Subgroups — C₃×D₅×#450 #14423230

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65507	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65458	C₂	1	2	yes	maximal, complemented
7	C₃×#65335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65065	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
10	C₃×#65020	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#450	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×D₅	—	2	1	no	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
16	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×D₄×D₅	—	2	8	no	—
18	C₂×C₃×D₄×D₅	—	2	1	no	—
19	C₂×C₃×D₄×D₅	—	2	1	no	—
20	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
21	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
22	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×#4092	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#688	C₂²	1	2	yes	complemented
28	C₂×C₃×#687	C₂²	1	2	yes	complemented
29	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
30	C₃×D₅×SD₁₆	—	2	8	no	—
31	C₂×C₃×#677	C₂²	1	2	yes	complemented
32	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
33	C₃×#4043	C₂²	1	1	yes	characteristic, complemented
34	C₃×#4042	—	2	1	no	—
35	C₃×D₅×C₄⋊C₄	—	2	1	no	—
36	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
38	C₃×#4024	—	2	1	no	—
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×#3964	C₂²	1	2	yes	complemented
42	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
43	C₃×#3953	C₂²	1	2	yes	complemented
44	C₃×#3952	C₂²	1	2	yes	complemented
45	C₃×#3941	C₂²	1	2	yes	complemented
46	C₂×C₃×#450	—	5	1	no	maximal, Hall
47	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic
48	C₂×D₅×SD₁₆	C₂×C₃	1	2	yes	complemented
49	D₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
51	#65507	C₂×C₃	1	1	yes	characteristic, complemented
52	#65458	C₂×C₃	1	2	yes	complemented
53	#65335	C₂×C₃	1	1	yes	characteristic, complemented
54	#65065	C₂×C₃	1	2	yes	complemented
55	D₅×#102	C₂×C₃	1	2	yes	complemented
56	#65020	C₂×C₃	1	1	yes	characteristic, complemented
57	D₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂⁴×C₃×C₅	—	2	1	no	—
59	C₂³×C₃×D₅	—	2	8	no	—
60	C₂³×C₃×D₅	—	2	1	no	—
61	C₂³×C₃×D₅	—	2	2	no	—
62	C₂³×C₃×D₅	—	2	2	no	—
63	C₂³×C₃×D₅	—	4	4	no	—
64	C₂³×C₃×D₅	—	4	4	no	—
65	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
66	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
67	C₂×C₃×C₅×D₄	—	2	4	no	—
68	C₂×C₃×C₅×D₄	—	2	1	no	—
69	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
72	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
73	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
74	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
75	C₃×Q₈×D₅	—	2	4	no	—
76	C₃×D₄×D₅	—	2	8	no	—
77	C₃×D₄×D₅	—	2	8	no	—
78	C₃×D₄×D₅	—	2	4	no	—
79	C₃×D₄×D₅	—	2	4	no	—
80	C₃×D₄×D₅	—	2	4	no	—
81	C₃×D₄×D₅	D₄	1	8	yes	—
82	C₂×C₃×D₂₀	—	2	1	no	—
83	C₂×C₃×D₂₀	—	2	4	no	—
84	C₂×C₃×D₂₀	C₂³	1	2	yes	—
85	C₂×C₃×C₄×D₅	—	2	4	no	—
86	C₂×C₃×C₄×D₅	—	2	1	no	—
87	C₂×C₃×C₄×D₅	—	2	1	no	—
88	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
92	C₂×C₃×Dic₁₀	—	2	1	no	—
93	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
94	C₃×C₅×SD₁₆	—	2	4	no	—
95	C₂×C₃×C₅×C₈	C₂³	1	2	yes	complemented
96	C₃×C₅×C₄⋊C₄	—	2	1	no	—
97	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
98	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₃×C₂²⋊Dic₅	—	2	1	no	—
100	C₃×#688	—	2	4	no	—
101	C₃×#687	—	2	4	no	—
102	C₃×#685	—	2	1	no	—
103	C₃×#685	—	2	1	no	—
104	C₃×C₄⋊Dic₅	—	2	1	no	—
105	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
106	C₃×#683	—	2	1	no	—
107	C₃×#683	—	2	1	no	—
108	C₃×#683	—	2	1	no	—
109	C₂×C₃×#168	C₂³	1	2	yes	complemented
110	C₃×#677	—	2	4	no	—
111	C₃×C₈×D₅	—	2	4	no	—
112	C₂³×C₃×D₄	—	5	1	no	—
113	C₂²×C₃×SD₁₆	—	5	2	no	—
114	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
115	C₃×#450	—	5	1	no	—
116	C₃×#450	—	5	2	no	—
117	C₃×#450	—	5	1	no	—
118	C₃×#450	—	5	2	no	—
119	C₃×#450	—	5	1	no	—
120	C₃×#450	D₅	1	1	yes	characteristic, direct product factor
121	C₂×C₃×#102	—	5	2	no	—
122	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
123	C₂⁴×D₅	—	2	1	no	—
124	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₂²⋊D₅	—	2	1	no	—
126	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×D₄×D₅	—	2	8	no	—
128	C₂×D₄×D₅	—	2	1	no	—
129	C₂×D₄×D₅	—	2	1	no	—
130	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
131	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
132	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
133	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
135	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
136	#4092	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂×#688	C₂²×C₃	1	2	yes	complemented
138	C₂×#687	C₂²×C₃	1	2	yes	complemented
139	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
140	D₅×SD₁₆	—	2	8	no	—
141	C₂×#677	C₂²×C₃	1	2	yes	complemented
142	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
143	#4043	C₂²×C₃	1	1	yes	characteristic, complemented
144	#4042	—	2	1	no	—
145	D₅×C₄⋊C₄	—	2	1	no	—
146	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
147	D₅×C₂²⋊C₄	—	2	1	no	—
148	#4024	—	2	1	no	—
149	C₅×#102	C₂²×C₃	1	2	yes	complemented
150	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
151	#3964	C₂²×C₃	1	2	yes	complemented
152	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
153	#3953	C₂²×C₃	1	2	yes	complemented
154	#3952	C₂²×C₃	1	2	yes	complemented
155	#3941	C₂²×C₃	1	2	yes	complemented
156	C₂×#450	—	5	1	no	Sylow
157	C₂³×C₃×C₅	—	2	4	no	—
158	C₂³×C₃×C₅	—	2	2	no	—
159	C₂³×C₃×C₅	—	4	2	no	—
160	C₂³×C₃×C₅	—	4	2	no	—
161	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₃×D₅	—	2	2	no	—
163	C₂²×C₃×D₅	—	2	2	no	—
164	C₂²×C₃×D₅	—	2	4	no	—
165	C₂²×C₃×D₅	—	2	8	no	—
166	C₂²×C₃×D₅	—	2	2	no	—
167	C₂²×C₃×D₅	—	2	8	no	—
168	C₂²×C₃×D₅	—	4	4	no	—
169	C₂²×C₃×D₅	—	4	32	no	—
170	C₂²×C₃×D₅	—	4	2	no	—
171	C₂²×C₃×D₅	—	4	2	no	—
172	C₂²×C₃×D₅	—	4	4	no	—
173	C₂²×C₃×D₅	—	4	4	no	—
174	C₂²×C₃×D₅	—	4	4	no	—
175	C₂²×C₃×D₅	SD₁₆	1	4	yes	complemented
176	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
178	C₃×C₅×Q₈	—	2	2	no	—
179	C₃×C₅×D₄	—	2	4	no	—
180	C₃×C₅×D₄	—	2	2	no	—
181	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
182	C₂×C₃×C₄×C₅	—	2	2	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₃×C₂²⋊D₅	—	2	8	no	—
188	C₃×C₂²⋊D₅	—	2	8	no	—
189	C₂×C₃×Dic₅	—	2	2	no	—
190	C₂×C₃×Dic₅	—	2	1	no	—
191	C₂×C₃×Dic₅	—	2	1	no	—
192	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
193	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
194	C₃×D₂₀	—	2	4	no	—
195	C₃×D₂₀	—	2	2	no	—
196	C₃×D₂₀	C₂×D₄	1	4	yes	—
197	C₃×C₄×D₅	—	2	2	no	—
198	C₃×C₄×D₅	—	2	2	no	—
199	C₃×C₄×D₅	—	2	2	no	—
200	C₃×C₄×D₅	—	4	2	no	—
201	C₃×C₄×D₅	—	4	2	no	—
202	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
203	C₃×Dic₁₀	—	2	2	no	—
204	C₃×Dic₁₀	—	4	2	no	—
205	C₃×C₅×C₈	—	2	2	no	—
206	C₃×#168	—	2	2	no	—
207	C₂⁵×C₃	—	10	1	no	—
208	C₂²×C₃×Q₈	—	5	1	no	—
209	C₂²×C₃×D₄	—	5	2	no	—
210	C₂²×C₃×D₄	—	5	2	no	—
211	C₂²×C₃×D₄	—	5	1	no	—
212	C₂²×C₃×D₄	—	10	1	no	—
213	C₂²×C₃×D₄	—	10	1	no	—
214	C₂²×C₃×D₄	—	10	1	no	—
215	C₂²×C₃×D₄	—	10	8	no	—
216	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
217	C₂³×C₃×C₄	—	5	1	no	—
218	C₂×C₃×SD₁₆	—	5	2	no	—
219	C₂×C₃×SD₁₆	—	5	2	no	—
220	C₂×C₃×SD₁₆	—	5	2	no	—
221	C₂×C₃×SD₁₆	—	10	8	no	—
222	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
223	C₂²×C₃×C₈	—	5	2	no	—
224	C₃×C₂²⋊Q₈	—	5	1	no	—
225	C₃×C₂²⋊Q₈	—	5	1	no	—
226	C₃×C₂²⋊Q₈	—	5	1	no	—
227	C₃×C₂²⋊Q₈	—	10	1	no	—
228	C₃×C₂²⋊Q₈	—	10	1	no	—
229	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
230	C₂×C₃×C₄⋊C₄	—	5	1	no	—
231	C₂×C₃×C₄⋊C₄	—	10	1	no	—
232	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
233	C₃×#102	—	5	2	no	—
234	C₃×#102	—	5	2	no	—
235	C₃×#102	—	5	2	no	—
236	C₃×#102	C₂×D₅	1	2	yes	complemented
237	C₃×C₂²⋊C₈	—	5	1	no	—
238	C₃×C₂²⋊C₈	—	5	2	no	—
239	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
240	C₂⁴×C₅	—	2	1	no	—
241	C₂³×D₅	—	2	8	no	—
242	C₂³×D₅	—	2	1	no	—
243	C₂³×D₅	—	2	2	no	—
244	C₂³×D₅	—	2	2	no	—
245	C₂³×D₅	—	4	4	no	—
246	C₂³×D₅	—	4	4	no	—
247	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
248	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
249	C₂×C₅×D₄	—	2	4	no	—
250	C₂×C₅×D₄	—	2	1	no	—
251	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₂²⋊D₅	—	2	8	no	—
254	C₂×C₂²⋊D₅	—	2	2	no	—
255	C₂×C₂²⋊D₅	—	2	2	no	—
256	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
257	Q₈×D₅	—	2	4	no	—
258	D₄×D₅	—	2	8	no	—
259	D₄×D₅	—	2	8	no	—
260	D₄×D₅	—	2	4	no	—
261	D₄×D₅	—	2	4	no	—
262	D₄×D₅	—	2	4	no	—
263	D₄×D₅	C₃×D₄	1	8	yes	—
264	C₂×D₂₀	—	2	1	no	—
265	C₂×D₂₀	—	2	4	no	—
266	C₂×D₂₀	C₂³×C₃	1	2	yes	—
267	C₂×C₄×D₅	—	2	4	no	—
268	C₂×C₄×D₅	—	2	1	no	—
269	C₂×C₄×D₅	—	2	1	no	—
270	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
271	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
272	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
274	C₂×Dic₁₀	—	2	1	no	—
275	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic, complemented
276	C₅×SD₁₆	—	2	4	no	—
277	C₂×C₅×C₈	C₂³×C₃	1	2	yes	complemented
278	C₅×C₄⋊C₄	—	2	1	no	—
279	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
280	C₅×C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊Dic₅	—	2	1	no	—
282	#688	—	2	4	no	—
283	#687	—	2	4	no	—
284	#685	—	2	1	no	—
285	#685	—	2	1	no	—
286	C₄⋊Dic₅	—	2	1	no	—
287	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic, complemented
288	#683	—	2	1	no	—
289	#683	—	2	1	no	—
290	#683	—	2	1	no	—
291	C₂×#168	C₂³×C₃	1	2	yes	complemented
292	#677	—	2	4	no	—
293	C₈×D₅	—	2	4	no	—
294	C₂³×D₄	—	5	1	no	—
295	C₂²×SD₁₆	—	5	2	no	—
296	C₂×C₂²⋊Q₈	—	5	1	no	—
297	#450	—	5	1	no	—
298	#450	—	5	2	no	—
299	#450	—	5	1	no	—
300	#450	—	5	2	no	—
301	#450	—	5	1	no	—
302	#450	C₃×D₅	1	1	yes	characteristic, direct product factor
303	C₂×#102	—	5	2	no	—
304	C₂×C₂²⋊C₈	—	5	1	no	—
305	C₂²×C₃×C₅	—	2	1	no	—
306	C₂²×C₃×C₅	—	2	1	no	—
307	C₂²×C₃×C₅	—	2	4	no	—
308	C₂²×C₃×C₅	—	4	8	no	—
309	C₂²×C₃×C₅	—	4	2	no	—
310	C₂²×C₃×C₅	—	4	2	no	—
311	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	complemented
312	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₃×D₅	—	2	1	no	—
314	C₂×C₃×D₅	—	2	1	no	—
315	C₂×C₃×D₅	—	2	8	no	—
316	C₂×C₃×D₅	—	2	4	no	—
317	C₂×C₃×D₅	—	4	16	no	—
318	C₂×C₃×D₅	—	4	8	no	—
319	C₂×C₃×D₅	—	4	2	no	—
320	C₂×C₃×D₅	—	4	2	no	—
321	C₂×C₃×D₅	—	4	16	no	—
322	C₂×C₃×D₅	#120	1	2	yes	—
323	C₂×C₃×D₅	C₂×SD₁₆	1	2	yes	—
324	C₂×C₃×D₅	C₂×SD₁₆	1	2	yes	complemented
325	C₂×C₃×D₅	AGL(1,ℤ/8)	1	2	yes	—
326	C₃×C₄×C₅	—	2	1	no	—
327	C₃×C₄×C₅	—	4	1	no	—
328	C₃×C₄×C₅	—	4	1	no	—
329	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
330	C₃×Dic₅	—	2	1	no	—
331	C₃×Dic₅	—	4	1	no	—
332	C₃×Dic₅	—	4	1	no	—
333	C₃×Dic₅	#120	1	2	yes	—
334	C₂⁴×C₃	—	2	1	no	—
335	C₂⁴×C₃	—	5	1	no	—
336	C₂⁴×C₃	—	10	2	no	—
337	C₂⁴×C₃	—	10	2	no	—
338	C₂⁴×C₃	—	10	8	no	—
339	C₂⁴×C₃	—	10	1	no	—
340	C₂⁴×C₃	—	20	4	no	—
341	C₂⁴×C₃	—	20	4	no	—
342	C₂×C₃×Q₈	—	5	1	no	—
343	C₂×C₃×Q₈	—	10	1	no	—
344	C₂×C₃×Q₈	—	10	4	no	—
345	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	2	1	no	—
348	C₂×C₃×D₄	—	5	8	no	—
349	C₂×C₃×D₄	—	5	2	no	—
350	C₂×C₃×D₄	—	10	4	no	—
351	C₂×C₃×D₄	—	10	4	no	—
352	C₂×C₃×D₄	—	10	2	no	—
353	C₂×C₃×D₄	—	10	2	no	—
354	C₂×C₃×D₄	—	10	4	no	—
355	C₂×C₃×D₄	—	10	8	no	—
356	C₂×C₃×D₄	—	10	8	no	—
357	C₂×C₃×D₄	—	10	8	no	—
358	C₂×C₃×D₄	—	10	4	no	—
359	C₂×C₃×D₄	—	10	1	no	—
360	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
361	C₂²×C₃×C₄	—	5	1	no	—
362	C₂²×C₃×C₄	—	5	1	no	—
363	C₂²×C₃×C₄	—	5	1	no	—
364	C₂²×C₃×C₄	—	5	1	no	—
365	C₂²×C₃×C₄	—	5	1	no	—
366	C₂²×C₃×C₄	—	10	4	no	—
367	C₂²×C₃×C₄	—	10	1	no	—
368	C₂²×C₃×C₄	—	10	1	no	—
369	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
370	C₃×SD₁₆	—	2	4	no	—
371	C₃×SD₁₆	—	10	4	no	—
372	C₃×SD₁₆	—	10	4	no	—
373	C₃×SD₁₆	—	10	4	no	—
374	C₂×C₃×C₈	—	5	2	no	—
375	C₂×C₃×C₈	—	10	4	no	—
376	C₂×C₃×C₈	C₂²×D₅	1	2	yes	complemented
377	C₃×C₄⋊C₄	—	2	1	no	—
378	C₃×C₄⋊C₄	—	5	1	no	—
379	C₃×C₄⋊C₄	—	10	1	no	—
380	C₃×C₄⋊C₄	—	10	1	no	—
381	C₃×C₄⋊C₄	—	10	1	no	—
382	C₃×C₄⋊C₄	—	10	1	no	—
383	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
384	C₃×C₂²⋊C₄	—	2	1	no	—
385	C₃×C₂²⋊C₄	—	10	1	no	—
386	C₃×C₂²⋊C₄	—	10	1	no	—
387	C₃×C₂²⋊C₄	—	10	1	no	—
388	C₂³×C₅	—	2	4	no	—
389	C₂³×C₅	—	2	2	no	—
390	C₂³×C₅	—	4	2	no	—
391	C₂³×C₅	—	4	2	no	—
392	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
393	C₂²×D₅	—	2	2	no	—
394	C₂²×D₅	—	2	2	no	—
395	C₂²×D₅	—	2	4	no	—
396	C₂²×D₅	—	2	8	no	—
397	C₂²×D₅	—	2	2	no	—
398	C₂²×D₅	—	2	8	no	—
399	C₂²×D₅	—	4	4	no	—
400	C₂²×D₅	—	4	32	no	—
401	C₂²×D₅	—	4	2	no	—
402	C₂²×D₅	—	4	2	no	—
403	C₂²×D₅	—	4	4	no	—
404	C₂²×D₅	—	4	4	no	—
405	C₂²×D₅	—	4	4	no	—
406	C₂²×D₅	C₃×SD₁₆	1	4	yes	complemented
407	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
408	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
409	C₅×Q₈	—	2	2	no	—
410	C₅×D₄	—	2	4	no	—
411	C₅×D₄	—	2	2	no	—
412	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
413	C₂×C₄×C₅	—	2	2	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
418	C₂²⋊D₅	—	2	8	no	—
419	C₂²⋊D₅	—	2	8	no	—
420	C₂×Dic₅	—	2	2	no	—
421	C₂×Dic₅	—	2	1	no	—
422	C₂×Dic₅	—	2	1	no	—
423	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
424	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
425	D₂₀	—	2	4	no	—
426	D₂₀	—	2	2	no	—
427	D₂₀	C₂×C₃×D₄	1	4	yes	—
428	C₄×D₅	—	2	2	no	—
429	C₄×D₅	—	2	2	no	—
430	C₄×D₅	—	2	2	no	—
431	C₄×D₅	—	4	2	no	—
432	C₄×D₅	—	4	2	no	—
433	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
434	Dic₁₀	—	2	2	no	—
435	Dic₁₀	—	4	2	no	—
436	C₅×C₈	—	2	2	no	—
437	#168	—	2	2	no	—
438	C₂⁵	—	10	1	no	—
439	C₂²×Q₈	—	5	1	no	—
440	C₂²×D₄	—	5	2	no	—
441	C₂²×D₄	—	5	2	no	—
442	C₂²×D₄	—	5	1	no	—
443	C₂²×D₄	—	10	1	no	—
444	C₂²×D₄	—	10	1	no	—
445	C₂²×D₄	—	10	1	no	—
446	C₂²×D₄	—	10	8	no	—
447	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
448	C₂³×C₄	—	5	1	no	—
449	C₂×SD₁₆	—	5	2	no	—
450	C₂×SD₁₆	—	5	2	no	—
451	C₂×SD₁₆	—	5	2	no	—
452	C₂×SD₁₆	—	10	8	no	—
453	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
454	C₂²×C₈	—	5	2	no	—
455	C₂²⋊Q₈	—	5	1	no	—
456	C₂²⋊Q₈	—	5	1	no	—
457	C₂²⋊Q₈	—	5	1	no	—
458	C₂²⋊Q₈	—	10	1	no	—
459	C₂²⋊Q₈	—	10	1	no	—
460	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₄	—	5	1	no	—
462	C₂×C₄⋊C₄	—	10	1	no	—
463	C₂×C₂²⋊C₄	—	10	1	no	—
464	#102	—	5	2	no	—
465	#102	—	5	2	no	—
466	#102	—	5	2	no	—
467	#102	C₂×C₃×D₅	1	2	yes	complemented
468	C₂²⋊C₈	—	5	1	no	—
469	C₂²⋊C₈	—	5	2	no	—
470	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
471	C₂×C₃×C₅	—	2	2	no	—
472	C₂×C₃×C₅	—	4	4	no	—
473	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
474	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
475	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
476	C₃×D₅	—	2	2	no	—
477	C₃×D₅	—	4	4	no	—
478	C₃×D₅	#450	1	4	yes	direct product factor
479	C₂³×C₃	—	2	4	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	4	2	no	—
482	C₂³×C₃	—	4	2	no	—
483	C₂³×C₃	—	5	1	no	—
484	C₂³×C₃	—	5	1	no	—
485	C₂³×C₃	—	5	4	no	—
486	C₂³×C₃	—	10	2	no	—
487	C₂³×C₃	—	10	2	no	—
488	C₂³×C₃	—	10	8	no	—
489	C₂³×C₃	—	10	4	no	—
490	C₂³×C₃	—	10	8	no	—
491	C₂³×C₃	—	10	2	no	—
492	C₂³×C₃	—	20	2	no	—
493	C₂³×C₃	—	20	4	no	—
494	C₂³×C₃	—	20	4	no	—
495	C₂³×C₃	—	20	4	no	—
496	C₂³×C₃	—	20	32	no	—
497	C₂³×C₃	—	20	4	no	—
498	C₂³×C₃	—	20	2	no	—
499	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
500	C₃×Q₈	—	2	2	no	—
501	C₃×Q₈	—	10	2	no	—
502	C₃×Q₈	—	20	2	no	—
503	C₃×D₄	—	2	4	no	—
504	C₃×D₄	—	2	2	no	—
505	C₃×D₄	—	5	4	no	—
506	C₃×D₄	—	10	4	no	—
507	C₃×D₄	—	10	8	no	—
508	C₃×D₄	—	10	8	no	—
509	C₃×D₄	—	10	2	no	—
510	C₃×D₄	D₄×D₅	1	4	yes	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	5	1	no	—
515	C₂×C₃×C₄	—	5	4	no	—
516	C₂×C₃×C₄	—	5	1	no	—
517	C₂×C₃×C₄	—	10	2	no	—
518	C₂×C₃×C₄	—	10	2	no	—
519	C₂×C₃×C₄	—	10	2	no	—
520	C₂×C₃×C₄	—	10	2	no	—
521	C₂×C₃×C₄	—	10	1	no	—
522	C₂×C₃×C₄	—	10	1	no	—
523	C₂×C₃×C₄	—	20	2	no	—
524	C₂×C₃×C₄	—	20	2	no	—
525	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
527	C₃×C₈	—	2	2	no	—
528	C₃×C₈	—	10	2	no	—
529	C₂²×C₅	—	2	1	no	—
530	C₂²×C₅	—	2	1	no	—
531	C₂²×C₅	—	2	4	no	—
532	C₂²×C₅	—	4	8	no	—
533	C₂²×C₅	—	4	2	no	—
534	C₂²×C₅	—	4	2	no	—
535	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	complemented
536	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
537	C₂×D₅	—	2	1	no	—
538	C₂×D₅	—	2	1	no	—
539	C₂×D₅	—	2	8	no	—
540	C₂×D₅	—	2	4	no	—
541	C₂×D₅	—	4	16	no	—
542	C₂×D₅	—	4	8	no	—
543	C₂×D₅	—	4	2	no	—
544	C₂×D₅	—	4	2	no	—
545	C₂×D₅	—	4	16	no	—
546	C₂×D₅	C₃×#120	1	2	yes	—
547	C₂×D₅	C₂×C₃×SD₁₆	1	2	yes	—
548	C₂×D₅	C₂×C₃×SD₁₆	1	2	yes	complemented
549	C₂×D₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
550	C₄×C₅	—	2	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
554	Dic₅	—	2	1	no	—
555	Dic₅	—	4	1	no	—
556	Dic₅	—	4	1	no	—
557	Dic₅	C₃×#120	1	2	yes	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	5	1	no	—
560	C₂⁴	—	10	2	no	—
561	C₂⁴	—	10	2	no	—
562	C₂⁴	—	10	8	no	—
563	C₂⁴	—	10	1	no	—
564	C₂⁴	—	20	4	no	—
565	C₂⁴	—	20	4	no	—
566	C₂×Q₈	—	5	1	no	—
567	C₂×Q₈	—	10	1	no	—
568	C₂×Q₈	—	10	4	no	—
569	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	5	8	no	—
573	C₂×D₄	—	5	2	no	—
574	C₂×D₄	—	10	4	no	—
575	C₂×D₄	—	10	4	no	—
576	C₂×D₄	—	10	2	no	—
577	C₂×D₄	—	10	2	no	—
578	C₂×D₄	—	10	4	no	—
579	C₂×D₄	—	10	8	no	—
580	C₂×D₄	—	10	8	no	—
581	C₂×D₄	—	10	8	no	—
582	C₂×D₄	—	10	4	no	—
583	C₂×D₄	—	10	1	no	—
584	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
585	C₂²×C₄	—	5	1	no	—
586	C₂²×C₄	—	5	1	no	—
587	C₂²×C₄	—	5	1	no	—
588	C₂²×C₄	—	5	1	no	—
589	C₂²×C₄	—	5	1	no	—
590	C₂²×C₄	—	10	4	no	—
591	C₂²×C₄	—	10	1	no	—
592	C₂²×C₄	—	10	1	no	—
593	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
594	SD₁₆	—	2	4	no	—
595	SD₁₆	—	10	4	no	—
596	SD₁₆	—	10	4	no	—
597	SD₁₆	—	10	4	no	—
598	C₂×C₈	—	5	2	no	—
599	C₂×C₈	—	10	4	no	—
600	C₂×C₈	C₂²×C₃×D₅	1	2	yes	complemented
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	5	1	no	—
603	C₄⋊C₄	—	10	1	no	—
604	C₄⋊C₄	—	10	1	no	—
605	C₄⋊C₄	—	10	1	no	—
606	C₄⋊C₄	—	10	1	no	—
607	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	10	1	no	—
610	C₂²⋊C₄	—	10	1	no	—
611	C₂²⋊C₄	—	10	1	no	—
612	C₃×C₅	C₂×#450	1	1	yes	characteristic, complemented, Hall
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	4	no	—
616	C₂²×C₃	—	4	8	no	—
617	C₂²×C₃	—	4	2	no	—
618	C₂²×C₃	—	4	2	no	—
619	C₂²×C₃	—	5	2	no	—
620	C₂²×C₃	—	5	2	no	—
621	C₂²×C₃	—	5	2	no	—
622	C₂²×C₃	—	5	2	no	—
623	C₂²×C₃	—	10	8	no	—
624	C₂²×C₃	—	10	1	no	—
625	C₂²×C₃	—	10	1	no	—
626	C₂²×C₃	—	10	4	no	—
627	C₂²×C₃	—	20	8	no	—
628	C₂²×C₃	—	20	16	no	—
629	C₂²×C₃	—	20	16	no	—
630	C₂²×C₃	—	20	2	no	—
631	C₂²×C₃	—	20	2	no	—
632	C₂²×C₃	D₅×SD₁₆	1	2	yes	complemented
633	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	4	1	no	—
636	C₃×C₄	—	4	1	no	—
637	C₃×C₄	—	5	2	no	—
638	C₃×C₄	—	10	1	no	—
639	C₃×C₄	—	20	1	no	—
640	C₃×C₄	—	20	1	no	—
641	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
642	C₂×C₅	—	2	2	no	—
643	C₂×C₅	—	4	4	no	—
644	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
645	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
646	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
647	D₅	—	2	2	no	—
648	D₅	—	4	4	no	—
649	D₅	C₃×#450	1	4	yes	direct product factor
650	C₂³	—	2	4	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	5	1	no	—
655	C₂³	—	5	1	no	—
656	C₂³	—	5	4	no	—
657	C₂³	—	10	2	no	—
658	C₂³	—	10	2	no	—
659	C₂³	—	10	8	no	—
660	C₂³	—	10	4	no	—
661	C₂³	—	10	8	no	—
662	C₂³	—	10	2	no	—
663	C₂³	—	20	2	no	—
664	C₂³	—	20	4	no	—
665	C₂³	—	20	4	no	—
666	C₂³	—	20	4	no	—
667	C₂³	—	20	32	no	—
668	C₂³	—	20	4	no	—
669	C₂³	—	20	2	no	—
670	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	10	2	no	—
673	Q₈	—	20	2	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	2	no	—
676	D₄	—	5	4	no	—
677	D₄	—	10	4	no	—
678	D₄	—	10	8	no	—
679	D₄	—	10	8	no	—
680	D₄	—	10	2	no	—
681	D₄	C₃×D₄×D₅	1	4	yes	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	5	1	no	—
686	C₂×C₄	—	5	4	no	—
687	C₂×C₄	—	5	1	no	—
688	C₂×C₄	—	10	2	no	—
689	C₂×C₄	—	10	2	no	—
690	C₂×C₄	—	10	2	no	—
691	C₂×C₄	—	10	2	no	—
692	C₂×C₄	—	10	1	no	—
693	C₂×C₄	—	10	1	no	—
694	C₂×C₄	—	20	2	no	—
695	C₂×C₄	—	20	2	no	—
696	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
697	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	10	2	no	—
700	C₂×C₃	—	2	2	no	—
701	C₂×C₃	—	4	4	no	—
702	C₂×C₃	—	5	4	no	—
703	C₂×C₃	—	10	2	no	—
704	C₂×C₃	—	20	4	no	—
705	C₂×C₃	D₅×#120	1	1	yes	characteristic
706	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
707	C₂×C₃	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
708	C₅	C₂×C₃×#450	1	1	yes	characteristic, complemented, Sylow
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	4	8	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	5	2	no	—
716	C₂²	—	5	2	no	—
717	C₂²	—	5	2	no	—
718	C₂²	—	5	2	no	—
719	C₂²	—	10	8	no	—
720	C₂²	—	10	1	no	—
721	C₂²	—	10	1	no	—
722	C₂²	—	10	4	no	—
723	C₂²	—	20	8	no	—
724	C₂²	—	20	16	no	—
725	C₂²	—	20	16	no	—
726	C₂²	—	20	2	no	—
727	C₂²	—	20	2	no	—
728	C₂²	C₃×D₅×SD₁₆	1	2	yes	complemented
729	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	5	2	no	—
734	C₄	—	10	1	no	—
735	C₄	—	20	1	no	—
736	C₄	—	20	1	no	—
737	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
738	C₃	D₅×#450	1	1	yes	characteristic, direct product factor, Sylow
739	C₂	—	2	2	no	—
740	C₂	—	4	4	no	—
741	C₂	—	5	4	no	—
742	C₂	—	10	2	no	—
743	C₂	—	20	4	no	—
744	C₂	C₃×D₅×#120	1	1	yes	characteristic
745	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
746	C₂	C₃×D₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#450	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₄×D₅	C₂
hypercenter	C₃×#450	D₅
hypocenter	C₅	C₂×C₃×#450
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#450

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×D₅×SD₁₆	C₂	semidirect
3. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
4. C₃×C₅×#450	C₂	semidirect
5. C₃×#65507	C₂	semidirect
6. C₃×#65458	C₂	semidirect
7. C₃×#65335	C₂	semidirect
8. C₃×#65065	C₂	semidirect
9. C₃×D₅×#102	C₂	semidirect
10. C₃×#65020	C₂	semidirect
11. C₃×D₅×C₂²⋊C₈	C₂	semidirect
12. D₅×#450	C₃	direct (N × H)
16. C₂×C₃×Q₈×D₅	C₂²	semidirect
24. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
25. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₃×#4092	C₂²	semidirect
27. C₂×C₃×#688	C₂²	semidirect
28. C₂×C₃×#687	C₂²	semidirect
29. C₃×#4070	C₂²	semidirect
31. C₂×C₃×#677	C₂²	semidirect
32. C₂×C₃×C₈×D₅	C₂²	semidirect
33. C₃×#4043	C₂²	semidirect
36. C₃×D₅×C₄⋊C₄	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
41. C₃×#3964	C₂²	semidirect
42. C₃×C₂²⋊#168	C₂²	semidirect
43. C₃×#3953	C₂²	semidirect
44. C₃×#3952	C₂²	semidirect
45. C₃×#3941	C₂²	semidirect
48. C₂×D₅×SD₁₆	C₂×C₃	semidirect
49. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
50. C₅×#450	C₂×C₃	semidirect
51. #65507	C₂×C₃	semidirect
52. #65458	C₂×C₃	semidirect
53. #65335	C₂×C₃	semidirect
54. #65065	C₂×C₃	semidirect
55. D₅×#102	C₂×C₃	semidirect
56. #65020	C₂×C₃	semidirect
57. D₅×C₂²⋊C₈	C₂×C₃	semidirect
66. C₂×C₃×C₅×Q₈	C₂³	semidirect
93. C₂×C₃×Dic₁₀	C₂³	semidirect
95. C₂×C₃×C₅×C₈	C₂³	semidirect
97. C₃×C₅×C₄⋊C₄	C₂³	semidirect
105. C₃×C₄⋊Dic₅	C₂³	semidirect
109. C₂×C₃×#168	C₂³	semidirect
120. C₃×#450	D₅	direct (N × H)
126. C₂×Q₈×D₅	C₂²×C₃	semidirect
134. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
135. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
136. #4092	C₂²×C₃	semidirect
137. C₂×#688	C₂²×C₃	semidirect
138. C₂×#687	C₂²×C₃	semidirect
139. #4070	C₂²×C₃	semidirect
141. C₂×#677	C₂²×C₃	semidirect
142. C₂×C₈×D₅	C₂²×C₃	semidirect
143. #4043	C₂²×C₃	semidirect
146. D₅×C₄⋊C₄	C₂²×C₃	semidirect
149. C₅×#102	C₂²×C₃	semidirect
150. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
151. #3964	C₂²×C₃	semidirect
152. C₂²⋊#168	C₂²×C₃	semidirect
153. #3953	C₂²×C₃	semidirect
154. #3952	C₂²×C₃	semidirect
155. #3941	C₂²×C₃	semidirect
175. C₂²×C₃×D₅	SD₁₆	semidirect
222. C₂×C₃×SD₁₆	C₂×D₅	semidirect
229. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
236. C₃×#102	C₂×D₅	semidirect
239. C₃×C₂²⋊C₈	C₂×D₅	semidirect
248. C₂×C₅×Q₈	C₂³×C₃	semidirect
275. C₂×Dic₁₀	C₂³×C₃	semidirect
277. C₂×C₅×C₈	C₂³×C₃	semidirect
279. C₅×C₄⋊C₄	C₂³×C₃	semidirect
287. C₄⋊Dic₅	C₂³×C₃	semidirect
291. C₂×#168	C₂³×C₃	semidirect
302. #450	C₃×D₅	direct (N × H)
311. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
324. C₂×C₃×D₅	C₂×SD₁₆	semidirect
345. C₂×C₃×Q₈	C₂²×D₅	semidirect
376. C₂×C₃×C₈	C₂²×D₅	semidirect
383. C₃×C₄⋊C₄	C₂²×D₅	semidirect
406. C₂²×D₅	C₃×SD₁₆	semidirect
453. C₂×SD₁₆	C₂×C₃×D₅	semidirect
460. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
467. #102	C₂×C₃×D₅	semidirect
470. C₂²⋊C₈	C₂×C₃×D₅	semidirect
478. C₃×D₅	#450	direct (N × H)
535. C₂²×C₅	C₂×C₃×SD₁₆	semidirect
548. C₂×D₅	C₂×C₃×SD₁₆	semidirect
569. C₂×Q₈	C₂²×C₃×D₅	semidirect
600. C₂×C₈	C₂²×C₃×D₅	semidirect
607. C₄⋊C₄	C₂²×C₃×D₅	semidirect
612. C₃×C₅	C₂×#450	semidirect
632. C₂²×C₃	D₅×SD₁₆	semidirect
649. D₅	C₃×#450	direct (N × H)
708. C₅	C₂×C₃×#450	semidirect
728. C₂²	C₃×D₅×SD₁₆	semidirect
738. C₃	D₅×#450	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×C₃×D₄×D₅	2
C₂×C₃×D₅×SD₁₆	2
C₃×D₅×C₂²⋊Q₈	2
C₃×C₅×#450	2
C₃×#65507	2
C₃×#65458	2
C₃×#65335	2
C₃×#65065	2
C₃×D₅×#102	2
C₃×#65020	2
C₃×D₅×C₂²⋊C₈	2
D₅×#450	3
C₂×C₃×#450	5

Subgroups — C3×D5×#450 #14423230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#450 #14423230