Subgroups — C₁₃×#61893 #15748232

Order 3328.

1698 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3398	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×#3218	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#3117	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	C₂²	1	2	yes	—
15	C₁₃×#557	—	2	2	no	—
16	C₁₃×#557	—	2	2	no	—
17	C₁₃×#557	C₂²	1	4	yes	—
18	C₁₃×#557	C₂²	1	4	yes	—
19	C₁₃×#557	C₂²	1	2	yes	—
20	C₁₃×#556	—	2	2	no	—
21	C₁₃×#556	C₂²	1	2	yes	—
22	C₁₃×#554	C₂²	1	2	yes	—
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#539	—	2	2	no	—
25	C₁₃×#536	—	2	1	no	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₁₃×#529	C₂²	1	4	yes	—
31	C₂×C₁₃×#125	—	2	1	no	—
32	C₂×C₁₃×#125	—	2	2	no	—
33	C₁₃×#520	—	2	1	no	—
34	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#497	C₂²	1	8	yes	—
39	C₁₃×#494	C₂²	1	2	yes	—
40	C₁₃×#492	C₂²	1	2	yes	—
41	C₁₃×#491	C₂²	1	8	yes	—
42	C₁₃×#487	C₂²	1	2	yes	—
43	C₁₃×#487	C₂²	1	2	yes	—
44	C₁₃×#484	C₂²	1	2	yes	—
45	C₁₃×#481	C₂²	1	2	yes	—
46	C₁₃×#479	C₂²	1	8	yes	—
47	C₁₃×#477	C₂²	1	2	yes	—
48	C₁₃×#475	C₂²	1	2	yes	—
49	C₁₃×#464	C₂²	1	8	yes	—
50	C₁₃×#462	C₂²	1	2	yes	—
51	C₁₃×#462	C₂²	1	8	yes	—
52	C₁₃×#462	C₂²	1	4	yes	—
53	C₁₃×#461	C₂²	1	4	yes	—
54	C₁₃×#461	C₂²	1	8	yes	—
55	C₁₃×#460	C₂²	1	2	yes	—
56	C₁₃×#451	C₂²	1	2	yes	—
57	C₁₃×#451	C₂²	1	4	yes	—
58	C₁₃×#448	C₂²	1	2	yes	—
59	C₁₃×#448	C₂²	1	4	yes	—
60	C₁₃×#446	C₂²	1	4	yes	—
61	C₁₃×#446	C₂²	1	4	yes	—
62	C₁₃×#441	C₂²	1	8	yes	—
63	C₁₃×#440	C₂²	1	8	yes	—
64	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
65	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
66	C₁₃×#432	C₂²	1	4	yes	—
67	C₁₃×#431	C₂²	1	1	yes	characteristic
68	C₁₃×#431	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	4	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×#127	C₂³	1	1	yes	characteristic
88	C₁₃×#126	—	2	4	no	—
89	C₁₃×#126	—	2	4	no	—
90	C₁₃×#125	—	2	4	no	—
91	C₁₃×#125	—	2	4	no	—
92	C₁₃×#125	—	2	8	no	—
93	C₁₃×#125	—	2	8	no	—
94	C₁₃×#125	—	2	4	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	C₂³	1	4	yes	—
97	C₁₃×#124	—	2	2	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	C₂³	1	4	yes	—
100	C₁₃×#123	—	2	4	no	—
101	C₁₃×#123	—	2	4	no	—
102	C₁₃×C₂²⋊Q₈	—	2	2	no	—
103	C₁₃×C₂²⋊Q₈	—	2	2	no	—
104	C₁₃×C₂²⋊Q₈	—	2	1	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×#121	—	2	1	no	—
108	C₁₃×#121	C₂³	1	2	yes	—
109	C₄×Q₈×C₁₃	—	2	4	no	—
110	C₄×Q₈×C₁₃	—	2	4	no	—
111	C₄×Q₈×C₁₃	—	2	2	no	—
112	C₄×Q₈×C₁₃	—	2	4	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	D₄	1	2	yes	—
117	C₄×Q₈×C₁₃	D₄	1	2	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₄×D₄×C₁₃	—	2	4	no	—
126	C₄×D₄×C₁₃	—	2	2	no	—
127	C₄×D₄×C₁₃	—	2	1	no	—
128	C₄×D₄×C₁₃	C₂³	1	2	yes	—
129	C₄×D₄×C₁₃	C₂³	1	4	yes	—
130	C₁₃×#117	—	2	1	no	—
131	C₁₃×#117	—	2	2	no	—
132	C₁₃×#117	—	2	4	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	—	2	2	no	—
144	C₂×C₄²×C₁₃	—	2	1	no	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
147	C₁₃×#107	C₂³	1	4	yes	—
148	C₁₃×#106	C₂³	1	4	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	4	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#103	C₂³	1	8	yes	—
156	C₁₃×#103	C₂³	1	8	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
160	C₁₃×#97	C₂³	1	8	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	2	yes	—
163	#61893	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₁₃×#41	—	4	4	no	—
165	C₂×Q₈×C₁₃	—	2	4	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	4	2	no	—
171	C₂×Q₈×C₁₃	—	4	4	no	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
177	C₂×D₄×C₁₃	—	2	2	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×Q₁₆	—	4	4	no	—
192	C₁₃×Q₁₆	—	4	8	no	—
193	C₁₃×SD₁₆	—	4	8	no	—
194	C₁₃×SD₁₆	—	4	4	no	—
195	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
196	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	8	no	—
200	C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	8	no	—
203	C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₁₃×C₄⋊C₄	—	2	8	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
219	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
222	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
223	C₁₃×C₂²⋊C₄	—	2	2	no	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₄²×C₁₃	—	2	8	no	—
230	C₄²×C₁₃	—	2	2	no	—
231	C₄²×C₁₃	—	2	2	no	—
232	C₄²×C₁₃	—	2	4	no	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	C₂×D₄	1	4	yes	—
235	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₄²×C₁₃	C₂⁴	1	4	yes	—
240	#3507	C₂×C₁₃	1	1	yes	characteristic
241	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3400	C₂×C₁₃	1	4	yes	complemented
243	#3398	C₂×C₁₃	1	4	yes	complemented
244	#3374	C₂×C₁₃	1	4	yes	complemented
245	#3372	C₂×C₁₃	1	4	yes	complemented
246	#3218	C₂×C₁₃	1	4	yes	complemented
247	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#3206	C₂×C₁₃	1	1	yes	characteristic
249	#3117	C₂×C₁₃	1	4	yes	complemented
250	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3103	C₂×C₁₃	1	1	yes	characteristic
252	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₃	—	2	4	no	—
256	Q₈×C₁₃	—	2	4	no	—
257	Q₈×C₁₃	—	2	2	no	—
258	Q₈×C₁₃	—	2	8	no	—
259	Q₈×C₁₃	—	2	4	no	—
260	Q₈×C₁₃	—	2	2	no	—
261	Q₈×C₁₃	—	4	2	no	—
262	Q₈×C₁₃	—	4	4	no	—
263	Q₈×C₁₃	—	4	2	no	—
264	Q₈×C₁₃	—	8	1	no	—
265	D₄×C₁₃	—	2	4	no	—
266	D₄×C₁₃	—	4	4	no	—
267	D₄×C₁₃	—	4	2	no	—
268	D₄×C₁₃	—	8	1	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	2	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	8	4	no	—
284	C₂×C₄×C₁₃	#137	1	4	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₁₃	—	2	4	no	—
294	C₈×C₁₃	—	2	4	no	—
295	#559	C₂²×C₁₃	1	2	yes	—
296	#557	—	2	2	no	—
297	#557	—	2	2	no	—
298	#557	C₂²×C₁₃	1	4	yes	—
299	#557	C₂²×C₁₃	1	4	yes	—
300	#557	C₂²×C₁₃	1	2	yes	—
301	#556	—	2	2	no	—
302	#556	C₂²×C₁₃	1	2	yes	—
303	#554	C₂²×C₁₃	1	2	yes	—
304	#552	—	2	2	no	—
305	#539	—	2	2	no	—
306	#536	—	2	1	no	—
307	#533	C₂²×C₁₃	1	1	yes	characteristic
308	#532	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
311	#529	C₂²×C₁₃	1	4	yes	—
312	C₂×#125	—	2	1	no	—
313	C₂×#125	—	2	2	no	—
314	#520	—	2	1	no	—
315	C₂×C₄×Q₈	—	2	1	no	—
316	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
318	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	#497	C₂²×C₁₃	1	8	yes	—
320	#494	C₂²×C₁₃	1	2	yes	—
321	#492	C₂²×C₁₃	1	2	yes	—
322	#491	C₂²×C₁₃	1	8	yes	—
323	#487	C₂²×C₁₃	1	2	yes	—
324	#487	C₂²×C₁₃	1	2	yes	—
325	#484	C₂²×C₁₃	1	2	yes	—
326	#481	C₂²×C₁₃	1	2	yes	—
327	#479	C₂²×C₁₃	1	8	yes	—
328	#477	C₂²×C₁₃	1	2	yes	—
329	#475	C₂²×C₁₃	1	2	yes	—
330	#464	C₂²×C₁₃	1	8	yes	—
331	#462	C₂²×C₁₃	1	2	yes	—
332	#462	C₂²×C₁₃	1	8	yes	—
333	#462	C₂²×C₁₃	1	4	yes	—
334	#461	C₂²×C₁₃	1	4	yes	—
335	#461	C₂²×C₁₃	1	8	yes	—
336	#460	C₂²×C₁₃	1	2	yes	—
337	#451	C₂²×C₁₃	1	2	yes	—
338	#451	C₂²×C₁₃	1	4	yes	—
339	#448	C₂²×C₁₃	1	2	yes	—
340	#448	C₂²×C₁₃	1	4	yes	—
341	#446	C₂²×C₁₃	1	4	yes	—
342	#446	C₂²×C₁₃	1	4	yes	—
343	#441	C₂²×C₁₃	1	8	yes	—
344	#440	C₂²×C₁₃	1	8	yes	—
345	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
346	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
347	#432	C₂²×C₁₃	1	4	yes	—
348	#431	C₂²×C₁₃	1	1	yes	characteristic
349	#431	C₂²×C₁₃	1	1	yes	characteristic
350	C₂²×C₁₃	—	2	1	no	—
351	C₂²×C₁₃	—	2	1	no	—
352	C₂²×C₁₃	—	4	2	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	2	no	—
355	C₂²×C₁₃	C₂×#137	1	2	yes	—
356	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₁₃	—	2	4	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	2	1	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	4	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	2	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	4	no	—
366	C₄×C₁₃	—	4	2	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	C₂×#137	1	2	yes	—
369	C₄×C₁₃	C₂×#137	1	2	yes	—
370	C₄×C₁₃	#585	1	2	yes	—
371	C₂×#41	—	2	1	no	—
372	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
373	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
375	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
376	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
377	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
378	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
379	C₄⋊Q₈	—	2	2	no	—
380	C₄⋊Q₈	—	2	4	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	—	2	1	no	—
383	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
384	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
385	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
386	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	#127	C₂³×C₁₃	1	1	yes	characteristic
390	#126	—	2	4	no	—
391	#126	—	2	4	no	—
392	#125	—	2	4	no	—
393	#125	—	2	4	no	—
394	#125	—	2	8	no	—
395	#125	—	2	8	no	—
396	#125	—	2	4	no	—
397	#125	—	2	1	no	—
398	#125	C₂³×C₁₃	1	4	yes	—
399	#124	—	2	2	no	—
400	#124	—	2	1	no	—
401	#124	C₂³×C₁₃	1	4	yes	—
402	#123	—	2	4	no	—
403	#123	—	2	4	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	1	no	—
407	C₂²⋊Q₈	—	2	4	no	—
408	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
409	#121	—	2	1	no	—
410	#121	C₂³×C₁₃	1	2	yes	—
411	C₄×Q₈	—	2	4	no	—
412	C₄×Q₈	—	2	4	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	—	2	4	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	D₄×C₁₃	1	2	yes	—
419	C₄×Q₈	D₄×C₁₃	1	2	yes	—
420	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
421	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
422	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
427	C₄×D₄	—	2	4	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	C₂³×C₁₃	1	4	yes	—
431	C₄×D₄	C₂³×C₁₃	1	2	yes	—
432	#117	—	2	1	no	—
433	#117	—	2	2	no	—
434	#117	—	2	4	no	—
435	C₂×C₄⋊C₄	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	2	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄²	—	2	2	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
448	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
449	#107	C₂³×C₁₃	1	4	yes	—
450	#106	C₂³×C₁₃	1	4	yes	—
451	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
452	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
453	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
454	#103	C₂³×C₁₃	1	4	yes	—
455	#103	C₂³×C₁₃	1	4	yes	—
456	#103	C₂³×C₁₃	1	4	yes	—
457	#103	C₂³×C₁₃	1	8	yes	—
458	#103	C₂³×C₁₃	1	8	yes	—
459	#102	C₂³×C₁₃	1	4	yes	—
460	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
461	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
462	#97	C₂³×C₁₃	1	8	yes	—
463	C₄×C₈	C₂³×C₁₃	1	2	yes	—
464	C₄×C₈	C₂³×C₁₃	1	2	yes	—
465	C₂×C₁₃	—	2	2	no	—
466	C₂×C₁₃	—	8	2	no	—
467	C₂×C₁₃	#3487	1	1	yes	characteristic
468	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
469	C₂×C₁₃	#3586	1	1	yes	characteristic
470	#41	—	4	4	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	4	2	no	—
477	C₂×Q₈	—	4	4	no	—
478	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
479	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
480	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
481	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
482	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	Q₁₆	—	4	4	no	—
498	Q₁₆	—	4	8	no	—
499	SD₁₆	—	4	8	no	—
500	SD₁₆	—	4	4	no	—
501	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
502	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
523	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
524	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
525	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
526	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₄²	—	2	8	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	2	no	—
540	C₄²	C₂×D₄×C₁₃	1	4	yes	—
541	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
544	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
545	C₄²	C₂⁴×C₁₃	1	4	yes	—
546	C₁₃	#61893	1	1	yes	characteristic, direct product factor, Sylow
547	C₂³	—	2	2	no	—
548	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
549	Q₈	—	2	4	no	—
550	Q₈	—	2	4	no	—
551	Q₈	—	2	2	no	—
552	Q₈	—	2	8	no	—
553	Q₈	—	2	4	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	4	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	8	1	no	—
559	D₄	—	2	4	no	—
560	D₄	—	4	4	no	—
561	D₄	—	4	2	no	—
562	D₄	—	8	1	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	8	4	no	—
578	C₂×C₄	C₁₃×#137	1	4	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
587	C₈	—	2	4	no	—
588	C₈	—	2	4	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	C₂×C₁₃×#137	1	2	yes	—
595	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
596	C₄	—	2	4	no	—
597	C₄	—	2	4	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	2	no	—
607	C₄	C₂×C₁₃×#137	1	2	yes	—
608	C₄	C₂×C₁₃×#137	1	2	yes	—
609	C₄	C₁₃×#585	1	2	yes	—
610	C₂	—	2	2	no	—
611	C₂	—	8	2	no	—
612	C₂	C₁₃×#3487	1	1	yes	characteristic
613	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
614	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3374	C₂	semidirect
6. C₁₃×#3372	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3209	C₂	semidirect
10. C₁₃×#3117	C₂	semidirect
11. C₁₃×#3104	C₂	semidirect
13. C₁₃×#2983	C₂	semidirect
163. #61893	C₁₃	direct (N × H)
241. C₂×#557	C₂×C₁₃	semidirect
242. #3400	C₂×C₁₃	semidirect
243. #3398	C₂×C₁₃	semidirect
244. #3374	C₂×C₁₃	semidirect
245. #3372	C₂×C₁₃	semidirect
246. #3218	C₂×C₁₃	semidirect
247. #3209	C₂×C₁₃	semidirect
249. #3117	C₂×C₁₃	semidirect
250. #3104	C₂×C₁₃	semidirect
252. #2983	C₂×C₁₃	semidirect
546. C₁₃	#61893	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×#3507	2
C₂×C₁₃×#557	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3374	2
C₁₃×#3372	2
C₁₃×#3218	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3117	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#2983	2
#61893	13

Subgroups — C13×#61893 #15748232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61893 #15748232