Subgroups — C₂×C₁₃×#2325 #15720405

Order 3328.

4150 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2325	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#121	C₄	1	16	yes	complemented
18	C₂×C₁₃×#121	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₁₃	—	2	16	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#388	C₂²	1	16	yes	complemented
32	C₁₃×#387	C₂²	1	16	yes	complemented
33	C₁₃×#386	C₂²	1	16	yes	complemented
34	C₁₃×#386	C₂²	1	16	yes	complemented
35	C₁₃×#385	C₂²	1	16	yes	complemented
36	C₁₃×#380	C₂²	1	8	yes	complemented
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₃	C₂³	1	2	yes	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	8	no	—
46	C₂²×D₄×C₁₃	—	2	8	no	—
47	C₂²×D₄×C₁₃	—	4	2	no	—
48	C₂²×D₄×C₁₃	—	4	2	no	—
49	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
50	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
51	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	—	2	4	no	—
54	C₂³×C₄×C₁₃	—	2	8	no	—
55	C₂³×C₄×C₁₃	—	4	2	no	—
56	C₂³×C₄×C₁₃	—	4	2	no	—
57	C₂³×C₄×C₁₃	—	4	2	no	—
58	C₂³×C₄×C₁₃	—	4	2	no	—
59	C₂³×C₄×C₁₃	—	4	4	no	—
60	C₂³×C₄×C₁₃	—	4	4	no	—
61	C₂³×C₄×C₁₃	—	4	2	no	—
62	C₂³×C₄×C₁₃	—	4	2	no	—
63	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
64	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₁₃×#121	C₂×C₄	1	64	yes	complemented
77	C₄×D₄×C₁₃	—	2	64	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
79	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
81	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
90	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₃	—	2	8	no	—
97	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
98	C₁₃×#95	C₂³	1	8	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₂×#2325	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	—	2	4	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
115	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
116	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
117	C₂⁴×C₁₃	#41	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	64	no	—
122	C₂×D₄×C₁₃	—	2	16	no	—
123	C₂×D₄×C₁₃	—	2	16	no	—
124	C₂×D₄×C₁₃	—	4	16	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
128	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	complemented
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	16	no	—
148	C₂²×C₄×C₁₃	—	4	16	no	—
149	C₂²×C₄×C₁₃	—	4	16	no	—
150	C₂²×C₄×C₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₃	—	4	4	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	4	8	no	—
155	C₂²×C₄×C₁₃	—	4	8	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	—	4	32	no	—
159	C₂²×C₄×C₁₃	—	4	16	no	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
162	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	complemented
164	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
173	C₁₃×C₄⋊C₄	—	2	16	no	—
174	C₁₃×C₄⋊C₄	—	4	4	no	—
175	C₁₃×C₄⋊C₄	—	4	4	no	—
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
177	C₁₃×C₂²⋊C₄	—	2	16	no	—
178	C₁₃×C₂²⋊C₄	—	2	16	no	—
179	C₁₃×C₂²⋊C₄	—	4	8	no	—
180	C₁₃×C₂²⋊C₄	—	4	8	no	—
181	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
182	C₄²×C₁₃	—	2	16	no	—
183	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
184	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
185	#2325	C₂×C₁₃	1	16	yes	direct product factor
186	C₂×#388	C₂×C₁₃	1	2	yes	complemented
187	C₂×#387	C₂×C₁₃	1	2	yes	complemented
188	C₂×#386	C₂×C₁₃	1	2	yes	complemented
189	C₂×#386	C₂×C₁₃	1	2	yes	complemented
190	C₂×#385	C₂×C₁₃	1	2	yes	complemented
191	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	2	8	no	—
195	C₂³×C₁₃	—	2	8	no	—
196	C₂³×C₁₃	—	2	8	no	—
197	C₂³×C₁₃	—	2	8	no	—
198	C₂³×C₁₃	—	2	8	no	—
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	2	16	no	—
204	C₂³×C₁₃	—	2	16	no	—
205	C₂³×C₁₃	—	2	16	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	4	8	no	—
213	C₂³×C₁₃	—	4	8	no	—
214	C₂³×C₁₃	—	4	8	no	—
215	C₂³×C₁₃	—	4	8	no	—
216	C₂³×C₁₃	C₄×D₄	1	16	yes	—
217	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
218	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
219	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
220	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
221	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂³×C₁₃	C₂×#41	1	4	yes	—
223	C₂³×C₁₃	C₂×#41	1	2	yes	—
224	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
225	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
226	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
227	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
228	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
229	D₄×C₁₃	—	2	64	no	—
230	D₄×C₁₃	—	4	16	no	—
231	C₂×C₄×C₁₃	—	2	16	no	—
232	C₂×C₄×C₁₃	—	2	8	no	—
233	C₂×C₄×C₁₃	—	2	8	no	—
234	C₂×C₄×C₁₃	—	2	16	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	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	2	no	—
243	C₂×C₄×C₁₃	—	2	4	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	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	4	16	no	—
253	C₂×C₄×C₁₃	—	4	16	no	—
254	C₂×C₄×C₁₃	—	4	32	no	—
255	C₂×C₄×C₁₃	—	4	16	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	—	4	8	no	—
259	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
260	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
261	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
263	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
264	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
266	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#121	C₄×C₁₃	1	16	yes	complemented
270	C₂×#121	C₂²×C₁₃	1	8	yes	—
271	C₂×C₄×D₄	—	2	16	no	—
272	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
280	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
283	#388	C₂²×C₁₃	1	16	yes	complemented
284	#387	C₂²×C₁₃	1	16	yes	complemented
285	#386	C₂²×C₁₃	1	16	yes	complemented
286	#386	C₂²×C₁₃	1	16	yes	complemented
287	#385	C₂²×C₁₃	1	16	yes	complemented
288	#380	C₂²×C₁₃	1	8	yes	complemented
289	C₂×#95	C₂²×C₁₃	1	2	yes	—
290	C₂×#95	C₂²×C₁₃	1	2	yes	—
291	C₂×#95	C₂²×C₁₃	1	2	yes	—
292	C₂×#95	C₂²×C₁₃	1	2	yes	—
293	C₂×#95	C₂²×C₁₃	1	2	yes	—
294	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
295	C₂²×C₁₃	—	2	32	no	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	2	4	no	—
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	2	4	no	—
302	C₂²×C₁₃	—	2	8	no	—
303	C₂²×C₁₃	—	2	8	no	—
304	C₂²×C₁₃	—	2	8	no	—
305	C₂²×C₁₃	—	4	32	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	4	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	C₂×C₄×D₄	1	8	yes	—
311	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
312	C₂²×C₁₃	#518	1	4	yes	—
313	C₂²×C₁₃	#520	1	4	yes	—
314	C₂²×C₁₃	#534	1	4	yes	—
315	C₂²×C₁₃	#537	1	4	yes	—
316	C₂²×C₁₃	#538	1	4	yes	—
317	C₂²×C₁₃	#539	1	4	yes	—
318	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
319	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
320	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₄×C₁₃	—	2	8	no	—
326	C₄×C₁₃	—	2	4	no	—
327	C₄×C₁₃	—	2	4	no	—
328	C₄×C₁₃	—	2	8	no	—
329	C₄×C₁₃	—	4	4	no	—
330	C₄×C₁₃	—	4	4	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₂⁵	C₂³×C₁₃	1	2	yes	—
333	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×D₄	—	2	8	no	—
335	C₂²×D₄	—	2	8	no	—
336	C₂²×D₄	—	4	2	no	—
337	C₂²×D₄	—	4	2	no	—
338	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
339	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
340	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
341	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
342	C₂³×C₄	—	2	4	no	—
343	C₂³×C₄	—	2	8	no	—
344	C₂³×C₄	—	4	2	no	—
345	C₂³×C₄	—	4	2	no	—
346	C₂³×C₄	—	4	2	no	—
347	C₂³×C₄	—	4	2	no	—
348	C₂³×C₄	—	4	4	no	—
349	C₂³×C₄	—	4	4	no	—
350	C₂³×C₄	—	4	2	no	—
351	C₂³×C₄	—	4	2	no	—
352	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
353	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
354	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
359	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
362	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
363	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
365	#121	C₂×C₄×C₁₃	1	64	yes	complemented
366	C₄×D₄	—	2	64	no	—
367	C₂×C₄⋊C₄	—	2	8	no	—
368	C₂×C₄⋊C₄	—	4	2	no	—
369	C₂×C₄⋊C₄	—	4	2	no	—
370	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	—	4	4	no	—
378	C₂×C₂²⋊C₄	—	4	4	no	—
379	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
380	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	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	8	yes	—
385	C₂×C₄²	—	2	8	no	—
386	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
387	#95	C₂³×C₁₃	1	8	yes	—
388	#95	C₂³×C₁₃	1	8	yes	—
389	#95	C₂³×C₁₃	1	8	yes	—
390	#95	C₂³×C₁₃	1	8	yes	—
391	#95	C₂³×C₁₃	1	8	yes	—
392	C₂×C₁₃	—	2	8	no	—
393	C₂×C₁₃	—	4	8	no	—
394	C₂×C₁₃	#2325	1	8	yes	direct product factor
395	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
396	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
397	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
398	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
399	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
401	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	4	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
413	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
414	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
415	C₂⁴	C₁₃×#41	1	4	yes	—
416	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
417	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
418	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
419	C₂×D₄	—	2	64	no	—
420	C₂×D₄	—	2	16	no	—
421	C₂×D₄	—	2	16	no	—
422	C₂×D₄	—	4	16	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	complemented
426	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	complemented
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	16	no	—
446	C₂²×C₄	—	4	16	no	—
447	C₂²×C₄	—	4	16	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	8	no	—
453	C₂²×C₄	—	4	8	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	32	no	—
457	C₂²×C₄	—	4	16	no	—
458	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
459	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
460	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
462	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
464	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
471	C₄⋊C₄	—	2	16	no	—
472	C₄⋊C₄	—	4	4	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
475	C₂²⋊C₄	—	2	16	no	—
476	C₂²⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	4	8	no	—
478	C₂²⋊C₄	—	4	8	no	—
479	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
480	C₄²	—	2	16	no	—
481	C₁₃	C₂×#2325	1	1	yes	characteristic, direct product factor, Sylow
482	C₂³	—	2	8	no	—
483	C₂³	—	2	8	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	16	no	—
494	C₂³	—	2	16	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	4	8	no	—
502	C₂³	—	4	8	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	4	8	no	—
505	C₂³	C₄×D₄×C₁₃	1	16	yes	—
506	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
507	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
508	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
509	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
510	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
511	C₂³	C₂×C₁₃×#41	1	4	yes	—
512	C₂³	C₂×C₁₃×#41	1	2	yes	—
513	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
514	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
515	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
516	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
517	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
518	D₄	—	2	64	no	—
519	D₄	—	4	16	no	—
520	C₂×C₄	—	2	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	16	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	4	16	no	—
542	C₂×C₄	—	4	16	no	—
543	C₂×C₄	—	4	32	no	—
544	C₂×C₄	—	4	16	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
549	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
550	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
552	C₂²	—	2	32	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	2	4	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	2	8	no	—
560	C₂²	—	2	8	no	—
561	C₂²	—	2	8	no	—
562	C₂²	—	4	32	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	C₂×C₄×D₄×C₁₃	1	8	yes	—
568	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
569	C₂²	C₁₃×#518	1	4	yes	—
570	C₂²	C₁₃×#520	1	4	yes	—
571	C₂²	C₁₃×#534	1	4	yes	—
572	C₂²	C₁₃×#537	1	4	yes	—
573	C₂²	C₁₃×#538	1	4	yes	—
574	C₂²	C₁₃×#539	1	4	yes	—
575	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
576	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
577	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
578	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
582	C₄	—	2	8	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	8	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	4	no	—
589	C₂	—	2	8	no	—
590	C₂	—	4	8	no	—
591	C₂	C₁₃×#2325	1	8	yes	direct product factor
592	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
593	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
594	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
595	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
596	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
597	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
598	C₂	C₂×C₁₃×#539	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2325	C₂	direct (N × H)
4. C₂×C₁₃×#388	C₂	semidirect
5. C₂×C₁₃×#387	C₂	semidirect
6. C₂×C₁₃×#386	C₂	semidirect
7. C₂×C₁₃×#386	C₂	semidirect
8. C₂×C₁₃×#385	C₂	semidirect
9. C₂×C₁₃×#380	C₂	semidirect
10. C₂²×C₁₃×#95	C₂	semidirect
17. C₂×C₁₃×#121	C₄	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₁₃×#388	C₂²	semidirect
32. C₁₃×#387	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#386	C₂²	semidirect
35. C₁₃×#385	C₂²	semidirect
36. C₁₃×#380	C₂²	semidirect
42. C₂×C₁₃×#95	C₂²	semidirect
49. C₂²×D₄×C₁₃	C₂×C₄	semidirect
50. C₂²×D₄×C₁₃	C₂×C₄	semidirect
63. C₂³×C₄×C₁₃	C₂×C₄	semidirect
64. C₂³×C₄×C₁₃	D₄	semidirect
76. C₁₃×#121	C₂×C₄	semidirect
81. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
90. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
103. C₂×#2325	C₁₃	direct (N × H)
127. C₂×D₄×C₁₃	C₂²×C₄	semidirect
128. C₂×D₄×C₁₃	C₂²×C₄	semidirect
163. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
165. C₂²×C₄×C₁₃	C₂×D₄	semidirect
176. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
181. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
184. C₂²×C₄×D₄	C₂×C₁₃	semidirect
185. #2325	C₂×C₁₃	direct (N × H)
186. C₂×#388	C₂×C₁₃	semidirect
187. C₂×#387	C₂×C₁₃	semidirect
188. C₂×#386	C₂×C₁₃	semidirect
189. C₂×#386	C₂×C₁₃	semidirect
190. C₂×#385	C₂×C₁₃	semidirect
191. C₂×#380	C₂×C₁₃	semidirect
192. C₂²×#95	C₂×C₁₃	semidirect
269. C₂×#121	C₄×C₁₃	semidirect
272. C₂×C₄×D₄	C₂²×C₁₃	semidirect
283. #388	C₂²×C₁₃	semidirect
284. #387	C₂²×C₁₃	semidirect
285. #386	C₂²×C₁₃	semidirect
286. #386	C₂²×C₁₃	semidirect
287. #385	C₂²×C₁₃	semidirect
288. #380	C₂²×C₁₃	semidirect
294. C₂×#95	C₂²×C₁₃	semidirect
338. C₂²×D₄	C₂×C₄×C₁₃	semidirect
339. C₂²×D₄	C₂×C₄×C₁₃	semidirect
352. C₂³×C₄	C₂×C₄×C₁₃	semidirect
353. C₂³×C₄	D₄×C₁₃	semidirect
365. #121	C₂×C₄×C₁₃	semidirect
370. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
379. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
394. C₂×C₁₃	#2325	direct (N × H)
425. C₂×D₄	C₂²×C₄×C₁₃	semidirect
426. C₂×D₄	C₂²×C₄×C₁₃	semidirect
461. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
463. C₂²×C₄	C₂×D₄×C₁₃	semidirect
474. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
479. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
481. C₁₃	C₂×#2325	direct (N × H)
591. C₂	C₁₃×#2325	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2325	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂²×C₁₃×#95	2
C₂×#2325	13

Subgroups — C2×C13×#2325 #15720405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2325 #15720405