Subgroups — C₂×C₄×C₁₃×#123 #15720368

Order 3328.

4070 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂³×C₄²×C₁₃	C₂	semidirect
4. C₄×C₁₃×#123	C₂	direct (N × H)
5. C₂×C₁₃×#388	C₂	semidirect
6. C₂×C₁₃×#387	C₂	semidirect
8. C₂×C₁₃×#385	C₂	semidirect
9. C₂×C₁₃×#381	C₂	semidirect
10. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
11. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₂×C₁₃×#123	C₄	direct (N × H)
36. C₂²×C₄²×C₁₃	C₂²	semidirect
37. C₁₃×#388	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
40. C₁₃×#385	C₂²	semidirect
41. C₁₃×#381	C₂²	semidirect
42. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
63. C₂³×C₄×C₁₃	C₂×C₄	semidirect
78. C₁₃×#123	C₂×C₄	direct (N × H)
82. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
90. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
91. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
112. C₂×C₄×#123	C₁₃	direct (N × H)
160. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
177. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
182. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
183. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
190. C₂³×C₄²	C₂×C₁₃	semidirect
191. C₄×#123	C₂×C₁₃	direct (N × H)
192. C₂×#388	C₂×C₁₃	semidirect
193. C₂×#387	C₂×C₁₃	semidirect
195. C₂×#385	C₂×C₁₃	semidirect
196. C₂×#381	C₂×C₁₃	semidirect
197. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
198. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
199. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
255. C₂×C₄×C₁₃	#123	direct (N × H)
268. C₂×#123	C₄×C₁₃	direct (N × H)
286. C₂²×C₄²	C₂²×C₁₃	semidirect
287. #388	C₂²×C₁₃	semidirect
288. #387	C₂²×C₁₃	semidirect
290. #385	C₂²×C₁₃	semidirect
291. #381	C₂²×C₁₃	semidirect
292. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
293. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
294. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
330. C₄×C₁₃	C₂×#123	direct (N × H)
344. C₂³×C₄	C₂×C₄×C₁₃	semidirect
359. #123	C₂×C₄×C₁₃	direct (N × H)
363. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
371. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
372. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
395. C₂×C₁₃	C₄×#123	direct (N × H)
448. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
465. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
470. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
471. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
476. C₁₃	C₂×C₄×#123	direct (N × H)
532. C₂×C₄	C₁₃×#123	direct (N × H)
570. C₄	C₂×C₁₃×#123	direct (N × H)
573. C₂	C₄×C₁₃×#123	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×#123	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₄²×C₁₃	2
C₄×C₁₃×#123	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#381	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×C₄×#123	13

Subgroups — C2×C4×C13×#123 #15720368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₃×#123 #15720368