Subgroups — C₄×C₁₃×#541 #15720434

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2336	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2334	C₂	1	4	yes	maximal
4	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2323	C₂	1	2	yes	maximal
7	C₁₃×#2320	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#125	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#126	C₂	1	4	yes	maximal
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
14	C₄²×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#541	C₄	1	16	yes	direct product factor
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#126	C₂²	1	4	yes	—
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	2	yes	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	4	yes	—
33	C₁₃×#389	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×#387	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×#387	C₂²	1	4	yes	—
46	C₁₃×#387	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic
49	C₁₃×#383	C₂²	1	4	yes	—
50	C₁₃×#382	C₂²	1	1	yes	characteristic
51	C₁₃×#382	C₂²	1	4	yes	—
52	C₁₃×#380	C₂²	1	2	yes	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₁₃×#376	C₂²	1	1	yes	characteristic
68	C₁₃×#376	C₂²	1	1	yes	characteristic
69	C₄³×C₁₃	C₂²	1	1	yes	characteristic
70	C₄³×C₁₃	C₂²	1	1	yes	characteristic
71	C₄³×C₁₃	C₂²	1	4	yes	—
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
77	C₁₃×#126	C₂×C₄	1	32	yes	—
78	C₁₃×#125	C₂×C₄	1	8	yes	complemented
79	C₁₃×#125	C₂×C₄	1	32	yes	complemented
80	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
81	C₄×Q₈×C₁₃	—	2	8	no	—
82	C₄×Q₈×C₁₃	—	2	8	no	—
83	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
84	C₁₃×#117	—	2	4	no	—
85	C₁₃×#117	C₂×C₄	1	8	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₄²×C₁₃	—	2	4	no	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#95	C₂³	1	2	yes	—
124	C₁₃×#95	C₂³	1	2	yes	—
125	C₁₃×#95	C₂³	1	2	yes	—
126	C₁₃×#95	C₂³	1	2	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	4	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₄×#541	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	4	4	no	—
170	C₁₃×C₄⋊C₄	—	4	4	no	—
171	C₁₃×C₄⋊C₄	—	4	4	no	—
172	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
173	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
174	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
177	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
178	C₁₃×C₂²⋊C₄	—	2	4	no	—
179	C₁₃×C₂²⋊C₄	—	4	4	no	—
180	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
181	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	2	2	no	—
185	C₄²×C₁₃	—	2	2	no	—
186	C₄²×C₁₃	—	2	8	no	—
187	C₄²×C₁₃	—	2	8	no	—
188	C₄²×C₁₃	—	2	4	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	2	8	no	—
191	C₄²×C₁₃	—	4	2	no	—
192	C₄²×C₁₃	—	4	4	no	—
193	C₄²×C₁₃	—	4	4	no	—
194	C₄²×C₁₃	—	4	2	no	—
195	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
196	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
197	C₄²×C₁₃	C₂²×C₄	1	16	yes	—
198	C₄²×C₁₃	#41	1	4	yes	—
199	C₄²×C₁₃	#41	1	4	yes	—
200	C₂×#541	C₂×C₁₃	1	1	yes	characteristic
201	#2336	C₂×C₁₃	1	4	yes	complemented
202	#2334	C₂×C₁₃	1	4	yes	—
203	#2330	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2327	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2323	C₂×C₁₃	1	2	yes	—
206	#2320	C₂×C₁₃	1	2	yes	complemented
207	#2314	C₂×C₁₃	1	1	yes	characteristic
208	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₄×#125	C₂×C₁₃	1	4	yes	complemented
211	C₄×#126	C₂×C₁₃	1	4	yes	—
212	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	—
213	C₄²×Q₈	C₂×C₁₃	1	2	yes	complemented
214	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
220	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
221	Q₈×C₁₃	—	2	16	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
252	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
254	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
255	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
256	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
258	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
261	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
262	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
263	#541	C₄×C₁₃	1	16	yes	direct product factor
264	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#126	C₂²×C₁₃	1	4	yes	—
266	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#125	C₂²×C₁₃	1	4	yes	—
268	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
269	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
272	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
275	#391	C₂²×C₁₃	1	2	yes	—
276	#391	C₂²×C₁₃	1	2	yes	—
277	#389	C₂²×C₁₃	1	2	yes	—
278	#389	C₂²×C₁₃	1	4	yes	—
279	#389	C₂²×C₁₃	1	4	yes	—
280	#389	C₂²×C₁₃	1	4	yes	—
281	#389	C₂²×C₁₃	1	2	yes	—
282	#388	C₂²×C₁₃	1	4	yes	—
283	#388	C₂²×C₁₃	1	4	yes	—
284	#388	C₂²×C₁₃	1	4	yes	—
285	#387	C₂²×C₁₃	1	4	yes	—
286	#387	C₂²×C₁₃	1	4	yes	—
287	#387	C₂²×C₁₃	1	4	yes	—
288	#387	C₂²×C₁₃	1	4	yes	—
289	#387	C₂²×C₁₃	1	4	yes	—
290	#387	C₂²×C₁₃	1	4	yes	—
291	#387	C₂²×C₁₃	1	4	yes	—
292	#387	C₂²×C₁₃	1	4	yes	—
293	#387	C₂²×C₁₃	1	4	yes	—
294	#385	C₂²×C₁₃	1	4	yes	—
295	#384	C₂²×C₁₃	1	1	yes	characteristic
296	#383	C₂²×C₁₃	1	4	yes	—
297	#382	C₂²×C₁₃	1	1	yes	characteristic
298	#382	C₂²×C₁₃	1	4	yes	—
299	#380	C₂²×C₁₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
301	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
302	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
303	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
305	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
308	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
309	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
310	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
313	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
314	#376	C₂²×C₁₃	1	1	yes	characteristic
315	#376	C₂²×C₁₃	1	1	yes	characteristic
316	C₄³	C₂²×C₁₃	1	4	yes	—
317	C₄³	C₂²×C₁₃	1	1	yes	characteristic
318	C₄³	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	4	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
325	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
328	C₂²×C₁₃	#585	1	2	yes	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	8	no	—
331	C₄×C₁₃	—	2	4	no	—
332	C₄×C₁₃	—	2	4	no	—
333	C₄×C₁₃	—	2	8	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	4	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	4	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	C₄×#41	1	4	yes	—
342	C₄×C₁₃	#541	1	4	yes	direct product factor
343	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
348	#126	C₂×C₄×C₁₃	1	32	yes	—
349	#125	C₂×C₄×C₁₃	1	8	yes	complemented
350	#125	C₂×C₄×C₁₃	1	32	yes	complemented
351	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×Q₈	—	2	8	no	—
354	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
355	#117	—	2	4	no	—
356	#117	C₂×C₄×C₁₃	1	8	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₄²	—	2	4	no	—
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
379	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
386	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
387	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
388	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
392	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	#95	C₂³×C₁₃	1	2	yes	—
395	#95	C₂³×C₁₃	1	2	yes	—
396	#95	C₂³×C₁₃	1	2	yes	—
397	#95	C₂³×C₁₃	1	2	yes	—
398	#95	C₂³×C₁₃	1	4	yes	—
399	#95	C₂³×C₁₃	1	4	yes	—
400	#95	C₂³×C₁₃	1	4	yes	—
401	#95	C₂³×C₁₃	1	4	yes	—
402	#95	C₂³×C₁₃	1	4	yes	—
403	#95	C₂³×C₁₃	1	4	yes	—
404	#95	C₂³×C₁₃	1	4	yes	—
405	#95	C₂³×C₁₃	1	4	yes	—
406	#95	C₂³×C₁₃	1	4	yes	—
407	#95	C₂³×C₁₃	1	4	yes	—
408	#95	C₂³×C₁₃	1	4	yes	—
409	C₂×C₁₃	—	4	2	no	—
410	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
411	C₂×C₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
412	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
413	C₂×C₁₃	#3455	1	1	yes	characteristic
414	C₂×C₁₃	#3461	1	2	yes	—
415	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	—	4	4	no	—
447	C₄⋊C₄	—	4	4	no	—
448	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
449	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
450	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
451	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
452	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
453	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
457	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	8	no	—
463	C₄²	—	2	8	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	8	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	4	2	no	—
468	C₄²	—	4	4	no	—
469	C₄²	—	4	4	no	—
470	C₄²	—	4	2	no	—
471	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
472	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
473	C₄²	C₂²×C₄×C₁₃	1	16	yes	—
474	C₄²	C₁₃×#41	1	4	yes	—
475	C₄²	C₁₃×#41	1	4	yes	—
476	C₁₃	C₄×#541	1	1	yes	characteristic, direct product factor, Sylow
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
482	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
483	Q₈	—	2	16	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
514	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
515	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
516	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
517	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
519	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
520	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
521	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
522	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
523	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
524	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
531	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
532	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
533	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
534	C₂²	C₁₃×#585	1	2	yes	—
535	C₄	—	2	2	no	—
536	C₄	—	2	8	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	4	no	—
539	C₄	—	2	8	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	4	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	C₄×C₁₃×#41	1	4	yes	—
548	C₄	C₁₃×#541	1	4	yes	direct product factor
549	C₂	—	4	2	no	—
550	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
551	C₂	C₄×C₁₃×2₋¹⁺⁴	1	2	yes	—
552	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
553	C₂	C₁₃×#3455	1	1	yes	characteristic
554	C₂	C₁₃×#3461	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2336	C₂	semidirect
4. C₁₃×#2330	C₂	semidirect
5. C₁₃×#2327	C₂	semidirect
7. C₁₃×#2320	C₂	semidirect
9. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
10. C₄×C₁₃×#125	C₂	semidirect
11. C₄×C₁₃×#125	C₂	semidirect
14. C₄²×Q₈×C₁₃	C₂	semidirect
16. C₁₃×#541	C₄	direct (N × H)
76. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
78. C₁₃×#125	C₂×C₄	semidirect
79. C₁₃×#125	C₂×C₄	semidirect
83. C₄×Q₈×C₁₃	C₂×C₄	semidirect
138. C₄×#541	C₁₃	direct (N × H)
201. #2336	C₂×C₁₃	semidirect
203. #2330	C₂×C₁₃	semidirect
204. #2327	C₂×C₁₃	semidirect
206. #2320	C₂×C₁₃	semidirect
208. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
209. C₄×#125	C₂×C₁₃	semidirect
210. C₄×#125	C₂×C₁₃	semidirect
213. C₄²×Q₈	C₂×C₁₃	semidirect
263. #541	C₄×C₁₃	direct (N × H)
342. C₄×C₁₃	#541	direct (N × H)
347. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
349. #125	C₂×C₄×C₁₃	semidirect
350. #125	C₂×C₄×C₁₃	semidirect
354. C₄×Q₈	C₂×C₄×C₁₃	semidirect
476. C₁₃	C₄×#541	direct (N × H)
548. C₄	C₁₃×#541	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×#541	2
C₁₃×#2336	2
C₁₃×#2334	2
C₁₃×#2330	2
C₁₃×#2327	2
C₁₃×#2323	2
C₁₃×#2320	2
C₁₃×#2314	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₄×C₁₃×#126	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄²×Q₈×C₁₃	2
C₄×C₁₃×#117	2
C₄×#541	13

Subgroups — C4×C13×#541 #15720434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#541 #15720434