Subgroups — C₁₃×#36718 #15723057

Order 3328.

2842 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2848	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2681	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2672	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2583	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2435	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2405	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2405	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#543	—	2	8	no	—
17	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#121	—	2	8	no	—
26	C₂×C₁₃×#121	C₂²	1	8	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₁₃×#399	C₂²	1	4	yes	complemented
32	C₁₃×#398	C₂²	1	4	yes	complemented
33	C₁₃×#396	C₂²	1	8	yes	complemented
34	C₁₃×#395	C₂²	1	4	yes	complemented
35	C₁₃×#394	C₂²	1	8	yes	complemented
36	C₁₃×#394	C₂²	1	8	yes	complemented
37	C₁₃×#394	C₂²	1	8	yes	complemented
38	C₁₃×#393	C₂²	1	4	yes	complemented
39	C₁₃×#390	C₂²	1	4	yes	complemented
40	C₁₃×#389	C₂²	1	8	yes	complemented
41	C₁₃×#388	C₂²	1	8	yes	complemented
42	C₁₃×#386	C₂²	1	4	yes	complemented
43	C₁₃×#386	C₂²	1	4	yes	complemented
44	C₁₃×#385	C₂²	1	4	yes	—
45	C₁₃×#385	C₂²	1	4	yes	—
46	C₁₃×#385	C₂²	1	8	yes	complemented
47	C₁₃×#380	C₂²	1	2	yes	—
48	C₁₃×#380	C₂²	1	4	yes	complemented
49	C₁₃×#379	C₂²	1	2	yes	—
50	C₁₃×#379	C₂²	1	4	yes	—
51	C₁₃×#379	C₂²	1	4	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	—	2	4	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	4	4	no	—
62	C₂²×D₄×C₁₃	—	4	4	no	—
63	C₂²×D₄×C₁₃	—	4	4	no	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	—	2	4	no	—
68	C₂³×C₄×C₁₃	—	4	4	no	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#124	—	4	8	no	—
77	C₁₃×#123	—	4	8	no	—
78	C₁₃×#123	—	4	8	no	—
79	C₁₃×C₂²⋊Q₈	—	2	8	no	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	16	no	—
82	C₁₃×C₂²⋊Q₈	—	2	16	no	—
83	C₁₃×C₂²⋊Q₈	—	4	8	no	—
84	C₁₃×#121	—	2	32	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	8	yes	—
112	C₁₃×#95	C₂³	1	8	yes	—
113	#36718	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	2	no	—
118	C₂⁴×C₁₃	—	2	4	no	—
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₂⁴×C₁₃	—	4	2	no	—
121	C₂⁴×C₁₃	—	4	2	no	—
122	C₂⁴×C₁₃	—	4	2	no	—
123	C₂⁴×C₁₃	—	4	2	no	—
124	C₂⁴×C₁₃	—	4	2	no	—
125	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	4	4	no	—
133	C₂×Q₈×C₁₃	—	4	4	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	8	no	—
137	C₂×D₄×C₁₃	—	2	8	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	4	4	no	—
141	C₂×D₄×C₁₃	—	4	4	no	—
142	C₂×D₄×C₁₃	—	4	4	no	—
143	C₂×D₄×C₁₃	—	4	16	no	—
144	C₂×D₄×C₁₃	—	4	16	no	—
145	C₂×D₄×C₁₃	—	4	16	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	—	4	16	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	8	no	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	16	no	—
175	C₁₃×C₄⋊C₄	—	4	4	no	—
176	C₁₃×C₄⋊C₄	—	4	8	no	—
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊C₄	—	2	8	no	—
179	C₁₃×C₂²⋊C₄	—	2	16	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	4	8	no	—
183	C₁₃×C₂²⋊C₄	—	4	4	no	—
184	C₁₃×C₂²⋊C₄	—	4	4	no	—
185	C₁₃×C₂²⋊C₄	—	4	8	no	—
186	C₁₃×C₂²⋊C₄	—	4	8	no	—
187	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
188	C₄²×C₁₃	—	4	4	no	—
189	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
191	#2848	C₂×C₁₃	1	2	yes	complemented
192	#2681	C₂×C₁₃	1	8	yes	complemented
193	#2672	C₂×C₁₃	1	8	yes	complemented
194	#2626	C₂×C₁₃	1	2	yes	complemented
195	#2583	C₂×C₁₃	1	2	yes	complemented
196	#2435	C₂×C₁₃	1	2	yes	complemented
197	#2405	C₂×C₁₃	1	2	yes	complemented
198	#2405	C₂×C₁₃	1	2	yes	complemented
199	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	8	no	—
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	8	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	4	4	no	—
216	C₂³×C₁₃	—	4	4	no	—
217	C₂³×C₁₃	—	4	16	no	—
218	C₂³×C₁₃	—	4	4	no	—
219	C₂³×C₁₃	—	4	4	no	—
220	C₂³×C₁₃	—	4	4	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	—	4	4	no	—
223	C₂³×C₁₃	—	8	8	no	—
224	C₂³×C₁₃	—	8	8	no	—
225	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
226	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
228	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
229	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
230	Q₈×C₁₃	—	8	4	no	—
231	Q₈×C₁₃	—	8	4	no	—
232	D₄×C₁₃	—	4	16	no	—
233	D₄×C₁₃	—	4	16	no	—
234	D₄×C₁₃	—	4	16	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	8	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	2	8	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	8	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	—	4	16	no	—
252	C₂×C₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	8	4	no	—
254	C₂×C₄×C₁₃	—	8	4	no	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
258	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
262	#543	—	2	8	no	—
263	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
264	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
265	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
266	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
268	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
269	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
270	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
271	C₂×#121	—	2	8	no	—
272	C₂×#121	C₂²×C₁₃	1	8	yes	—
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	#399	C₂²×C₁₃	1	4	yes	complemented
278	#398	C₂²×C₁₃	1	4	yes	complemented
279	#396	C₂²×C₁₃	1	8	yes	complemented
280	#395	C₂²×C₁₃	1	4	yes	complemented
281	#394	C₂²×C₁₃	1	8	yes	complemented
282	#394	C₂²×C₁₃	1	8	yes	complemented
283	#394	C₂²×C₁₃	1	8	yes	complemented
284	#393	C₂²×C₁₃	1	4	yes	complemented
285	#390	C₂²×C₁₃	1	4	yes	complemented
286	#389	C₂²×C₁₃	1	8	yes	complemented
287	#388	C₂²×C₁₃	1	8	yes	complemented
288	#386	C₂²×C₁₃	1	4	yes	complemented
289	#386	C₂²×C₁₃	1	4	yes	complemented
290	#385	C₂²×C₁₃	1	4	yes	—
291	#385	C₂²×C₁₃	1	4	yes	—
292	#385	C₂²×C₁₃	1	8	yes	complemented
293	#380	C₂²×C₁₃	1	2	yes	—
294	#380	C₂²×C₁₃	1	4	yes	complemented
295	#379	C₂²×C₁₃	1	2	yes	—
296	#379	C₂²×C₁₃	1	4	yes	—
297	#379	C₂²×C₁₃	1	4	yes	—
298	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	8	no	—
302	C₂²×C₁₃	—	2	4	no	—
303	C₂²×C₁₃	—	2	4	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	8	no	—
307	C₂²×C₁₃	—	4	16	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	—	4	8	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	8	no	—
316	C₂²×C₁₃	—	8	8	no	—
317	C₂²×C₁₃	—	8	8	no	—
318	C₂²×C₁₃	#536	1	4	yes	—
319	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
320	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
321	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
322	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
323	C₄×C₁₃	—	2	4	no	—
324	C₄×C₁₃	—	2	4	no	—
325	C₄×C₁₃	—	2	4	no	—
326	C₄×C₁₃	—	4	2	no	—
327	C₄×C₁₃	—	4	4	no	—
328	C₄×C₁₃	—	4	4	no	—
329	C₄×C₁₃	—	4	8	no	—
330	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
331	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
332	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
334	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
335	C₂²×D₄	—	2	4	no	—
336	C₂²×D₄	—	2	4	no	—
337	C₂²×D₄	—	2	4	no	—
338	C₂²×D₄	—	4	4	no	—
339	C₂²×D₄	—	4	4	no	—
340	C₂²×D₄	—	4	4	no	—
341	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
342	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
343	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
344	C₂³×C₄	—	2	4	no	—
345	C₂³×C₄	—	4	4	no	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
353	#124	—	4	8	no	—
354	#123	—	4	8	no	—
355	#123	—	4	8	no	—
356	C₂²⋊Q₈	—	2	8	no	—
357	C₂²⋊Q₈	—	2	8	no	—
358	C₂²⋊Q₈	—	2	16	no	—
359	C₂²⋊Q₈	—	2	16	no	—
360	C₂²⋊Q₈	—	4	8	no	—
361	#121	—	2	32	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
386	#95	C₂³×C₁₃	1	4	yes	—
387	#95	C₂³×C₁₃	1	4	yes	—
388	#95	C₂³×C₁₃	1	8	yes	—
389	#95	C₂³×C₁₃	1	8	yes	—
390	C₂×C₁₃	—	2	4	no	—
391	C₂×C₁₃	—	4	4	no	—
392	C₂×C₁₃	—	4	4	no	—
393	C₂×C₁₃	—	8	2	no	—
394	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
395	C₂×C₁₃	#3484	1	1	yes	characteristic
396	C₂×C₁₃	#3484	1	1	yes	characteristic
397	C₂×C₁₃	#3536	1	4	yes	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	—	4	2	no	—
406	C₂⁴	—	4	2	no	—
407	C₂⁴	—	4	2	no	—
408	C₂⁴	—	4	2	no	—
409	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
410	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
411	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
412	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
413	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×Q₈	—	4	4	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	16	no	—
428	C₂×D₄	—	4	16	no	—
429	C₂×D₄	—	4	16	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	8	no	—
436	C₂²×C₄	—	2	8	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	—	4	16	no	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
445	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	16	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	—	4	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	16	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	4	8	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	8	no	—
470	C₂²⋊C₄	—	4	8	no	—
471	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
472	C₄²	—	4	4	no	—
473	C₁₃	#36718	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	16	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	8	8	no	—
498	C₂³	—	8	8	no	—
499	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
500	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
501	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
502	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
503	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
504	Q₈	—	8	4	no	—
505	Q₈	—	8	4	no	—
506	D₄	—	4	16	no	—
507	D₄	—	4	16	no	—
508	D₄	—	4	16	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	8	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	8	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	16	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
531	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	16	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	8	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	8	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	8	no	—
550	C₂²	—	8	8	no	—
551	C₂²	C₁₃×#536	1	4	yes	—
552	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
553	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
554	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
555	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
556	C₄	—	2	4	no	—
557	C₄	—	2	4	no	—
558	C₄	—	2	4	no	—
559	C₄	—	4	8	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	4	no	—
563	C₂	—	2	4	no	—
564	C₂	—	4	4	no	—
565	C₂	—	4	4	no	—
566	C₂	—	8	2	no	—
567	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
568	C₂	C₁₃×#3484	1	1	yes	characteristic
569	C₂	C₁₃×#3484	1	1	yes	characteristic
570	C₂	C₁₃×#3536	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#543	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2681	C₂	semidirect
5. C₁₃×#2672	C₂	semidirect
6. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2583	C₂	semidirect
8. C₁₃×#2435	C₂	semidirect
9. C₁₃×#2405	C₂	semidirect
10. C₁₃×#2405	C₂	semidirect
11. C₁₃×#2312	C₂	semidirect
17. C₂×C₁₃×#124	C₂²	semidirect
18. C₂×C₁₃×#123	C₂²	semidirect
19. C₂×C₁₃×#123	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₁₃×#399	C₂²	semidirect
32. C₁₃×#398	C₂²	semidirect
33. C₁₃×#396	C₂²	semidirect
34. C₁₃×#395	C₂²	semidirect
35. C₁₃×#394	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#394	C₂²	semidirect
38. C₁₃×#393	C₂²	semidirect
39. C₁₃×#390	C₂²	semidirect
40. C₁₃×#389	C₂²	semidirect
41. C₁₃×#388	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
46. C₁₃×#385	C₂²	semidirect
48. C₁₃×#380	C₂²	semidirect
113. #36718	C₁₃	direct (N × H)
189. C₂×#543	C₂×C₁₃	semidirect
191. #2848	C₂×C₁₃	semidirect
192. #2681	C₂×C₁₃	semidirect
193. #2672	C₂×C₁₃	semidirect
194. #2626	C₂×C₁₃	semidirect
195. #2583	C₂×C₁₃	semidirect
196. #2435	C₂×C₁₃	semidirect
197. #2405	C₂×C₁₃	semidirect
198. #2405	C₂×C₁₃	semidirect
199. #2312	C₂×C₁₃	semidirect
263. C₂×#124	C₂²×C₁₃	semidirect
264. C₂×#123	C₂²×C₁₃	semidirect
265. C₂×#123	C₂²×C₁₃	semidirect
268. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
269. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
270. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
277. #399	C₂²×C₁₃	semidirect
278. #398	C₂²×C₁₃	semidirect
279. #396	C₂²×C₁₃	semidirect
280. #395	C₂²×C₁₃	semidirect
281. #394	C₂²×C₁₃	semidirect
282. #394	C₂²×C₁₃	semidirect
283. #394	C₂²×C₁₃	semidirect
284. #393	C₂²×C₁₃	semidirect
285. #390	C₂²×C₁₃	semidirect
286. #389	C₂²×C₁₃	semidirect
287. #388	C₂²×C₁₃	semidirect
288. #386	C₂²×C₁₃	semidirect
289. #386	C₂²×C₁₃	semidirect
292. #385	C₂²×C₁₃	semidirect
294. #380	C₂²×C₁₃	semidirect
473. C₁₃	#36718	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#543	2
C₂²×C₁₃×#121	2
C₁₃×#2848	2
C₁₃×#2681	2
C₁₃×#2672	2
C₁₃×#2626	2
C₁₃×#2583	2
C₁₃×#2435	2
C₁₃×#2405	2
C₁₃×#2312	2
#36718	13

Subgroups — C13×#36718 #15723057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36718 #15723057