	—
182	C₁₃×#41	—	2	4	no	—
183	C₁₃×#41	—	2	4	no	—
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
188	C₂×D₄×C₁₃	—	2	2	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	2	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₁₃×M₁₆	—	2	2	no	—
204	C₁₃×M₁₆	—	2	2	no	—
205	C₂×C₈×C₁₃	—	2	2	no	—
206	C₂×C₈×C₁₃	—	2	2	no	—
207	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
208	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	4	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	4	no	—
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	2	4	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	2	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	—	2	4	no	—
226	C₁₃×C₄⋊C₄	—	2	2	no	—
227	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
228	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	2	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
241	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
242	C₄²×C₁₃	—	2	4	no	—
243	C₄²×C₁₃	—	2	4	no	—
244	C₄²×C₁₃	—	2	2	no	—
245	C₄²×C₁₃	C₂×D₄	1	4	yes	—
246	C₄²×C₁₃	C₂×D₄	1	2	yes	—
247	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₄²×C₁₃	C₂⁴	1	2	yes	—
250	#3512	C₂×C₁₃	1	1	yes	characteristic
251	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3242	C₂×C₁₃	1	4	yes	complemented
253	#3241	C₂×C₁₃	1	4	yes	complemented
254	#3233	C₂×C₁₃	1	4	yes	complemented
255	#3232	C₂×C₁₃	1	4	yes	complemented
256	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#3099	C₂×C₁₃	1	2	yes	complemented
261	#3098	C₂×C₁₃	1	2	yes	complemented
262	#3084	C₂×C₁₃	1	2	yes	complemented
263	#3083	C₂×C₁₃	1	2	yes	complemented
264	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
265	C₂³×C₁₃	—	2	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	2	no	—
270	Q₈×C₁₃	—	2	2	no	—
271	Q₈×C₁₃	—	8	4	no	—
272	Q₈×C₁₃	—	8	2	no	—
273	D₄×C₁₃	—	2	4	no	—
274	D₄×C₁₃	—	2	2	no	—
275	D₄×C₁₃	—	2	2	no	—
276	D₄×C₁₃	—	2	2	no	—
277	D₄×C₁₃	—	4	4	no	—
278	D₄×C₁₃	—	8	2	no	—
279	D₄×C₁₃	—	8	4	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	4	4	no	—
288	C₂×C₄×C₁₃	—	4	2	no	—
289	C₂×C₄×C₁₃	—	4	4	no	—
290	C₂×C₄×C₁₃	—	8	4	no	—
291	C₂×C₄×C₁₃	—	8	2	no	—
292	C₂×C₄×C₁₃	—	8	2	no	—
293	C₂×C₄×C₁₃	—	8	4	no	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
300	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
301	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
302	C₈×C₁₃	—	2	2	no	—
303	C₈×C₁₃	—	2	2	no	—
304	C₈×C₁₃	—	2	2	no	—
305	C₈×C₁₃	—	2	2	no	—
306	#557	—	2	2	no	—
307	#554	—	2	4	no	—
308	#554	—	2	2	no	—
309	#553	—	2	4	no	—
310	#553	—	2	2	no	—
311	#552	—	2	2	no	—
312	#544	C₂²×C₁₃	1	2	yes	—
313	#544	C₂²×C₁₃	1	4	yes	—
314	#541	C₂²×C₁₃	1	2	yes	—
315	#540	C₂²×C₁₃	1	2	yes	—
316	#537	C₂²×C₁₃	1	2	yes	—
317	#533	C₂²×C₁₃	1	1	yes	characteristic
318	#533	C₂²×C₁₃	1	2	yes	—
319	#532	C₂²×C₁₃	1	1	yes	characteristic
320	#529	C₂²×C₁₃	1	4	yes	—
321	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#125	C₂²×C₁₃	1	2	yes	—
324	#520	C₂²×C₁₃	1	2	yes	—
325	#520	C₂²×C₁₃	1	2	yes	—
326	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
327	#501	C₂²×C₁₃	1	4	yes	—
328	#499	C₂²×C₁₃	1	4	yes	—
329	#499	C₂²×C₁₃	1	4	yes	—
330	#499	C₂²×C₁₃	1	2	yes	—
331	#499	C₂²×C₁₃	1	2	yes	—
332	#491	C₂²×C₁₃	1	2	yes	—
333	#490	C₂²×C₁₃	1	2	yes	—
334	#488	C₂²×C₁₃	1	2	yes	—
335	#488	C₂²×C₁₃	1	2	yes	—
336	#488	C₂²×C₁₃	1	4	yes	—
337	#487	C₂²×C₁₃	1	2	yes	—
338	#486	C₂²×C₁₃	1	2	yes	—
339	#485	C₂²×C₁₃	1	4	yes	—
340	#485	C₂²×C₁₃	1	4	yes	—
341	#484	C₂²×C₁₃	1	4	yes	—
342	#483	C₂²×C₁₃	1	4	yes	—
343	#482	C₂²×C₁₃	1	4	yes	—
344	#482	C₂²×C₁₃	1	4	yes	—
345	#481	C₂²×C₁₃	1	4	yes	—
346	#480	C₂²×C₁₃	1	4	yes	—
347	#479	C₂²×C₁₃	1	4	yes	—
348	#479	C₂²×C₁₃	1	4	yes	—
349	#478	C₂²×C₁₃	1	4	yes	—
350	#478	C₂²×C₁₃	1	4	yes	—
351	#477	C₂²×C₁₃	1	4	yes	—
352	#476	C₂²×C₁₃	1	4	yes	—
353	#475	C₂²×C₁₃	1	4	yes	—
354	#474	C₂²×C₁₃	1	4	yes	—
355	#433	C₂²×C₁₃	1	4	yes	—
356	#431	C₂²×C₁₃	1	4	yes	—
357	#428	C₂²×C₁₃	1	2	yes	—
358	#428	C₂²×C₁₃	1	2	yes	—
359	C₂×#107	C₂²×C₁₃	1	2	yes	—
360	C₂×#106	C₂²×C₁₃	1	2	yes	—
361	#424	C₂²×C₁₃	1	1	yes	characteristic
362	#424	C₂²×C₁₃	1	1	yes	characteristic
363	#417	C₂²×C₁₃	1	2	yes	—
364	#417	C₂²×C₁₃	1	2	yes	—
365	#416	C₂²×C₁₃	1	2	yes	—
366	#416	C₂²×C₁₃	1	2	yes	—
367	#408	C₂²×C₁₃	1	1	yes	characteristic
368	#408	C₂²×C₁₃	1	1	yes	characteristic
369	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₁₃	—	2	2	no	—
372	C₂²×C₁₃	—	2	4	no	—
373	C₂²×C₁₃	—	2	2	no	—
374	C₂²×C₁₃	—	4	2	no	—
375	C₂²×C₁₃	—	4	2	no	—
376	C₂²×C₁₃	—	4	2	no	—
377	C₂²×C₁₃	#536	1	2	yes	—
378	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	2	4	no	—
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	—	2	2	no	—
383	C₄×C₁₃	—	4	4	no	—
384	C₄×C₁₃	—	4	4	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	4	2	no	—
387	C₄×C₁₃	—	4	2	no	—
388	C₄×C₁₃	#536	1	2	yes	—
389	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
390	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
391	C₂×#41	C₂³×C₁₃	1	2	yes	—
392	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊Q₈	—	2	2	no	—
398	C₄⋊Q₈	—	2	4	no	—
399	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
401	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
402	#127	C₂³×C₁₃	1	1	yes	characteristic
403	#126	—	2	4	no	—
404	#126	—	2	4	no	—
405	#125	—	2	4	no	—
406	#125	—	2	2	no	—
407	#125	—	2	4	no	—
408	#125	—	2	2	no	—
409	#125	—	2	4	no	—
410	#125	—	2	2	no	—
411	#125	C₂³×C₁₃	1	2	yes	—
412	#125	C₂³×C₁₃	1	1	yes	characteristic
413	#125	C₂³×C₁₃	1	2	yes	—
414	#125	C₂³×C₁₃	1	2	yes	—
415	#125	C₂³×C₁₃	1	4	yes	—
416	#125	C₂³×C₁₃	1	2	yes	—
417	#125	C₂³×C₁₃	1	1	yes	characteristic
418	#124	C₂³×C₁₃	1	2	yes	—
419	#123	—	2	4	no	—
420	#123	—	2	4	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	4	no	—
424	C₂²⋊Q₈	—	2	4	no	—
425	C₂²⋊Q₈	—	2	4	no	—
426	C₂²⋊Q₈	—	2	4	no	—
427	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
428	#121	—	2	2	no	—
429	#121	—	2	4	no	—
430	#121	—	2	2	no	—
431	#121	—	2	4	no	—
432	#121	C₂³×C₁₃	1	4	yes	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	4	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	D₄×C₁₃	1	2	yes	—
437	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	4	no	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	D₄×C₁₃	1	4	yes	—
444	C₄×D₄	D₄×C₁₃	1	2	yes	—
445	C₄×D₄	C₂³×C₁₃	1	4	yes	—
446	#117	—	2	2	no	—
447	#117	—	2	4	no	—
448	#117	C₂³×C₁₃	1	2	yes	—
449	#117	C₂³×C₁₃	1	4	yes	—
450	#117	C₂³×C₁₃	1	1	yes	characteristic
451	#117	C₂³×C₁₃	1	2	yes	—
452	C₂×C₄⋊C₄	—	2	2	no	—
453	C₂×C₄⋊C₄	—	2	2	no	—
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₄⋊C₄	—	2	2	no	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
461	#107	C₂³×C₁₃	1	4	yes	—
462	#107	C₂³×C₁₃	1	4	yes	—
463	#107	C₂³×C₁₃	1	4	yes	—
464	#107	C₂³×C₁₃	1	4	yes	—
465	#106	C₂³×C₁₃	1	4	yes	—
466	#106	C₂³×C₁₃	1	4	yes	—
467	#106	C₂³×C₁₃	1	4	yes	—
468	#106	C₂³×C₁₃	1	4	yes	—
469	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
470	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
471	#103	C₂³×C₁₃	1	2	yes	—
472	#103	C₂³×C₁₃	1	2	yes	—
473	#103	C₂³×C₁₃	1	2	yes	—
474	#103	C₂³×C₁₃	1	2	yes	—
475	#103	C₂³×C₁₃	1	4	yes	—
476	#103	C₂³×C₁₃	1	4	yes	—
477	#102	C₂³×C₁₃	1	2	yes	—
478	#102	C₂³×C₁₃	1	2	yes	—
479	#102	C₂³×C₁₃	1	2	yes	—
480	#102	C₂³×C₁₃	1	2	yes	—
481	#102	C₂³×C₁₃	1	4	yes	—
482	#102	C₂³×C₁₃	1	4	yes	—
483	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
484	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
485	#97	C₂³×C₁₃	1	2	yes	—
486	C₄×C₈	C₂³×C₁₃	1	2	yes	—
487	C₄×C₈	C₂³×C₁₃	1	2	yes	—
488	C₄×C₈	C₂³×C₁₃	1	2	yes	—
489	C₂×C₁₃	—	2	2	no	—
490	C₂×C₁₃	—	4	2	no	—
491	C₂×C₁₃	—	8	2	no	—
492	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
493	C₂×C₁₃	#3584	1	2	yes	—
494	#41	—	2	2	no	—
495	#41	—	2	2	no	—
496	#41	—	2	4	no	—
497	#41	—	2	4	no	—
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
506	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
517	M₁₆	—	2	2	no	—
518	M₁₆	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
522	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
523	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
524	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
542	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
543	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
544	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
545	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	2	no	—
559	C₄²	C₂×D₄×C₁₃	1	4	yes	—
560	C₄²	C₂×D₄×C₁₃	1	2	yes	—
561	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
562	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₄²	C₂⁴×C₁₃	1	2	yes	—
564	C₁₃	#60882	1	1	yes	characteristic, direct product factor, Sylow
565	C₂³	—	2	2	no	—
566	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
567	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	8	4	no	—
572	Q₈	—	8	2	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	8	2	no	—
579	D₄	—	8	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
599	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
600	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
601	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	2	2	no	—
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	C₁₃×#536	1	2	yes	—
613	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
614	C₄	—	2	2	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	4	no	—
619	C₄	—	4	4	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	C₁₃×#536	1	2	yes	—
624	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
625	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
626	C₂	—	2	2	no	—
627	C₂	—	4	2	no	—
628	C₂	—	8	2	no	—
629	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
630	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3512	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
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3242	C₂	semidirect
4. C₁₃×#3241	C₂	semidirect
5. C₁₃×#3233	C₂	semidirect
6. C₁₃×#3232	C₂	semidirect
7. C₁₃×#3166	C₂	semidirect
8. C₂×C₁₃×#499	C₂	semidirect
9. C₁₃×#3142	C₂	semidirect
10. C₁₃×#3131	C₂	semidirect
11. C₁₃×#3099	C₂	semidirect
12. C₁₃×#3098	C₂	semidirect
13. C₁₃×#3084	C₂	semidirect
14. C₁₃×#3083	C₂	semidirect
15. C₁₃×#2922	C₂	semidirect
179. #60882	C₁₃	direct (N × H)
251. #3504	C₂×C₁₃	semidirect
252. #3242	C₂×C₁₃	semidirect
253. #3241	C₂×C₁₃	semidirect
254. #3233	C₂×C₁₃	semidirect
255. #3232	C₂×C₁₃	semidirect
256. #3166	C₂×C₁₃	semidirect
257. C₂×#499	C₂×C₁₃	semidirect
258. #3142	C₂×C₁₃	semidirect
259. #3131	C₂×C₁₃	semidirect
260. #3099	C₂×C₁₃	semidirect
261. #3098	C₂×C₁₃	semidirect
262. #3084	C₂×C₁₃	semidirect
263. #3083	C₂×C₁₃	semidirect
264. #2922	C₂×C₁₃	semidirect
564. C₁₃	#60882	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×#3512	2
C₁₃×#3504	2
C₁₃×#3242	2
C₁₃×#3241	2
C₁₃×#3233	2
C₁₃×#3232	2
C₁₃×#3166	2
C₂×C₁₃×#499	2
C₁₃×#3142	2
C₁₃×#3131	2
C₁₃×#3099	2
C₁₃×#3098	2
C₁₃×#3084	2
C₁₃×#3083	2
C₁₃×#2922	2
#60882	13

Subgroups — C13×#60882 #15747221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60882 #15747221