Subgroups — C₁₃×#34241 #15720580

Order 3328.

2330 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2373	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2364	C₂	1	2	yes	maximal
5	C₁₃×#2355	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
8	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2314	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2274	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₄	1	16	yes	complemented
17	C₂×C₁₃×#126	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	4	yes	—
34	C₁₃×#389	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#388	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	4	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#387	C₂²	1	4	yes	—
40	C₁₃×#387	C₂²	1	4	yes	—
41	C₁₃×#387	C₂²	1	4	yes	—
42	C₁₃×#387	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	—
44	C₁₃×#387	C₂²	1	4	yes	—
45	C₁₃×#386	C₂²	1	4	yes	—
46	C₁₃×#386	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₁₃×#384	C₂²	1	2	yes	—
50	C₁₃×#383	C₂²	1	2	yes	—
51	C₁₃×#382	C₂²	1	2	yes	—
52	C₁₃×#382	C₂²	1	2	yes	—
53	C₁₃×#381	C₂²	1	2	yes	—
54	C₁₃×#380	C₂²	1	1	yes	characteristic
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#380	C₂²	1	2	yes	—
57	C₁₃×#380	C₂²	1	2	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₁₃×#376	C₂²	1	2	yes	—
75	C₂×C₁₃×#95	C₂²	1	2	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#126	C₂×C₄	1	16	yes	complemented
86	C₁₃×#125	C₂×C₄	1	8	yes	complemented
87	C₁₃×#124	C₂×C₄	1	8	yes	complemented
88	C₁₃×#123	C₂×C₄	1	16	yes	complemented
89	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
90	C₁₃×#121	C₂×C₄	1	8	yes	—
91	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
92	C₄×D₄×C₁₃	—	4	8	no	—
93	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
94	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
95	C₁₃×#117	—	2	8	no	—
96	C₁₃×#117	C₂×C₄	1	16	yes	complemented
97	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃	—	4	4	no	—
124	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
125	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	#34241	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	—	4	2	no	—
155	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
160	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	—	4	4	no	—
172	C₂²×C₄×C₁₃	—	4	4	no	—
173	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
176	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	8	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	4	4	no	—
196	C₁₃×C₄⋊C₄	—	4	4	no	—
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
199	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
200	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
201	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
202	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
203	C₁₃×C₄⋊C₄	#41	1	8	yes	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	8	no	—
207	C₁₃×C₂²⋊C₄	—	4	4	no	—
208	C₁₃×C₂²⋊C₄	—	4	4	no	—
209	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
210	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
211	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
212	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
213	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
214	C₄²×C₁₃	—	2	8	no	—
215	C₄²×C₁₃	—	4	2	no	—
216	C₄²×C₁₃	—	4	4	no	—
217	C₄²×C₁₃	—	4	2	no	—
218	C₄²×C₁₃	—	4	4	no	—
219	C₄²×C₁₃	—	4	4	no	—
220	C₄²×C₁₃	—	4	4	no	—
221	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
222	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
223	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
224	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
225	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
226	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
227	#2373	C₂×C₁₃	1	4	yes	complemented
228	#2368	C₂×C₁₃	1	2	yes	complemented
229	#2364	C₂×C₁₃	1	2	yes	—
230	#2355	C₂×C₁₃	1	2	yes	complemented
231	#2352	C₂×C₁₃	1	2	yes	complemented
232	#2352	C₂×C₁₃	1	2	yes	complemented
233	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
234	#2337	C₂×C₁₃	1	2	yes	complemented
235	#2336	C₂×C₁₃	1	2	yes	complemented
236	#2314	C₂×C₁₃	1	2	yes	complemented
237	C₄×#123	C₂×C₁₃	1	4	yes	complemented
238	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2274	C₂×C₁₃	1	2	yes	complemented
240	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	—	2	2	no	—
245	C₂³×C₁₃	—	2	2	no	—
246	C₂³×C₁₃	—	2	2	no	—
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	2	2	no	—
249	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
250	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
251	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
252	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
253	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
254	Q₈×C₁₃	—	4	4	no	—
255	D₄×C₁₃	—	2	16	no	—
256	D₄×C₁₃	—	4	4	no	—
257	C₂×C₄×C₁₃	—	2	8	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	8	no	—
274	C₂×C₄×C₁₃	—	2	16	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	4	4	no	—
285	C₂×C₄×C₁₃	—	4	16	no	—
286	C₂×C₄×C₁₃	—	8	8	no	—
287	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
297	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
298	#529	C₄×C₁₃	1	16	yes	complemented
299	C₂×#126	C₂²×C₁₃	1	2	yes	—
300	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#123	C₂²×C₁₃	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
307	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#117	C₂²×C₁₃	1	2	yes	—
310	C₂×#117	C₂²×C₁₃	1	2	yes	—
311	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
313	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
315	#391	C₂²×C₁₃	1	4	yes	—
316	#389	C₂²×C₁₃	1	4	yes	—
317	#388	C₂²×C₁₃	1	4	yes	—
318	#388	C₂²×C₁₃	1	4	yes	—
319	#388	C₂²×C₁₃	1	4	yes	—
320	#388	C₂²×C₁₃	1	4	yes	—
321	#387	C₂²×C₁₃	1	4	yes	—
322	#387	C₂²×C₁₃	1	4	yes	—
323	#387	C₂²×C₁₃	1	4	yes	—
324	#387	C₂²×C₁₃	1	4	yes	—
325	#387	C₂²×C₁₃	1	4	yes	—
326	#387	C₂²×C₁₃	1	4	yes	—
327	#386	C₂²×C₁₃	1	4	yes	—
328	#386	C₂²×C₁₃	1	4	yes	—
329	#385	C₂²×C₁₃	1	4	yes	—
330	#385	C₂²×C₁₃	1	4	yes	—
331	#384	C₂²×C₁₃	1	2	yes	—
332	#383	C₂²×C₁₃	1	2	yes	—
333	#382	C₂²×C₁₃	1	2	yes	—
334	#382	C₂²×C₁₃	1	2	yes	—
335	#381	C₂²×C₁₃	1	2	yes	—
336	#380	C₂²×C₁₃	1	2	yes	—
337	#380	C₂²×C₁₃	1	2	yes	—
338	#380	C₂²×C₁₃	1	1	yes	characteristic
339	#380	C₂²×C₁₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
343	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
344	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
347	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
348	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
349	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
355	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
356	#376	C₂²×C₁₃	1	2	yes	—
357	C₂×#95	C₂²×C₁₃	1	2	yes	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	2	4	no	—
361	C₂²×C₁₃	—	2	4	no	—
362	C₂²×C₁₃	—	2	4	no	—
363	C₂²×C₁₃	—	2	4	no	—
364	C₂²×C₁₃	—	2	4	no	—
365	C₂²×C₁₃	—	4	2	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	4	2	no	—
368	C₂²×C₁₃	—	4	2	no	—
369	C₂²×C₁₃	#520	1	4	yes	—
370	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
371	C₂²×C₁₃	C₂²×#41	1	2	yes	—
372	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂²×C₁₃	#585	1	2	yes	—
375	C₄×C₁₃	—	2	4	no	—
376	C₄×C₁₃	—	2	2	no	—
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	2	4	no	—
380	C₄×C₁₃	—	2	2	no	—
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	—	2	4	no	—
383	C₄×C₁₃	—	2	8	no	—
384	C₄×C₁₃	—	4	4	no	—
385	C₄×C₁₃	—	4	4	no	—
386	C₄×C₁₃	—	4	4	no	—
387	C₄×C₁₃	C₄×#41	1	4	yes	—
388	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
390	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
392	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
394	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
396	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
397	#126	C₂×C₄×C₁₃	1	16	yes	complemented
398	#125	C₂×C₄×C₁₃	1	8	yes	complemented
399	#124	C₂×C₄×C₁₃	1	8	yes	complemented
400	#123	C₂×C₄×C₁₃	1	16	yes	complemented
401	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
402	#121	C₂×C₄×C₁₃	1	8	yes	—
403	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
404	C₄×D₄	—	4	8	no	—
405	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
406	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
407	#117	—	2	8	no	—
408	#117	C₂×C₄×C₁₃	1	16	yes	complemented
409	C₂×C₄⋊C₄	—	2	8	no	—
410	C₂×C₄⋊C₄	—	2	8	no	—
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄²	—	4	4	no	—
436	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
437	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
438	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
439	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
440	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
441	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
442	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
443	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
449	#95	C₂³×C₁₃	1	2	yes	—
450	#95	C₂³×C₁₃	1	4	yes	—
451	#95	C₂³×C₁₃	1	2	yes	—
452	#95	C₂³×C₁₃	1	4	yes	—
453	#95	C₂³×C₁₃	1	2	yes	—
454	#95	C₂³×C₁₃	1	2	yes	—
455	#95	C₂³×C₁₃	1	4	yes	—
456	#95	C₂³×C₁₃	1	4	yes	—
457	#95	C₂³×C₁₃	1	4	yes	—
458	#95	C₂³×C₁₃	1	4	yes	—
459	#95	C₂³×C₁₃	1	4	yes	—
460	#95	C₂³×C₁₃	1	4	yes	—
461	#95	C₂³×C₁₃	1	4	yes	—
462	#95	C₂³×C₁₃	1	4	yes	—
463	C₂×C₁₃	—	2	4	no	—
464	C₂×C₁₃	—	4	4	no	—
465	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
466	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
467	C₂×C₁₃	#3428	1	1	yes	characteristic
468	C₂×C₁₃	#3513	1	2	yes	—
469	C₂×C₁₃	#3516	1	2	yes	—
470	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
471	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
478	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	4	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
492	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
494	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₄⋊C₄	—	4	4	no	—
515	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
516	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
517	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
518	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
519	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
520	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
521	C₄⋊C₄	C₁₃×#41	1	8	yes	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	8	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	4	no	—
527	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
528	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
529	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
530	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
531	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
532	C₄²	—	2	8	no	—
533	C₄²	—	4	2	no	—
534	C₄²	—	4	4	no	—
535	C₄²	—	4	2	no	—
536	C₄²	—	4	4	no	—
537	C₄²	—	4	4	no	—
538	C₄²	—	4	4	no	—
539	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
540	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
541	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
542	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
543	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
544	C₁₃	#34241	1	1	yes	characteristic, direct product factor, Sylow
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
554	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
555	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
556	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
557	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
558	Q₈	—	4	4	no	—
559	D₄	—	2	16	no	—
560	D₄	—	4	4	no	—
561	C₂×C₄	—	2	8	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	16	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	16	no	—
590	C₂×C₄	—	8	8	no	—
591	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
593	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
594	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
595	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
596	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
597	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
598	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
599	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
600	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
601	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	C₁₃×#520	1	4	yes	—
614	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
615	C₂²	C₂²×C₁₃×#41	1	2	yes	—
616	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
618	C₂²	C₁₃×#585	1	2	yes	—
619	C₄	—	2	4	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	4	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	4	no	—
627	C₄	—	2	8	no	—
628	C₄	—	4	4	no	—
629	C₄	—	4	4	no	—
630	C₄	—	4	4	no	—
631	C₄	C₄×C₁₃×#41	1	4	yes	—
632	C₂	—	2	4	no	—
633	C₂	—	4	4	no	—
634	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
635	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
636	C₂	C₁₃×#3428	1	1	yes	characteristic
637	C₂	C₁₃×#3513	1	2	yes	—
638	C₂	C₁₃×#3516	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2373	C₂	semidirect
3. C₁₃×#2368	C₂	semidirect
5. C₁₃×#2355	C₂	semidirect
6. C₁₃×#2352	C₂	semidirect
7. C₁₃×#2352	C₂	semidirect
8. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
9. C₁₃×#2337	C₂	semidirect
10. C₁₃×#2336	C₂	semidirect
11. C₁₃×#2314	C₂	semidirect
12. C₄×C₁₃×#123	C₂	semidirect
13. C₁₃×#2283	C₂	semidirect
14. C₁₃×#2274	C₂	semidirect
15. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
16. C₁₃×#529	C₄	semidirect
85. C₁₃×#126	C₂×C₄	semidirect
86. C₁₃×#125	C₂×C₄	semidirect
87. C₁₃×#124	C₂×C₄	semidirect
88. C₁₃×#123	C₂×C₄	semidirect
89. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₄×Q₈×C₁₃	C₂×C₄	semidirect
93. C₄×D₄×C₁₃	C₂×C₄	semidirect
94. C₄×D₄×C₁₃	C₂×C₄	semidirect
96. C₁₃×#117	C₂×C₄	semidirect
124. C₂×C₄²×C₁₃	C₂×C₄	semidirect
151. #34241	C₁₃	direct (N × H)
227. #2373	C₂×C₁₃	semidirect
228. #2368	C₂×C₁₃	semidirect
230. #2355	C₂×C₁₃	semidirect
231. #2352	C₂×C₁₃	semidirect
232. #2352	C₂×C₁₃	semidirect
233. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
234. #2337	C₂×C₁₃	semidirect
235. #2336	C₂×C₁₃	semidirect
236. #2314	C₂×C₁₃	semidirect
237. C₄×#123	C₂×C₁₃	semidirect
238. #2283	C₂×C₁₃	semidirect
239. #2274	C₂×C₁₃	semidirect
240. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
298. #529	C₄×C₁₃	semidirect
397. #126	C₂×C₄×C₁₃	semidirect
398. #125	C₂×C₄×C₁₃	semidirect
399. #124	C₂×C₄×C₁₃	semidirect
400. #123	C₂×C₄×C₁₃	semidirect
401. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
403. C₄×Q₈	C₂×C₄×C₁₃	semidirect
405. C₄×D₄	C₂×C₄×C₁₃	semidirect
406. C₄×D₄	C₂×C₄×C₁₃	semidirect
408. #117	C₂×C₄×C₁₃	semidirect
436. C₂×C₄²	C₂×C₄×C₁₃	semidirect
544. C₁₃	#34241	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×#529	2
C₁₃×#2373	2
C₁₃×#2368	2
C₁₃×#2364	2
C₁₃×#2355	2
C₁₃×#2352	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2337	2
C₁₃×#2336	2
C₁₃×#2314	2
C₄×C₁₃×#123	2
C₁₃×#2283	2
C₁₃×#2274	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34241	13

Subgroups — C13×#34241 #15720580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34241 #15720580