Subgroups — C₁₃×#32430 #15718769

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2512	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#126	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#397	—	2	1	no	—
32	C₁₃×#396	—	2	1	no	—
33	C₁₃×#395	—	2	1	no	—
34	C₁₃×#395	—	2	1	no	—
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#390	C₂²	1	1	yes	characteristic
40	C₁₃×#389	—	2	1	no	—
41	C₁₃×#389	—	2	1	no	—
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#388	—	2	1	no	—
44	C₁₃×#384	C₂²	1	1	yes	characteristic
45	C₁₃×#384	C₂²	1	1	yes	characteristic
46	C₁₃×#384	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	4	1	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	—	4	1	no	—
70	C₁₃×C₄⋊Q₈	—	4	1	no	—
71	C₁₃×#126	—	4	4	no	—
72	C₄×Q₈×C₁₃	—	4	1	no	—
73	C₄×Q₈×C₁₃	—	4	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#106	—	4	1	no	—
103	C₁₃×#106	—	4	1	no	—
104	C₁₃×#106	—	4	1	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#103	—	4	1	no	—
109	C₁₃×#102	—	4	1	no	—
110	C₁₃×#102	—	4	1	no	—
111	C₁₃×#102	—	4	1	no	—
112	C₄×C₈×C₁₃	—	2	2	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	D₄	1	1	yes	characteristic
120	C₁₃×#95	D₄	1	1	yes	characteristic
121	#32430	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	—	8	1	no	—
130	C₂×Q₈×C₁₃	—	8	1	no	—
131	C₂×Q₈×C₁₃	#41	1	2	yes	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×SD₁₆	—	4	4	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	#41	1	2	yes	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	4	2	no	—
179	C₁₃×C₄⋊C₄	—	4	2	no	—
180	C₁₃×C₄⋊C₄	—	4	2	no	—
181	C₁₃×C₄⋊C₄	—	4	2	no	—
182	C₁₃×C₄⋊C₄	—	8	1	no	—
183	C₁₃×C₄⋊C₄	—	8	1	no	—
184	C₁₃×C₄⋊C₄	—	8	1	no	—
185	C₁₃×C₄⋊C₄	—	8	1	no	—
186	C₁₃×C₄⋊C₄	—	8	1	no	—
187	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
188	C₁₃×C₂²⋊C₄	—	4	2	no	—
189	C₁₃×C₂²⋊C₄	—	4	2	no	—
190	C₁₃×C₂²⋊C₄	—	4	2	no	—
191	C₁₃×C₂²⋊C₄	—	4	2	no	—
192	C₁₃×C₂²⋊C₄	—	8	1	no	—
193	C₁₃×C₂²⋊C₄	—	8	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	4	2	no	—
201	C₄²×C₁₃	—	4	2	no	—
202	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2512	C₂×C₁₃	1	1	yes	characteristic
204	#2094	C₂×C₁₃	1	1	yes	characteristic
205	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2071	C₂×C₁₃	1	1	yes	characteristic
207	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2055	C₂×C₁₃	1	1	yes	characteristic
209	#2023	C₂×C₁₃	1	1	yes	characteristic
210	#1968	C₂×C₁₃	1	1	yes	characteristic
211	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1880	C₂×C₁₃	1	1	yes	characteristic
215	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	—	4	1	no	—
223	C₂³×C₁₃	—	4	1	no	—
224	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	2	no	—
226	Q₈×C₁₃	—	2	2	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	8	4	no	—
230	D₄×C₁₃	—	4	1	no	—
231	D₄×C₁₃	—	4	1	no	—
232	D₄×C₁₃	—	4	1	no	—
233	D₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	2	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	2	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	—	2	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	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	—	4	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	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
270	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
271	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
272	C₂×C₄×C₁₃	#137	1	2	yes	—
273	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#126	—	2	1	no	—
286	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	#397	—	2	1	no	—
299	#396	—	2	1	no	—
300	#395	—	2	1	no	—
301	#395	—	2	1	no	—
302	#391	C₂²×C₁₃	1	1	yes	characteristic
303	#391	C₂²×C₁₃	1	1	yes	characteristic
304	#390	C₂²×C₁₃	1	1	yes	characteristic
305	#390	C₂²×C₁₃	1	1	yes	characteristic
306	#390	C₂²×C₁₃	1	1	yes	characteristic
307	#389	—	2	1	no	—
308	#389	—	2	1	no	—
309	#389	C₂²×C₁₃	1	1	yes	characteristic
310	#388	—	2	1	no	—
311	#384	C₂²×C₁₃	1	1	yes	characteristic
312	#384	C₂²×C₁₃	1	1	yes	characteristic
313	#384	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
316	#340	C₂²×C₁₃	1	1	yes	characteristic
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	#340	C₂²×C₁₃	1	1	yes	characteristic
319	#340	C₂²×C₁₃	1	1	yes	characteristic
320	#340	C₂²×C₁₃	1	1	yes	characteristic
321	#340	C₂²×C₁₃	1	1	yes	characteristic
322	#336	C₂²×C₁₃	1	1	yes	characteristic
323	#336	C₂²×C₁₃	1	1	yes	characteristic
324	#336	C₂²×C₁₃	1	1	yes	characteristic
325	#336	C₂²×C₁₃	1	1	yes	characteristic
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	—	8	1	no	—
332	C₂²×C₁₃	—	8	1	no	—
333	C₂²×C₁₃	#535	1	1	yes	characteristic
334	C₂²×C₁₃	#547	1	1	yes	characteristic
335	C₂²×C₁₃	#548	1	1	yes	characteristic
336	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
337	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
338	C₂²×C₁₃	#576	1	1	yes	characteristic
339	C₂²×C₁₃	#577	1	1	yes	characteristic
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	—	8	1	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	#539	1	1	yes	characteristic
354	C₄×C₁₃	#542	1	1	yes	characteristic
355	C₄×C₁₃	#551	1	1	yes	characteristic
356	C₄×C₁₃	#563	1	1	yes	characteristic
357	C₂²×Q₈	—	2	1	no	—
358	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×SD₁₆	—	2	2	no	—
362	C₂×SD₁₆	—	4	1	no	—
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₄⋊Q₈	—	4	1	no	—
368	C₄⋊Q₈	—	4	1	no	—
369	#126	—	4	4	no	—
370	C₄×Q₈	—	4	1	no	—
371	C₄×Q₈	—	4	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	#106	—	4	1	no	—
401	#106	—	4	1	no	—
402	#106	—	4	1	no	—
403	C₄⋊C₈	—	2	2	no	—
404	#103	—	2	2	no	—
405	#103	—	2	2	no	—
406	#103	—	4	1	no	—
407	#102	—	4	1	no	—
408	#102	—	4	1	no	—
409	#102	—	4	1	no	—
410	C₄×C₈	—	2	2	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	D₄×C₁₃	1	1	yes	characteristic
418	#95	D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₁₃	—	16	1	no	—
420	C₂×C₁₃	#2723	1	1	yes	characteristic
421	C₂×C₁₃	#3206	1	1	yes	characteristic
422	C₂×C₁₃	#3224	1	1	yes	characteristic
423	C₂×C₁₃	#3335	1	1	yes	characteristic
424	C₂×C₁₃	#3346	1	1	yes	characteristic
425	C₂×C₁₃	#3362	1	1	yes	characteristic
426	C₂×C₁₃	#3369	1	1	yes	characteristic
427	C₂⁴	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	4	2	no	—
434	C₂×Q₈	—	8	1	no	—
435	C₂×Q₈	—	8	1	no	—
436	C₂×Q₈	C₁₃×#41	1	2	yes	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
457	SD₁₆	—	4	4	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	C₁₃×#41	1	2	yes	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	8	1	no	—
488	C₄⋊C₄	—	8	1	no	—
489	C₄⋊C₄	—	8	1	no	—
490	C₄⋊C₄	—	8	1	no	—
491	C₄⋊C₄	—	8	1	no	—
492	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	8	1	no	—
498	C₂²⋊C₄	—	8	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₁₃	#32430	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	8	4	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	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	—	4	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	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
561	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
562	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
563	C₂×C₄	C₁₃×#137	1	2	yes	—
564	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
565	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
566	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
569	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	C₁₃×#535	1	1	yes	characteristic
582	C₂²	C₁₃×#547	1	1	yes	characteristic
583	C₂²	C₁₃×#548	1	1	yes	characteristic
584	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
585	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
586	C₂²	C₁₃×#576	1	1	yes	characteristic
587	C₂²	C₁₃×#577	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	C₁₃×#539	1	1	yes	characteristic
602	C₄	C₁₃×#542	1	1	yes	characteristic
603	C₄	C₁₃×#551	1	1	yes	characteristic
604	C₄	C₁₃×#563	1	1	yes	characteristic
605	C₂	—	16	1	no	—
606	C₂	C₁₃×#2723	1	1	yes	characteristic
607	C₂	C₁₃×#3206	1	1	yes	characteristic
608	C₂	C₁₃×#3224	1	1	yes	characteristic
609	C₂	C₁₃×#3335	1	1	yes	characteristic
610	C₂	C₁₃×#3346	1	1	yes	characteristic
611	C₂	C₁₃×#3362	1	1	yes	characteristic
612	C₂	C₁₃×#3369	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2567	C₂	semidirect
4. C₁₃×#2072	C₂	semidirect
6. C₁₃×#2058	C₂	semidirect
10. C₁₃×#1948	C₂	semidirect
11. C₁₃×#1927	C₂	semidirect
12. C₁₃×#1916	C₂	semidirect
14. C₁₃×#1865	C₂	semidirect
15. C₁₃×#1834	C₂	semidirect
121. #32430	C₁₃	direct (N × H)
187. C₁₃×C₄⋊C₄	SD₁₆	semidirect
202. #2567	C₂×C₁₃	semidirect
205. #2072	C₂×C₁₃	semidirect
207. #2058	C₂×C₁₃	semidirect
211. #1948	C₂×C₁₃	semidirect
212. #1927	C₂×C₁₃	semidirect
213. #1916	C₂×C₁₃	semidirect
215. #1865	C₂×C₁₃	semidirect
216. #1834	C₂×C₁₃	semidirect
492. C₄⋊C₄	C₁₃×SD₁₆	semidirect
507. C₁₃	#32430	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×#2567	2
C₁₃×#2512	2
C₁₃×#2094	2
C₁₃×#2072	2
C₁₃×#2071	2
C₁₃×#2058	2
C₁₃×#2055	2
C₁₃×#2023	2
C₁₃×#1968	2
C₁₃×#1948	2
C₁₃×#1927	2
C₁₃×#1916	2
C₁₃×#1880	2
C₁₃×#1865	2
C₁₃×#1834	2
#32430	13

Subgroups — C13×#32430 #15718769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32430 #15718769