Subgroups — C₄×C₁₃×#540 #15720432

Order 3328.

2518 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2335	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2333	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2324	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
14	C₄²×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#540	C₄	1	16	yes	direct product factor
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#123	C₂²	1	4	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₁₃×#121	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#390	C₂²	1	4	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	4	yes	—
35	C₁₃×#389	C₂²	1	2	yes	—
36	C₁₃×#389	C₂²	1	4	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	4	yes	—
41	C₁₃×#388	C₂²	1	4	yes	—
42	C₁₃×#388	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×#386	C₂²	1	4	yes	—
47	C₁₃×#386	C₂²	1	4	yes	—
48	C₁₃×#386	C₂²	1	4	yes	—
49	C₁₃×#386	C₂²	1	4	yes	—
50	C₁₃×#385	C₂²	1	4	yes	—
51	C₁₃×#384	C₂²	1	1	yes	characteristic
52	C₁₃×#382	C₂²	1	1	yes	characteristic
53	C₁₃×#381	C₂²	1	4	yes	—
54	C₁₃×#380	C₂²	1	2	yes	—
55	C₁₃×#380	C₂²	1	4	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	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	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
68	C₁₃×#376	C₂²	1	1	yes	characteristic
69	C₁₃×#376	C₂²	1	1	yes	characteristic
70	C₄³×C₁₃	C₂²	1	1	yes	characteristic
71	C₄³×C₁₃	C₂²	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
81	C₁₃×#127	C₂×C₄	1	8	yes	complemented
82	C₁₃×#125	C₂×C₄	1	8	yes	complemented
83	C₁₃×#123	C₂×C₄	1	32	yes	complemented
84	C₁₃×#121	C₂×C₄	1	32	yes	complemented
85	C₁₃×#121	C₂×C₄	1	16	yes	complemented
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	8	no	—
88	C₄×D₄×C₁₃	—	4	8	no	—
89	C₄×D₄×C₁₃	—	4	8	no	—
90	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
91	C₁₃×#117	—	2	4	no	—
92	C₁₃×#117	C₂×C₄	1	8	yes	complemented
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃	—	2	4	no	—
114	C₂×C₄²×C₁₃	—	4	8	no	—
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
134	C₁₃×#95	C₂³	1	2	yes	—
135	C₁₃×#95	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	2	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₄×#540	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	4	4	no	—
147	C₂×D₄×C₁₃	—	4	4	no	—
148	C₂×D₄×C₁₃	—	4	4	no	—
149	C₂×D₄×C₁₃	—	4	4	no	—
150	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
151	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
152	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	8	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	4	4	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	—	4	4	no	—
167	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	4	4	no	—
186	C₁₃×C₄⋊C₄	—	4	4	no	—
187	C₁₃×C₄⋊C₄	—	4	4	no	—
188	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
189	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	8	no	—
194	C₁₃×C₂²⋊C₄	—	4	4	no	—
195	C₁₃×C₂²⋊C₄	—	4	4	no	—
196	C₁₃×C₂²⋊C₄	—	4	4	no	—
197	C₁₃×C₂²⋊C₄	—	4	4	no	—
198	C₁₃×C₂²⋊C₄	—	4	4	no	—
199	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
200	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
201	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
202	C₄²×C₁₃	—	2	2	no	—
203	C₄²×C₁₃	—	2	2	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	—	2	2	no	—
206	C₄²×C₁₃	—	2	4	no	—
207	C₄²×C₁₃	—	2	8	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	4	4	no	—
210	C₄²×C₁₃	—	4	4	no	—
211	C₄²×C₁₃	—	4	2	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
214	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
215	C₄²×C₁₃	#41	1	4	yes	—
216	C₄²×C₁₃	#41	1	4	yes	—
217	C₂×#540	C₂×C₁₃	1	1	yes	characteristic
218	#2335	C₂×C₁₃	1	4	yes	complemented
219	#2333	C₂×C₁₃	1	4	yes	complemented
220	#2330	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2328	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2324	C₂×C₁₃	1	2	yes	complemented
223	#2319	C₂×C₁₃	1	2	yes	complemented
224	#2314	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₄×#123	C₂×C₁₃	1	4	yes	complemented
228	C₄×#121	C₂×C₁₃	1	2	yes	complemented
229	C₄×#121	C₂×C₁₃	1	4	yes	complemented
230	C₄²×D₄	C₂×C₁₃	1	2	yes	complemented
231	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	2	4	no	—
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	4	no	—
239	C₂³×C₁₃	—	2	4	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
243	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
244	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
245	D₄×C₁₃	—	2	16	no	—
246	D₄×C₁₃	—	4	16	no	—
247	D₄×C₁₃	—	4	16	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	8	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	4	16	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	16	no	—
276	C₂×C₄×C₁₃	—	4	4	no	—
277	C₂×C₄×C₁₃	—	4	16	no	—
278	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
279	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
280	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
282	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
284	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
285	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
287	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
288	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
289	#540	C₄×C₁₃	1	16	yes	direct product factor
290	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#123	C₂²×C₁₃	1	4	yes	—
293	C₂×#121	C₂²×C₁₃	1	2	yes	—
294	C₂×#121	C₂²×C₁₃	1	4	yes	—
295	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
300	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
304	#390	C₂²×C₁₃	1	2	yes	—
305	#390	C₂²×C₁₃	1	4	yes	—
306	#390	C₂²×C₁₃	1	2	yes	—
307	#390	C₂²×C₁₃	1	4	yes	—
308	#389	C₂²×C₁₃	1	2	yes	—
309	#389	C₂²×C₁₃	1	2	yes	—
310	#389	C₂²×C₁₃	1	4	yes	—
311	#388	C₂²×C₁₃	1	4	yes	—
312	#388	C₂²×C₁₃	1	4	yes	—
313	#388	C₂²×C₁₃	1	4	yes	—
314	#388	C₂²×C₁₃	1	4	yes	—
315	#388	C₂²×C₁₃	1	4	yes	—
316	#387	C₂²×C₁₃	1	4	yes	—
317	#387	C₂²×C₁₃	1	4	yes	—
318	#387	C₂²×C₁₃	1	4	yes	—
319	#386	C₂²×C₁₃	1	4	yes	—
320	#386	C₂²×C₁₃	1	4	yes	—
321	#386	C₂²×C₁₃	1	4	yes	—
322	#386	C₂²×C₁₃	1	4	yes	—
323	#385	C₂²×C₁₃	1	4	yes	—
324	#384	C₂²×C₁₃	1	1	yes	characteristic
325	#382	C₂²×C₁₃	1	1	yes	characteristic
326	#381	C₂²×C₁₃	1	4	yes	—
327	#380	C₂²×C₁₃	1	2	yes	—
328	#380	C₂²×C₁₃	1	4	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
331	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
332	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
333	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
334	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
336	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
338	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
339	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
340	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
341	#376	C₂²×C₁₃	1	1	yes	characteristic
342	#376	C₂²×C₁₃	1	1	yes	characteristic
343	C₄³	C₂²×C₁₃	1	1	yes	characteristic
344	C₄³	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	8	no	—
347	C₂²×C₁₃	—	2	8	no	—
348	C₂²×C₁₃	—	2	4	no	—
349	C₂²×C₁₃	—	2	8	no	—
350	C₂²×C₁₃	—	4	4	no	—
351	C₂²×C₁₃	—	4	1	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	4	4	no	—
354	C₂²×C₁₃	—	4	4	no	—
355	C₂²×C₁₃	—	4	2	no	—
356	C₂²×C₁₃	—	4	4	no	—
357	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
358	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
361	C₂²×C₁₃	#585	1	2	yes	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	4	no	—
364	C₄×C₁₃	—	2	8	no	—
365	C₄×C₁₃	—	2	4	no	—
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	2	4	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	4	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	4	4	no	—
373	C₄×C₁₃	C₄×#41	1	4	yes	—
374	C₄×C₁₃	#540	1	4	yes	direct product factor
375	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
377	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
380	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
384	#127	C₂×C₄×C₁₃	1	8	yes	complemented
385	#125	C₂×C₄×C₁₃	1	8	yes	complemented
386	#123	C₂×C₄×C₁₃	1	32	yes	complemented
387	#121	C₂×C₄×C₁₃	1	32	yes	complemented
388	#121	C₂×C₄×C₁₃	1	16	yes	complemented
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	8	no	—
391	C₄×D₄	—	4	8	no	—
392	C₄×D₄	—	4	8	no	—
393	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
394	#117	—	2	4	no	—
395	#117	C₂×C₄×C₁₃	1	8	yes	complemented
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₄²	—	2	4	no	—
417	C₂×C₄²	—	4	8	no	—
418	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
426	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	#95	C₂³×C₁₃	1	2	yes	—
434	#95	C₂³×C₁₃	1	2	yes	—
435	#95	C₂³×C₁₃	1	2	yes	—
436	#95	C₂³×C₁₃	1	2	yes	—
437	#95	C₂³×C₁₃	1	4	yes	—
438	#95	C₂³×C₁₃	1	4	yes	—
439	#95	C₂³×C₁₃	1	4	yes	—
440	#95	C₂³×C₁₃	1	4	yes	—
441	#95	C₂³×C₁₃	1	4	yes	—
442	#95	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	4	yes	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	4	8	no	—
446	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
447	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
448	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
449	C₂×C₁₃	#3455	1	1	yes	characteristic
450	C₂×C₁₃	#3460	1	2	yes	—
451	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
460	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
461	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	2	8	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
477	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	4	4	no	—
495	C₄⋊C₄	—	4	4	no	—
496	C₄⋊C₄	—	4	4	no	—
497	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
498	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
499	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	4	4	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	4	4	no	—
507	C₂²⋊C₄	—	4	4	no	—
508	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
509	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
510	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	8	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	4	4	no	—
519	C₄²	—	4	4	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	4	2	no	—
522	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
523	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
524	C₄²	C₁₃×#41	1	4	yes	—
525	C₄²	C₁₃×#41	1	4	yes	—
526	C₁₃	C₄×#540	1	1	yes	characteristic, direct product factor, Sylow
527	C₂³	—	2	1	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
538	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
539	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
540	D₄	—	2	16	no	—
541	D₄	—	4	16	no	—
542	D₄	—	4	16	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	4	16	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	16	no	—
573	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
574	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
575	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
576	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
577	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
578	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
579	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
580	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
581	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
582	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
583	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	8	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	4	no	—
596	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
597	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
598	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
599	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
600	C₂²	C₁₃×#585	1	2	yes	—
601	C₄	—	2	2	no	—
602	C₄	—	2	4	no	—
603	C₄	—	2	8	no	—
604	C₄	—	2	4	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	4	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	4	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	4	no	—
612	C₄	C₄×C₁₃×#41	1	4	yes	—
613	C₄	C₁₃×#540	1	4	yes	direct product factor
614	C₂	—	4	2	no	—
615	C₂	—	4	8	no	—
616	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
617	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
618	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
619	C₂	C₁₃×#3455	1	1	yes	characteristic
620	C₂	C₁₃×#3460	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	C₂×C₁₃×#540	C₂
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×#2335	C₂	semidirect
3. C₁₃×#2333	C₂	semidirect
4. C₁₃×#2330	C₂	semidirect
5. C₁₃×#2328	C₂	semidirect
6. C₁₃×#2324	C₂	semidirect
7. C₁₃×#2319	C₂	semidirect
8. C₁₃×#2314	C₂	semidirect
9. C₄×C₁₃×#127	C₂	semidirect
10. C₄×C₁₃×#125	C₂	semidirect
11. C₄×C₁₃×#123	C₂	semidirect
12. C₄×C₁₃×#121	C₂	semidirect
13. C₄×C₁₃×#121	C₂	semidirect
14. C₄²×D₄×C₁₃	C₂	semidirect
15. C₄×C₁₃×#117	C₂	semidirect
16. C₁₃×#540	C₄	direct (N × H)
81. C₁₃×#127	C₂×C₄	semidirect
82. C₁₃×#125	C₂×C₄	semidirect
83. C₁₃×#123	C₂×C₄	semidirect
84. C₁₃×#121	C₂×C₄	semidirect
85. C₁₃×#121	C₂×C₄	semidirect
90. C₄×D₄×C₁₃	C₂×C₄	semidirect
92. C₁₃×#117	C₂×C₄	semidirect
141. C₄×#540	C₁₃	direct (N × H)
218. #2335	C₂×C₁₃	semidirect
219. #2333	C₂×C₁₃	semidirect
220. #2330	C₂×C₁₃	semidirect
221. #2328	C₂×C₁₃	semidirect
222. #2324	C₂×C₁₃	semidirect
223. #2319	C₂×C₁₃	semidirect
224. #2314	C₂×C₁₃	semidirect
225. C₄×#127	C₂×C₁₃	semidirect
226. C₄×#125	C₂×C₁₃	semidirect
227. C₄×#123	C₂×C₁₃	semidirect
228. C₄×#121	C₂×C₁₃	semidirect
229. C₄×#121	C₂×C₁₃	semidirect
230. C₄²×D₄	C₂×C₁₃	semidirect
231. C₄×#117	C₂×C₁₃	semidirect
289. #540	C₄×C₁₃	direct (N × H)
374. C₄×C₁₃	#540	direct (N × H)
384. #127	C₂×C₄×C₁₃	semidirect
385. #125	C₂×C₄×C₁₃	semidirect
386. #123	C₂×C₄×C₁₃	semidirect
387. #121	C₂×C₄×C₁₃	semidirect
388. #121	C₂×C₄×C₁₃	semidirect
393. C₄×D₄	C₂×C₄×C₁₃	semidirect
395. #117	C₂×C₄×C₁₃	semidirect
526. C₁₃	C₄×#540	direct (N × H)
613. C₄	C₁₃×#540	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×#540	2
C₁₃×#2335	2
C₁₃×#2333	2
C₁₃×#2330	2
C₁₃×#2328	2
C₁₃×#2324	2
C₁₃×#2319	2
C₁₃×#2314	2
C₄×C₁₃×#127	2
C₄×C₁₃×#125	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
C₄×#540	13

Subgroups — C4×C13×#540 #15720432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#540 #15720432