Subgroups — C₁₃×#60880 #15747219

Order 3328.

1722 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3243	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3230	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3228	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3226	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3098	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3083	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈²×C₁₃	—	2	1	no	—
16	C₁₃×#557	—	2	1	no	—
17	C₁₃×#556	—	2	1	no	—
18	C₁₃×#555	—	2	1	no	—
19	C₁₃×#554	—	2	1	no	—
20	C₁₃×#554	—	2	2	no	—
21	C₁₃×#554	—	2	1	no	—
22	C₁₃×#553	—	2	2	no	—
23	D₄×Q₈×C₁₃	—	2	1	no	—
24	D₄×Q₈×C₁₃	—	2	2	no	—
25	C₁₃×#548	—	2	2	no	—
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#544	C₂²	1	4	yes	—
29	C₁₃×#542	C₂²	1	4	yes	—
30	C₁₃×#537	C₂²	1	2	yes	—
31	C₁₃×#533	C₂²	1	2	yes	—
32	C₁₃×#533	C₂²	1	1	yes	characteristic
33	C₁₃×#533	C₂²	1	2	yes	—
34	C₁₃×#532	C₂²	1	1	yes	characteristic
35	C₁₃×#532	C₂²	1	2	yes	—
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#520	C₂²	1	2	yes	—
41	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
42	C₁₃×#501	C₂²	1	4	yes	—
43	C₁₃×#500	C₂²	1	2	yes	—
44	C₁₃×#500	C₂²	1	2	yes	—
45	C₁₃×#500	C₂²	1	4	yes	—
46	C₁₃×#500	C₂²	1	2	yes	—
47	C₁₃×#498	C₂²	1	2	yes	—
48	C₁₃×#489	C₂²	1	4	yes	—
49	C₁₃×#488	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	1	yes	characteristic
51	C₁₃×#487	C₂²	1	1	yes	characteristic
52	C₁₃×#487	C₂²	1	2	yes	—
53	C₁₃×#486	C₂²	1	1	yes	characteristic
54	C₁₃×#486	C₂²	1	1	yes	characteristic
55	C₁₃×#486	C₂²	1	2	yes	—
56	C₁₃×#485	C₂²	1	8	yes	—
57	C₁₃×#484	C₂²	1	8	yes	—
58	C₁₃×#482	C₂²	1	8	yes	—
59	C₁₃×#480	C₂²	1	8	yes	—
60	C₁₃×#479	C₂²	1	8	yes	—
61	C₁₃×#478	C₂²	1	8	yes	—
62	C₁₃×#477	C₂²	1	8	yes	—
63	C₁₃×#474	C₂²	1	8	yes	—
64	C₁₃×#433	C₂²	1	4	yes	—
65	C₁₃×#431	C₂²	1	2	yes	—
66	C₁₃×#431	C₂²	1	2	yes	—
67	C₁₃×#428	C₂²	1	4	yes	—
68	C₂×C₁₃×#107	C₂²	1	4	yes	—
69	C₁₃×#424	C₂²	1	2	yes	—
70	C₁₃×#417	C₂²	1	4	yes	—
71	C₁₃×#416	C₂²	1	4	yes	—
72	C₁₃×#408	C₂²	1	2	yes	—
73	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#41	—	2	2	no	—
76	C₂×C₁₃×#41	C₂³	1	2	yes	—
77	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	—	2	1	no	—
79	C₂²×Q₈×C₁₃	—	2	1	no	—
80	C₂²×Q₈×C₁₃	—	2	2	no	—
81	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	—	2	4	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	—	2	1	no	—
87	C₁₃×C₄⋊Q₈	—	2	2	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	—	2	2	no	—
90	C₁₃×C₄⋊Q₈	—	2	1	no	—
91	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₃×#127	C₂³	1	1	yes	characteristic
100	C₁₃×#126	—	2	4	no	—
101	C₁₃×#125	—	2	2	no	—
102	C₁₃×#125	—	2	4	no	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	C₂³	1	4	yes	—
105	C₁₃×#125	C₂³	1	2	yes	—
106	C₁₃×#124	—	2	4	no	—
107	C₁₃×#124	—	2	2	no	—
108	C₁₃×#124	C₂³	1	2	yes	—
109	C₁₃×#123	—	2	4	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	4	no	—
117	C₁₃×C₂²⋊Q₈	—	2	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	4	no	—
123	C₁₃×#121	—	2	1	no	—
124	C₁₃×#121	—	2	1	no	—
125	C₁₃×#121	—	2	2	no	—
126	C₁₃×#121	C₂³	1	4	yes	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	2	no	—
129	C₄×Q₈×C₁₃	—	2	1	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	—	2	1	no	—
133	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
134	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
135	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
136	C₄×D₄×C₁₃	—	2	4	no	—
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
143	C₄×D₄×C₁₃	D₄	1	2	yes	—
144	C₄×D₄×C₁₃	D₄	1	2	yes	—
145	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
146	C₄×D₄×C₁₃	C₂³	1	4	yes	—
147	C₁₃×#117	—	2	2	no	—
148	C₁₃×#117	—	2	2	no	—
149	C₁₃×#117	C₂³	1	2	yes	—
150	C₁₃×#117	C₂³	1	4	yes	—
151	C₁₃×#117	C₂³	1	1	yes	characteristic
152	C₁₃×#117	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₁₃×#107	C₂³	1	8	yes	—
163	C₁₃×#107	C₂³	1	8	yes	—
164	C₁₃×#107	C₂³	1	8	yes	—
165	C₁₃×#106	C₂³	1	8	yes	—
166	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
167	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
168	C₁₃×#103	C₂³	1	4	yes	—
169	C₁₃×#103	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	8	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	8	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	2	yes	—
177	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₃	C₂³	1	2	yes	—
180	C₄×C₈×C₁₃	C₂³	1	2	yes	—
181	#60880	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₁₃×#41	—	2	4	no	—
183	C₁₃×#41	—	2	8	no	—
184	C₁₃×#41	—	8	4	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	2	4	no	—
192	C₂×Q₈×C₁₃	—	8	2	no	—
193	C₂×Q₈×C₁₃	—	8	2	no	—
194	C₂×Q₈×C₁₃	—	8	4	no	—
195	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	4	no	—
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₁₃×M₁₆	—	2	4	no	—
216	C₂×C₈×C₁₃	—	2	4	no	—
217	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
218	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
219	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	4	no	—
226	C₁₃×C₄⋊C₄	—	2	2	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
241	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
244	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
245	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	2	2	no	—
253	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
254	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
255	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
256	C₄²×C₁₃	—	2	4	no	—
257	C₄²×C₁₃	—	2	4	no	—
258	C₄²×C₁₃	—	2	2	no	—
259	C₄²×C₁₃	C₂×D₄	1	2	yes	—
260	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₁₃	C₂×D₄	1	2	yes	—
263	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₄²×C₁₃	C₂⁴	1	2	yes	—
266	#3511	C₂×C₁₃	1	1	yes	characteristic
267	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#3243	C₂×C₁₃	1	8	yes	complemented
269	#3231	C₂×C₁₃	1	2	yes	complemented
270	#3230	C₂×C₁₃	1	2	yes	complemented
271	#3228	C₂×C₁₃	1	2	yes	complemented
272	#3226	C₂×C₁₃	1	2	yes	complemented
273	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#3098	C₂×C₁₃	1	4	yes	complemented
278	#3083	C₂×C₁₃	1	4	yes	complemented
279	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₁₃	—	2	2	no	—
284	Q₈×C₁₃	—	2	4	no	—
285	Q₈×C₁₃	—	4	4	no	—
286	Q₈×C₁₃	—	4	2	no	—
287	Q₈×C₁₃	—	4	4	no	—
288	Q₈×C₁₃	—	4	2	no	—
289	Q₈×C₁₃	—	8	4	no	—
290	Q₈×C₁₃	—	8	2	no	—
291	Q₈×C₁₃	—	8	2	no	—
292	D₄×C₁₃	—	2	4	no	—
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	4	no	—
295	D₄×C₁₃	—	4	4	no	—
296	D₄×C₁₃	—	4	2	no	—
297	D₄×C₁₃	—	4	2	no	—
298	D₄×C₁₃	—	8	4	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	4	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	4	4	no	—
310	C₂×C₄×C₁₃	—	8	4	no	—
311	C₂×C₄×C₁₃	—	8	2	no	—
312	C₂×C₄×C₁₃	—	8	2	no	—
313	C₂×C₄×C₁₃	—	8	4	no	—
314	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
323	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
324	C₈×C₁₃	—	2	2	no	—
325	C₈×C₁₃	—	2	2	no	—
326	C₈×C₁₃	—	2	4	no	—
327	Q₈²	—	2	1	no	—
328	#557	—	2	1	no	—
329	#556	—	2	1	no	—
330	#555	—	2	1	no	—
331	#554	—	2	1	no	—
332	#554	—	2	2	no	—
333	#554	—	2	1	no	—
334	#553	—	2	2	no	—
335	D₄×Q₈	—	2	1	no	—
336	D₄×Q₈	—	2	2	no	—
337	#548	—	2	2	no	—
338	#547	—	2	1	no	—
339	#544	C₂²×C₁₃	1	2	yes	—
340	#544	C₂²×C₁₃	1	4	yes	—
341	#542	C₂²×C₁₃	1	4	yes	—
342	#537	C₂²×C₁₃	1	2	yes	—
343	#533	C₂²×C₁₃	1	2	yes	—
344	#533	C₂²×C₁₃	1	1	yes	characteristic
345	#533	C₂²×C₁₃	1	2	yes	—
346	#532	C₂²×C₁₃	1	1	yes	characteristic
347	#532	C₂²×C₁₃	1	2	yes	—
348	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
351	#520	C₂²×C₁₃	1	2	yes	—
352	#520	C₂²×C₁₃	1	2	yes	—
353	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
354	#501	C₂²×C₁₃	1	4	yes	—
355	#500	C₂²×C₁₃	1	2	yes	—
356	#500	C₂²×C₁₃	1	2	yes	—
357	#500	C₂²×C₁₃	1	4	yes	—
358	#500	C₂²×C₁₃	1	2	yes	—
359	#498	C₂²×C₁₃	1	2	yes	—
360	#489	C₂²×C₁₃	1	4	yes	—
361	#488	C₂²×C₁₃	1	4	yes	—
362	#487	C₂²×C₁₃	1	1	yes	characteristic
363	#487	C₂²×C₁₃	1	1	yes	characteristic
364	#487	C₂²×C₁₃	1	2	yes	—
365	#486	C₂²×C₁₃	1	1	yes	characteristic
366	#486	C₂²×C₁₃	1	1	yes	characteristic
367	#486	C₂²×C₁₃	1	2	yes	—
368	#485	C₂²×C₁₃	1	8	yes	—
369	#484	C₂²×C₁₃	1	8	yes	—
370	#482	C₂²×C₁₃	1	8	yes	—
371	#480	C₂²×C₁₃	1	8	yes	—
372	#479	C₂²×C₁₃	1	8	yes	—
373	#478	C₂²×C₁₃	1	8	yes	—
374	#477	C₂²×C₁₃	1	8	yes	—
375	#474	C₂²×C₁₃	1	8	yes	—
376	#433	C₂²×C₁₃	1	4	yes	—
377	#431	C₂²×C₁₃	1	2	yes	—
378	#431	C₂²×C₁₃	1	2	yes	—
379	#428	C₂²×C₁₃	1	4	yes	—
380	C₂×#107	C₂²×C₁₃	1	4	yes	—
381	#424	C₂²×C₁₃	1	2	yes	—
382	#417	C₂²×C₁₃	1	4	yes	—
383	#416	C₂²×C₁₃	1	4	yes	—
384	#408	C₂²×C₁₃	1	2	yes	—
385	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₁₃	—	2	1	no	—
388	C₂²×C₁₃	—	2	1	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	2	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	#536	1	2	yes	—
396	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	1	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	1	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	4	4	no	—
404	C₄×C₁₃	—	4	4	no	—
405	C₄×C₁₃	—	4	2	no	—
406	C₄×C₁₃	—	4	2	no	—
407	C₄×C₁₃	#536	1	2	yes	—
408	C₄×C₁₃	#576	1	2	yes	—
409	C₄×C₁₃	#578	1	2	yes	—
410	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
411	C₂×#41	—	2	2	no	—
412	C₂×#41	C₂³×C₁₃	1	2	yes	—
413	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×Q₈	—	2	1	no	—
415	C₂²×Q₈	—	2	1	no	—
416	C₂²×Q₈	—	2	2	no	—
417	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
418	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
419	C₄⋊Q₈	—	2	2	no	—
420	C₄⋊Q₈	—	2	4	no	—
421	C₄⋊Q₈	—	2	1	no	—
422	C₄⋊Q₈	—	2	1	no	—
423	C₄⋊Q₈	—	2	2	no	—
424	C₄⋊Q₈	—	2	1	no	—
425	C₄⋊Q₈	—	2	2	no	—
426	C₄⋊Q₈	—	2	1	no	—
427	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
429	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
431	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
432	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
433	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
434	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
435	#127	C₂³×C₁₃	1	1	yes	characteristic
436	#126	—	2	4	no	—
437	#125	—	2	2	no	—
438	#125	—	2	4	no	—
439	#125	—	2	2	no	—
440	#125	C₂³×C₁₃	1	4	yes	—
441	#125	C₂³×C₁₃	1	2	yes	—
442	#124	—	2	4	no	—
443	#124	—	2	2	no	—
444	#124	C₂³×C₁₃	1	2	yes	—
445	#123	—	2	4	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	1	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	4	no	—
453	C₂²⋊Q₈	—	2	4	no	—
454	C₂²⋊Q₈	—	2	4	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
457	#121	—	2	2	no	—
458	#121	—	2	4	no	—
459	#121	—	2	1	no	—
460	#121	—	2	1	no	—
461	#121	—	2	2	no	—
462	#121	C₂³×C₁₃	1	4	yes	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	1	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
470	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
471	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	1	no	—
478	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
479	C₄×D₄	D₄×C₁₃	1	2	yes	—
480	C₄×D₄	D₄×C₁₃	1	2	yes	—
481	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
482	C₄×D₄	C₂³×C₁₃	1	4	yes	—
483	#117	—	2	2	no	—
484	#117	—	2	2	no	—
485	#117	C₂³×C₁₃	1	2	yes	—
486	#117	C₂³×C₁₃	1	4	yes	—
487	#117	C₂³×C₁₃	1	1	yes	characteristic
488	#117	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	2	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
496	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
498	#107	C₂³×C₁₃	1	8	yes	—
499	#107	C₂³×C₁₃	1	8	yes	—
500	#107	C₂³×C₁₃	1	8	yes	—
501	#106	C₂³×C₁₃	1	8	yes	—
502	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
503	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
504	#103	C₂³×C₁₃	1	4	yes	—
505	#103	C₂³×C₁₃	1	4	yes	—
506	#103	C₂³×C₁₃	1	8	yes	—
507	#102	C₂³×C₁₃	1	4	yes	—
508	#102	C₂³×C₁₃	1	4	yes	—
509	#102	C₂³×C₁₃	1	8	yes	—
510	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
511	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
512	#97	C₂³×C₁₃	1	2	yes	—
513	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₄×C₈	C₂³×C₁₃	1	2	yes	—
516	C₄×C₈	C₂³×C₁₃	1	2	yes	—
517	C₂×C₁₃	—	2	2	no	—
518	C₂×C₁₃	—	4	2	no	—
519	C₂×C₁₃	—	8	2	no	—
520	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
521	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
522	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
523	#41	—	2	4	no	—
524	#41	—	2	8	no	—
525	#41	—	8	4	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	8	2	no	—
534	C₂×Q₈	—	8	2	no	—
535	C₂×Q₈	—	8	4	no	—
536	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
543	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
556	M₁₆	—	2	4	no	—
557	C₂×C₈	—	2	4	no	—
558	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
559	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
560	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
583	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
586	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
596	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	2	no	—
600	C₄²	C₂×D₄×C₁₃	1	2	yes	—
601	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₄²	C₂×D₄×C₁₃	1	2	yes	—
604	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₄²	C₂⁴×C₁₃	1	2	yes	—
607	C₁₃	#60880	1	1	yes	characteristic, direct product factor, Sylow
608	C₂³	—	2	2	no	—
609	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
610	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
611	Q₈	—	2	2	no	—
612	Q₈	—	2	4	no	—
613	Q₈	—	4	4	no	—
614	Q₈	—	4	2	no	—
615	Q₈	—	4	4	no	—
616	Q₈	—	4	2	no	—
617	Q₈	—	8	4	no	—
618	Q₈	—	8	2	no	—
619	Q₈	—	8	2	no	—
620	D₄	—	2	4	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	4	no	—
623	D₄	—	4	4	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	2	no	—
626	D₄	—	8	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	8	4	no	—
639	C₂×C₄	—	8	2	no	—
640	C₂×C₄	—	8	2	no	—
641	C₂×C₄	—	8	4	no	—
642	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
644	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
651	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
652	C₈	—	2	2	no	—
653	C₈	—	2	2	no	—
654	C₈	—	2	4	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	C₁₃×#536	1	2	yes	—
664	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	C₁₃×#536	1	2	yes	—
676	C₄	C₁₃×#576	1	2	yes	—
677	C₄	C₁₃×#578	1	2	yes	—
678	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
679	C₂	—	2	2	no	—
680	C₂	—	4	2	no	—
681	C₂	—	8	2	no	—
682	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
683	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
684	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3511	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×#3503	C₂	semidirect
3. C₁₃×#3243	C₂	semidirect
4. C₁₃×#3231	C₂	semidirect
5. C₁₃×#3230	C₂	semidirect
6. C₁₃×#3228	C₂	semidirect
7. C₁₃×#3226	C₂	semidirect
8. C₁₃×#3165	C₂	semidirect
9. C₂×C₁₃×#500	C₂	semidirect
10. C₁₃×#3141	C₂	semidirect
11. C₁₃×#3131	C₂	semidirect
12. C₁₃×#3098	C₂	semidirect
13. C₁₃×#3083	C₂	semidirect
14. C₁₃×#2922	C₂	semidirect
181. #60880	C₁₃	direct (N × H)
267. #3503	C₂×C₁₃	semidirect
268. #3243	C₂×C₁₃	semidirect
269. #3231	C₂×C₁₃	semidirect
270. #3230	C₂×C₁₃	semidirect
271. #3228	C₂×C₁₃	semidirect
272. #3226	C₂×C₁₃	semidirect
273. #3165	C₂×C₁₃	semidirect
274. C₂×#500	C₂×C₁₃	semidirect
275. #3141	C₂×C₁₃	semidirect
276. #3131	C₂×C₁₃	semidirect
277. #3098	C₂×C₁₃	semidirect
278. #3083	C₂×C₁₃	semidirect
279. #2922	C₂×C₁₃	semidirect
607. C₁₃	#60880	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×#3511	2
C₁₃×#3503	2
C₁₃×#3243	2
C₁₃×#3231	2
C₁₃×#3230	2
C₁₃×#3228	2
C₁₃×#3226	2
C₁₃×#3165	2
C₂×C₁₃×#500	2
C₁₃×#3141	2
C₁₃×#3131	2
C₁₃×#3098	2
C₁₃×#3083	2
C₁₃×#2922	2
#60880	13

Subgroups — C13×#60880 #15747219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60880 #15747219