Subgroups — C₂×C₁₃×#2392 #15720878

Order 3328.

4134 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2392	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#396	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#392	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	—	2	16	no	—
18	C₂×C₄×D₄×C₁₃	—	2	8	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
20	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#117	—	2	8	no	—
22	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#398	C₂²	1	8	yes	complemented
39	C₁₃×#397	C₂²	1	8	yes	complemented
40	C₁₃×#396	C₂²	1	16	yes	complemented
41	C₁₃×#394	C₂²	1	16	yes	complemented
42	C₁₃×#394	C₂²	1	8	yes	complemented
43	C₁₃×#392	C₂²	1	8	yes	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂⁵×C₁₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	2	8	no	—
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	—	2	8	no	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
59	C₂³×C₄×C₁₃	—	2	4	no	—
60	C₂³×C₄×C₁₃	—	2	4	no	—
61	C₂³×C₄×C₁₃	—	2	8	no	—
62	C₂³×C₄×C₁₃	—	2	8	no	—
63	C₂³×C₄×C₁₃	—	2	8	no	—
64	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
65	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₁₃	—	2	64	no	—
77	C₄×D₄×C₁₃	—	2	32	no	—
78	C₁₃×#117	—	2	32	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₄²×C₁₃	—	2	4	no	—
104	C₂×C₄²×C₁₃	—	2	8	no	—
105	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	8	yes	—
110	C₁₃×#95	C₂³	1	8	yes	—
111	C₁₃×#95	C₂³	1	4	yes	—
112	C₁₃×#95	C₂³	1	4	yes	—
113	C₂×#2392	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	2	2	no	—
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₂⁴×C₁₃	—	2	4	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	4	no	—
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
125	C₂⁴×C₁₃	#41	1	8	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×D₄×C₁₃	—	2	32	no	—
130	C₂×D₄×C₁₃	—	2	64	no	—
131	C₂×D₄×C₁₃	—	2	16	no	—
132	C₂×D₄×C₁₃	—	2	16	no	—
133	C₂×D₄×C₁₃	—	2	16	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	16	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	32	no	—
143	C₂²×C₄×C₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	16	no	—
156	C₂²×C₄×C₁₃	—	2	16	no	—
157	C₂²×C₄×C₁₃	—	2	16	no	—
158	C₂²×C₄×C₁₃	—	4	32	no	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
165	C₂²×C₄×C₁₃	#41	1	8	yes	—
166	C₂²×C₄×C₁₃	#41	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	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	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	2	16	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	16	no	—
181	C₁₃×C₂²⋊C₄	—	2	16	no	—
182	C₁₃×C₂²⋊C₄	—	2	16	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	16	no	—
186	C₁₃×C₂²⋊C₄	—	2	16	no	—
187	C₁₃×C₂²⋊C₄	—	2	16	no	—
188	C₄²×C₁₃	—	2	8	no	—
189	C₄²×C₁₃	—	2	16	no	—
190	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
191	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
193	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2392	C₂×C₁₃	1	16	yes	direct product factor
195	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#396	C₂×C₁₃	1	2	yes	complemented
198	C₂×#394	C₂×C₁₃	1	2	yes	complemented
199	C₂×#394	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#392	C₂×C₁₃	1	1	yes	characteristic
201	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
203	C₂³×C₁₃	—	2	8	no	—
204	C₂³×C₁₃	—	2	16	no	—
205	C₂³×C₁₃	—	2	16	no	—
206	C₂³×C₁₃	—	2	16	no	—
207	C₂³×C₁₃	—	2	16	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	4	8	no	—
219	C₂³×C₁₃	—	4	4	no	—
220	C₂³×C₁₃	—	4	8	no	—
221	C₂³×C₁₃	—	4	8	no	—
222	C₂³×C₁₃	—	4	8	no	—
223	C₂³×C₁₃	—	4	4	no	—
224	C₂³×C₁₃	—	4	8	no	—
225	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
226	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂³×C₁₃	C₂×#41	1	8	yes	—
229	C₂³×C₁₃	C₂×#41	1	2	yes	—
230	C₂³×C₁₃	C₂×#41	1	4	yes	—
231	C₂³×C₁₃	C₂×#41	1	4	yes	—
232	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
233	D₄×C₁₃	—	2	32	no	—
234	D₄×C₁₃	—	2	64	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	16	no	—
238	C₂×C₄×C₁₃	—	2	8	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	4	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	32	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	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	32	no	—
261	C₂×C₄×C₁₃	#121	1	16	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
268	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
269	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
271	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
272	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄×D₄	—	2	16	no	—
274	C₂×C₄×D₄	—	2	8	no	—
275	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
276	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
277	C₂×#117	—	2	8	no	—
278	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
279	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
287	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
290	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
291	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
293	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
294	#398	C₂²×C₁₃	1	8	yes	complemented
295	#397	C₂²×C₁₃	1	8	yes	complemented
296	#396	C₂²×C₁₃	1	16	yes	complemented
297	#394	C₂²×C₁₃	1	16	yes	complemented
298	#394	C₂²×C₁₃	1	8	yes	complemented
299	#392	C₂²×C₁₃	1	8	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
301	C₄×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	complemented
302	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#95	C₂²×C₁₃	1	2	yes	—
305	C₂×#95	C₂²×C₁₃	1	2	yes	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	2	8	no	—
308	C₂²×C₁₃	—	2	8	no	—
309	C₂²×C₁₃	—	2	8	no	—
310	C₂²×C₁₃	—	2	8	no	—
311	C₂²×C₁₃	—	4	16	no	—
312	C₂²×C₁₃	—	4	32	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	C₂×#121	1	4	yes	—
321	C₂²×C₁₃	#525	1	4	yes	—
322	C₂²×C₁₃	#525	1	8	yes	—
323	C₂²×C₁₃	#529	1	8	yes	—
324	C₂²×C₁₃	#532	1	4	yes	—
325	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
326	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
327	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₁₃	C₂²×#41	1	2	yes	—
329	C₂²×C₁₃	C₂²×#41	1	2	yes	—
330	C₄×C₁₃	—	2	4	no	—
331	C₄×C₁₃	—	2	4	no	—
332	C₄×C₁₃	—	2	8	no	—
333	C₄×C₁₃	—	2	4	no	—
334	C₄×C₁₃	—	4	4	no	—
335	C₄×C₁₃	—	4	4	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	C₂×#121	1	8	yes	—
339	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
340	C₂⁵	C₂³×C₁₃	1	2	yes	—
341	C₂²×D₄	—	2	8	no	—
342	C₂²×D₄	—	2	8	no	—
343	C₂²×D₄	—	2	8	no	—
344	C₂²×D₄	—	2	4	no	—
345	C₂²×D₄	—	2	8	no	—
346	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
347	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
348	C₂³×C₄	—	2	4	no	—
349	C₂³×C₄	—	2	4	no	—
350	C₂³×C₄	—	2	8	no	—
351	C₂³×C₄	—	2	8	no	—
352	C₂³×C₄	—	2	8	no	—
353	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
354	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
359	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
363	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
364	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₄×D₄	—	2	64	no	—
366	C₄×D₄	—	2	32	no	—
367	#117	—	2	32	no	—
368	C₂×C₄⋊C₄	—	2	4	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	8	no	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	—	2	8	no	—
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
378	C₂×C₂²⋊C₄	—	2	8	no	—
379	C₂×C₂²⋊C₄	—	2	8	no	—
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	—	2	8	no	—
383	C₂×C₂²⋊C₄	—	2	8	no	—
384	C₂×C₂²⋊C₄	—	2	8	no	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
392	C₂×C₄²	—	2	4	no	—
393	C₂×C₄²	—	2	8	no	—
394	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
395	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
396	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
397	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
398	#95	C₂³×C₁₃	1	8	yes	—
399	#95	C₂³×C₁₃	1	8	yes	—
400	#95	C₂³×C₁₃	1	4	yes	—
401	#95	C₂³×C₁₃	1	4	yes	—
402	C₂×C₁₃	—	4	4	no	—
403	C₂×C₁₃	—	4	8	no	—
404	C₂×C₁₃	#2392	1	8	yes	direct product factor
405	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
406	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
407	C₂×C₁₃	C₂×#525	1	2	yes	—
408	C₂×C₁₃	C₂×#529	1	2	yes	—
409	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	4	no	—
416	C₂⁴	—	2	4	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	2	4	no	—
420	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
421	C₂⁴	C₁₃×#41	1	8	yes	—
422	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
423	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
424	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₂×D₄	—	2	32	no	—
426	C₂×D₄	—	2	64	no	—
427	C₂×D₄	—	2	16	no	—
428	C₂×D₄	—	2	16	no	—
429	C₂×D₄	—	2	16	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	16	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	32	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	16	no	—
452	C₂²×C₄	—	2	16	no	—
453	C₂²×C₄	—	2	16	no	—
454	C₂²×C₄	—	4	32	no	—
455	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
461	C₂²×C₄	C₁₃×#41	1	8	yes	—
462	C₂²×C₄	C₁₃×#41	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	16	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	2	16	no	—
478	C₂²⋊C₄	—	2	16	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	16	no	—
482	C₂²⋊C₄	—	2	16	no	—
483	C₂²⋊C₄	—	2	16	no	—
484	C₄²	—	2	8	no	—
485	C₄²	—	2	16	no	—
486	C₄²	C₂×D₄×C₁₃	1	16	yes	complemented
487	C₁₃	C₂×#2392	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	8	no	—
489	C₂³	—	2	16	no	—
490	C₂³	—	2	16	no	—
491	C₂³	—	2	16	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	4	4	no	—
505	C₂³	—	4	8	no	—
506	C₂³	—	4	8	no	—
507	C₂³	—	4	8	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	8	no	—
510	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
511	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
512	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
513	C₂³	C₂×C₁₃×#41	1	8	yes	—
514	C₂³	C₂×C₁₃×#41	1	2	yes	—
515	C₂³	C₂×C₁₃×#41	1	4	yes	—
516	C₂³	C₂×C₁₃×#41	1	4	yes	—
517	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
518	D₄	—	2	32	no	—
519	D₄	—	2	64	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	16	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	32	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	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	8	no	—
542	C₂×C₄	—	4	8	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	32	no	—
546	C₂×C₄	C₁₃×#121	1	16	yes	—
547	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
548	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
552	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
553	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	8	no	—
556	C₂²	—	2	8	no	—
557	C₂²	—	2	8	no	—
558	C₂²	—	2	8	no	—
559	C₂²	—	4	16	no	—
560	C₂²	—	4	32	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	4	no	—
568	C₂²	C₂×C₁₃×#121	1	4	yes	—
569	C₂²	C₁₃×#525	1	4	yes	—
570	C₂²	C₁₃×#525	1	8	yes	—
571	C₂²	C₁₃×#529	1	8	yes	—
572	C₂²	C₁₃×#532	1	4	yes	—
573	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
574	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
575	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
576	C₂²	C₂²×C₁₃×#41	1	2	yes	—
577	C₂²	C₂²×C₁₃×#41	1	2	yes	—
578	C₄	—	2	4	no	—
579	C₄	—	2	4	no	—
580	C₄	—	2	8	no	—
581	C₄	—	2	4	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	C₂×C₁₃×#121	1	8	yes	—
587	C₂	—	4	4	no	—
588	C₂	—	4	8	no	—
589	C₂	C₁₃×#2392	1	8	yes	direct product factor
590	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
591	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
592	C₂	C₂×C₁₃×#525	1	2	yes	—
593	C₂	C₂×C₁₃×#529	1	2	yes	—
594	C₂	C₂×C₁₃×#532	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂×C₁₃×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₄×C₁₃	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₂²×C₁₃×#117	C₂	semidirect
4. C₁₃×#2392	C₂	direct (N × H)
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#396	C₂	semidirect
8. C₂×C₁₃×#394	C₂	semidirect
9. C₂×C₁₃×#394	C₂	semidirect
11. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#397	C₂²	semidirect
40. C₁₃×#396	C₂²	semidirect
41. C₁₃×#394	C₂²	semidirect
42. C₁₃×#394	C₂²	semidirect
44. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
64. C₂³×C₄×C₁₃	D₄	semidirect
105. C₂×C₄²×C₁₃	D₄	semidirect
113. C₂×#2392	C₁₃	direct (N × H)
164. C₂²×C₄×C₁₃	C₂×D₄	semidirect
190. C₄²×C₁₃	C₂×D₄	semidirect
191. C₂²×C₄×D₄	C₂×C₁₃	semidirect
192. C₂²×C₄×D₄	C₂×C₁₃	semidirect
193. C₂²×#117	C₂×C₁₃	semidirect
194. #2392	C₂×C₁₃	direct (N × H)
195. C₂×#398	C₂×C₁₃	semidirect
196. C₂×#397	C₂×C₁₃	semidirect
197. C₂×#396	C₂×C₁₃	semidirect
198. C₂×#394	C₂×C₁₃	semidirect
199. C₂×#394	C₂×C₁₃	semidirect
201. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
202. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
275. C₂×C₄×D₄	C₂²×C₁₃	semidirect
276. C₂×C₄×D₄	C₂²×C₁₃	semidirect
278. C₂×#117	C₂²×C₁₃	semidirect
294. #398	C₂²×C₁₃	semidirect
295. #397	C₂²×C₁₃	semidirect
296. #396	C₂²×C₁₃	semidirect
297. #394	C₂²×C₁₃	semidirect
298. #394	C₂²×C₁₃	semidirect
300. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
301. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
353. C₂³×C₄	D₄×C₁₃	semidirect
394. C₂×C₄²	D₄×C₁₃	semidirect
404. C₂×C₁₃	#2392	direct (N × H)
460. C₂²×C₄	C₂×D₄×C₁₃	semidirect
486. C₄²	C₂×D₄×C₁₃	semidirect
487. C₁₃	C₂×#2392	direct (N × H)
589. C₂	C₁₃×#2392	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×C₄×D₄×C₁₃	2
C₂²×C₁₃×#117	2
C₁₃×#2392	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#396	2
C₂×C₁₃×#394	2
C₂×C₁₃×#392	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2392	13

Subgroups — C2×C13×#2392 #15720878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2392 #15720878