Subgroups — C₂×C₁₃×#2430 #15721069

Order 3328.

6042 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2430	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	16	no	—
14	C₂²×C₁₃×#41	—	2	8	no	—
15	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
20	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	—	2	8	no	—
25	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
26	C₂×C₁₃×#121	—	2	16	no	—
27	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₁₃×#395	C₂²	1	8	yes	complemented
39	C₁₃×#394	C₂²	1	8	yes	complemented
40	C₁₃×#393	C₂²	1	8	yes	complemented
41	C₁₃×#392	C₂²	1	8	yes	complemented
42	C₁₃×#386	C₂²	1	16	yes	complemented
43	C₁₃×#386	C₂²	1	16	yes	complemented
44	C₁₃×#385	C₂²	1	16	yes	complemented
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂×C₁₃×#95	C₂²	1	2	yes	—
50	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃	C₂³	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×#41	—	2	128	no	—
55	C₂×C₁₃×#41	—	2	64	no	—
56	C₂×C₁₃×#41	—	2	32	no	—
57	C₂²×Q₈×C₁₃	—	2	8	no	—
58	C₂²×Q₈×C₁₃	—	2	4	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	2	8	no	—
62	C₂²×D₄×C₁₃	—	2	8	no	—
63	C₂²×D₄×C₁₃	—	2	8	no	—
64	C₂²×D₄×C₁₃	—	2	8	no	—
65	C₂²×D₄×C₁₃	—	2	4	no	—
66	C₂²×D₄×C₁₃	—	2	4	no	—
67	C₂²×D₄×C₁₃	—	2	8	no	—
68	C₂²×D₄×C₁₃	—	4	4	no	—
69	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
74	C₂³×C₄×C₁₃	—	2	8	no	—
75	C₂³×C₄×C₁₃	—	2	8	no	—
76	C₂³×C₄×C₁₃	—	2	8	no	—
77	C₂³×C₄×C₁₃	—	2	8	no	—
78	C₂³×C₄×C₁₃	—	2	8	no	—
79	C₂³×C₄×C₁₃	—	2	8	no	—
80	C₂³×C₄×C₁₃	—	4	4	no	—
81	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
82	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#123	—	2	32	no	—
94	C₁₃×#121	—	2	64	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
115	C₁₃×#95	C₂³	1	8	yes	—
116	C₁₃×#95	C₂³	1	8	yes	—
117	C₁₃×#95	C₂³	1	8	yes	—
118	C₁₃×#95	C₂³	1	4	yes	—
119	C₁₃×#95	C₂³	1	4	yes	—
120	C₂×#2430	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	2	no	—
123	C₂⁴×C₁₃	—	2	2	no	—
124	C₂⁴×C₁₃	—	2	4	no	—
125	C₂⁴×C₁₃	—	2	4	no	—
126	C₂⁴×C₁₃	—	2	4	no	—
127	C₂⁴×C₁₃	—	2	4	no	—
128	C₂⁴×C₁₃	—	2	4	no	—
129	C₂⁴×C₁₃	—	2	4	no	—
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂⁴×C₁₃	—	2	4	no	—
132	C₂⁴×C₁₃	—	2	4	no	—
133	C₂⁴×C₁₃	—	2	2	no	—
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
136	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
137	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
138	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
139	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
140	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×#41	—	2	256	no	—
143	C₂×Q₈×C₁₃	—	2	32	no	—
144	C₂×Q₈×C₁₃	—	2	16	no	—
145	C₂×Q₈×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	32	no	—
147	C₂×D₄×C₁₃	—	2	64	no	—
148	C₂×D₄×C₁₃	—	2	16	no	—
149	C₂×D₄×C₁₃	—	2	16	no	—
150	C₂×D₄×C₁₃	—	2	16	no	—
151	C₂×D₄×C₁₃	—	2	16	no	—
152	C₂×D₄×C₁₃	—	2	16	no	—
153	C₂×D₄×C₁₃	—	2	8	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	2	16	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	—	4	32	no	—
158	C₂×D₄×C₁₃	—	4	16	no	—
159	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	complemented
160	C₂²×C₄×C₁₃	—	2	64	no	—
161	C₂²×C₄×C₁₃	—	2	32	no	—
162	C₂²×C₄×C₁₃	—	2	4	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	4	no	—
167	C₂²×C₄×C₁₃	—	2	16	no	—
168	C₂²×C₄×C₁₃	—	2	16	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	16	no	—
171	C₂²×C₄×C₁₃	—	2	16	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	16	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	16	no	—
184	C₂²×C₄×C₁₃	—	4	8	no	—
185	C₂²×C₄×C₁₃	—	4	32	no	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
190	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
191	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
199	C₁₃×C₄⋊C₄	—	2	16	no	—
200	C₁₃×C₄⋊C₄	—	2	8	no	—
201	C₁₃×C₄⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	16	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	16	no	—
205	C₁₃×C₂²⋊C₄	—	2	8	no	—
206	C₁₃×C₂²⋊C₄	—	2	8	no	—
207	C₁₃×C₂²⋊C₄	—	2	16	no	—
208	C₁₃×C₂²⋊C₄	—	4	8	no	—
209	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
212	#2430	C₂×C₁₃	1	16	yes	direct product factor
213	C₂×#395	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#394	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#393	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#392	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#386	C₂×C₁₃	1	2	yes	complemented
218	C₂×#386	C₂×C₁₃	1	2	yes	complemented
219	C₂×#385	C₂×C₁₃	1	2	yes	complemented
220	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂³×C₁₃	—	2	8	no	—
222	C₂³×C₁₃	—	2	8	no	—
223	C₂³×C₁₃	—	2	16	no	—
224	C₂³×C₁₃	—	2	16	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	16	no	—
229	C₂³×C₁₃	—	2	16	no	—
230	C₂³×C₁₃	—	2	16	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	2	4	no	—
235	C₂³×C₁₃	—	2	4	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	2	no	—
242	C₂³×C₁₃	—	4	8	no	—
243	C₂³×C₁₃	—	4	8	no	—
244	C₂³×C₁₃	—	4	8	no	—
245	C₂³×C₁₃	—	4	8	no	—
246	C₂³×C₁₃	—	4	4	no	—
247	C₂³×C₁₃	—	4	4	no	—
248	C₂³×C₁₃	—	4	4	no	—
249	C₂³×C₁₃	—	4	8	no	—
250	C₂³×C₁₃	—	4	8	no	—
251	C₂³×C₁₃	#120	1	16	yes	—
252	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
253	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
254	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
255	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
256	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
257	C₂³×C₁₃	C₂×#41	1	4	yes	—
258	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
259	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
260	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
261	Q₈×C₁₃	—	2	32	no	—
262	D₄×C₁₃	—	2	32	no	—
263	D₄×C₁₃	—	2	64	no	—
264	D₄×C₁₃	—	4	32	no	—
265	D₄×C₁₃	—	4	16	no	—
266	C₂×C₄×C₁₃	—	2	64	no	—
267	C₂×C₄×C₁₃	—	2	8	no	—
268	C₂×C₄×C₁₃	—	2	16	no	—
269	C₂×C₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	2	32	no	—
271	C₂×C₄×C₁₃	—	2	16	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	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	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	4	32	no	—
289	C₂×C₄×C₁₃	—	4	4	no	—
290	C₂×C₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	4	4	no	—
292	C₂×C₄×C₁₃	—	4	8	no	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₁₃	C₂×#41	1	8	yes	complemented
297	C₂²×#41	—	2	16	no	—
298	C₂²×#41	—	2	8	no	—
299	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
300	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
304	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
305	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
306	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
307	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#123	—	2	8	no	—
309	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
310	C₂×#121	—	2	16	no	—
311	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
312	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
317	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
318	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
322	#395	C₂²×C₁₃	1	8	yes	complemented
323	#394	C₂²×C₁₃	1	8	yes	complemented
324	#393	C₂²×C₁₃	1	8	yes	complemented
325	#392	C₂²×C₁₃	1	8	yes	complemented
326	#386	C₂²×C₁₃	1	16	yes	complemented
327	#386	C₂²×C₁₃	1	16	yes	complemented
328	#385	C₂²×C₁₃	1	16	yes	complemented
329	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#95	C₂²×C₁₃	1	2	yes	—
332	C₂×#95	C₂²×C₁₃	1	2	yes	—
333	C₂×#95	C₂²×C₁₃	1	2	yes	—
334	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
335	C₂²×C₁₃	—	2	4	no	—
336	C₂²×C₁₃	—	2	4	no	—
337	C₂²×C₁₃	—	2	32	no	—
338	C₂²×C₁₃	—	2	8	no	—
339	C₂²×C₁₃	—	2	8	no	—
340	C₂²×C₁₃	—	2	8	no	—
341	C₂²×C₁₃	—	2	8	no	—
342	C₂²×C₁₃	—	2	8	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	32	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	—	4	4	no	—
348	C₂²×C₁₃	—	4	2	no	—
349	C₂²×C₁₃	—	4	2	no	—
350	C₂²×C₁₃	—	4	2	no	—
351	C₂²×C₁₃	—	4	4	no	—
352	C₂²×C₁₃	—	4	4	no	—
353	C₂²×C₁₃	—	8	8	no	—
354	C₂²×C₁₃	C₂×#120	1	8	yes	—
355	C₂²×C₁₃	C₂×#120	1	4	yes	—
356	C₂²×C₁₃	#532	1	4	yes	—
357	C₂²×C₁₃	#537	1	4	yes	—
358	C₂²×C₁₃	#546	1	8	yes	—
359	C₂²×C₁₃	#547	1	8	yes	—
360	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
361	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
362	C₂²×C₁₃	C₂²×#41	1	2	yes	—
363	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
365	C₄×C₁₃	—	2	4	no	—
366	C₄×C₁₃	—	2	8	no	—
367	C₄×C₁₃	—	2	4	no	—
368	C₄×C₁₃	—	2	8	no	—
369	C₄×C₁₃	—	4	2	no	—
370	C₄×C₁₃	—	4	2	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	4	4	no	—
373	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
374	C₂⁵	C₂³×C₁₃	1	2	yes	—
375	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×#41	—	2	128	no	—
377	C₂×#41	—	2	64	no	—
378	C₂×#41	—	2	32	no	—
379	C₂²×Q₈	—	2	8	no	—
380	C₂²×Q₈	—	2	4	no	—
381	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
382	C₂²×D₄	—	2	8	no	—
383	C₂²×D₄	—	2	8	no	—
384	C₂²×D₄	—	2	8	no	—
385	C₂²×D₄	—	2	8	no	—
386	C₂²×D₄	—	2	8	no	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	—	2	4	no	—
389	C₂²×D₄	—	2	8	no	—
390	C₂²×D₄	—	4	4	no	—
391	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
392	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
393	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
394	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
395	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
396	C₂³×C₄	—	2	8	no	—
397	C₂³×C₄	—	2	8	no	—
398	C₂³×C₄	—	2	8	no	—
399	C₂³×C₄	—	2	8	no	—
400	C₂³×C₄	—	2	8	no	—
401	C₂³×C₄	—	2	8	no	—
402	C₂³×C₄	—	4	4	no	—
403	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
404	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
407	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
409	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
410	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
412	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
414	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
415	#123	—	2	32	no	—
416	#121	—	2	64	no	—
417	C₂×C₄⋊C₄	—	2	8	no	—
418	C₂×C₄⋊C₄	—	2	4	no	—
419	C₂×C₄⋊C₄	—	2	4	no	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	—	2	4	no	—
425	C₂×C₂²⋊C₄	—	2	8	no	—
426	C₂×C₂²⋊C₄	—	2	4	no	—
427	C₂×C₂²⋊C₄	—	2	4	no	—
428	C₂×C₂²⋊C₄	—	2	8	no	—
429	C₂×C₂²⋊C₄	—	4	4	no	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
437	#95	C₂³×C₁₃	1	8	yes	—
438	#95	C₂³×C₁₃	1	4	yes	—
439	#95	C₂³×C₁₃	1	4	yes	—
440	#95	C₂³×C₁₃	1	8	yes	—
441	#95	C₂³×C₁₃	1	8	yes	—
442	C₂×C₁₃	—	2	8	no	—
443	C₂×C₁₃	—	4	8	no	—
444	C₂×C₁₃	—	8	2	no	—
445	C₂×C₁₃	#2430	1	8	yes	direct product factor
446	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
447	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
448	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
449	C₂×C₁₃	C₂×#546	1	2	yes	—
450	C₂×C₁₃	C₂×#547	1	2	yes	—
451	C₂⁴	—	2	4	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	2	2	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	4	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	—	2	2	no	—
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	4	no	—
463	C₂⁴	—	2	2	no	—
464	C₂⁴	—	2	2	no	—
465	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
466	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
467	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
468	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
469	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
470	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
471	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
472	#41	—	2	256	no	—
473	C₂×Q₈	—	2	32	no	—
474	C₂×Q₈	—	2	16	no	—
475	C₂×Q₈	—	2	8	no	—
476	C₂×D₄	—	2	32	no	—
477	C₂×D₄	—	2	64	no	—
478	C₂×D₄	—	2	16	no	—
479	C₂×D₄	—	2	16	no	—
480	C₂×D₄	—	2	16	no	—
481	C₂×D₄	—	2	16	no	—
482	C₂×D₄	—	2	16	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	2	16	no	—
486	C₂×D₄	—	4	8	no	—
487	C₂×D₄	—	4	32	no	—
488	C₂×D₄	—	4	16	no	—
489	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	complemented
490	C₂²×C₄	—	2	64	no	—
491	C₂²×C₄	—	2	32	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	16	no	—
498	C₂²×C₄	—	2	16	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	16	no	—
501	C₂²×C₄	—	2	16	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	16	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	16	no	—
514	C₂²×C₄	—	4	8	no	—
515	C₂²×C₄	—	4	32	no	—
516	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
517	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
518	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
519	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
520	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
521	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
529	C₄⋊C₄	—	2	16	no	—
530	C₄⋊C₄	—	2	8	no	—
531	C₄⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	16	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	16	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	16	no	—
538	C₂²⋊C₄	—	4	8	no	—
539	C₁₃	C₂×#2430	1	1	yes	characteristic, direct product factor, Sylow
540	C₂³	—	2	8	no	—
541	C₂³	—	2	8	no	—
542	C₂³	—	2	16	no	—
543	C₂³	—	2	16	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	16	no	—
548	C₂³	—	2	16	no	—
549	C₂³	—	2	16	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	8	no	—
562	C₂³	—	4	8	no	—
563	C₂³	—	4	8	no	—
564	C₂³	—	4	8	no	—
565	C₂³	—	4	4	no	—
566	C₂³	—	4	4	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	4	8	no	—
569	C₂³	—	4	8	no	—
570	C₂³	C₁₃×#120	1	16	yes	—
571	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
572	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
573	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
574	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
575	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
576	C₂³	C₂×C₁₃×#41	1	4	yes	—
577	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
578	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
579	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
580	Q₈	—	2	32	no	—
581	D₄	—	2	32	no	—
582	D₄	—	2	64	no	—
583	D₄	—	4	32	no	—
584	D₄	—	4	16	no	—
585	C₂×C₄	—	2	64	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	16	no	—
588	C₂×C₄	—	2	8	no	—
589	C₂×C₄	—	2	32	no	—
590	C₂×C₄	—	2	16	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	32	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	4	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
613	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
614	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
615	C₂×C₄	C₂×C₁₃×#41	1	8	yes	complemented
616	C₂²	—	2	4	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	32	no	—
619	C₂²	—	2	8	no	—
620	C₂²	—	2	8	no	—
621	C₂²	—	2	8	no	—
622	C₂²	—	2	8	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	4	4	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	32	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	8	8	no	—
635	C₂²	C₂×C₁₃×#120	1	8	yes	—
636	C₂²	C₂×C₁₃×#120	1	4	yes	—
637	C₂²	C₁₃×#532	1	4	yes	—
638	C₂²	C₁₃×#537	1	4	yes	—
639	C₂²	C₁₃×#546	1	8	yes	—
640	C₂²	C₁₃×#547	1	8	yes	—
641	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
642	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
643	C₂²	C₂²×C₁₃×#41	1	2	yes	—
644	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
646	C₄	—	2	4	no	—
647	C₄	—	2	8	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	8	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	4	no	—
654	C₂	—	2	8	no	—
655	C₂	—	4	8	no	—
656	C₂	—	8	2	no	—
657	C₂	C₁₃×#2430	1	8	yes	direct product factor
658	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
659	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
660	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
661	C₂	C₂×C₁₃×#546	1	2	yes	—
662	C₂	C₂×C₁₃×#547	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×#41	C₂	semidirect
2. C₂²×C₁₃×#123	C₂	semidirect
3. C₂²×C₁₃×#121	C₂	semidirect
4. C₁₃×#2430	C₂	direct (N × H)
5. C₂×C₁₃×#395	C₂	semidirect
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#393	C₂	semidirect
8. C₂×C₁₃×#392	C₂	semidirect
9. C₂×C₁₃×#386	C₂	semidirect
10. C₂×C₁₃×#386	C₂	semidirect
11. C₂×C₁₃×#385	C₂	semidirect
12. C₂²×C₁₃×#95	C₂	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
38. C₁₃×#395	C₂²	semidirect
39. C₁₃×#394	C₂²	semidirect
40. C₁₃×#393	C₂²	semidirect
41. C₁₃×#392	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
44. C₁₃×#385	C₂²	semidirect
50. C₂×C₁₃×#95	C₂²	semidirect
69. C₂²×D₄×C₁₃	D₄	semidirect
81. C₂³×C₄×C₁₃	D₄	semidirect
120. C₂×#2430	C₁₃	direct (N × H)
159. C₂×D₄×C₁₃	C₂×D₄	semidirect
189. C₂²×C₄×C₁₃	C₂×D₄	semidirect
190. C₂²×C₄×C₁₃	#41	semidirect
209. C₂³×#41	C₂×C₁₃	semidirect
210. C₂²×#123	C₂×C₁₃	semidirect
211. C₂²×#121	C₂×C₁₃	semidirect
212. #2430	C₂×C₁₃	direct (N × H)
213. C₂×#395	C₂×C₁₃	semidirect
214. C₂×#394	C₂×C₁₃	semidirect
215. C₂×#393	C₂×C₁₃	semidirect
216. C₂×#392	C₂×C₁₃	semidirect
217. C₂×#386	C₂×C₁₃	semidirect
218. C₂×#386	C₂×C₁₃	semidirect
219. C₂×#385	C₂×C₁₃	semidirect
220. C₂²×#95	C₂×C₁₃	semidirect
296. C₂×C₄×C₁₃	C₂×#41	semidirect
299. C₂²×#41	C₂²×C₁₃	semidirect
309. C₂×#123	C₂²×C₁₃	semidirect
311. C₂×#121	C₂²×C₁₃	semidirect
322. #395	C₂²×C₁₃	semidirect
323. #394	C₂²×C₁₃	semidirect
324. #393	C₂²×C₁₃	semidirect
325. #392	C₂²×C₁₃	semidirect
326. #386	C₂²×C₁₃	semidirect
327. #386	C₂²×C₁₃	semidirect
328. #385	C₂²×C₁₃	semidirect
334. C₂×#95	C₂²×C₁₃	semidirect
391. C₂²×D₄	D₄×C₁₃	semidirect
403. C₂³×C₄	D₄×C₁₃	semidirect
445. C₂×C₁₃	#2430	direct (N × H)
489. C₂×D₄	C₂×D₄×C₁₃	semidirect
519. C₂²×C₄	C₂×D₄×C₁₃	semidirect
520. C₂²×C₄	C₁₃×#41	semidirect
539. C₁₃	C₂×#2430	direct (N × H)
615. C₂×C₄	C₂×C₁₃×#41	semidirect
657. C₂	C₁₃×#2430	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×#121	2
C₁₃×#2430	2
C₂×C₁₃×#395	2
C₂×C₁₃×#394	2
C₂×C₁₃×#393	2
C₂×C₁₃×#392	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂²×C₁₃×#95	2
C₂×#2430	13

Subgroups — C2×C13×#2430 #15721069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2430 #15721069