Subgroups — C₁₃×#17988 #15704327

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2993	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1582	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
14	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#533	C₂²	1	1	yes	characteristic
17	C₁₃×#529	C₂²	1	1	yes	characteristic
18	C₁₃×#501	C₄	1	1	yes	characteristic
19	C₁₃×#497	C₄	1	1	yes	characteristic
20	C₁₃×#491	C₄	1	1	yes	characteristic
21	C₁₃×#489	C₄	1	1	yes	characteristic
22	C₁₃×#470	C₄	1	1	yes	characteristic
23	C₁₃×#470	C₄	1	1	yes	characteristic
24	C₁₃×#468	C₄	1	1	yes	characteristic
25	C₁₃×#468	C₄	1	1	yes	characteristic
26	C₁₃×#446	—	2	1	no	—
27	C₁₃×#446	—	2	1	no	—
28	C₁₃×#446	C₂²	1	1	yes	characteristic
29	C₁₃×#446	C₂²	1	1	yes	characteristic
30	C₁₃×#446	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×#436	—	2	1	no	—
39	C₁₃×#436	C₂²	1	1	yes	characteristic
40	C₁₃×#435	—	2	1	no	—
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#433	—	2	1	no	—
43	C₁₃×#433	—	2	1	no	—
44	C₁₃×#433	—	2	1	no	—
45	C₁₃×#432	C₂²	1	1	yes	characteristic
46	C₁₃×#431	C₂²	1	1	yes	characteristic
47	C₁₃×#424	—	2	1	no	—
48	C₁₃×#423	C₂²	1	1	yes	characteristic
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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₃×Q₈⋊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×Q₁₆	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×M₁₆	—	2	1	no	—
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×#126	—	2	1	no	—
80	C₁₃×#125	—	2	1	no	—
81	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#123	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	—	2	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	—	2	1	no	—
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×#103	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#103	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	D₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
128	C₁₃×#97	—	2	1	no	—
129	C₁₃×#97	—	2	1	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	—	2	1	no	—
132	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
133	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
134	C₄×C₈×C₁₃	—	2	1	no	—
135	C₄×C₈×C₁₃	—	2	1	no	—
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	#17988	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
155	C₁₃×Q₁₆	—	4	1	no	—
156	C₁₃×Q₁₆	—	4	1	no	—
157	C₁₃×SD₁₆	—	4	1	no	—
158	C₁₃×SD₁₆	—	4	1	no	—
159	C₁₃×M₁₆	—	4	1	no	—
160	C₁₃×M₁₆	—	4	1	no	—
161	C₁₃×M₁₆	—	8	1	no	—
162	C₁₃×M₁₆	—	8	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	4	2	no	—
170	C₂×C₈×C₁₃	—	8	1	no	—
171	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₃	#41	1	1	yes	characteristic
207	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
208	#3172	C₂×C₁₃	1	1	yes	characteristic
209	#2993	C₂×C₁₃	1	1	yes	characteristic
210	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1588	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1585	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1569	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1494	C₂×C₁₃	1	1	yes	characteristic
221	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	2	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	8	1	no	—
232	D₄×C₁₃	—	2	1	no	—
233	D₄×C₁₃	—	2	1	no	—
234	D₄×C₁₃	—	8	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₈×C₁₃	—	2	2	no	—
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	—	2	1	no	—
259	C₈×C₁₃	—	2	1	no	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	#533	C₂²×C₁₃	1	1	yes	characteristic
270	#529	C₂²×C₁₃	1	1	yes	characteristic
271	#501	C₄×C₁₃	1	1	yes	characteristic
272	#497	C₄×C₁₃	1	1	yes	characteristic
273	#491	C₄×C₁₃	1	1	yes	characteristic
274	#489	C₄×C₁₃	1	1	yes	characteristic
275	#470	C₄×C₁₃	1	1	yes	characteristic
276	#470	C₄×C₁₃	1	1	yes	characteristic
277	#468	C₄×C₁₃	1	1	yes	characteristic
278	#468	C₄×C₁₃	1	1	yes	characteristic
279	#446	—	2	1	no	—
280	#446	—	2	1	no	—
281	#446	C₂²×C₁₃	1	1	yes	characteristic
282	#446	C₂²×C₁₃	1	1	yes	characteristic
283	#446	C₂²×C₁₃	1	1	yes	characteristic
284	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
288	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	#436	—	2	1	no	—
292	#436	C₂²×C₁₃	1	1	yes	characteristic
293	#435	—	2	1	no	—
294	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
295	#433	—	2	1	no	—
296	#433	—	2	1	no	—
297	#433	—	2	1	no	—
298	#432	C₂²×C₁₃	1	1	yes	characteristic
299	#431	C₂²×C₁₃	1	1	yes	characteristic
300	#424	—	2	1	no	—
301	#423	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
304	#335	C₂²×C₁₃	1	1	yes	characteristic
305	#335	C₂²×C₁₃	1	1	yes	characteristic
306	#334	C₂²×C₁₃	1	1	yes	characteristic
307	#334	C₂²×C₁₃	1	1	yes	characteristic
308	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
309	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
310	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
311	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
312	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
313	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
314	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	#322	C₂²×C₁₃	1	1	yes	characteristic
317	#322	C₂²×C₁₃	1	1	yes	characteristic
318	#322	C₂²×C₁₃	1	1	yes	characteristic
319	#322	C₂²×C₁₃	1	1	yes	characteristic
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	#568	1	1	yes	characteristic
339	C₄×C₁₃	#568	1	1	yes	characteristic
340	C₄×C₁₃	#577	1	1	yes	characteristic
341	C₄×C₁₃	#578	1	1	yes	characteristic
342	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
343	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
344	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
345	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
349	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
353	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
354	#126	—	2	1	no	—
355	#125	—	2	1	no	—
356	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
357	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
358	#123	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
361	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
362	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
363	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
374	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
375	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
376	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
385	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
390	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
391	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
392	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
393	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
394	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
395	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
396	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
397	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
402	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
403	#97	—	2	1	no	—
404	#97	—	2	1	no	—
405	#97	—	2	1	no	—
406	#97	—	2	1	no	—
407	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
408	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₁₃	—	4	1	no	—
420	C₂×C₁₃	—	8	1	no	—
421	C₂×C₁₃	#2932	1	1	yes	characteristic
422	C₂×C₁₃	#2947	1	1	yes	characteristic
423	C₂×C₁₃	#2956	1	1	yes	characteristic
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
426	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
427	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
434	Q₁₆	—	4	1	no	—
435	Q₁₆	—	4	1	no	—
436	SD₁₆	—	4	1	no	—
437	SD₁₆	—	4	1	no	—
438	M₁₆	—	4	1	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	—	8	1	no	—
441	M₁₆	—	8	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	4	2	no	—
449	C₂×C₈	—	8	1	no	—
450	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
451	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
452	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
453	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₄²	C₁₃×#41	1	1	yes	characteristic
486	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
487	C₁₃	#17988	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	1	no	—
489	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	8	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	2	1	no	—
499	D₄	—	8	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	C₁₃×#568	1	1	yes	characteristic
553	C₄	C₁₃×#568	1	1	yes	characteristic
554	C₄	C₁₃×#577	1	1	yes	characteristic
555	C₄	C₁₃×#578	1	1	yes	characteristic
556	C₂	—	4	1	no	—
557	C₂	—	8	1	no	—
558	C₂	C₁₃×#2932	1	1	yes	characteristic
559	C₂	C₁₃×#2947	1	1	yes	characteristic
560	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×#121	C₂×C₄
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
3. C₁₃×#2985	C₂	semidirect
4. C₁₃×#1588	C₂	semidirect
5. C₁₃×#1587	C₂	semidirect
6. C₁₃×#1587	C₂	semidirect
7. C₁₃×#1585	C₂	semidirect
8. C₁₃×#1584	C₂	semidirect
9. C₁₃×#1584	C₂	semidirect
10. C₁₃×#1583	C₂	semidirect
11. C₁₃×#1582	C₂	semidirect
12. C₁₃×#1569	C₂	semidirect
14. C₁₃×#1493	C₂	semidirect
15. C₁₃×#1451	C₂	semidirect
144. #17988	C₁₃	direct (N × H)
210. #2985	C₂×C₁₃	semidirect
211. #1588	C₂×C₁₃	semidirect
212. #1587	C₂×C₁₃	semidirect
213. #1587	C₂×C₁₃	semidirect
214. #1585	C₂×C₁₃	semidirect
215. #1584	C₂×C₁₃	semidirect
216. #1584	C₂×C₁₃	semidirect
217. #1583	C₂×C₁₃	semidirect
218. #1582	C₂×C₁₃	semidirect
219. #1569	C₂×C₁₃	semidirect
221. #1493	C₂×C₁₃	semidirect
222. #1451	C₂×C₁₃	semidirect
487. C₁₃	#17988	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×#3172	2
C₁₃×#2993	2
C₁₃×#2985	2
C₁₃×#1588	2
C₁₃×#1587	2
C₁₃×#1585	2
C₁₃×#1584	2
C₁₃×#1583	2
C₁₃×#1582	2
C₁₃×#1569	2
C₁₃×#1494	2
C₁₃×#1493	2
C₁₃×#1451	2
#17988	13

Subgroups — C13×#17988 #15704327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17988 #15704327