Subgroups — C₁₃×#18029 #15704368

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1495	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₁₃×#485	C₄	1	1	yes	characteristic
19	C₁₃×#482	C₄	1	1	yes	characteristic
20	C₁₃×#479	C₄	1	1	yes	characteristic
21	C₁₃×#478	C₄	1	1	yes	characteristic
22	C₁₃×#464	C₄	1	1	yes	characteristic
23	C₁₃×#463	C₄	1	1	yes	characteristic
24	C₁₃×#452	C₄	1	1	yes	characteristic
25	C₁₃×#449	C₄	1	1	yes	characteristic
26	C₁₃×#446	C₂²	1	1	yes	characteristic
27	C₁₃×#446	C₂²	1	1	yes	characteristic
28	C₁₃×#446	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₁₃×#436	C₂²	1	1	yes	characteristic
35	C₁₃×#435	—	2	1	no	—
36	C₁₃×#435	—	2	1	no	—
37	C₁₃×#435	—	2	1	no	—
38	C₈×D₄×C₁₃	—	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	—	2	1	no	—
44	C₁₃×#431	C₂²	1	1	yes	characteristic
45	C₁₃×#431	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	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₁₃×#334	C₂²	1	1	yes	characteristic
52	C₁₃×#334	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×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	C₈²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	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×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₁₃×#126	—	2	1	no	—
79	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#123	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#117	—	2	1	no	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	—	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	C₂×C₄	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	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×#102	C₂×C₄	1	1	yes	characteristic
124	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
131	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
134	C₁₃×#97	—	2	1	no	—
135	C₁₃×#97	—	2	1	no	—
136	C₁₃×#97	—	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	#18029	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	2	2	no	—
146	C₁₃×#41	—	4	1	no	—
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	—	2	1	no	—
151	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
160	C₁₃×Q₁₆	—	4	1	no	—
161	C₁₃×SD₁₆	—	2	2	no	—
162	C₁₃×SD₁₆	—	4	1	no	—
163	C₁₃×D₈	—	2	2	no	—
164	C₁₃×M₁₆	—	8	1	no	—
165	C₁₃×M₁₆	—	8	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	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	8	1	no	—
173	C₂×C₈×C₁₃	—	8	1	no	—
174	C₂×C₈×C₁₃	—	8	1	no	—
175	C₂×C₈×C₁₃	—	8	1	no	—
176	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	#41	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	#3102	C₂×C₁₃	1	1	yes	characteristic
211	#2994	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1593	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1590	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1570	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1495	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1477	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1454	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	D₄×C₁₃	—	2	1	no	—
233	D₄×C₁₃	—	2	1	no	—
234	D₄×C₁₃	—	2	1	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	#131	1	2	yes	—
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	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	—	2	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	#529	C₂²×C₁₃	1	1	yes	characteristic
276	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
277	#485	C₄×C₁₃	1	1	yes	characteristic
278	#482	C₄×C₁₃	1	1	yes	characteristic
279	#479	C₄×C₁₃	1	1	yes	characteristic
280	#478	C₄×C₁₃	1	1	yes	characteristic
281	#464	C₄×C₁₃	1	1	yes	characteristic
282	#463	C₄×C₁₃	1	1	yes	characteristic
283	#452	C₄×C₁₃	1	1	yes	characteristic
284	#449	C₄×C₁₃	1	1	yes	characteristic
285	#446	C₂²×C₁₃	1	1	yes	characteristic
286	#446	C₂²×C₁₃	1	1	yes	characteristic
287	#446	C₂²×C₁₃	1	1	yes	characteristic
288	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
292	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
293	#436	C₂²×C₁₃	1	1	yes	characteristic
294	#435	—	2	1	no	—
295	#435	—	2	1	no	—
296	#435	—	2	1	no	—
297	C₈×D₄	—	2	1	no	—
298	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
301	#433	—	2	1	no	—
302	#432	—	2	1	no	—
303	#431	C₂²×C₁₃	1	1	yes	characteristic
304	#431	C₂²×C₁₃	1	1	yes	characteristic
305	#431	C₂²×C₁₃	1	1	yes	characteristic
306	#424	—	2	1	no	—
307	#423	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₈	—	2	1	no	—
309	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
310	#334	C₂²×C₁₃	1	1	yes	characteristic
311	#334	C₂²×C₁₃	1	1	yes	characteristic
312	#334	C₂²×C₁₃	1	1	yes	characteristic
313	#334	C₂²×C₁₃	1	1	yes	characteristic
314	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	#322	C₂²×C₁₃	1	1	yes	characteristic
323	#322	C₂²×C₁₃	1	1	yes	characteristic
324	#322	C₂²×C₁₃	1	1	yes	characteristic
325	C₈²	C₂²×C₁₃	1	1	yes	characteristic
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
347	C₄×C₁₃	#568	1	1	yes	characteristic
348	C₄×C₁₃	#577	1	1	yes	characteristic
349	C₄×C₁₃	#577	1	1	yes	characteristic
350	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
351	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
352	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
353	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
354	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	#126	—	2	1	no	—
362	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
363	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
364	#123	—	2	1	no	—
365	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
366	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
367	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
368	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
374	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
382	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
384	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
394	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
395	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
400	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
401	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
402	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
403	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
404	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
405	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
406	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
407	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
414	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
415	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
416	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
417	#97	—	2	1	no	—
418	#97	—	2	1	no	—
419	#97	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₁₃	—	4	1	no	—
428	C₂×C₁₃	—	4	2	no	—
429	C₂×C₁₃	—	8	1	no	—
430	C₂×C₁₃	#2933	1	1	yes	characteristic
431	C₂×C₁₃	#2952	1	1	yes	characteristic
432	C₂×C₁₃	#2955	1	1	yes	characteristic
433	#41	—	2	2	no	—
434	#41	—	4	1	no	—
435	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
436	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
440	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
448	Q₁₆	—	4	1	no	—
449	SD₁₆	—	2	2	no	—
450	SD₁₆	—	4	1	no	—
451	D₈	—	2	2	no	—
452	M₁₆	—	8	1	no	—
453	M₁₆	—	8	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	8	1	no	—
461	C₂×C₈	—	8	1	no	—
462	C₂×C₈	—	8	1	no	—
463	C₂×C₈	—	8	1	no	—
464	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
467	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄²	C₁₃×#41	1	1	yes	characteristic
497	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₁₃	#18029	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	C₁₃×#131	1	2	yes	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
530	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
570	C₄	C₁₃×#568	1	1	yes	characteristic
571	C₄	C₁₃×#577	1	1	yes	characteristic
572	C₄	C₁₃×#577	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	C₁₃×#2933	1	1	yes	characteristic
577	C₂	C₁₃×#2952	1	1	yes	characteristic
578	C₂	C₁₃×#2955	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×#449	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
2. C₁₃×#2994	C₂	semidirect
3. C₁₃×#2990	C₂	semidirect
4. C₁₃×#1593	C₂	semidirect
5. C₁₃×#1590	C₂	semidirect
6. C₁₃×#1587	C₂	semidirect
7. C₁₃×#1586	C₂	semidirect
8. C₁₃×#1582	C₂	semidirect
9. C₁₃×#1582	C₂	semidirect
10. C₁₃×#1580	C₂	semidirect
11. C₈×C₁₃×SD₁₆	C₂	semidirect
12. C₁₃×#1570	C₂	semidirect
13. C₁₃×#1495	C₂	semidirect
14. C₁₃×#1477	C₂	semidirect
15. C₁₃×#1454	C₂	semidirect
144. #18029	C₁₃	direct (N × H)
211. #2994	C₂×C₁₃	semidirect
212. #2990	C₂×C₁₃	semidirect
213. #1593	C₂×C₁₃	semidirect
214. #1590	C₂×C₁₃	semidirect
215. #1587	C₂×C₁₃	semidirect
216. #1586	C₂×C₁₃	semidirect
217. #1582	C₂×C₁₃	semidirect
218. #1582	C₂×C₁₃	semidirect
219. #1580	C₂×C₁₃	semidirect
220. C₈×SD₁₆	C₂×C₁₃	semidirect
221. #1570	C₂×C₁₃	semidirect
222. #1495	C₂×C₁₃	semidirect
223. #1477	C₂×C₁₃	semidirect
224. #1454	C₂×C₁₃	semidirect
498. C₁₃	#18029	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×#3102	2
C₁₃×#2994	2
C₁₃×#2990	2
C₁₃×#1593	2
C₁₃×#1590	2
C₁₃×#1587	2
C₁₃×#1586	2
C₁₃×#1582	2
C₁₃×#1580	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1570	2
C₁₃×#1495	2
C₁₃×#1477	2
C₁₃×#1454	2
#18029	13

Subgroups — C13×#18029 #15704368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18029 #15704368