Subgroups — C₁₃×#61338 #15747677

Order 3328.

1732 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3374	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3372	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3046	C₂	1	2	yes	maximal
12	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₁₃×#557	C₂²	1	4	yes	—
19	C₁₃×#557	C₂²	1	4	yes	—
20	C₁₃×#556	C₂²	1	4	yes	—
21	C₁₃×#554	—	2	4	no	—
22	C₁₃×#554	C₂²	1	4	yes	—
23	C₁₃×#552	—	2	4	no	—
24	C₁₃×#544	—	2	2	no	—
25	C₁₃×#544	C₂²	1	2	yes	—
26	C₁₃×#541	—	2	1	no	—
27	C₁₃×#541	—	2	1	no	—
28	C₁₃×#536	C₂²	1	2	yes	—
29	C₁₃×#533	—	2	2	no	—
30	C₁₃×#533	—	2	1	no	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#125	—	2	1	no	—
34	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₁₃×#519	C₂²	1	2	yes	—
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₁₃×#491	C₂²	1	4	yes	—
40	C₁₃×#491	C₂²	1	4	yes	—
41	C₁₃×#491	C₂²	1	4	yes	—
42	C₁₃×#489	C₂²	1	4	yes	—
43	C₁₃×#488	C₂²	1	4	yes	—
44	C₁₃×#487	C₂²	1	4	yes	—
45	C₁₃×#479	C₂²	1	4	yes	—
46	C₁₃×#479	C₂²	1	4	yes	—
47	C₁₃×#479	C₂²	1	4	yes	—
48	C₁₃×#478	C₂²	1	4	yes	—
49	C₁₃×#477	C₂²	1	4	yes	—
50	C₁₃×#475	C₂²	1	4	yes	—
51	C₁₃×#464	C₂²	1	4	yes	—
52	C₁₃×#463	C₂²	1	4	yes	—
53	C₁₃×#462	C₂²	1	4	yes	—
54	C₁₃×#462	C₂²	1	4	yes	—
55	C₁₃×#461	C₂²	1	4	yes	—
56	C₁₃×#461	C₂²	1	4	yes	—
57	C₁₃×#446	C₂²	1	4	yes	—
58	C₁₃×#446	C₂²	1	4	yes	—
59	C₁₃×#442	C₂²	1	2	yes	—
60	C₁₃×#441	C₂²	1	2	yes	—
61	C₁₃×#441	C₂²	1	4	yes	—
62	C₁₃×#440	C₂²	1	2	yes	—
63	C₁₃×#440	C₂²	1	4	yes	—
64	C₁₃×#440	C₂²	1	2	yes	—
65	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
66	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
67	C₁₃×#428	C₂²	1	2	yes	—
68	C₁₃×#427	C₂²	1	1	yes	characteristic
69	C₁₃×#424	C₂²	1	2	yes	—
70	C₁₃×#423	C₂²	1	1	yes	characteristic
71	C₁₃×#419	C₂²	1	2	yes	—
72	C₁₃×#417	C₂²	1	2	yes	—
73	C₁₃×#416	C₂²	1	1	yes	characteristic
74	C₁₃×#416	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#103	C₂²	1	2	yes	—
76	C₂×C₁₃×#103	C₂²	1	2	yes	—
77	C₁₃×#405	C₂²	1	2	yes	—
78	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
79	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
82	C₁₃×#137	—	2	8	no	—
83	C₁₃×#135	—	2	4	no	—
84	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
85	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	—	2	4	no	—
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	2	1	no	—
96	C₁₃×C₄⋊Q₈	—	2	1	no	—
97	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×#126	—	2	4	no	—
102	C₁₃×#126	—	2	4	no	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	—	2	4	no	—
105	C₁₃×#125	—	2	4	no	—
106	C₁₃×#125	—	2	4	no	—
107	C₁₃×#125	—	2	4	no	—
108	C₁₃×#125	—	2	4	no	—
109	C₁₃×#125	—	2	1	no	—
110	C₁₃×#125	—	2	1	no	—
111	C₁₃×#125	D₄	1	1	yes	characteristic
112	C₁₃×#125	D₄	1	1	yes	characteristic
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#125	C₂³	1	4	yes	—
115	C₁₃×#124	C₂³	1	4	yes	—
116	C₁₃×#123	—	2	4	no	—
117	C₁₃×C₂²⋊Q₈	—	2	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	4	no	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
125	C₄×Q₈×C₁₃	—	2	4	no	—
126	C₄×Q₈×C₁₃	—	2	2	no	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	4	no	—
129	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
132	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	2	yes	—
140	C₄×D₄×C₁₃	C₂³	1	2	yes	—
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	—	2	4	no	—
143	C₁₃×#117	—	2	4	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	C₂³	1	1	yes	characteristic
147	C₁₃×#117	C₂³	1	1	yes	characteristic
148	C₁₃×#117	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃	—	2	1	no	—
155	C₂×C₄²×C₁₃	—	2	1	no	—
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₁₃×#107	C₂³	1	2	yes	—
158	C₁₃×#107	C₂³	1	4	yes	—
159	C₁₃×#106	C₂³	1	2	yes	—
160	C₁₃×#106	C₂³	1	4	yes	—
161	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
162	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
163	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
164	C₁₃×#103	C₂³	1	4	yes	—
165	C₁₃×#103	C₂³	1	4	yes	—
166	C₁₃×#103	C₂³	1	4	yes	—
167	C₁₃×#103	C₂³	1	4	yes	—
168	C₁₃×#103	C₂³	1	2	yes	—
169	C₁₃×#103	C₂³	1	2	yes	—
170	C₁₃×#103	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	4	yes	—
172	C₁₃×#103	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	2	yes	—
174	C₁₃×#102	C₂³	1	2	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	2	yes	—
177	C₁₃×#97	C₂³	1	2	yes	—
178	C₁₃×#97	C₂³	1	4	yes	—
179	C₄×C₈×C₁₃	C₂³	1	4	yes	—
180	#61338	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃×#41	—	2	2	no	—
182	C₁₃×#41	—	2	2	no	—
183	C₁₃×#41	—	2	2	no	—
184	C₁₃×#41	#41	1	4	yes	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	—	2	4	no	—
187	C₂×Q₈×C₁₃	—	2	4	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
190	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
191	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₁₃×Q₁₆	—	2	2	no	—
207	C₁₃×Q₁₆	—	2	8	no	—
208	C₁₃×SD₁₆	—	2	2	no	—
209	C₁₃×SD₁₆	—	2	2	no	—
210	C₁₃×SD₁₆	—	2	8	no	—
211	C₁₃×D₈	—	2	2	no	—
212	C₁₃×M₁₆	—	2	4	no	—
213	C₂×C₈×C₁₃	—	2	2	no	—
214	C₂×C₈×C₁₃	—	2	2	no	—
215	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
216	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
217	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	4	no	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
235	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
239	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
242	C₁₃×C₂²⋊C₄	—	2	1	no	—
243	C₁₃×C₂²⋊C₄	—	2	1	no	—
244	C₁₃×C₂²⋊C₄	—	2	2	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	2	2	no	—
253	C₄²×C₁₃	—	2	2	no	—
254	C₄²×C₁₃	—	2	4	no	—
255	C₄²×C₁₃	—	2	4	no	—
256	C₄²×C₁₃	—	2	4	no	—
257	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₁₃	C₂⁴	1	4	yes	—
260	C₄²×C₁₃	C₂⁴	1	2	yes	—
261	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#3377	C₂×C₁₃	1	4	yes	complemented
264	#3376	C₂×C₁₃	1	4	yes	complemented
265	#3374	C₂×C₁₃	1	4	yes	complemented
266	#3372	C₂×C₁₃	1	4	yes	complemented
267	#3137	C₂×C₁₃	1	2	yes	complemented
268	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#3082	C₂×C₁₃	1	2	yes	complemented
270	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#3046	C₂×C₁₃	1	2	yes	—
272	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2947	C₂×C₁₃	1	2	yes	complemented
275	#2943	C₂×C₁₃	1	1	yes	characteristic
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₁₃	—	2	1	no	—
280	Q₈×C₁₃	—	2	4	no	—
281	Q₈×C₁₃	—	2	1	no	—
282	Q₈×C₁₃	—	2	4	no	—
283	Q₈×C₁₃	—	2	1	no	—
284	Q₈×C₁₃	—	4	4	no	—
285	Q₈×C₁₃	—	4	4	no	—
286	Q₈×C₁₃	—	8	4	no	—
287	Q₈×C₁₃	C₂×#41	1	2	yes	—
288	D₄×C₁₃	—	2	4	no	—
289	D₄×C₁₃	—	2	1	no	—
290	D₄×C₁₃	—	2	1	no	—
291	D₄×C₁₃	—	2	1	no	—
292	D₄×C₁₃	—	4	2	no	—
293	D₄×C₁₃	C₂×#41	1	2	yes	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	4	2	no	—
302	C₂×C₄×C₁₃	—	4	4	no	—
303	C₂×C₄×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	4	2	no	—
305	C₂×C₄×C₁₃	—	8	2	no	—
306	C₂×C₄×C₁₃	—	8	4	no	—
307	C₂×C₄×C₁₃	—	8	2	no	—
308	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
309	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
316	C₈×C₁₃	—	2	1	no	—
317	C₈×C₁₃	—	2	1	no	—
318	C₈×C₁₃	—	2	4	no	—
319	C₈×C₁₃	—	2	2	no	—
320	C₂×#137	C₂²×C₁₃	1	2	yes	—
321	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
322	#557	C₂²×C₁₃	1	4	yes	—
323	#557	C₂²×C₁₃	1	4	yes	—
324	#556	C₂²×C₁₃	1	4	yes	—
325	#554	—	2	4	no	—
326	#554	C₂²×C₁₃	1	4	yes	—
327	#552	—	2	4	no	—
328	#544	—	2	2	no	—
329	#544	C₂²×C₁₃	1	2	yes	—
330	#541	—	2	1	no	—
331	#541	—	2	1	no	—
332	#536	C₂²×C₁₃	1	2	yes	—
333	#533	—	2	2	no	—
334	#533	—	2	1	no	—
335	#533	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#125	—	2	1	no	—
338	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
339	#520	C₂²×C₁₃	1	2	yes	—
340	#519	C₂²×C₁₃	1	2	yes	—
341	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
342	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
343	#491	C₂²×C₁₃	1	4	yes	—
344	#491	C₂²×C₁₃	1	4	yes	—
345	#491	C₂²×C₁₃	1	4	yes	—
346	#489	C₂²×C₁₃	1	4	yes	—
347	#488	C₂²×C₁₃	1	4	yes	—
348	#487	C₂²×C₁₃	1	4	yes	—
349	#479	C₂²×C₁₃	1	4	yes	—
350	#479	C₂²×C₁₃	1	4	yes	—
351	#479	C₂²×C₁₃	1	4	yes	—
352	#478	C₂²×C₁₃	1	4	yes	—
353	#477	C₂²×C₁₃	1	4	yes	—
354	#475	C₂²×C₁₃	1	4	yes	—
355	#464	C₂²×C₁₃	1	4	yes	—
356	#463	C₂²×C₁₃	1	4	yes	—
357	#462	C₂²×C₁₃	1	4	yes	—
358	#462	C₂²×C₁₃	1	4	yes	—
359	#461	C₂²×C₁₃	1	4	yes	—
360	#461	C₂²×C₁₃	1	4	yes	—
361	#446	C₂²×C₁₃	1	4	yes	—
362	#446	C₂²×C₁₃	1	4	yes	—
363	#442	C₂²×C₁₃	1	2	yes	—
364	#441	C₂²×C₁₃	1	2	yes	—
365	#441	C₂²×C₁₃	1	4	yes	—
366	#440	C₂²×C₁₃	1	2	yes	—
367	#440	C₂²×C₁₃	1	4	yes	—
368	#440	C₂²×C₁₃	1	2	yes	—
369	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
370	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
371	#428	C₂²×C₁₃	1	2	yes	—
372	#427	C₂²×C₁₃	1	1	yes	characteristic
373	#424	C₂²×C₁₃	1	2	yes	—
374	#423	C₂²×C₁₃	1	1	yes	characteristic
375	#419	C₂²×C₁₃	1	2	yes	—
376	#417	C₂²×C₁₃	1	2	yes	—
377	#416	C₂²×C₁₃	1	1	yes	characteristic
378	#416	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#103	C₂²×C₁₃	1	2	yes	—
380	C₂×#103	C₂²×C₁₃	1	2	yes	—
381	#405	C₂²×C₁₃	1	2	yes	—
382	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	#548	1	2	yes	—
389	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
390	C₄×C₁₃	—	2	2	no	—
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	2	4	no	—
393	C₄×C₁₃	—	2	4	no	—
394	C₄×C₁₃	—	2	2	no	—
395	C₄×C₁₃	—	4	2	no	—
396	C₄×C₁₃	—	4	4	no	—
397	C₄×C₁₃	—	4	2	no	—
398	C₄×C₁₃	—	4	1	no	—
399	C₄×C₁₃	—	4	4	no	—
400	C₄×C₁₃	#548	1	2	yes	—
401	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
402	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
406	#137	—	2	8	no	—
407	#135	—	2	4	no	—
408	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
410	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
413	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
415	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄⋊Q₈	—	2	4	no	—
418	C₄⋊Q₈	—	2	2	no	—
419	C₄⋊Q₈	—	2	1	no	—
420	C₄⋊Q₈	—	2	1	no	—
421	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
422	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
423	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
424	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
425	#126	—	2	4	no	—
426	#126	—	2	4	no	—
427	#125	—	2	2	no	—
428	#125	—	2	4	no	—
429	#125	—	2	4	no	—
430	#125	—	2	4	no	—
431	#125	—	2	4	no	—
432	#125	—	2	4	no	—
433	#125	—	2	1	no	—
434	#125	—	2	1	no	—
435	#125	D₄×C₁₃	1	1	yes	characteristic
436	#125	D₄×C₁₃	1	1	yes	characteristic
437	#125	C₂³×C₁₃	1	4	yes	—
438	#125	C₂³×C₁₃	1	4	yes	—
439	#124	C₂³×C₁₃	1	4	yes	—
440	#123	—	2	4	no	—
441	C₂²⋊Q₈	—	2	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	4	no	—
446	C₂²⋊Q₈	—	2	4	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
449	C₄×Q₈	—	2	4	no	—
450	C₄×Q₈	—	2	2	no	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	—	2	4	no	—
453	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
454	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
455	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
456	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
457	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
458	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	4	no	—
462	C₄×D₄	C₂³×C₁₃	1	2	yes	—
463	C₄×D₄	C₂³×C₁₃	1	2	yes	—
464	C₄×D₄	C₂³×C₁₃	1	4	yes	—
465	#117	—	2	2	no	—
466	#117	—	2	4	no	—
467	#117	—	2	4	no	—
468	#117	—	2	1	no	—
469	#117	—	2	1	no	—
470	#117	C₂³×C₁₃	1	1	yes	characteristic
471	#117	C₂³×C₁₃	1	1	yes	characteristic
472	#117	C₂³×C₁₃	1	2	yes	—
473	C₂×C₄⋊C₄	—	2	2	no	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	—	2	2	no	—
476	C₂×C₄⋊C₄	—	2	4	no	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
478	C₂×C₄²	—	2	1	no	—
479	C₂×C₄²	—	2	1	no	—
480	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
481	#107	C₂³×C₁₃	1	2	yes	—
482	#107	C₂³×C₁₃	1	4	yes	—
483	#106	C₂³×C₁₃	1	2	yes	—
484	#106	C₂³×C₁₃	1	4	yes	—
485	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
486	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
487	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
488	#103	C₂³×C₁₃	1	4	yes	—
489	#103	C₂³×C₁₃	1	4	yes	—
490	#103	C₂³×C₁₃	1	4	yes	—
491	#103	C₂³×C₁₃	1	4	yes	—
492	#103	C₂³×C₁₃	1	2	yes	—
493	#103	C₂³×C₁₃	1	2	yes	—
494	#103	C₂³×C₁₃	1	4	yes	—
495	#103	C₂³×C₁₃	1	4	yes	—
496	#103	C₂³×C₁₃	1	4	yes	—
497	#102	C₂³×C₁₃	1	2	yes	—
498	#102	C₂³×C₁₃	1	2	yes	—
499	#102	C₂³×C₁₃	1	4	yes	—
500	#97	C₂³×C₁₃	1	2	yes	—
501	#97	C₂³×C₁₃	1	2	yes	—
502	#97	C₂³×C₁₃	1	4	yes	—
503	C₄×C₈	C₂³×C₁₃	1	4	yes	—
504	C₂×C₁₃	—	2	2	no	—
505	C₂×C₁₃	—	4	2	no	—
506	C₂×C₁₃	—	8	1	no	—
507	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
508	C₂×C₁₃	#3586	1	2	yes	—
509	#41	—	2	2	no	—
510	#41	—	2	2	no	—
511	#41	—	2	2	no	—
512	#41	C₁₃×#41	1	4	yes	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	2	4	no	—
515	C₂×Q₈	—	2	4	no	—
516	C₂×Q₈	—	2	4	no	—
517	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
518	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
519	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
520	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
534	Q₁₆	—	2	2	no	—
535	Q₁₆	—	2	8	no	—
536	SD₁₆	—	2	2	no	—
537	SD₁₆	—	2	2	no	—
538	SD₁₆	—	2	8	no	—
539	D₈	—	2	2	no	—
540	M₁₆	—	2	4	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
544	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
545	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
546	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
563	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
564	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
565	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
566	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
567	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
568	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	2	4	no	—
583	C₄²	—	2	4	no	—
584	C₄²	—	2	4	no	—
585	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₄²	C₂⁴×C₁₃	1	4	yes	—
588	C₄²	C₂⁴×C₁₃	1	2	yes	—
589	C₁₃	#61338	1	1	yes	characteristic, direct product factor, Sylow
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
593	Q₈	—	2	1	no	—
594	Q₈	—	2	4	no	—
595	Q₈	—	2	1	no	—
596	Q₈	—	2	4	no	—
597	Q₈	—	2	1	no	—
598	Q₈	—	4	4	no	—
599	Q₈	—	4	4	no	—
600	Q₈	—	8	4	no	—
601	Q₈	C₂×C₁₃×#41	1	2	yes	—
602	D₄	—	2	4	no	—
603	D₄	—	2	1	no	—
604	D₄	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	4	2	no	—
607	D₄	C₂×C₁₃×#41	1	2	yes	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	8	2	no	—
620	C₂×C₄	—	8	4	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
623	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
628	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
629	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
630	C₈	—	2	1	no	—
631	C₈	—	2	1	no	—
632	C₈	—	2	4	no	—
633	C₈	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	1	no	—
639	C₂²	C₁₃×#548	1	2	yes	—
640	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	4	no	—
645	C₄	—	2	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	4	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	4	no	—
651	C₄	C₁₃×#548	1	2	yes	—
652	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
653	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
654	C₂	—	2	2	no	—
655	C₂	—	4	2	no	—
656	C₂	—	8	1	no	—
657	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
658	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3377	C₂	semidirect
4. C₁₃×#3376	C₂	semidirect
5. C₁₃×#3374	C₂	semidirect
6. C₁₃×#3372	C₂	semidirect
7. C₁₃×#3137	C₂	semidirect
8. C₂×C₁₃×#491	C₂	semidirect
9. C₁₃×#3082	C₂	semidirect
10. C₁₃×#3080	C₂	semidirect
12. C₁₃×#3039	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2947	C₂	semidirect
180. #61338	C₁₃	direct (N × H)
261. #3509	C₂×C₁₃	semidirect
262. #3504	C₂×C₁₃	semidirect
263. #3377	C₂×C₁₃	semidirect
264. #3376	C₂×C₁₃	semidirect
265. #3374	C₂×C₁₃	semidirect
266. #3372	C₂×C₁₃	semidirect
267. #3137	C₂×C₁₃	semidirect
268. C₂×#491	C₂×C₁₃	semidirect
269. #3082	C₂×C₁₃	semidirect
270. #3080	C₂×C₁₃	semidirect
272. #3039	C₂×C₁₃	semidirect
273. #2961	C₂×C₁₃	semidirect
274. #2947	C₂×C₁₃	semidirect
589. C₁₃	#61338	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×#3509	2
C₁₃×#3504	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3374	2
C₁₃×#3372	2
C₁₃×#3137	2
C₂×C₁₃×#491	2
C₁₃×#3082	2
C₁₃×#3080	2
C₁₃×#3046	2
C₁₃×#3039	2
C₁₃×#2961	2
C₁₃×#2947	2
C₁₃×#2943	2
#61338	13

Subgroups — C13×#61338 #15747677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61338 #15747677