Subgroups — C₁₃×#17987 #15704326

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3171	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#532	C₂²	1	1	yes	characteristic
17	C₁₃×#529	C₂²	1	1	yes	characteristic
18	C₁₃×#501	C₄	1	1	yes	characteristic
19	C₁₃×#496	C₄	1	1	yes	characteristic
20	C₁₃×#490	C₄	1	1	yes	characteristic
21	C₁₃×#489	C₄	1	1	yes	characteristic
22	C₁₃×#469	C₄	1	1	yes	characteristic
23	C₁₃×#469	C₄	1	1	yes	characteristic
24	C₁₃×#468	C₄	1	1	yes	characteristic
25	C₁₃×#468	C₄	1	1	yes	characteristic
26	C₁₃×#446	C₂²	1	1	yes	characteristic
27	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₁₃×#436	—	2	1	no	—
33	C₁₃×#436	C₂²	1	1	yes	characteristic
34	C₁₃×#436	C₂²	1	1	yes	characteristic
35	C₁₃×#436	C₂²	1	1	yes	characteristic
36	C₁₃×#435	—	2	1	no	—
37	C₁₃×#435	—	2	1	no	—
38	C₁₃×#435	—	2	1	no	—
39	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#433	—	2	1	no	—
43	C₁₃×#432	C₂²	1	1	yes	characteristic
44	C₁₃×#431	C₂²	1	1	yes	characteristic
45	C₁₃×#424	—	2	1	no	—
46	C₁₃×#423	C₂²	1	1	yes	characteristic
47	C₁₃×#408	—	2	1	no	—
48	C₁₃×#408	—	2	1	no	—
49	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×#335	C₂²	1	1	yes	characteristic
53	C₁₃×#334	C₂²	1	1	yes	characteristic
54	C₁₃×#334	C₂²	1	1	yes	characteristic
55	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×#322	C₂²	1	1	yes	characteristic
64	C₁₃×#322	C₂²	1	1	yes	characteristic
65	C₁₃×#322	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#126	—	2	1	no	—
85	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#124	—	2	1	no	—
87	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#123	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#117	—	2	1	no	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
104	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	—	2	1	no	—
108	C₁₃×C₄⋊C₈	—	2	1	no	—
109	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
122	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
123	C₁₃×C₂²⋊C₈	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	1	no	—
125	C₁₃×C₂²⋊C₈	—	2	1	no	—
126	C₁₃×C₂²⋊C₈	—	2	1	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
132	C₁₃×#97	—	2	1	no	—
133	C₁₃×#97	—	2	1	no	—
134	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
135	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
136	C₄×C₈×C₁₃	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#17987	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	8	1	no	—
146	C₁₃×#41	—	8	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
163	C₁₃×SD₁₆	—	4	1	no	—
164	C₁₃×SD₁₆	—	4	1	no	—
165	C₁₃×D₈	—	4	1	no	—
166	C₁₃×D₈	—	4	1	no	—
167	C₁₃×M₁₆	—	4	1	no	—
168	C₁₃×M₁₆	—	4	1	no	—
169	C₁₃×M₁₆	—	8	1	no	—
170	C₁₃×M₁₆	—	8	1	no	—
171	C₁₃×M₁₆	—	8	1	no	—
172	C₁₃×M₁₆	—	8	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	4	2	no	—
180	C₂×C₈×C₁₃	—	8	1	no	—
181	C₂×C₈×C₁₃	—	8	1	no	—
182	C₂×C₈×C₁₃	—	8	1	no	—
183	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	#41	1	1	yes	characteristic
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3171	C₂×C₁₃	1	1	yes	characteristic
215	#2993	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1588	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1585	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1569	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	8	1	no	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	8	1	no	—
243	D₄×C₁₃	—	8	1	no	—
244	D₄×C₁₃	—	8	1	no	—
245	D₄×C₁₃	—	8	1	no	—
246	D₄×C₁₃	—	8	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	2	1	no	—
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	#532	C₂²×C₁₃	1	1	yes	characteristic
284	#529	C₂²×C₁₃	1	1	yes	characteristic
285	#501	C₄×C₁₃	1	1	yes	characteristic
286	#496	C₄×C₁₃	1	1	yes	characteristic
287	#490	C₄×C₁₃	1	1	yes	characteristic
288	#489	C₄×C₁₃	1	1	yes	characteristic
289	#469	C₄×C₁₃	1	1	yes	characteristic
290	#469	C₄×C₁₃	1	1	yes	characteristic
291	#468	C₄×C₁₃	1	1	yes	characteristic
292	#468	C₄×C₁₃	1	1	yes	characteristic
293	#446	C₂²×C₁₃	1	1	yes	characteristic
294	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
296	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
299	#436	—	2	1	no	—
300	#436	C₂²×C₁₃	1	1	yes	characteristic
301	#436	C₂²×C₁₃	1	1	yes	characteristic
302	#436	C₂²×C₁₃	1	1	yes	characteristic
303	#435	—	2	1	no	—
304	#435	—	2	1	no	—
305	#435	—	2	1	no	—
306	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	#433	—	2	1	no	—
310	#432	C₂²×C₁₃	1	1	yes	characteristic
311	#431	C₂²×C₁₃	1	1	yes	characteristic
312	#424	—	2	1	no	—
313	#423	C₂²×C₁₃	1	1	yes	characteristic
314	#408	—	2	1	no	—
315	#408	—	2	1	no	—
316	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
318	#335	C₂²×C₁₃	1	1	yes	characteristic
319	#335	C₂²×C₁₃	1	1	yes	characteristic
320	#334	C₂²×C₁₃	1	1	yes	characteristic
321	#334	C₂²×C₁₃	1	1	yes	characteristic
322	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
324	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
327	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	#322	C₂²×C₁₃	1	1	yes	characteristic
331	#322	C₂²×C₁₃	1	1	yes	characteristic
332	#322	C₂²×C₁₃	1	1	yes	characteristic
333	#322	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	#568	1	1	yes	characteristic
357	C₄×C₁₃	#568	1	1	yes	characteristic
358	C₄×C₁₃	#576	1	1	yes	characteristic
359	C₄×C₁₃	#577	1	1	yes	characteristic
360	C₂×#41	—	2	1	no	—
361	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
362	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
363	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
364	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
370	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
376	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
377	#126	—	2	1	no	—
378	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
379	#124	—	2	1	no	—
380	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
381	#123	—	2	1	no	—
382	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#121	—	2	1	no	—
384	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
385	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
386	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
387	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
393	#117	—	2	1	no	—
394	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
395	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
396	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
397	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
398	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
408	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
409	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
410	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
411	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
412	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
413	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
414	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
415	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
424	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
425	#97	—	2	1	no	—
426	#97	—	2	1	no	—
427	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
428	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
429	C₄×C₈	—	2	1	no	—
430	C₄×C₈	—	2	1	no	—
431	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₁₃	—	4	1	no	—
438	C₂×C₁₃	—	8	1	no	—
439	C₂×C₁₃	—	8	1	no	—
440	C₂×C₁₃	—	8	1	no	—
441	C₂×C₁₃	#2932	1	1	yes	characteristic
442	C₂×C₁₃	#2946	1	1	yes	characteristic
443	C₂×C₁₃	#2956	1	1	yes	characteristic
444	#41	—	8	1	no	—
445	#41	—	8	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
462	SD₁₆	—	4	1	no	—
463	SD₁₆	—	4	1	no	—
464	D₈	—	4	1	no	—
465	D₈	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	8	1	no	—
469	M₁₆	—	8	1	no	—
470	M₁₆	—	8	1	no	—
471	M₁₆	—	8	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	4	2	no	—
479	C₂×C₈	—	8	1	no	—
480	C₂×C₈	—	8	1	no	—
481	C₂×C₈	—	8	1	no	—
482	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
483	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
484	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₁₃×#41	1	1	yes	characteristic
512	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₁₃	#17987	1	1	yes	characteristic, direct product factor, Sylow
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	8	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	1	no	—
531	D₄	—	8	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
554	C₈	—	2	2	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	C₁₃×#568	1	1	yes	characteristic
591	C₄	C₁₃×#568	1	1	yes	characteristic
592	C₄	C₁₃×#576	1	1	yes	characteristic
593	C₄	C₁₃×#577	1	1	yes	characteristic
594	C₂	—	4	1	no	—
595	C₂	—	8	1	no	—
596	C₂	—	8	1	no	—
597	C₂	—	8	1	no	—
598	C₂	C₁₃×#2932	1	1	yes	characteristic
599	C₂	C₁₃×#2946	1	1	yes	characteristic
600	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#3171	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2993	C₂	semidirect
3. C₁₃×#2981	C₂	semidirect
4. C₁₃×#1588	C₂	semidirect
5. C₁₃×#1586	C₂	semidirect
6. C₁₃×#1586	C₂	semidirect
7. C₁₃×#1585	C₂	semidirect
8. C₁₃×#1583	C₂	semidirect
9. C₁₃×#1582	C₂	semidirect
10. C₁₃×#1581	C₂	semidirect
11. C₁₃×#1581	C₂	semidirect
12. C₁₃×#1569	C₂	semidirect
13. C₁₃×#1494	C₂	semidirect
14. C₁₃×#1492	C₂	semidirect
15. C₁₃×#1451	C₂	semidirect
144. #17987	C₁₃	direct (N × H)
215. #2993	C₂×C₁₃	semidirect
216. #2981	C₂×C₁₃	semidirect
217. #1588	C₂×C₁₃	semidirect
218. #1586	C₂×C₁₃	semidirect
219. #1586	C₂×C₁₃	semidirect
220. #1585	C₂×C₁₃	semidirect
221. #1583	C₂×C₁₃	semidirect
222. #1582	C₂×C₁₃	semidirect
223. #1581	C₂×C₁₃	semidirect
224. #1581	C₂×C₁₃	semidirect
225. #1569	C₂×C₁₃	semidirect
226. #1494	C₂×C₁₃	semidirect
227. #1492	C₂×C₁₃	semidirect
228. #1451	C₂×C₁₃	semidirect
513. C₁₃	#17987	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×#3171	2
C₁₃×#2993	2
C₁₃×#2981	2
C₁₃×#1588	2
C₁₃×#1586	2
C₁₃×#1585	2
C₁₃×#1583	2
C₁₃×#1582	2
C₁₃×#1581	2
C₁₃×#1569	2
C₁₃×#1494	2
C₁₃×#1492	2
C₁₃×#1451	2
#17987	13

Subgroups — C13×#17987 #15704326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17987 #15704326