Subgroups — C₃×#65988 #11755665

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4085	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4031	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4030	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4028	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4028	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#65988	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×D₄×D₅	—	2	4	no	—
27	C₃×#709	—	2	4	no	—
28	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
29	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
30	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
43	C₃×#685	C₂²	1	1	yes	characteristic
44	C₃×#685	C₂²	1	1	yes	characteristic
45	C₃×#685	C₂²	1	1	yes	characteristic
46	C₃×#685	C₂²	1	1	yes	characteristic, complemented
47	C₃×#685	C₂²	1	1	yes	characteristic, complemented
48	C₃×#685	C₂²	1	1	yes	characteristic, complemented
49	C₃×#685	C₂²	1	1	yes	characteristic, complemented
50	C₃×#685	C₂²	1	1	yes	characteristic, complemented
51	C₃×#683	C₂²	1	1	yes	characteristic, complemented
52	C₃×#683	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
54	C₃×#546	—	5	1	no	maximal, Hall
55	C₂×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#709	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
58	#4085	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#685	C₂×C₃	1	1	yes	characteristic, complemented
60	#4042	C₂×C₃	1	1	yes	characteristic, complemented
61	#4041	C₂×C₃	1	1	yes	characteristic, complemented
62	#4040	C₂×C₃	1	1	yes	characteristic, complemented
63	#4039	C₂×C₃	1	1	yes	characteristic, complemented
64	#4031	C₂×C₃	1	1	yes	characteristic, complemented
65	#4030	C₂×C₃	1	1	yes	characteristic, complemented
66	#4028	C₂×C₃	1	1	yes	characteristic, complemented
67	#4028	C₂×C₃	1	1	yes	characteristic, complemented
68	#4027	C₂×C₃	1	1	yes	characteristic, complemented
69	D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×D₅	—	2	2	no	—
73	C₂²×C₃×D₅	—	2	2	no	—
74	C₂²×C₃×D₅	—	2	2	no	—
75	C₂²×C₃×D₅	—	2	2	no	—
76	C₂²×C₃×D₅	—	4	1	no	—
77	C₂²×C₃×D₅	—	4	1	no	—
78	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
82	C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₃×C₂²⋊D₅	—	2	2	no	—
90	C₃×C₂²⋊D₅	—	2	2	no	—
91	C₃×C₂²⋊D₅	—	4	1	no	—
92	C₃×C₂²⋊D₅	D₄	1	4	yes	complemented
93	C₂×C₃×Dic₅	—	4	1	no	—
94	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
95	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
97	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
98	C₃×D₂₀	—	2	2	no	—
99	C₃×D₂₀	—	2	2	no	—
100	C₃×D₂₀	—	2	2	no	—
101	C₃×D₂₀	—	4	1	no	—
102	C₃×C₄×D₅	—	2	2	no	—
103	C₃×C₄×D₅	—	2	2	no	—
104	C₃×C₄×D₅	—	2	2	no	—
105	C₃×C₄×D₅	—	4	1	no	—
106	C₃×Dic₁₀	—	2	2	no	—
107	C₂×C₃×#41	—	5	1	no	—
108	C₂²×C₃×D₄	—	5	1	no	—
109	C₃×#124	—	5	1	no	—
110	C₃×#123	—	5	1	no	—
111	C₃×#123	D₅	1	1	yes	characteristic, complemented
112	C₃×C₂²⋊Q₈	—	5	1	no	—
113	C₃×#121	—	5	1	no	—
114	C₃×#121	—	5	1	no	—
115	C₃×#121	—	5	1	no	—
116	C₃×#120	—	5	1	no	—
117	C₃×#120	—	5	1	no	—
118	C₃×C₄×D₄	—	5	1	no	—
119	C₃×C₄×D₄	—	5	1	no	—
120	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
121	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
122	C₂³×D₅	C₂²×C₃	1	1	yes	characteristic
123	C₂³×D₅	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
131	D₄×D₅	—	2	4	no	—
132	#709	—	2	4	no	—
133	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
134	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
135	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
136	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
148	#685	C₂²×C₃	1	1	yes	characteristic
149	#685	C₂²×C₃	1	1	yes	characteristic
150	#685	C₂²×C₃	1	1	yes	characteristic
151	#685	C₂²×C₃	1	1	yes	characteristic, complemented
152	#685	C₂²×C₃	1	1	yes	characteristic, complemented
153	#685	C₂²×C₃	1	1	yes	characteristic, complemented
154	#685	C₂²×C₃	1	1	yes	characteristic, complemented
155	#685	C₂²×C₃	1	1	yes	characteristic, complemented
156	#683	C₂²×C₃	1	1	yes	characteristic, complemented
157	#683	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
159	#546	—	5	1	no	Sylow
160	C₂²×C₃×C₅	—	2	1	no	—
161	C₂²×C₃×C₅	—	2	1	no	—
162	C₂²×C₃×C₅	—	2	1	no	—
163	C₂²×C₃×C₅	—	2	1	no	—
164	C₂²×C₃×C₅	—	2	1	no	—
165	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
166	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
167	C₂×C₃×D₅	—	2	1	no	—
168	C₂×C₃×D₅	—	2	1	no	—
169	C₂×C₃×D₅	—	2	1	no	—
170	C₂×C₃×D₅	—	2	1	no	—
171	C₂×C₃×D₅	—	2	1	no	—
172	C₂×C₃×D₅	—	2	1	no	—
173	C₂×C₃×D₅	—	2	1	no	—
174	C₂×C₃×D₅	—	2	1	no	—
175	C₂×C₃×D₅	—	2	1	no	—
176	C₂×C₃×D₅	—	2	1	no	—
177	C₂×C₃×D₅	—	4	4	no	—
178	C₂×C₃×D₅	—	4	4	no	—
179	C₂×C₃×D₅	C₂×D₄	1	2	yes	—
180	C₂×C₃×D₅	#41	1	2	yes	complemented
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	—	2	1	no	—
184	C₃×C₄×C₅	—	2	1	no	—
185	C₃×C₄×C₅	—	2	1	no	—
186	C₃×Dic₅	—	2	1	no	—
187	C₃×Dic₅	—	2	1	no	—
188	C₃×Dic₅	—	2	1	no	—
189	C₃×Dic₅	C₂×D₄	1	2	yes	—
190	C₂⁴×C₃	—	5	1	no	—
191	C₂⁴×C₃	—	5	1	no	—
192	C₃×#41	—	10	4	no	—
193	C₂×C₃×Q₈	—	5	1	no	—
194	C₂×C₃×D₄	—	5	1	no	—
195	C₂×C₃×D₄	—	5	1	no	—
196	C₂×C₃×D₄	—	5	1	no	—
197	C₂×C₃×D₄	—	5	1	no	—
198	C₂×C₃×D₄	—	5	1	no	—
199	C₂×C₃×D₄	—	5	1	no	—
200	C₂×C₃×D₄	—	5	1	no	—
201	C₂×C₃×D₄	—	5	1	no	—
202	C₂×C₃×D₄	—	10	4	no	—
203	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	5	1	no	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
210	C₃×C₄⋊C₄	—	5	1	no	—
211	C₃×C₄⋊C₄	—	5	1	no	—
212	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
213	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
214	C₃×C₂²⋊C₄	—	5	1	no	—
215	C₃×C₂²⋊C₄	—	5	1	no	—
216	C₃×C₂²⋊C₄	—	5	1	no	—
217	C₃×C₂²⋊C₄	—	5	1	no	—
218	C₃×C₂²⋊C₄	—	5	1	no	—
219	C₃×C₂²⋊C₄	—	5	1	no	—
220	C₃×C₂²⋊C₄	—	5	1	no	—
221	C₃×C₂²⋊C₄	—	5	1	no	—
222	C₃×C₂²⋊C₄	—	5	1	no	—
223	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
224	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
225	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
226	C₃×C₄²	—	5	1	no	—
227	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
228	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
229	C₂²×D₅	—	2	2	no	—
230	C₂²×D₅	—	2	2	no	—
231	C₂²×D₅	—	2	2	no	—
232	C₂²×D₅	—	2	2	no	—
233	C₂²×D₅	—	4	1	no	—
234	C₂²×D₅	—	4	1	no	—
235	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
236	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
237	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
238	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
239	C₅×D₄	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₂²⋊D₅	—	2	2	no	—
247	C₂²⋊D₅	—	2	2	no	—
248	C₂²⋊D₅	—	4	1	no	—
249	C₂²⋊D₅	C₃×D₄	1	4	yes	complemented
250	C₂×Dic₅	—	4	1	no	—
251	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
252	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
253	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
254	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
255	D₂₀	—	2	2	no	—
256	D₂₀	—	2	2	no	—
257	D₂₀	—	2	2	no	—
258	D₂₀	—	4	1	no	—
259	C₄×D₅	—	2	2	no	—
260	C₄×D₅	—	2	2	no	—
261	C₄×D₅	—	2	2	no	—
262	C₄×D₅	—	4	1	no	—
263	Dic₁₀	—	2	2	no	—
264	C₂×#41	—	5	1	no	—
265	C₂²×D₄	—	5	1	no	—
266	#124	—	5	1	no	—
267	#123	—	5	1	no	—
268	#123	C₃×D₅	1	1	yes	characteristic, complemented
269	C₂²⋊Q₈	—	5	1	no	—
270	#121	—	5	1	no	—
271	#121	—	5	1	no	—
272	#121	—	5	1	no	—
273	#120	—	5	1	no	—
274	#120	—	5	1	no	—
275	C₄×D₄	—	5	1	no	—
276	C₄×D₄	—	5	1	no	—
277	C₂×C₂²⋊C₄	—	5	1	no	—
278	C₂×C₂²⋊C₄	—	5	1	no	—
279	C₂×C₃×C₅	—	2	2	no	—
280	C₂×C₃×C₅	—	4	1	no	—
281	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
283	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
284	C₃×D₅	—	2	2	no	—
285	C₃×D₅	—	2	2	no	—
286	C₃×D₅	—	4	1	no	—
287	C₃×D₅	—	4	1	no	—
288	C₂³×C₃	—	5	1	no	—
289	C₂³×C₃	—	5	1	no	—
290	C₂³×C₃	—	5	1	no	—
291	C₂³×C₃	—	5	1	no	—
292	C₂³×C₃	—	10	2	no	—
293	C₂³×C₃	—	10	2	no	—
294	C₂³×C₃	—	10	2	no	—
295	C₂³×C₃	—	10	2	no	—
296	C₂³×C₃	—	20	1	no	—
297	C₂³×C₃	—	20	1	no	—
298	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
299	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
300	C₃×Q₈	—	10	2	no	—
301	C₃×D₄	—	2	2	no	—
302	C₃×D₄	—	5	4	no	—
303	C₃×D₄	—	10	2	no	—
304	C₃×D₄	—	10	2	no	—
305	C₃×D₄	—	10	2	no	—
306	C₃×D₄	—	10	2	no	—
307	C₃×D₄	—	10	2	no	—
308	C₃×D₄	—	20	1	no	—
309	C₃×D₄	—	20	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	5	1	no	—
314	C₂×C₃×C₄	—	5	1	no	—
315	C₂×C₃×C₄	—	10	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	20	1	no	—
319	C₂×C₃×C₄	—	20	1	no	—
320	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	C₂×C₃×D₄	1	2	yes	—
331	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
332	C₂×D₅	—	2	1	no	—
333	C₂×D₅	—	2	1	no	—
334	C₂×D₅	—	2	1	no	—
335	C₂×D₅	—	2	1	no	—
336	C₂×D₅	—	2	1	no	—
337	C₂×D₅	—	2	1	no	—
338	C₂×D₅	—	2	1	no	—
339	C₂×D₅	—	2	1	no	—
340	C₂×D₅	—	2	1	no	—
341	C₂×D₅	—	2	1	no	—
342	C₂×D₅	—	4	4	no	—
343	C₂×D₅	—	4	4	no	—
344	C₂×D₅	C₂×C₃×D₄	1	2	yes	—
345	C₂×D₅	C₃×#41	1	2	yes	complemented
346	C₄×C₅	—	2	1	no	—
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	2	1	no	—
350	C₄×C₅	—	2	1	no	—
351	Dic₅	—	2	1	no	—
352	Dic₅	—	2	1	no	—
353	Dic₅	—	2	1	no	—
354	Dic₅	C₂×C₃×D₄	1	2	yes	—
355	C₂⁴	—	5	1	no	—
356	C₂⁴	—	5	1	no	—
357	#41	—	10	4	no	—
358	C₂×Q₈	—	5	1	no	—
359	C₂×D₄	—	5	1	no	—
360	C₂×D₄	—	5	1	no	—
361	C₂×D₄	—	5	1	no	—
362	C₂×D₄	—	5	1	no	—
363	C₂×D₄	—	5	1	no	—
364	C₂×D₄	—	5	1	no	—
365	C₂×D₄	—	5	1	no	—
366	C₂×D₄	—	5	1	no	—
367	C₂×D₄	—	10	4	no	—
368	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	5	1	no	—
372	C₂²×C₄	—	5	1	no	—
373	C₂²×C₄	—	5	1	no	—
374	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
375	C₄⋊C₄	—	5	1	no	—
376	C₄⋊C₄	—	5	1	no	—
377	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
378	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
379	C₂²⋊C₄	—	5	1	no	—
380	C₂²⋊C₄	—	5	1	no	—
381	C₂²⋊C₄	—	5	1	no	—
382	C₂²⋊C₄	—	5	1	no	—
383	C₂²⋊C₄	—	5	1	no	—
384	C₂²⋊C₄	—	5	1	no	—
385	C₂²⋊C₄	—	5	1	no	—
386	C₂²⋊C₄	—	5	1	no	—
387	C₂²⋊C₄	—	5	1	no	—
388	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
389	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
390	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
391	C₄²	—	5	1	no	—
392	C₃×C₅	#546	1	1	yes	characteristic, complemented, Hall
393	C₂²×C₃	—	2	1	no	—
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	5	2	no	—
399	C₂²×C₃	—	5	2	no	—
400	C₂²×C₃	—	10	1	no	—
401	C₂²×C₃	—	10	1	no	—
402	C₂²×C₃	—	10	1	no	—
403	C₂²×C₃	—	10	1	no	—
404	C₂²×C₃	—	10	1	no	—
405	C₂²×C₃	—	10	1	no	—
406	C₂²×C₃	—	10	1	no	—
407	C₂²×C₃	—	10	1	no	—
408	C₂²×C₃	—	10	1	no	—
409	C₂²×C₃	—	10	1	no	—
410	C₂²×C₃	—	20	4	no	—
411	C₂²×C₃	—	20	4	no	—
412	C₂²×C₃	D₄×D₅	1	2	yes	—
413	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	5	2	no	—
420	C₃×C₄	—	10	1	no	—
421	C₃×C₄	—	10	1	no	—
422	C₃×C₄	—	10	1	no	—
423	C₂×C₅	—	2	2	no	—
424	C₂×C₅	—	4	1	no	—
425	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
426	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
427	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
428	D₅	—	2	2	no	—
429	D₅	—	2	2	no	—
430	D₅	—	4	1	no	—
431	D₅	—	4	1	no	—
432	C₂³	—	5	1	no	—
433	C₂³	—	5	1	no	—
434	C₂³	—	5	1	no	—
435	C₂³	—	5	1	no	—
436	C₂³	—	10	2	no	—
437	C₂³	—	10	2	no	—
438	C₂³	—	10	2	no	—
439	C₂³	—	10	2	no	—
440	C₂³	—	20	1	no	—
441	C₂³	—	20	1	no	—
442	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
443	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
444	Q₈	—	10	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	5	4	no	—
447	D₄	—	10	2	no	—
448	D₄	—	10	2	no	—
449	D₄	—	10	2	no	—
450	D₄	—	10	2	no	—
451	D₄	—	10	2	no	—
452	D₄	—	20	1	no	—
453	D₄	—	20	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	5	1	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	10	2	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	10	2	no	—
462	C₂×C₄	—	20	1	no	—
463	C₂×C₄	—	20	1	no	—
464	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	—	4	1	no	—
471	C₂×C₃	—	10	2	no	—
472	C₂×C₃	—	10	2	no	—
473	C₂×C₃	—	20	1	no	—
474	C₂×C₃	—	20	1	no	—
475	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
476	C₂×C₃	D₅×#41	1	1	yes	characteristic
477	C₂×C₃	#4149	1	1	yes	characteristic
478	C₅	C₃×#546	1	1	yes	characteristic, complemented, Sylow
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	5	2	no	—
485	C₂²	—	5	2	no	—
486	C₂²	—	10	1	no	—
487	C₂²	—	10	1	no	—
488	C₂²	—	10	1	no	—
489	C₂²	—	10	1	no	—
490	C₂²	—	10	1	no	—
491	C₂²	—	10	1	no	—
492	C₂²	—	10	1	no	—
493	C₂²	—	10	1	no	—
494	C₂²	—	10	1	no	—
495	C₂²	—	10	1	no	—
496	C₂²	—	20	4	no	—
497	C₂²	—	20	4	no	—
498	C₂²	C₃×D₄×D₅	1	2	yes	—
499	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	5	2	no	—
506	C₄	—	10	1	no	—
507	C₄	—	10	1	no	—
508	C₄	—	10	1	no	—
509	C₃	#65988	1	1	yes	characteristic, direct product factor, Sylow
510	C₂	—	2	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	10	2	no	—
513	C₂	—	10	2	no	—
514	C₂	—	20	1	no	—
515	C₂	—	20	1	no	—
516	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic
517	C₂	C₃×D₅×#41	1	1	yes	characteristic
518	C₂	C₃×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×#123	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₃×#123	D₅
hypocenter	C₅	C₃×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₅	C₂	semidirect
2. C₂×C₃×#709	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₃×#4085	C₂	semidirect
5. C₂×C₃×#685	C₂	semidirect
6. C₃×#4042	C₂	semidirect
7. C₃×#4041	C₂	semidirect
8. C₃×#4040	C₂	semidirect
9. C₃×#4039	C₂	semidirect
10. C₃×#4031	C₂	semidirect
11. C₃×#4030	C₂	semidirect
12. C₃×#4028	C₂	semidirect
13. C₃×#4028	C₂	semidirect
14. C₃×#4027	C₂	semidirect
15. C₃×D₅×C₂²⋊C₄	C₂	semidirect
16. #65988	C₃	direct (N × H)
20. C₂²×C₃×C₄×C₅	C₂²	semidirect
23. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
24. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
25. C₂²×C₃×Dic₅	C₂²	semidirect
30. C₂×C₃×D₂₀	C₂²	semidirect
31. C₂×C₃×D₂₀	C₂²	semidirect
33. C₂×C₃×C₄×D₅	C₂²	semidirect
34. C₂×C₃×C₄×D₅	C₂²	semidirect
35. C₂×C₃×C₄×D₅	C₂²	semidirect
36. C₂×C₃×Dic₁₀	C₂²	semidirect
37. C₃×C₅×C₄⋊C₄	C₂²	semidirect
38. C₃×C₅×C₄⋊C₄	C₂²	semidirect
39. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
40. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
41. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
42. C₃×C₂²⋊Dic₅	C₂²	semidirect
46. C₃×#685	C₂²	semidirect
47. C₃×#685	C₂²	semidirect
48. C₃×#685	C₂²	semidirect
49. C₃×#685	C₂²	semidirect
50. C₃×#685	C₂²	semidirect
51. C₃×#683	C₂²	semidirect
52. C₃×#683	C₂²	semidirect
53. C₃×C₄×Dic₅	C₂²	semidirect
55. C₂×D₄×D₅	C₂×C₃	semidirect
56. C₂×#709	C₂×C₃	semidirect
57. C₅×#123	C₂×C₃	semidirect
58. #4085	C₂×C₃	semidirect
59. C₂×#685	C₂×C₃	semidirect
60. #4042	C₂×C₃	semidirect
61. #4041	C₂×C₃	semidirect
62. #4040	C₂×C₃	semidirect
63. #4039	C₂×C₃	semidirect
64. #4031	C₂×C₃	semidirect
65. #4030	C₂×C₃	semidirect
66. #4028	C₂×C₃	semidirect
67. #4028	C₂×C₃	semidirect
68. #4027	C₂×C₃	semidirect
69. D₅×C₂²⋊C₄	C₂×C₃	semidirect
92. C₃×C₂²⋊D₅	D₄	semidirect
111. C₃×#123	D₅	semidirect
125. C₂²×C₄×C₅	C₂²×C₃	semidirect
128. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
129. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
130. C₂²×Dic₅	C₂²×C₃	semidirect
135. C₂×D₂₀	C₂²×C₃	semidirect
136. C₂×D₂₀	C₂²×C₃	semidirect
138. C₂×C₄×D₅	C₂²×C₃	semidirect
139. C₂×C₄×D₅	C₂²×C₃	semidirect
140. C₂×C₄×D₅	C₂²×C₃	semidirect
141. C₂×Dic₁₀	C₂²×C₃	semidirect
142. C₅×C₄⋊C₄	C₂²×C₃	semidirect
143. C₅×C₄⋊C₄	C₂²×C₃	semidirect
144. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
145. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
146. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
147. C₂²⋊Dic₅	C₂²×C₃	semidirect
151. #685	C₂²×C₃	semidirect
152. #685	C₂²×C₃	semidirect
153. #685	C₂²×C₃	semidirect
154. #685	C₂²×C₃	semidirect
155. #685	C₂²×C₃	semidirect
156. #683	C₂²×C₃	semidirect
157. #683	C₂²×C₃	semidirect
158. C₄×Dic₅	C₂²×C₃	semidirect
180. C₂×C₃×D₅	#41	semidirect
209. C₂²×C₃×C₄	C₂×D₅	semidirect
212. C₃×C₄⋊C₄	C₂×D₅	semidirect
213. C₃×C₄⋊C₄	C₂×D₅	semidirect
223. C₃×C₂²⋊C₄	C₂×D₅	semidirect
224. C₃×C₂²⋊C₄	C₂×D₅	semidirect
225. C₃×C₂²⋊C₄	C₂×D₅	semidirect
249. C₂²⋊D₅	C₃×D₄	semidirect
268. #123	C₃×D₅	semidirect
345. C₂×D₅	C₃×#41	semidirect
374. C₂²×C₄	C₂×C₃×D₅	semidirect
377. C₄⋊C₄	C₂×C₃×D₅	semidirect
378. C₄⋊C₄	C₂×C₃×D₅	semidirect
388. C₂²⋊C₄	C₂×C₃×D₅	semidirect
389. C₂²⋊C₄	C₂×C₃×D₅	semidirect
390. C₂²⋊C₄	C₂×C₃×D₅	semidirect
392. C₃×C₅	#546	semidirect
478. C₅	C₃×#546	semidirect
509. C₃	#65988	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×C₃×D₄×D₅	2
C₂×C₃×#709	2
C₃×C₅×#123	2
C₃×#4085	2
C₂×C₃×#685	2
C₃×#4042	2
C₃×#4041	2
C₃×#4040	2
C₃×#4039	2
C₃×#4031	2
C₃×#4030	2
C₃×#4028	2
C₃×#4027	2
C₃×D₅×C₂²⋊C₄	2
#65988	3
C₃×#546	5

Subgroups — C3×#65988 #11755665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65988 #11755665