Subgroups — C₂×C₃⋊D₃×#6038 #72259812

Order 7200.

3636 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268265	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14268269	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14268264	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#6038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃⋊D₃×#6038	C₂	1	8	yes	maximal, direct product factor
6	C₂×D₃×#6038	—	3	4	no	maximal
7	C₂×C₅×C₃⋊D₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×D₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₃⋊D₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₃²×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃²×C₅⋊D₅	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₅²×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊D₁₅	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃⋊(C₃⋊(C₅⋊D₅))	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃⋊D₃×C₅⋊D₅	—	2	4	no	—
16	C₂×C₃⋊D₃×C₅⋊D₅	C₂²	1	4	yes	complemented
17	C₂×C₅×D₅×C₃⋊D₃	—	2	4	no	—
18	C₂×C₅×D₅×C₃⋊D₃	C₂²	1	4	yes	complemented
19	C₂×C₅×C₃⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃²×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
21	#14268269	C₂²	1	4	yes	complemented
22	#14268265	C₂²	1	4	yes	complemented
23	#14268264	C₂²	1	4	yes	complemented
24	C₅×C₃⋊D₃×Dic₅	C₂²	1	4	yes	complemented
25	C₃²×#6038	C₂²	1	4	yes	complemented
26	C₂×C₃⋊D₃×C₂²⋊D₅	—	5	1	no	maximal
27	C₂×C₃⋊D₃×D₂₀	—	5	1	no	maximal
28	C₂²×D₃×C₅⋊D₅	—	3	4	no	—
29	C₂²×C₅×D₃×D₅	—	3	4	no	—
30	C₂×#10597127	—	3	4	no	—
31	C₂×#10597123	—	3	4	no	—
32	C₂×#10597122	—	3	4	no	—
33	C₂×C₅×D₃×Dic₅	—	3	4	no	—
34	C₂×C₃×#6038	D₃	1	4	yes	complemented
35	D₃×#6038	—	3	32	no	—
36	C₂²×C₃²×C₅²	C₂³	1	1	yes	characteristic
37	C₂×C₃⋊(C₃⋊(C₅⋊D₅))	—	2	2	no	—
38	C₂×C₃⋊(C₃⋊(C₅⋊D₅))	C₂³	1	2	yes	complemented
39	C₂×C₅×C₃⋊D₁₅	—	2	2	no	—
40	C₂×C₅×C₃⋊D₁₅	C₂³	1	2	yes	complemented
41	C₂×C₅²×C₃⋊D₃	D₄	1	4	yes	complemented
42	C₂×C₅²×C₃⋊D₃	C₂³	1	2	yes	—
43	C₂×C₃²×C₅⋊D₅	—	2	2	no	—
44	C₂×C₃²×C₅⋊D₅	C₂³	1	2	yes	complemented
45	C₂×C₃²×C₅×D₅	—	2	2	no	—
46	C₂×C₃²×C₅×D₅	C₂³	1	2	yes	complemented
47	C₃⋊D₃×C₅⋊D₅	—	2	8	no	—
48	C₅×D₅×C₃⋊D₃	—	2	8	no	—
49	C₅×C₃⋊Dic₁₅	C₂³	1	2	yes	complemented
50	C₃²×C₅×Dic₅	C₂³	1	2	yes	complemented
51	C₂²×#6038	—	9	1	no	Hall
52	C₂³×C₅×C₃⋊D₃	—	5	1	no	—
53	C₂²×D₅×C₃⋊D₃	—	5	1	no	—
54	C₂²×D₅×C₃⋊D₃	—	5	1	no	—
55	C₂²×D₅×C₃⋊D₃	—	10	2	no	—
56	C₂²×D₅×C₃⋊D₃	D₅	1	1	yes	characteristic, complemented
57	C₂×#67184	—	5	1	no	—
58	C₂×C₄⋊(C₃⋊D₁₅)	—	5	1	no	—
59	C₂×C₄×C₅×C₃⋊D₃	—	5	1	no	—
60	C₂×C₃²×C₂²⋊D₅	—	5	1	no	—
61	C₂×C₃²×D₂₀	—	5	1	no	—
62	C₃⋊D₃×C₂²⋊D₅	—	5	8	no	—
63	C₂×#67140	—	5	1	no	—
64	C₂×#67139	—	5	1	no	—
65	C₂×#67139	—	5	1	no	—
66	C₂×#67138	—	5	1	no	—
67	C₂×C₃⋊D₃×Dic₅	D₅	1	1	yes	characteristic, complemented
68	C₃⋊D₃×D₂₀	—	5	8	no	—
69	C₂²×C₃⋊(C₅⋊D₅)	—	3	4	no	—
70	C₂²×C₅×D₁₅	—	3	4	no	—
71	C₂²×C₅²×D₃	—	3	4	no	—
72	C₂²×C₃×C₅⋊D₅	C₂×D₃	1	4	yes	complemented
73	C₂²×C₃×C₅×D₅	C₂×D₃	1	4	yes	complemented
74	C₂×D₃×C₅⋊D₅	—	3	16	no	—
75	C₂×D₃×C₅⋊D₅	—	6	16	no	—
76	C₂×C₅×D₃×D₅	—	3	16	no	—
77	C₂×C₅×D₃×D₅	—	6	16	no	—
78	C₂×C₅×Dic₁₅	—	3	4	no	—
79	C₂×C₃×C₅×Dic₅	C₂×D₃	1	4	yes	complemented
80	#10597127	—	3	16	no	—
81	#10597123	—	3	16	no	—
82	#10597122	—	3	16	no	—
83	C₅×D₃×Dic₅	—	3	16	no	—
84	C₃×#6038	C₂×D₃	1	16	yes	complemented
85	C₂×D₃×C₂²⋊D₅	—	15	4	no	—
86	C₂×D₃×D₂₀	—	15	4	no	—
87	C₂×C₃²×C₅²	C₂×D₄	1	2	yes	complemented
88	C₂×C₃²×C₅²	C₂⁴	1	1	yes	characteristic
89	C₃⋊(C₃⋊(C₅⋊D₅))	—	2	2	no	—
90	C₅×C₃⋊D₁₅	—	2	2	no	—
91	C₅²×C₃⋊D₃	C₂×D₄	1	4	yes	complemented
92	C₃²×C₅⋊D₅	—	2	2	no	—
93	C₃²×C₅×D₅	—	2	2	no	—
94	C₂³×C₅⋊D₅	—	9	1	no	—
95	C₂³×C₅×D₅	—	9	1	no	—
96	C₂²×C₅×Dic₅	—	9	1	no	—
97	C₂×#6038	—	9	1	no	—
98	C₂×#6038	—	9	1	no	—
99	C₂×#6038	—	9	1	no	—
100	C₂×#6038	—	9	8	no	—
101	C₂×#6038	C₃⋊D₃	1	1	yes	characteristic, direct product factor
102	C₂³×C₃²×C₅	—	5	1	no	—
103	C₂²×C₃⋊D₁₅	—	5	1	no	—
104	C₂²×C₃⋊D₁₅	—	5	1	no	—
105	C₂²×C₃⋊D₁₅	—	10	2	no	—
106	C₂²×C₃⋊D₁₅	C₂×D₅	1	1	yes	characteristic, complemented
107	C₂²×C₅×C₃⋊D₃	—	2	2	no	—
108	C₂²×C₅×C₃⋊D₃	—	5	1	no	—
109	C₂²×C₅×C₃⋊D₃	—	5	4	no	—
110	C₂²×C₅×C₃⋊D₃	—	10	4	no	—
111	C₂²×C₅×C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
112	C₂²×C₅×C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
113	C₂²×C₃²×D₅	—	5	1	no	—
114	C₂²×C₃²×D₅	—	5	1	no	—
115	C₂²×C₃²×D₅	—	10	2	no	—
116	C₂²×C₃²×D₅	C₂×D₅	1	1	yes	characteristic, complemented
117	C₂×D₅×C₃⋊D₃	—	2	4	no	—
118	C₂×D₅×C₃⋊D₃	—	5	4	no	—
119	C₂×D₅×C₃⋊D₃	—	5	4	no	—
120	C₂×D₅×C₃⋊D₃	—	10	8	no	—
121	C₂×D₅×C₃⋊D₃	—	10	16	no	—
122	C₂×D₅×C₃⋊D₃	—	10	4	no	—
123	C₂×D₅×C₃⋊D₃	—	10	4	no	—
124	C₂×D₅×C₃⋊D₃	C₂×D₅	1	4	yes	complemented
125	C₂×C₃²×C₄×C₅	—	5	1	no	—
126	#67184	—	5	4	no	—
127	C₂×C₃⋊Dic₁₅	C₂×D₅	1	1	yes	characteristic, complemented
128	C₄⋊(C₃⋊D₁₅)	—	5	4	no	—
129	C₂×C₅×C₃⋊Dic₃	—	5	1	no	—
130	C₄×C₅×C₃⋊D₃	—	5	4	no	—
131	C₃²×C₂²⋊D₅	—	5	4	no	—
132	C₂×C₃²×Dic₅	C₂×D₅	1	1	yes	characteristic, complemented
133	C₃²×D₂₀	—	5	4	no	—
134	#67140	—	5	4	no	—
135	#67139	—	5	4	no	—
136	#67139	—	5	4	no	—
137	#67138	—	5	4	no	—
138	C₃⋊D₃×Dic₅	C₂×D₅	1	4	yes	complemented
139	C₂²×C₃×C₅²	C₂²×D₃	1	4	yes	—
140	C₂×C₃⋊(C₅⋊D₅)	—	3	8	no	—
141	C₂×C₃⋊(C₅⋊D₅)	—	6	8	no	—
142	C₂×C₅×D₁₅	—	3	8	no	—
143	C₂×C₅×D₁₅	—	6	8	no	—
144	C₂×C₅²×D₃	—	3	16	no	—
145	C₂×C₅²×D₃	—	3	8	no	—
146	C₂×C₃×C₅⋊D₅	—	2	8	no	—
147	C₂×C₃×C₅⋊D₅	C₂²×D₃	1	8	yes	complemented
148	C₂×C₃×C₅×D₅	—	2	8	no	—
149	C₂×C₃×C₅×D₅	C₂²×D₃	1	8	yes	complemented
150	D₃×C₅⋊D₅	—	6	32	no	—
151	C₅×D₃×D₅	—	6	32	no	—
152	C₅×Dic₁₅	—	3	8	no	—
153	C₃×C₅×Dic₅	C₂²×D₃	1	8	yes	complemented
154	C₂×D₄×C₃⋊D₃	—	25	1	no	Hall
155	C₂³×C₅×D₃	—	15	4	no	—
156	C₂²×D₃×D₅	—	3	4	no	—
157	C₂²×D₃×D₅	—	15	4	no	—
158	C₂²×D₃×D₅	—	15	4	no	—
159	C₂²×D₃×D₅	—	30	8	no	—
160	C₂×#1220	—	15	4	no	—
161	C₂×D₆₀	—	15	4	no	—
162	C₂×C₄×C₅×D₃	—	15	4	no	—
163	C₂×C₃×C₂²⋊D₅	—	5	4	no	—
164	C₂×C₃×D₂₀	—	5	4	no	—
165	D₃×C₂²⋊D₅	—	15	32	no	—
166	C₂×#1203	—	15	4	no	—
167	C₂×#1202	—	15	4	no	—
168	C₂×#1202	—	15	4	no	—
169	C₂×#1201	—	15	4	no	—
170	C₂×D₃×Dic₅	—	3	4	no	—
171	D₃×D₂₀	—	15	32	no	—
172	C₃²×C₅²	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
173	C₂³×C₅²	—	9	1	no	—
174	C₂²×C₅⋊D₅	—	9	1	no	—
175	C₂²×C₅⋊D₅	—	9	4	no	—
176	C₂²×C₅⋊D₅	—	18	4	no	—
177	C₂²×C₅⋊D₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
178	C₂²×C₅×D₅	—	9	1	no	—
179	C₂²×C₅×D₅	—	9	4	no	—
180	C₂²×C₅×D₅	—	18	4	no	—
181	C₂²×C₅×D₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
182	C₂×C₅×Dic₅	—	9	1	no	—
183	C₂×C₅×Dic₅	—	9	4	no	—
184	C₂×C₅×Dic₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
185	#6038	—	9	4	no	—
186	#6038	—	9	4	no	—
187	#6038	—	9	4	no	—
188	#6038	C₂×C₃⋊D₃	1	4	yes	direct product factor
189	C₂²×C₃²×C₅	—	2	2	no	—
190	C₂²×C₃²×C₅	—	5	2	no	—
191	C₂²×C₃²×C₅	—	10	2	no	—
192	C₂²×C₃²×C₅	C₂²×D₅	1	1	yes	characteristic
193	C₂²×C₃²×C₅	C₂²×D₅	1	1	yes	characteristic
194	C₂×C₃⋊D₁₅	—	2	2	no	—
195	C₂×C₃⋊D₁₅	—	5	2	no	—
196	C₂×C₃⋊D₁₅	—	5	2	no	—
197	C₂×C₃⋊D₁₅	—	10	4	no	—
198	C₂×C₃⋊D₁₅	—	10	8	no	—
199	C₂×C₃⋊D₁₅	—	10	2	no	—
200	C₂×C₃⋊D₁₅	—	10	2	no	—
201	C₂×C₃⋊D₁₅	C₂²×D₅	1	2	yes	complemented
202	C₂×C₅×C₃⋊D₃	—	2	8	no	—
203	C₂×C₅×C₃⋊D₃	—	2	4	no	—
204	C₂×C₅×C₃⋊D₃	—	5	2	no	—
205	C₂×C₅×C₃⋊D₃	—	10	2	no	—
206	C₂×C₅×C₃⋊D₃	—	10	8	no	—
207	C₂×C₅×C₃⋊D₃	D₂₀	1	4	yes	complemented
208	C₂×C₅×C₃⋊D₃	C₂²⋊D₅	1	4	yes	complemented
209	C₂×C₅×C₃⋊D₃	C₂²×D₅	1	2	yes	—
210	C₂×C₅×C₃⋊D₃	C₂²×D₅	1	2	yes	—
211	C₂×C₃²×D₅	—	2	2	no	—
212	C₂×C₃²×D₅	—	5	2	no	—
213	C₂×C₃²×D₅	—	5	2	no	—
214	C₂×C₃²×D₅	—	10	4	no	—
215	C₂×C₃²×D₅	—	10	8	no	—
216	C₂×C₃²×D₅	—	10	2	no	—
217	C₂×C₃²×D₅	—	10	2	no	—
218	C₂×C₃²×D₅	C₂²×D₅	1	2	yes	complemented
219	D₅×C₃⋊D₃	—	2	8	no	—
220	D₅×C₃⋊D₃	—	10	32	no	—
221	D₅×C₃⋊D₃	—	10	8	no	—
222	D₅×C₃⋊D₃	—	10	8	no	—
223	C₃²×C₄×C₅	—	5	2	no	—
224	C₃⋊Dic₁₅	C₂²×D₅	1	2	yes	complemented
225	C₅×C₃⋊Dic₃	—	5	2	no	—
226	C₃²×Dic₅	C₂²×D₅	1	2	yes	complemented
227	C₂²×C₂²⋊D₅	—	45	1	no	—
228	C₂²×D₂₀	—	45	1	no	—
229	C₂×C₃×C₅²	D₃×D₄	1	8	yes	complemented
230	C₂×C₃×C₅²	C₂³×D₃	1	4	yes	—
231	C₃⋊(C₅⋊D₅)	—	6	8	no	—
232	C₅×D₁₅	—	6	8	no	—
233	C₅²×D₃	—	3	16	no	—
234	C₃×C₅⋊D₅	—	2	8	no	—
235	C₃×C₅×D₅	—	2	8	no	—
236	C₂³×C₃⋊D₃	—	5	1	no	—
237	C₂³×C₃⋊D₃	—	25	1	no	—
238	C₂×C₃²×D₄	—	25	1	no	—
239	C₂×#638	—	25	1	no	—
240	C₂×#638	—	25	1	no	—
241	D₄×C₃⋊D₃	—	25	8	no	—
242	C₂×C₄⋊(C₃⋊D₃)	—	25	1	no	—
243	C₂×C₄×C₃⋊D₃	—	5	1	no	—
244	C₂³×C₃×C₅	—	5	4	no	—
245	C₂²×D₁₅	—	3	4	no	—
246	C₂²×D₁₅	—	15	4	no	—
247	C₂²×D₁₅	—	15	4	no	—
248	C₂²×D₁₅	—	30	8	no	—
249	C₂²×C₅×D₃	—	3	4	no	—
250	C₂²×C₅×D₃	—	3	4	no	—
251	C₂²×C₅×D₃	—	6	8	no	—
252	C₂²×C₅×D₃	—	15	16	no	—
253	C₂²×C₅×D₃	—	15	4	no	—
254	C₂²×C₅×D₃	—	30	16	no	—
255	C₂²×C₃×D₅	—	5	4	no	—
256	C₂²×C₃×D₅	—	5	4	no	—
257	C₂²×C₃×D₅	—	10	8	no	—
258	C₂²×C₃×D₅	D₃×D₅	1	4	yes	complemented
259	C₂×D₃×D₅	—	3	16	no	—
260	C₂×D₃×D₅	—	6	16	no	—
261	C₂×D₃×D₅	—	15	16	no	—
262	C₂×D₃×D₅	—	15	16	no	—
263	C₂×D₃×D₅	—	30	16	no	—
264	C₂×D₃×D₅	—	30	16	no	—
265	C₂×D₃×D₅	—	30	32	no	—
266	C₂×D₃×D₅	—	30	64	no	—
267	C₂×C₃×C₄×C₅	—	5	4	no	—
268	#1220	—	15	16	no	—
269	C₂×Dic₁₅	—	3	4	no	—
270	D₆₀	—	15	16	no	—
271	C₂×C₅×Dic₃	—	15	4	no	—
272	C₄×C₅×D₃	—	15	16	no	—
273	C₃×C₂²⋊D₅	—	5	16	no	—
274	C₂×C₃×Dic₅	D₃×D₅	1	4	yes	complemented
275	C₃×D₂₀	—	5	16	no	—
276	#1203	—	15	16	no	—
277	#1202	—	15	16	no	—
278	#1202	—	15	16	no	—
279	#1201	—	15	16	no	—
280	D₃×Dic₅	—	3	16	no	—
281	C₂²×C₅²	—	9	2	no	—
282	C₂²×C₅²	—	9	4	no	—
283	C₂²×C₅²	C₂²×C₃⋊D₃	1	1	yes	characteristic
284	C₂×C₅⋊D₅	—	2	2	no	—
285	C₂×C₅⋊D₅	—	9	2	no	—
286	C₂×C₅⋊D₅	—	18	8	no	—
287	C₂×C₅⋊D₅	—	18	2	no	—
288	C₂×C₅⋊D₅	C₂²×C₃⋊D₃	1	2	yes	complemented
289	C₂×C₅×D₅	—	2	2	no	—
290	C₂×C₅×D₅	—	9	2	no	—
291	C₂×C₅×D₅	—	18	8	no	—
292	C₂×C₅×D₅	—	18	2	no	—
293	C₂×C₅×D₅	C₂²×C₃⋊D₃	1	2	yes	complemented
294	C₅×Dic₅	—	9	2	no	—
295	C₅×Dic₅	C₂²×C₃⋊D₃	1	2	yes	complemented
296	C₂×D₃×D₄	—	75	4	no	—
297	C₂×C₃²×C₅	—	2	4	no	—
298	C₂×C₃²×C₅	—	2	2	no	—
299	C₂×C₃²×C₅	—	10	2	no	—
300	C₂×C₃²×C₅	C₂×D₂₀	1	2	yes	complemented
301	C₂×C₃²×C₅	C₂×C₂²⋊D₅	1	2	yes	complemented
302	C₂×C₃²×C₅	C₂³×D₅	1	1	yes	characteristic
303	C₂×C₃²×C₅	C₂³×D₅	1	1	yes	characteristic
304	C₃⋊D₁₅	—	2	2	no	—
305	C₃⋊D₁₅	—	10	8	no	—
306	C₃⋊D₁₅	—	10	2	no	—
307	C₃⋊D₁₅	—	10	2	no	—
308	C₅×C₃⋊D₃	—	2	8	no	—
309	C₅×C₃⋊D₃	—	10	2	no	—
310	C₅×C₃⋊D₃	C₂×D₂₀	1	4	yes	complemented
311	C₅×C₃⋊D₃	C₂×C₂²⋊D₅	1	4	yes	complemented
312	C₃²×D₅	—	2	2	no	—
313	C₃²×D₅	—	10	8	no	—
314	C₃²×D₅	—	10	2	no	—
315	C₃²×D₅	—	10	2	no	—
316	C₂⁴×C₅	—	45	1	no	—
317	C₂³×D₅	—	9	1	no	—
318	C₂³×D₅	—	45	1	no	—
319	C₂³×D₅	—	45	1	no	—
320	C₂³×D₅	—	90	2	no	—
321	C₂²×C₄×C₅	—	45	1	no	—
322	C₂×C₂²⋊D₅	—	5	1	no	—
323	C₂×C₂²⋊D₅	—	45	8	no	—
324	C₂×C₂²⋊D₅	—	45	1	no	—
325	C₂×C₂²⋊D₅	—	45	1	no	—
326	C₂×C₂²⋊D₅	—	45	1	no	—
327	C₂²×Dic₅	—	9	1	no	—
328	C₂×D₂₀	—	5	1	no	—
329	C₂×D₂₀	—	45	8	no	—
330	C₂×D₂₀	—	45	1	no	—
331	C₂×D₂₀	—	45	1	no	—
332	C₂×D₂₀	—	45	1	no	—
333	C₃×C₅²	C₂×D₃×D₄	1	4	yes	complemented
334	C₂³×C₃²	—	5	1	no	—
335	C₂³×C₃²	—	25	1	no	—
336	C₂²×C₃⋊D₃	—	5	1	no	—
337	C₂²×C₃⋊D₃	—	5	4	no	—
338	C₂²×C₃⋊D₃	—	10	4	no	—
339	C₂²×C₃⋊D₃	—	25	1	no	—
340	C₂²×C₃⋊D₃	—	25	4	no	—
341	C₂²×C₃⋊D₃	—	50	4	no	—
342	C₂²×C₃⋊D₃	D₅²	1	1	yes	characteristic
343	C₃²×D₄	—	25	4	no	—
344	C₂×C₃²×C₄	—	5	1	no	—
345	#638	—	25	4	no	—
346	#638	—	25	4	no	—
347	C₂×C₃⋊Dic₃	—	5	1	no	—
348	C₄⋊(C₃⋊D₃)	—	25	4	no	—
349	C₄×C₃⋊D₃	—	5	4	no	—
350	C₂²×C₃×C₅	—	2	8	no	—
351	C₂²×C₃×C₅	—	5	8	no	—
352	C₂²×C₃×C₅	—	10	8	no	—
353	C₂²×C₃×C₅	C₂×D₃×D₅	1	4	yes	—
354	C₂²×C₃×C₅	C₂×D₃×D₅	1	4	yes	—
355	C₂×D₁₅	—	3	8	no	—
356	C₂×D₁₅	—	6	8	no	—
357	C₂×D₁₅	—	15	8	no	—
358	C₂×D₁₅	—	15	8	no	—
359	C₂×D₁₅	—	30	16	no	—
360	C₂×D₁₅	—	30	32	no	—
361	C₂×D₁₅	—	30	8	no	—
362	C₂×D₁₅	—	30	8	no	—
363	C₂×C₅×D₃	—	3	16	no	—
364	C₂×C₅×D₃	—	3	16	no	—
365	C₂×C₅×D₃	—	3	8	no	—
366	C₂×C₅×D₃	—	3	8	no	—
367	C₂×C₅×D₃	—	6	16	no	—
368	C₂×C₅×D₃	—	6	32	no	—
369	C₂×C₅×D₃	—	15	8	no	—
370	C₂×C₅×D₃	—	30	32	no	—
371	C₂×C₅×D₃	—	30	8	no	—
372	C₂×C₃×D₅	—	2	8	no	—
373	C₂×C₃×D₅	—	5	8	no	—
374	C₂×C₃×D₅	—	5	8	no	—
375	C₂×C₃×D₅	—	10	16	no	—
376	C₂×C₃×D₅	—	10	32	no	—
377	C₂×C₃×D₅	—	10	8	no	—
378	C₂×C₃×D₅	—	10	8	no	—
379	C₂×C₃×D₅	C₂×D₃×D₅	1	8	yes	complemented
380	D₃×D₅	—	6	32	no	—
381	D₃×D₅	—	30	32	no	—
382	D₃×D₅	—	30	32	no	—
383	D₃×D₅	—	30	128	no	—
384	C₃×C₄×C₅	—	5	8	no	—
385	Dic₁₅	—	3	8	no	—
386	C₃×Dic₅	C₂×D₃×D₅	1	8	yes	complemented
387	C₅×Dic₃	—	15	8	no	—
388	C₂×C₅²	—	9	4	no	—
389	C₂×C₅²	D₄×C₃⋊D₃	1	2	yes	complemented
390	C₂×C₅²	C₂³×C₃⋊D₃	1	1	yes	characteristic
391	C₅⋊D₅	—	2	2	no	—
392	C₅⋊D₅	—	18	2	no	—
393	C₅×D₅	—	2	2	no	—
394	C₅×D₅	—	18	2	no	—
395	C₂³×D₃	—	15	4	no	—
396	C₂³×D₃	—	75	4	no	—
397	C₂×C₃×D₄	—	25	4	no	—
398	C₂×#67	—	75	4	no	—
399	C₂×#67	—	75	4	no	—
400	D₃×D₄	—	75	32	no	—
401	C₂×D₁₂	—	75	4	no	—
402	C₂×C₄×D₃	—	15	4	no	—
403	C₃²×C₅	—	2	2	no	—
404	C₃²×C₅	C₂²×D₂₀	1	1	yes	characteristic, complemented
405	C₃²×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic, complemented
406	C₂³×C₅	—	5	1	no	—
407	C₂³×C₅	—	9	1	no	—
408	C₂³×C₅	—	9	1	no	—
409	C₂³×C₅	—	18	2	no	—
410	C₂³×C₅	—	45	4	no	—
411	C₂³×C₅	—	45	1	no	—
412	C₂³×C₅	—	90	4	no	—
413	C₂²×D₅	—	5	1	no	—
414	C₂²×D₅	—	5	1	no	—
415	C₂²×D₅	—	9	1	no	—
416	C₂²×D₅	—	9	4	no	—
417	C₂²×D₅	—	10	2	no	—
418	C₂²×D₅	—	18	4	no	—
419	C₂²×D₅	—	45	4	no	—
420	C₂²×D₅	—	45	4	no	—
421	C₂²×D₅	—	45	1	no	—
422	C₂²×D₅	—	45	1	no	—
423	C₂²×D₅	—	90	4	no	—
424	C₂²×D₅	—	90	4	no	—
425	C₂²×D₅	—	90	16	no	—
426	C₂²×D₅	—	90	8	no	—
427	C₂²×D₅	—	90	2	no	—
428	C₂²×D₅	D₅×C₃⋊D₃	1	1	yes	characteristic, complemented
429	C₂×C₄×C₅	—	5	1	no	—
430	C₂×C₄×C₅	—	45	4	no	—
431	C₂×C₄×C₅	—	45	1	no	—
432	C₂²⋊D₅	—	5	4	no	—
433	C₂²⋊D₅	—	45	4	no	—
434	C₂²⋊D₅	—	45	4	no	—
435	C₂²⋊D₅	—	45	4	no	—
436	C₂×Dic₅	—	9	1	no	—
437	C₂×Dic₅	—	9	4	no	—
438	C₂×Dic₅	D₅×C₃⋊D₃	1	1	yes	characteristic, complemented
439	D₂₀	—	5	4	no	—
440	D₂₀	—	45	4	no	—
441	D₂₀	—	45	4	no	—
442	D₂₀	—	45	4	no	—
443	C₂²×C₃²	—	5	2	no	—
444	C₂²×C₃²	—	10	2	no	—
445	C₂²×C₃²	—	25	2	no	—
446	C₂²×C₃²	—	50	2	no	—
447	C₂²×C₃²	C₂×D₅²	1	1	yes	characteristic
448	C₂×C₃⋊D₃	—	5	2	no	—
449	C₂×C₃⋊D₃	—	10	2	no	—
450	C₂×C₃⋊D₃	—	10	8	no	—
451	C₂×C₃⋊D₃	—	25	2	no	—
452	C₂×C₃⋊D₃	—	50	2	no	—
453	C₂×C₃⋊D₃	—	50	8	no	—
454	C₂×C₃⋊D₃	#6038	1	4	yes	direct product factor
455	C₂×C₃⋊D₃	C₂×D₅²	1	2	yes	—
456	C₃²×C₄	—	5	2	no	—
457	C₃⋊Dic₃	—	5	2	no	—
458	C₂²×D₄	—	225	1	no	Sylow
459	C₂×C₃×C₅	—	2	8	no	—
460	C₂×C₃×C₅	—	2	16	no	—
461	C₂×C₃×C₅	—	10	8	no	—
462	C₂×C₃×C₅	D₃×D₂₀	1	8	yes	complemented
463	C₂×C₃×C₅	D₃×C₂²⋊D₅	1	8	yes	complemented
464	C₂×C₃×C₅	C₂²×D₃×D₅	1	4	yes	—
465	C₂×C₃×C₅	C₂²×D₃×D₅	1	4	yes	—
466	D₁₅	—	6	8	no	—
467	D₁₅	—	30	32	no	—
468	D₁₅	—	30	8	no	—
469	D₁₅	—	30	8	no	—
470	C₃×D₅	—	2	8	no	—
471	C₃×D₅	—	10	32	no	—
472	C₃×D₅	—	10	8	no	—
473	C₃×D₅	—	10	8	no	—
474	C₅×D₃	—	3	16	no	—
475	C₅×D₃	—	3	16	no	—
476	C₅×D₃	—	6	32	no	—
477	C₅×D₃	—	30	8	no	—
478	C₅²	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
479	C₂³×C₃	—	5	4	no	—
480	C₂³×C₃	—	25	4	no	—
481	C₂²×D₃	—	3	4	no	—
482	C₂²×D₃	—	15	16	no	—
483	C₂²×D₃	—	15	4	no	—
484	C₂²×D₃	—	30	16	no	—
485	C₂²×D₃	—	75	16	no	—
486	C₂²×D₃	—	75	4	no	—
487	C₂²×D₃	—	150	16	no	—
488	C₃×D₄	—	25	16	no	—
489	C₂×C₃×C₄	—	5	4	no	—
490	#67	—	75	16	no	—
491	#67	—	75	16	no	—
492	C₂×Dic₃	—	15	4	no	—
493	D₁₂	—	75	16	no	—
494	C₄×D₃	—	15	16	no	—
495	C₂²×C₅	—	2	2	no	—
496	C₂²×C₅	—	5	2	no	—
497	C₂²×C₅	—	9	2	no	—
498	C₂²×C₅	—	9	2	no	—
499	C₂²×C₅	—	9	4	no	—
500	C₂²×C₅	—	9	4	no	—
501	C₂²×C₅	—	10	2	no	—
502	C₂²×C₅	—	18	8	no	—
503	C₂²×C₅	—	18	4	no	—
504	C₂²×C₅	—	45	2	no	—
505	C₂²×C₅	—	90	8	no	—
506	C₂²×C₅	—	90	2	no	—
507	C₂²×C₅	C₂×D₅×C₃⋊D₃	1	1	yes	characteristic
508	C₂²×C₅	C₂×D₅×C₃⋊D₃	1	1	yes	characteristic
509	C₂×D₅	—	2	2	no	—
510	C₂×D₅	—	5	2	no	—
511	C₂×D₅	—	5	2	no	—
512	C₂×D₅	—	9	2	no	—
513	C₂×D₅	—	10	4	no	—
514	C₂×D₅	—	10	8	no	—
515	C₂×D₅	—	10	2	no	—
516	C₂×D₅	—	10	2	no	—
517	C₂×D₅	—	18	8	no	—
518	C₂×D₅	—	18	2	no	—
519	C₂×D₅	—	45	2	no	—
520	C₂×D₅	—	45	2	no	—
521	C₂×D₅	—	90	8	no	—
522	C₂×D₅	—	90	8	no	—
523	C₂×D₅	—	90	32	no	—
524	C₂×D₅	—	90	8	no	—
525	C₂×D₅	—	90	2	no	—
526	C₂×D₅	—	90	2	no	—
527	C₂×D₅	—	90	4	no	—
528	C₂×D₅	C₂×D₅×C₃⋊D₃	1	2	yes	complemented
529	C₄×C₅	—	5	2	no	—
530	C₄×C₅	—	45	2	no	—
531	Dic₅	—	9	2	no	—
532	Dic₅	C₂×D₅×C₃⋊D₃	1	2	yes	complemented
533	C₂×C₃²	—	10	2	no	—
534	C₂×C₃²	—	50	2	no	—
535	C₂×C₃²	C₂×#6038	1	2	yes	complemented
536	C₂×C₃²	C₂²×D₅²	1	1	yes	characteristic
537	C₃⋊D₃	—	10	2	no	—
538	C₃⋊D₃	—	50	2	no	—
539	C₃⋊D₃	C₂×#6038	1	4	yes	direct product factor
540	C₂⁴	—	45	1	no	—
541	C₂⁴	—	225	1	no	—
542	C₂×D₄	—	25	1	no	—
543	C₂×D₄	—	225	1	no	—
544	C₂×D₄	—	225	8	no	—
545	C₂×D₄	—	225	1	no	—
546	C₂×D₄	—	225	1	no	—
547	C₂²×C₄	—	45	1	no	—
548	C₃×C₅	—	2	8	no	—
549	C₃×C₅	C₂×D₃×D₂₀	1	4	yes	complemented
550	C₃×C₅	C₂×D₃×C₂²⋊D₅	1	4	yes	complemented
551	C₂²×C₃	—	5	8	no	—
552	C₂²×C₃	—	10	8	no	—
553	C₂²×C₃	—	25	8	no	—
554	C₂²×C₃	—	50	8	no	—
555	C₂²×C₃	D₃×D₅²	1	4	yes	—
556	C₂×D₃	—	3	8	no	—
557	C₂×D₃	—	3	16	no	—
558	C₂×D₃	—	15	8	no	—
559	C₂×D₃	—	30	32	no	—
560	C₂×D₃	—	30	8	no	—
561	C₂×D₃	—	75	8	no	—
562	C₂×D₃	—	150	32	no	—
563	C₂×D₃	—	150	8	no	—
564	C₃×C₄	—	5	8	no	—
565	Dic₃	—	15	8	no	—
566	C₂×C₅	—	2	4	no	—
567	C₂×C₅	—	2	2	no	—
568	C₂×C₅	—	9	4	no	—
569	C₂×C₅	—	9	4	no	—
570	C₂×C₅	—	10	2	no	—
571	C₂×C₅	—	18	8	no	—
572	C₂×C₅	—	90	2	no	—
573	C₂×C₅	C₃⋊D₃×D₂₀	1	2	yes	complemented
574	C₂×C₅	C₃⋊D₃×C₂²⋊D₅	1	2	yes	complemented
575	C₂×C₅	C₂²×D₅×C₃⋊D₃	1	1	yes	characteristic
576	C₂×C₅	C₂²×D₅×C₃⋊D₃	1	1	yes	characteristic
577	D₅	—	2	2	no	—
578	D₅	—	10	8	no	—
579	D₅	—	10	2	no	—
580	D₅	—	10	2	no	—
581	D₅	—	18	2	no	—
582	D₅	—	90	8	no	—
583	D₅	—	90	2	no	—
584	D₅	—	90	2	no	—
585	C₃²	C₂²×#6038	1	1	yes	characteristic, complemented, Sylow
586	C₂³	—	5	1	no	—
587	C₂³	—	9	1	no	—
588	C₂³	—	25	1	no	—
589	C₂³	—	45	4	no	—
590	C₂³	—	45	1	no	—
591	C₂³	—	90	4	no	—
592	C₂³	—	450	4	no	—
593	C₂³	—	225	4	no	—
594	C₂³	—	225	1	no	—
595	D₄	—	25	4	no	—
596	D₄	—	225	4	no	—
597	D₄	—	225	4	no	—
598	D₄	—	225	4	no	—
599	C₂×C₄	—	5	1	no	—
600	C₂×C₄	—	45	4	no	—
601	C₂×C₄	—	45	1	no	—
602	C₂×C₃	—	10	8	no	—
603	C₂×C₃	—	50	8	no	—
604	C₂×C₃	D₃×#6038	1	8	yes	complemented
605	C₂×C₃	C₂×D₃×D₅²	1	4	yes	—
606	D₃	—	3	16	no	—
607	D₃	—	30	8	no	—
608	D₃	—	150	8	no	—
609	C₅	—	2	2	no	—
610	C₅	C₂×C₃⋊D₃×D₂₀	1	1	yes	characteristic, complemented
611	C₅	C₂×C₃⋊D₃×C₂²⋊D₅	1	1	yes	characteristic, complemented
612	C₂²	—	5	2	no	—
613	C₂²	—	9	4	no	—
614	C₂²	—	9	2	no	—
615	C₂²	—	10	2	no	—
616	C₂²	—	25	2	no	—
617	C₂²	—	45	2	no	—
618	C₂²	—	50	2	no	—
619	C₂²	—	90	8	no	—
620	C₂²	—	90	2	no	—
621	C₂²	—	450	8	no	—
622	C₂²	—	450	2	no	—
623	C₂²	—	225	2	no	—
624	C₂²	D₅²×C₃⋊D₃	1	1	yes	characteristic
625	C₄	—	5	2	no	—
626	C₄	—	45	2	no	—
627	C₃	C₂×D₃×#6038	1	4	yes	complemented
628	C₂	—	9	4	no	—
629	C₂	—	10	2	no	—
630	C₂	—	50	2	no	—
631	C₂	—	90	2	no	—
632	C₂	—	450	2	no	—
633	C₂	C₂×D₅²×C₃⋊D₃	1	1	yes	characteristic
634	C₂	C₃⋊D₃×#6038	1	2	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₅²×C₃⋊D₃
commutator, cosocle	C₂×C₃²×C₅²	C₂⁴
Frattini	C₂	C₂×D₅²×C₃⋊D₃
Fitting, socle	C₂²×C₃²×C₅²	C₂³
hypocenter	C₃²×C₅²	C₂²×D₄
LCS	G ▷ C₂×C₃²×C₅² ▷ C₃²×C₅²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#14268265	C₂	semidirect
2. C₂×#14268269	C₂	semidirect
3. C₂×#14268264	C₂	semidirect
4. C₂×C₃²×#6038	C₂	semidirect
5. C₃⋊D₃×#6038	C₂	direct (N × H)
7. C₂×C₅×C₃⋊D₃×Dic₅	C₂	semidirect
8. C₂²×C₅×D₅×C₃⋊D₃	C₂	semidirect
9. C₂²×C₃⋊D₃×C₅⋊D₅	C₂	semidirect
10. C₂²×C₃²×C₅×D₅	C₂²	semidirect
11. C₂²×C₃²×C₅⋊D₅	C₂²	semidirect
13. C₂²×C₅×C₃⋊D₁₅	C₂²	semidirect
14. C₂²×C₃⋊(C₃⋊(C₅⋊D₅))	C₂²	semidirect
16. C₂×C₃⋊D₃×C₅⋊D₅	C₂²	semidirect
18. C₂×C₅×D₅×C₃⋊D₃	C₂²	semidirect
19. C₂×C₅×C₃⋊Dic₁₅	C₂²	semidirect
20. C₂×C₃²×C₅×Dic₅	C₂²	semidirect
21. #14268269	C₂²	semidirect
22. #14268265	C₂²	semidirect
23. #14268264	C₂²	semidirect
24. C₅×C₃⋊D₃×Dic₅	C₂²	semidirect
25. C₃²×#6038	C₂²	semidirect
34. C₂×C₃×#6038	D₃	semidirect
38. C₂×C₃⋊(C₃⋊(C₅⋊D₅))	C₂³	semidirect
40. C₂×C₅×C₃⋊D₁₅	C₂³	semidirect
41. C₂×C₅²×C₃⋊D₃	D₄	semidirect
44. C₂×C₃²×C₅⋊D₅	C₂³	semidirect
46. C₂×C₃²×C₅×D₅	C₂³	semidirect
49. C₅×C₃⋊Dic₁₅	C₂³	semidirect
50. C₃²×C₅×Dic₅	C₂³	semidirect
56. C₂²×D₅×C₃⋊D₃	D₅	semidirect
67. C₂×C₃⋊D₃×Dic₅	D₅	semidirect
72. C₂²×C₃×C₅⋊D₅	C₂×D₃	semidirect
73. C₂²×C₃×C₅×D₅	C₂×D₃	semidirect
79. C₂×C₃×C₅×Dic₅	C₂×D₃	semidirect
84. C₃×#6038	C₂×D₃	semidirect
87. C₂×C₃²×C₅²	C₂×D₄	semidirect
91. C₅²×C₃⋊D₃	C₂×D₄	semidirect
101. C₂×#6038	C₃⋊D₃	direct (N × H)
106. C₂²×C₃⋊D₁₅	C₂×D₅	semidirect
116. C₂²×C₃²×D₅	C₂×D₅	semidirect
124. C₂×D₅×C₃⋊D₃	C₂×D₅	semidirect
127. C₂×C₃⋊Dic₁₅	C₂×D₅	semidirect
132. C₂×C₃²×Dic₅	C₂×D₅	semidirect
138. C₃⋊D₃×Dic₅	C₂×D₅	semidirect
147. C₂×C₃×C₅⋊D₅	C₂²×D₃	semidirect
149. C₂×C₃×C₅×D₅	C₂²×D₃	semidirect
153. C₃×C₅×Dic₅	C₂²×D₃	semidirect
172. C₃²×C₅²	C₂²×D₄	semidirect
177. C₂²×C₅⋊D₅	C₂×C₃⋊D₃	semidirect
181. C₂²×C₅×D₅	C₂×C₃⋊D₃	semidirect
184. C₂×C₅×Dic₅	C₂×C₃⋊D₃	semidirect
188. #6038	C₂×C₃⋊D₃	direct (N × H)
201. C₂×C₃⋊D₁₅	C₂²×D₅	semidirect
207. C₂×C₅×C₃⋊D₃	D₂₀	semidirect
208. C₂×C₅×C₃⋊D₃	C₂²⋊D₅	semidirect
218. C₂×C₃²×D₅	C₂²×D₅	semidirect
224. C₃⋊Dic₁₅	C₂²×D₅	semidirect
226. C₃²×Dic₅	C₂²×D₅	semidirect
229. C₂×C₃×C₅²	D₃×D₄	semidirect
258. C₂²×C₃×D₅	D₃×D₅	semidirect
274. C₂×C₃×Dic₅	D₃×D₅	semidirect
288. C₂×C₅⋊D₅	C₂²×C₃⋊D₃	semidirect
293. C₂×C₅×D₅	C₂²×C₃⋊D₃	semidirect
295. C₅×Dic₅	C₂²×C₃⋊D₃	semidirect
300. C₂×C₃²×C₅	C₂×D₂₀	semidirect
301. C₂×C₃²×C₅	C₂×C₂²⋊D₅	semidirect
310. C₅×C₃⋊D₃	C₂×D₂₀	semidirect
311. C₅×C₃⋊D₃	C₂×C₂²⋊D₅	semidirect
333. C₃×C₅²	C₂×D₃×D₄	semidirect
379. C₂×C₃×D₅	C₂×D₃×D₅	semidirect
386. C₃×Dic₅	C₂×D₃×D₅	semidirect
389. C₂×C₅²	D₄×C₃⋊D₃	semidirect
404. C₃²×C₅	C₂²×D₂₀	semidirect
405. C₃²×C₅	C₂²×C₂²⋊D₅	semidirect
428. C₂²×D₅	D₅×C₃⋊D₃	semidirect
438. C₂×Dic₅	D₅×C₃⋊D₃	semidirect
454. C₂×C₃⋊D₃	#6038	direct (N × H)
462. C₂×C₃×C₅	D₃×D₂₀	semidirect
463. C₂×C₃×C₅	D₃×C₂²⋊D₅	semidirect
478. C₅²	C₂×D₄×C₃⋊D₃	semidirect
528. C₂×D₅	C₂×D₅×C₃⋊D₃	semidirect
532. Dic₅	C₂×D₅×C₃⋊D₃	semidirect
535. C₂×C₃²	C₂×#6038	semidirect
539. C₃⋊D₃	C₂×#6038	direct (N × H)
549. C₃×C₅	C₂×D₃×D₂₀	semidirect
550. C₃×C₅	C₂×D₃×C₂²⋊D₅	semidirect
573. C₂×C₅	C₃⋊D₃×D₂₀	semidirect
574. C₂×C₅	C₃⋊D₃×C₂²⋊D₅	semidirect
585. C₃²	C₂²×#6038	semidirect
604. C₂×C₃	D₃×#6038	semidirect
610. C₅	C₂×C₃⋊D₃×D₂₀	semidirect
611. C₅	C₂×C₃⋊D₃×C₂²⋊D₅	semidirect
627. C₃	C₂×D₃×#6038	semidirect
634. C₂	C₃⋊D₃×#6038	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×#14268265	2
C₂×#14268269	2
C₂×#14268264	2
C₂×C₃²×#6038	2
C₃⋊D₃×#6038	2
C₂×D₃×#6038	3
C₂×C₅×C₃⋊D₃×Dic₅	2
C₂²×C₅×D₅×C₃⋊D₃	2
C₂²×C₃⋊D₃×C₅⋊D₅	2
C₂×C₃⋊D₃×C₂²⋊D₅	5
C₂×C₃⋊D₃×D₂₀	5

Subgroups — C2×C3⋊D3×#6038 #72259812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₃×#6038 #72259812