Subgroups — C₃×D₅×#540 #14481077

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66053	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66032	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65997	C₂	1	4	yes	maximal, complemented
7	C₃×D₅×#123	C₂	1	4	yes	maximal, complemented
8	C₃×#65953	C₂	1	2	yes	maximal, complemented
9	C₃×#65949	C₂	1	4	yes	maximal, complemented
10	C₃×D₅×#121	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#121	C₂	1	4	yes	maximal, complemented
12	C₃×#65896	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×D₄×D₅	C₂	1	2	yes	maximal, complemented
14	C₃×#65869	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×#540	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
18	C₂×C₃×D₄×D₅	C₂²	1	4	yes	—
19	C₂×C₃×D₄×D₅	C₂²	1	4	yes	—
20	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
22	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#123	C₂²	1	4	yes	complemented
25	C₃×C₅×#121	C₂²	1	4	yes	complemented
26	C₃×C₅×#121	C₂²	1	2	yes	complemented
27	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
29	C₃×#4086	C₂²	1	2	yes	complemented
30	C₃×#4086	C₂²	1	4	yes	complemented
31	C₃×#4085	C₂²	1	4	yes	complemented
32	C₃×#4085	C₂²	1	4	yes	complemented
33	C₃×#4085	C₂²	1	4	yes	complemented
34	C₃×#4084	C₂²	1	2	yes	complemented
35	C₃×#4084	C₂²	1	4	yes	complemented
36	C₃×#4081	C₂²	1	4	yes	complemented
37	C₃×D₄×Dic₅	C₂²	1	2	yes	complemented
38	C₃×#4076	C₂²	1	2	yes	complemented
39	C₃×#4076	C₂²	1	4	yes	complemented
40	C₃×#4075	C₂²	1	4	yes	complemented
41	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
42	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4041	C₂²	1	2	yes	complemented
44	C₃×#4041	C₂²	1	4	yes	complemented
45	C₃×#4040	C₂²	1	4	yes	complemented
46	C₃×#4040	C₂²	1	4	yes	complemented
47	C₃×#4039	C₂²	1	2	yes	complemented
48	C₃×#4038	C₂²	1	2	yes	complemented
49	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
50	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
51	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
52	C₃×#4036	C₂²	1	2	yes	complemented
53	C₃×#4035	C₂²	1	4	yes	complemented
54	C₃×#4032	C₂²	1	4	yes	complemented
55	C₃×#4030	C₂²	1	4	yes	complemented
56	C₃×#4030	C₂²	1	4	yes	complemented
57	C₃×#4030	C₂²	1	4	yes	complemented
58	C₃×#4029	C₂²	1	4	yes	complemented
59	C₃×#4029	C₂²	1	4	yes	complemented
60	C₃×#4027	C₂²	1	4	yes	complemented
61	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
62	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₃×#4023	C₂²	1	2	yes	complemented
65	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
67	C₃×#4018	C₂²	1	1	yes	characteristic, complemented
68	C₃×#4018	C₂²	1	1	yes	characteristic, complemented
69	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
70	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
71	C₃×#4016	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃×#540	—	5	1	no	maximal, Hall
73	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
74	#66053	C₂×C₃	1	1	yes	characteristic, complemented
75	D₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
76	#66032	C₂×C₃	1	1	yes	characteristic, complemented
77	D₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
78	#65997	C₂×C₃	1	4	yes	complemented
79	D₅×#123	C₂×C₃	1	4	yes	complemented
80	#65953	C₂×C₃	1	2	yes	complemented
81	#65949	C₂×C₃	1	4	yes	complemented
82	D₅×#121	C₂×C₃	1	4	yes	complemented
83	D₅×#121	C₂×C₃	1	2	yes	complemented
84	#65896	C₂×C₃	1	2	yes	complemented
85	C₄×D₄×D₅	C₂×C₃	1	2	yes	complemented
86	#65869	C₂×C₃	1	1	yes	characteristic, complemented
87	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
89	C₂³×C₃×D₅	C₂³	1	4	yes	—
90	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
91	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
92	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
95	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
96	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
97	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
98	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
99	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
100	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
101	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
102	C₃×D₄×D₅	—	2	8	no	—
103	C₃×D₄×D₅	—	4	8	no	—
104	C₃×D₄×D₅	—	4	8	no	—
105	C₂×C₃×D₂₀	C₂³	1	2	yes	—
106	C₂×C₃×D₂₀	C₂³	1	4	yes	—
107	C₂×C₃×D₂₀	C₂³	1	4	yes	—
108	C₂×C₃×C₄×D₅	—	2	4	no	—
109	C₂×C₃×C₄×D₅	—	4	8	no	—
110	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
112	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
113	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
115	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
116	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
117	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
118	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
119	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
122	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
126	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
128	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
129	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
130	C₃×#685	C₂³	1	2	yes	—
131	C₃×#685	C₂³	1	4	yes	—
132	C₃×#685	C₂³	1	4	yes	—
133	C₃×#685	C₂³	1	2	yes	—
134	C₃×#685	C₂³	1	4	yes	—
135	C₃×#685	C₂³	1	4	yes	—
136	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
137	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
138	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
139	C₃×#683	C₂³	1	2	yes	—
140	C₃×#683	C₂³	1	4	yes	—
141	C₃×#683	C₂³	1	4	yes	—
142	C₃×#683	C₂³	1	4	yes	—
143	C₃×#683	C₂³	1	2	yes	—
144	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
145	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
146	C₃×C₄×Dic₅	C₂³	1	2	yes	—
147	C₃×C₄×Dic₅	C₂³	1	2	yes	—
148	C₃×#540	—	5	1	no	—
149	C₃×#540	—	5	1	no	—
150	C₃×#540	—	5	4	no	—
151	C₃×#540	—	5	4	no	—
152	C₃×#540	—	5	2	no	—
153	C₃×#540	—	5	2	no	—
154	C₃×#540	—	5	1	no	—
155	C₃×#540	D₅	1	1	yes	characteristic, direct product factor
156	C₂×C₃×#127	—	5	1	no	—
157	C₂×C₃×#125	—	5	1	no	—
158	C₂×C₃×#123	—	5	4	no	—
159	C₂×C₃×#121	—	5	4	no	—
160	C₂×C₃×#121	—	5	2	no	—
161	C₂×C₃×C₄×D₄	—	5	2	no	—
162	C₂×C₃×#117	—	5	1	no	—
163	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
164	C₂×D₄×D₅	C₂²×C₃	1	4	yes	—
165	C₂×D₄×D₅	C₂²×C₃	1	4	yes	—
166	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
167	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
168	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#123	C₂²×C₃	1	4	yes	complemented
171	C₅×#121	C₂²×C₃	1	4	yes	complemented
172	C₅×#121	C₂²×C₃	1	2	yes	complemented
173	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
174	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
175	#4086	C₂²×C₃	1	2	yes	complemented
176	#4086	C₂²×C₃	1	4	yes	complemented
177	#4085	C₂²×C₃	1	4	yes	complemented
178	#4085	C₂²×C₃	1	4	yes	complemented
179	#4085	C₂²×C₃	1	4	yes	complemented
180	#4084	C₂²×C₃	1	2	yes	complemented
181	#4084	C₂²×C₃	1	4	yes	complemented
182	#4081	C₂²×C₃	1	4	yes	complemented
183	D₄×Dic₅	C₂²×C₃	1	2	yes	complemented
184	#4076	C₂²×C₃	1	2	yes	complemented
185	#4076	C₂²×C₃	1	4	yes	complemented
186	#4075	C₂²×C₃	1	4	yes	complemented
187	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
188	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
189	#4041	C₂²×C₃	1	2	yes	complemented
190	#4041	C₂²×C₃	1	4	yes	complemented
191	#4040	C₂²×C₃	1	4	yes	complemented
192	#4040	C₂²×C₃	1	4	yes	complemented
193	#4039	C₂²×C₃	1	2	yes	complemented
194	#4038	C₂²×C₃	1	2	yes	complemented
195	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
196	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
197	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
198	#4036	C₂²×C₃	1	2	yes	complemented
199	#4035	C₂²×C₃	1	4	yes	complemented
200	#4032	C₂²×C₃	1	4	yes	complemented
201	#4030	C₂²×C₃	1	4	yes	complemented
202	#4030	C₂²×C₃	1	4	yes	complemented
203	#4030	C₂²×C₃	1	4	yes	complemented
204	#4029	C₂²×C₃	1	4	yes	complemented
205	#4029	C₂²×C₃	1	4	yes	complemented
206	#4027	C₂²×C₃	1	4	yes	complemented
207	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
208	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
209	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
210	#4023	C₂²×C₃	1	2	yes	complemented
211	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
212	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
213	#4018	C₂²×C₃	1	1	yes	characteristic, complemented
214	#4018	C₂²×C₃	1	1	yes	characteristic, complemented
215	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
216	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
217	#4016	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₂×#540	—	5	1	no	Sylow
219	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
220	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
221	C₂²×C₃×D₅	—	2	2	no	—
222	C₂²×C₃×D₅	—	2	8	no	—
223	C₂²×C₃×D₅	—	2	8	no	—
224	C₂²×C₃×D₅	—	2	4	no	—
225	C₂²×C₃×D₅	—	2	8	no	—
226	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
227	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
228	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
229	C₃×C₅×D₄	—	2	4	no	—
230	C₃×C₅×D₄	—	4	4	no	—
231	C₃×C₅×D₄	—	4	4	no	—
232	C₂×C₃×C₄×C₅	—	2	2	no	—
233	C₂×C₃×C₄×C₅	—	4	4	no	—
234	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
236	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
237	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
238	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
239	C₃×C₂²⋊D₅	—	2	8	no	—
240	C₃×C₂²⋊D₅	—	4	4	no	—
241	C₃×C₂²⋊D₅	—	4	4	no	—
242	C₃×C₂²⋊D₅	—	4	4	no	—
243	C₃×C₂²⋊D₅	—	4	4	no	—
244	C₂×C₃×Dic₅	—	2	2	no	—
245	C₂×C₃×Dic₅	—	4	4	no	—
246	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
247	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
248	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
249	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
250	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
251	C₃×D₂₀	—	2	4	no	—
252	C₃×D₂₀	—	4	4	no	—
253	C₃×D₂₀	—	4	4	no	—
254	C₃×C₄×D₅	—	2	2	no	—
255	C₃×C₄×D₅	—	2	4	no	—
256	C₃×C₄×D₅	—	2	8	no	—
257	C₃×C₄×D₅	—	2	4	no	—
258	C₃×C₄×D₅	—	2	2	no	—
259	C₃×C₄×D₅	—	2	2	no	—
260	C₃×C₄×D₅	—	4	4	no	—
261	C₃×C₄×D₅	—	4	4	no	—
262	C₃×C₄×D₅	#41	1	4	yes	—
263	C₂²×C₃×D₄	—	5	2	no	—
264	C₂²×C₃×D₄	—	5	4	no	—
265	C₂²×C₃×D₄	—	5	4	no	—
266	C₂³×C₃×C₄	—	5	1	no	—
267	C₂³×C₃×C₄	—	5	4	no	—
268	C₃×#127	—	5	4	no	—
269	C₃×#127	—	5	2	no	—
270	C₃×#127	—	5	1	no	—
271	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
272	C₃×#125	—	5	4	no	—
273	C₃×#125	—	5	2	no	—
274	C₃×#125	—	5	1	no	—
275	C₃×#125	C₂×D₅	1	1	yes	characteristic, complemented
276	C₃×#123	—	5	4	no	—
277	C₃×#123	—	5	4	no	—
278	C₃×#123	—	5	4	no	—
279	C₃×#123	—	5	4	no	—
280	C₃×#123	—	5	4	no	—
281	C₃×#123	—	5	4	no	—
282	C₃×#123	—	5	4	no	—
283	C₃×#123	C₂×D₅	1	4	yes	complemented
284	C₃×#121	—	5	4	no	—
285	C₃×#121	—	5	2	no	—
286	C₃×#121	—	5	4	no	—
287	C₃×#121	—	5	4	no	—
288	C₃×#121	—	5	4	no	—
289	C₃×#121	—	5	4	no	—
290	C₃×#121	—	5	2	no	—
291	C₃×#121	—	5	4	no	—
292	C₃×#121	—	5	2	no	—
293	C₃×#121	—	5	4	no	—
294	C₃×#121	—	5	4	no	—
295	C₃×#121	—	5	4	no	—
296	C₃×#121	C₂×D₅	1	4	yes	complemented
297	C₃×#121	C₂×D₅	1	2	yes	complemented
298	C₃×C₄×D₄	—	5	2	no	—
299	C₃×C₄×D₄	—	5	4	no	—
300	C₃×C₄×D₄	—	5	2	no	—
301	C₃×C₄×D₄	—	5	4	no	—
302	C₃×C₄×D₄	—	5	2	no	—
303	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
304	C₃×#117	—	5	1	no	—
305	C₃×#117	—	5	2	no	—
306	C₃×#117	—	5	2	no	—
307	C₃×#117	—	5	1	no	—
308	C₃×#117	—	5	1	no	—
309	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
310	C₂×C₃×C₄⋊C₄	—	5	2	no	—
311	C₂×C₃×C₄⋊C₄	—	5	2	no	—
312	C₂×C₃×C₄⋊C₄	—	5	4	no	—
313	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
314	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
315	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
316	C₂×C₃×C₄²	—	5	1	no	—
317	C₂×C₃×C₄²	—	5	1	no	—
318	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
319	C₂³×D₅	C₂³×C₃	1	4	yes	—
320	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
321	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
322	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
323	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
325	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
326	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
327	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
328	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
329	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
330	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
331	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
332	D₄×D₅	—	2	8	no	—
333	D₄×D₅	—	4	8	no	—
334	D₄×D₅	—	4	8	no	—
335	C₂×D₂₀	C₂³×C₃	1	2	yes	—
336	C₂×D₂₀	C₂³×C₃	1	4	yes	—
337	C₂×D₂₀	C₂³×C₃	1	4	yes	—
338	C₂×C₄×D₅	—	2	4	no	—
339	C₂×C₄×D₅	—	4	8	no	—
340	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
341	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
342	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
343	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
344	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
345	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
346	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
347	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
348	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
349	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
350	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
351	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
352	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
353	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
354	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
356	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
358	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
359	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
360	#685	C₂³×C₃	1	2	yes	—
361	#685	C₂³×C₃	1	2	yes	—
362	#685	C₂³×C₃	1	4	yes	—
363	#685	C₂³×C₃	1	4	yes	—
364	#685	C₂³×C₃	1	4	yes	—
365	#685	C₂³×C₃	1	4	yes	—
366	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
367	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
368	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
369	#683	C₂³×C₃	1	4	yes	—
370	#683	C₂³×C₃	1	2	yes	—
371	#683	C₂³×C₃	1	2	yes	—
372	#683	C₂³×C₃	1	4	yes	—
373	#683	C₂³×C₃	1	4	yes	—
374	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
375	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
376	C₄×Dic₅	C₂³×C₃	1	2	yes	—
377	C₄×Dic₅	C₂³×C₃	1	2	yes	—
378	#540	—	5	1	no	—
379	#540	—	5	1	no	—
380	#540	—	5	4	no	—
381	#540	—	5	4	no	—
382	#540	—	5	2	no	—
383	#540	—	5	2	no	—
384	#540	—	5	1	no	—
385	#540	C₃×D₅	1	1	yes	characteristic, direct product factor
386	C₂×#127	—	5	1	no	—
387	C₂×#125	—	5	1	no	—
388	C₂×#123	—	5	4	no	—
389	C₂×#121	—	5	4	no	—
390	C₂×#121	—	5	2	no	—
391	C₂×C₄×D₄	—	5	2	no	—
392	C₂×#117	—	5	1	no	—
393	C₂²×C₃×C₅	—	2	1	no	—
394	C₂²×C₃×C₅	—	2	4	no	—
395	C₂²×C₃×C₅	—	2	4	no	—
396	C₂²×C₃×C₅	—	2	2	no	—
397	C₂²×C₃×C₅	—	2	4	no	—
398	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
399	C₂×C₃×D₅	—	2	1	no	—
400	C₂×C₃×D₅	—	2	4	no	—
401	C₂×C₃×D₅	—	2	4	no	—
402	C₂×C₃×D₅	—	2	2	no	—
403	C₂×C₃×D₅	—	2	4	no	—
404	C₂×C₃×D₅	—	4	4	no	—
405	C₂×C₃×D₅	—	4	16	no	—
406	C₂×C₃×D₅	C₂×#41	1	2	yes	—
407	C₂×C₃×D₅	H(5,𝔽₂)	1	4	yes	—
408	C₃×C₄×C₅	—	2	1	no	—
409	C₃×C₄×C₅	—	2	2	no	—
410	C₃×C₄×C₅	—	2	4	no	—
411	C₃×C₄×C₅	—	2	2	no	—
412	C₃×C₄×C₅	C₂×#41	1	2	yes	—
413	C₃×Dic₅	—	2	1	no	—
414	C₃×Dic₅	—	2	2	no	—
415	C₃×Dic₅	—	2	4	no	—
416	C₃×Dic₅	—	2	2	no	—
417	C₃×Dic₅	C₂×#41	1	2	yes	—
418	C₂⁴×C₃	—	5	1	no	—
419	C₂⁴×C₃	—	5	4	no	—
420	C₂×C₃×D₄	—	5	4	no	—
421	C₂×C₃×D₄	—	5	4	no	—
422	C₂×C₃×D₄	—	5	4	no	—
423	C₂×C₃×D₄	—	5	4	no	—
424	C₂×C₃×D₄	—	5	4	no	—
425	C₂×C₃×D₄	—	5	2	no	—
426	C₂×C₃×D₄	—	5	4	no	—
427	C₂×C₃×D₄	—	5	4	no	—
428	C₂×C₃×D₄	—	10	8	no	—
429	C₂×C₃×D₄	—	20	8	no	—
430	C₂×C₃×D₄	—	20	8	no	—
431	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
432	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
433	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
434	C₂²×C₃×C₄	—	5	1	no	—
435	C₂²×C₃×C₄	—	5	1	no	—
436	C₂²×C₃×C₄	—	5	4	no	—
437	C₂²×C₃×C₄	—	5	2	no	—
438	C₂²×C₃×C₄	—	5	2	no	—
439	C₂²×C₃×C₄	—	5	1	no	—
440	C₂²×C₃×C₄	—	5	4	no	—
441	C₂²×C₃×C₄	—	5	1	no	—
442	C₂²×C₃×C₄	—	5	1	no	—
443	C₂²×C₃×C₄	—	5	4	no	—
444	C₂²×C₃×C₄	—	5	4	no	—
445	C₂²×C₃×C₄	—	10	4	no	—
446	C₂²×C₃×C₄	—	20	8	no	—
447	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
449	C₃×C₄⋊C₄	—	5	2	no	—
450	C₃×C₄⋊C₄	—	5	2	no	—
451	C₃×C₄⋊C₄	—	5	4	no	—
452	C₃×C₄⋊C₄	—	5	4	no	—
453	C₃×C₄⋊C₄	—	5	4	no	—
454	C₃×C₄⋊C₄	—	5	2	no	—
455	C₃×C₄⋊C₄	—	5	2	no	—
456	C₃×C₄⋊C₄	—	5	4	no	—
457	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
458	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
459	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
460	C₃×C₂²⋊C₄	—	5	2	no	—
461	C₃×C₂²⋊C₄	—	5	4	no	—
462	C₃×C₂²⋊C₄	—	5	4	no	—
463	C₃×C₂²⋊C₄	—	5	2	no	—
464	C₃×C₂²⋊C₄	—	5	2	no	—
465	C₃×C₂²⋊C₄	—	5	4	no	—
466	C₃×C₂²⋊C₄	—	5	4	no	—
467	C₃×C₂²⋊C₄	—	5	4	no	—
468	C₃×C₂²⋊C₄	—	5	4	no	—
469	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
470	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
471	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
472	C₃×C₄²	—	5	2	no	—
473	C₃×C₄²	—	5	1	no	—
474	C₃×C₄²	—	5	2	no	—
475	C₃×C₄²	—	5	1	no	—
476	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
477	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
478	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
479	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
480	C₂²×D₅	—	2	2	no	—
481	C₂²×D₅	—	2	8	no	—
482	C₂²×D₅	—	2	8	no	—
483	C₂²×D₅	—	2	4	no	—
484	C₂²×D₅	—	2	8	no	—
485	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
486	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
487	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
488	C₅×D₄	—	2	4	no	—
489	C₅×D₄	—	4	4	no	—
490	C₅×D₄	—	4	4	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	4	4	no	—
493	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
494	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
495	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
496	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
497	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
498	C₂²⋊D₅	—	2	8	no	—
499	C₂²⋊D₅	—	4	4	no	—
500	C₂²⋊D₅	—	4	4	no	—
501	C₂²⋊D₅	—	4	4	no	—
502	C₂²⋊D₅	—	4	4	no	—
503	C₂×Dic₅	—	2	2	no	—
504	C₂×Dic₅	—	4	4	no	—
505	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
506	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
507	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
508	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
509	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
510	D₂₀	—	2	4	no	—
511	D₂₀	—	4	4	no	—
512	D₂₀	—	4	4	no	—
513	C₄×D₅	—	2	2	no	—
514	C₄×D₅	—	2	4	no	—
515	C₄×D₅	—	2	8	no	—
516	C₄×D₅	—	2	4	no	—
517	C₄×D₅	—	2	2	no	—
518	C₄×D₅	—	2	2	no	—
519	C₄×D₅	—	4	4	no	—
520	C₄×D₅	—	4	4	no	—
521	C₄×D₅	C₃×#41	1	4	yes	—
522	C₂²×D₄	—	5	2	no	—
523	C₂²×D₄	—	5	4	no	—
524	C₂²×D₄	—	5	4	no	—
525	C₂³×C₄	—	5	1	no	—
526	C₂³×C₄	—	5	4	no	—
527	#127	—	5	4	no	—
528	#127	—	5	2	no	—
529	#127	—	5	1	no	—
530	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
531	#125	—	5	4	no	—
532	#125	—	5	2	no	—
533	#125	—	5	1	no	—
534	#125	C₂×C₃×D₅	1	1	yes	characteristic, complemented
535	#123	—	5	4	no	—
536	#123	—	5	4	no	—
537	#123	—	5	4	no	—
538	#123	—	5	4	no	—
539	#123	—	5	4	no	—
540	#123	—	5	4	no	—
541	#123	—	5	4	no	—
542	#123	C₂×C₃×D₅	1	4	yes	complemented
543	#121	—	5	4	no	—
544	#121	—	5	2	no	—
545	#121	—	5	4	no	—
546	#121	—	5	4	no	—
547	#121	—	5	4	no	—
548	#121	—	5	4	no	—
549	#121	—	5	2	no	—
550	#121	—	5	4	no	—
551	#121	—	5	2	no	—
552	#121	—	5	4	no	—
553	#121	—	5	4	no	—
554	#121	—	5	4	no	—
555	#121	C₂×C₃×D₅	1	4	yes	complemented
556	#121	C₂×C₃×D₅	1	2	yes	complemented
557	C₄×D₄	—	5	2	no	—
558	C₄×D₄	—	5	4	no	—
559	C₄×D₄	—	5	2	no	—
560	C₄×D₄	—	5	4	no	—
561	C₄×D₄	—	5	2	no	—
562	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
563	#117	—	5	1	no	—
564	#117	—	5	2	no	—
565	#117	—	5	2	no	—
566	#117	—	5	1	no	—
567	#117	—	5	1	no	—
568	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
569	C₂×C₄⋊C₄	—	5	2	no	—
570	C₂×C₄⋊C₄	—	5	2	no	—
571	C₂×C₄⋊C₄	—	5	4	no	—
572	C₂×C₂²⋊C₄	—	5	2	no	—
573	C₂×C₂²⋊C₄	—	5	4	no	—
574	C₂×C₂²⋊C₄	—	5	4	no	—
575	C₂×C₄²	—	5	1	no	—
576	C₂×C₄²	—	5	1	no	—
577	C₂×C₃×C₅	—	4	1	no	—
578	C₂×C₃×C₅	—	4	4	no	—
579	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
580	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
581	C₃×D₅	—	4	1	no	—
582	C₃×D₅	—	4	4	no	—
583	C₃×D₅	#540	1	4	yes	direct product factor
584	C₂³×C₃	—	5	1	no	—
585	C₂³×C₃	—	5	1	no	—
586	C₂³×C₃	—	5	4	no	—
587	C₂³×C₃	—	10	2	no	—
588	C₂³×C₃	—	10	8	no	—
589	C₂³×C₃	—	10	8	no	—
590	C₂³×C₃	—	10	4	no	—
591	C₂³×C₃	—	10	8	no	—
592	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
593	C₂³×C₃	C₂³×D₅	1	4	yes	—
594	C₃×D₄	—	2	4	no	—
595	C₃×D₄	—	4	4	no	—
596	C₃×D₄	—	4	4	no	—
597	C₃×D₄	—	10	8	no	—
598	C₃×D₄	—	10	4	no	—
599	C₃×D₄	—	20	4	no	—
600	C₃×D₄	—	20	4	no	—
601	C₃×D₄	—	20	4	no	—
602	C₃×D₄	—	20	4	no	—
603	C₃×D₄	—	20	4	no	—
604	C₃×D₄	—	20	4	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	4	4	no	—
607	C₂×C₃×C₄	—	5	1	no	—
608	C₂×C₃×C₄	—	5	4	no	—
609	C₂×C₃×C₄	—	5	2	no	—
610	C₂×C₃×C₄	—	5	2	no	—
611	C₂×C₃×C₄	—	5	1	no	—
612	C₂×C₃×C₄	—	5	4	no	—
613	C₂×C₃×C₄	—	10	2	no	—
614	C₂×C₃×C₄	—	10	2	no	—
615	C₂×C₃×C₄	—	10	4	no	—
616	C₂×C₃×C₄	—	10	8	no	—
617	C₂×C₃×C₄	—	10	4	no	—
618	C₂×C₃×C₄	—	10	2	no	—
619	C₂×C₃×C₄	—	10	2	no	—
620	C₂×C₃×C₄	—	20	4	no	—
621	C₂×C₃×C₄	—	20	4	no	—
622	C₂×C₃×C₄	—	20	4	no	—
623	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
624	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
625	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
626	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
627	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
628	C₂²×C₅	—	2	1	no	—
629	C₂²×C₅	—	2	4	no	—
630	C₂²×C₅	—	2	4	no	—
631	C₂²×C₅	—	2	2	no	—
632	C₂²×C₅	—	2	4	no	—
633	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
634	C₂×D₅	—	2	1	no	—
635	C₂×D₅	—	2	4	no	—
636	C₂×D₅	—	2	4	no	—
637	C₂×D₅	—	2	2	no	—
638	C₂×D₅	—	2	4	no	—
639	C₂×D₅	—	4	4	no	—
640	C₂×D₅	—	4	16	no	—
641	C₂×D₅	C₂×C₃×#41	1	2	yes	—
642	C₂×D₅	C₃×H(5,𝔽₂)	1	4	yes	—
643	C₄×C₅	—	2	1	no	—
644	C₄×C₅	—	2	2	no	—
645	C₄×C₅	—	2	4	no	—
646	C₄×C₅	—	2	2	no	—
647	C₄×C₅	C₂×C₃×#41	1	2	yes	—
648	Dic₅	—	2	1	no	—
649	Dic₅	—	2	2	no	—
650	Dic₅	—	2	4	no	—
651	Dic₅	—	2	2	no	—
652	Dic₅	C₂×C₃×#41	1	2	yes	—
653	C₂⁴	—	5	1	no	—
654	C₂⁴	—	5	4	no	—
655	C₂×D₄	—	5	4	no	—
656	C₂×D₄	—	5	4	no	—
657	C₂×D₄	—	5	4	no	—
658	C₂×D₄	—	5	4	no	—
659	C₂×D₄	—	5	4	no	—
660	C₂×D₄	—	5	2	no	—
661	C₂×D₄	—	5	4	no	—
662	C₂×D₄	—	5	4	no	—
663	C₂×D₄	—	10	8	no	—
664	C₂×D₄	—	20	8	no	—
665	C₂×D₄	—	20	8	no	—
666	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
667	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
668	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
669	C₂²×C₄	—	5	1	no	—
670	C₂²×C₄	—	5	1	no	—
671	C₂²×C₄	—	5	4	no	—
672	C₂²×C₄	—	5	2	no	—
673	C₂²×C₄	—	5	2	no	—
674	C₂²×C₄	—	5	1	no	—
675	C₂²×C₄	—	5	4	no	—
676	C₂²×C₄	—	5	1	no	—
677	C₂²×C₄	—	5	1	no	—
678	C₂²×C₄	—	5	4	no	—
679	C₂²×C₄	—	5	4	no	—
680	C₂²×C₄	—	10	4	no	—
681	C₂²×C₄	—	20	8	no	—
682	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
683	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
684	C₄⋊C₄	—	5	2	no	—
685	C₄⋊C₄	—	5	2	no	—
686	C₄⋊C₄	—	5	2	no	—
687	C₄⋊C₄	—	5	4	no	—
688	C₄⋊C₄	—	5	2	no	—
689	C₄⋊C₄	—	5	4	no	—
690	C₄⋊C₄	—	5	4	no	—
691	C₄⋊C₄	—	5	4	no	—
692	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
693	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
694	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
695	C₂²⋊C₄	—	5	2	no	—
696	C₂²⋊C₄	—	5	4	no	—
697	C₂²⋊C₄	—	5	4	no	—
698	C₂²⋊C₄	—	5	2	no	—
699	C₂²⋊C₄	—	5	2	no	—
700	C₂²⋊C₄	—	5	4	no	—
701	C₂²⋊C₄	—	5	4	no	—
702	C₂²⋊C₄	—	5	4	no	—
703	C₂²⋊C₄	—	5	4	no	—
704	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
705	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
706	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
707	C₄²	—	5	2	no	—
708	C₄²	—	5	1	no	—
709	C₄²	—	5	2	no	—
710	C₄²	—	5	1	no	—
711	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
712	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
713	C₃×C₅	C₂×#540	1	1	yes	characteristic, complemented, Hall
714	C₂²×C₃	—	2	1	no	—
715	C₂²×C₃	—	2	4	no	—
716	C₂²×C₃	—	2	4	no	—
717	C₂²×C₃	—	2	2	no	—
718	C₂²×C₃	—	2	4	no	—
719	C₂²×C₃	—	5	2	no	—
720	C₂²×C₃	—	5	4	no	—
721	C₂²×C₃	—	10	1	no	—
722	C₂²×C₃	—	10	4	no	—
723	C₂²×C₃	—	10	4	no	—
724	C₂²×C₃	—	10	2	no	—
725	C₂²×C₃	—	10	4	no	—
726	C₂²×C₃	—	20	4	no	—
727	C₂²×C₃	—	20	16	no	—
728	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
729	C₃×C₄	—	2	1	no	—
730	C₃×C₄	—	2	2	no	—
731	C₃×C₄	—	2	4	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	5	2	no	—
734	C₃×C₄	—	10	1	no	—
735	C₃×C₄	—	10	2	no	—
736	C₃×C₄	—	10	4	no	—
737	C₃×C₄	—	10	2	no	—
738	C₃×C₄	D₅×#41	1	2	yes	—
739	C₂×C₅	—	4	1	no	—
740	C₂×C₅	—	4	4	no	—
741	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
742	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
743	D₅	—	4	1	no	—
744	D₅	—	4	4	no	—
745	D₅	C₃×#540	1	4	yes	direct product factor
746	C₂³	—	5	1	no	—
747	C₂³	—	5	1	no	—
748	C₂³	—	5	4	no	—
749	C₂³	—	10	2	no	—
750	C₂³	—	10	8	no	—
751	C₂³	—	10	8	no	—
752	C₂³	—	10	4	no	—
753	C₂³	—	10	8	no	—
754	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
755	C₂³	C₂³×C₃×D₅	1	4	yes	—
756	D₄	—	2	4	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	4	no	—
759	D₄	—	10	8	no	—
760	D₄	—	10	4	no	—
761	D₄	—	20	4	no	—
762	D₄	—	20	4	no	—
763	D₄	—	20	4	no	—
764	D₄	—	20	4	no	—
765	D₄	—	20	4	no	—
766	D₄	—	20	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	5	1	no	—
770	C₂×C₄	—	5	4	no	—
771	C₂×C₄	—	5	2	no	—
772	C₂×C₄	—	5	2	no	—
773	C₂×C₄	—	5	1	no	—
774	C₂×C₄	—	5	4	no	—
775	C₂×C₄	—	10	2	no	—
776	C₂×C₄	—	10	2	no	—
777	C₂×C₄	—	10	4	no	—
778	C₂×C₄	—	10	8	no	—
779	C₂×C₄	—	10	4	no	—
780	C₂×C₄	—	10	2	no	—
781	C₂×C₄	—	10	2	no	—
782	C₂×C₄	—	20	4	no	—
783	C₂×C₄	—	20	4	no	—
784	C₂×C₄	—	20	4	no	—
785	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
786	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
787	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
788	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
789	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
790	C₂×C₃	—	4	1	no	—
791	C₂×C₃	—	4	4	no	—
792	C₂×C₃	—	5	4	no	—
793	C₂×C₃	—	20	1	no	—
794	C₂×C₃	—	20	4	no	—
795	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
796	C₂×C₃	D₅×H(5,𝔽₂)	1	2	yes	—
797	C₅	C₂×C₃×#540	1	1	yes	characteristic, complemented, Sylow
798	C₂²	—	2	1	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	5	2	no	—
804	C₂²	—	5	4	no	—
805	C₂²	—	10	1	no	—
806	C₂²	—	10	4	no	—
807	C₂²	—	10	4	no	—
808	C₂²	—	10	2	no	—
809	C₂²	—	10	4	no	—
810	C₂²	—	20	4	no	—
811	C₂²	—	20	16	no	—
812	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	4	no	—
816	C₄	—	2	2	no	—
817	C₄	—	5	2	no	—
818	C₄	—	10	1	no	—
819	C₄	—	10	2	no	—
820	C₄	—	10	4	no	—
821	C₄	—	10	2	no	—
822	C₄	C₃×D₅×#41	1	2	yes	—
823	C₃	D₅×#540	1	1	yes	characteristic, direct product factor, Sylow
824	C₂	—	4	1	no	—
825	C₂	—	4	4	no	—
826	C₂	—	5	4	no	—
827	C₂	—	20	1	no	—
828	C₂	—	20	4	no	—
829	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
830	C₂	C₃×D₅×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#540	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#540	D₅
hypocenter	C₅	C₂×C₃×#540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#540

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#540	C₂	semidirect
2. C₃×#66053	C₂	semidirect
3. C₃×D₅×#127	C₂	semidirect
4. C₃×#66032	C₂	semidirect
5. C₃×D₅×#125	C₂	semidirect
6. C₃×#65997	C₂	semidirect
7. C₃×D₅×#123	C₂	semidirect
8. C₃×#65953	C₂	semidirect
9. C₃×#65949	C₂	semidirect
10. C₃×D₅×#121	C₂	semidirect
11. C₃×D₅×#121	C₂	semidirect
12. C₃×#65896	C₂	semidirect
13. C₃×C₄×D₄×D₅	C₂	semidirect
14. C₃×#65869	C₂	semidirect
15. C₃×D₅×#117	C₂	semidirect
16. D₅×#540	C₃	direct (N × H)
22. C₃×C₅×#127	C₂²	semidirect
23. C₃×C₅×#125	C₂²	semidirect
24. C₃×C₅×#123	C₂²	semidirect
25. C₃×C₅×#121	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
27. C₃×C₄×C₅×D₄	C₂²	semidirect
28. C₃×C₅×#117	C₂²	semidirect
29. C₃×#4086	C₂²	semidirect
30. C₃×#4086	C₂²	semidirect
31. C₃×#4085	C₂²	semidirect
32. C₃×#4085	C₂²	semidirect
33. C₃×#4085	C₂²	semidirect
34. C₃×#4084	C₂²	semidirect
35. C₃×#4084	C₂²	semidirect
36. C₃×#4081	C₂²	semidirect
37. C₃×D₄×Dic₅	C₂²	semidirect
38. C₃×#4076	C₂²	semidirect
39. C₃×#4076	C₂²	semidirect
40. C₃×#4075	C₂²	semidirect
41. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
42. C₃×#4072	C₂²	semidirect
43. C₃×#4041	C₂²	semidirect
44. C₃×#4041	C₂²	semidirect
45. C₃×#4040	C₂²	semidirect
46. C₃×#4040	C₂²	semidirect
47. C₃×#4039	C₂²	semidirect
48. C₃×#4038	C₂²	semidirect
52. C₃×#4036	C₂²	semidirect
53. C₃×#4035	C₂²	semidirect
54. C₃×#4032	C₂²	semidirect
55. C₃×#4030	C₂²	semidirect
56. C₃×#4030	C₂²	semidirect
57. C₃×#4030	C₂²	semidirect
58. C₃×#4029	C₂²	semidirect
59. C₃×#4029	C₂²	semidirect
60. C₃×#4027	C₂²	semidirect
64. C₃×#4023	C₂²	semidirect
65. C₃×#4020	C₂²	semidirect
66. C₃×C₄×D₂₀	C₂²	semidirect
67. C₃×#4018	C₂²	semidirect
68. C₃×#4018	C₂²	semidirect
71. C₃×#4016	C₂²	semidirect
73. C₅×#540	C₂×C₃	semidirect
74. #66053	C₂×C₃	semidirect
75. D₅×#127	C₂×C₃	semidirect
76. #66032	C₂×C₃	semidirect
77. D₅×#125	C₂×C₃	semidirect
78. #65997	C₂×C₃	semidirect
79. D₅×#123	C₂×C₃	semidirect
80. #65953	C₂×C₃	semidirect
81. #65949	C₂×C₃	semidirect
82. D₅×#121	C₂×C₃	semidirect
83. D₅×#121	C₂×C₃	semidirect
84. #65896	C₂×C₃	semidirect
85. C₄×D₄×D₅	C₂×C₃	semidirect
86. #65869	C₂×C₃	semidirect
87. D₅×#117	C₂×C₃	semidirect
155. C₃×#540	D₅	direct (N × H)
168. C₅×#127	C₂²×C₃	semidirect
169. C₅×#125	C₂²×C₃	semidirect
170. C₅×#123	C₂²×C₃	semidirect
171. C₅×#121	C₂²×C₃	semidirect
172. C₅×#121	C₂²×C₃	semidirect
173. C₄×C₅×D₄	C₂²×C₃	semidirect
174. C₅×#117	C₂²×C₃	semidirect
175. #4086	C₂²×C₃	semidirect
176. #4086	C₂²×C₃	semidirect
177. #4085	C₂²×C₃	semidirect
178. #4085	C₂²×C₃	semidirect
179. #4085	C₂²×C₃	semidirect
180. #4084	C₂²×C₃	semidirect
181. #4084	C₂²×C₃	semidirect
182. #4081	C₂²×C₃	semidirect
183. D₄×Dic₅	C₂²×C₃	semidirect
184. #4076	C₂²×C₃	semidirect
185. #4076	C₂²×C₃	semidirect
186. #4075	C₂²×C₃	semidirect
187. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
188. #4072	C₂²×C₃	semidirect
189. #4041	C₂²×C₃	semidirect
190. #4041	C₂²×C₃	semidirect
191. #4040	C₂²×C₃	semidirect
192. #4040	C₂²×C₃	semidirect
193. #4039	C₂²×C₃	semidirect
194. #4038	C₂²×C₃	semidirect
198. #4036	C₂²×C₃	semidirect
199. #4035	C₂²×C₃	semidirect
200. #4032	C₂²×C₃	semidirect
201. #4030	C₂²×C₃	semidirect
202. #4030	C₂²×C₃	semidirect
203. #4030	C₂²×C₃	semidirect
204. #4029	C₂²×C₃	semidirect
205. #4029	C₂²×C₃	semidirect
206. #4027	C₂²×C₃	semidirect
210. #4023	C₂²×C₃	semidirect
211. #4020	C₂²×C₃	semidirect
212. C₄×D₂₀	C₂²×C₃	semidirect
213. #4018	C₂²×C₃	semidirect
214. #4018	C₂²×C₃	semidirect
217. #4016	C₂²×C₃	semidirect
271. C₃×#127	C₂×D₅	semidirect
275. C₃×#125	C₂×D₅	semidirect
283. C₃×#123	C₂×D₅	semidirect
296. C₃×#121	C₂×D₅	semidirect
297. C₃×#121	C₂×D₅	semidirect
303. C₃×C₄×D₄	C₂×D₅	semidirect
309. C₃×#117	C₂×D₅	semidirect
385. #540	C₃×D₅	direct (N × H)
530. #127	C₂×C₃×D₅	semidirect
534. #125	C₂×C₃×D₅	semidirect
542. #123	C₂×C₃×D₅	semidirect
555. #121	C₂×C₃×D₅	semidirect
556. #121	C₂×C₃×D₅	semidirect
562. C₄×D₄	C₂×C₃×D₅	semidirect
568. #117	C₂×C₃×D₅	semidirect
583. C₃×D₅	#540	direct (N × H)
713. C₃×C₅	C₂×#540	semidirect
745. D₅	C₃×#540	direct (N × H)
797. C₅	C₂×C₃×#540	semidirect
823. C₃	D₅×#540	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#540	2
C₃×#66053	2
C₃×D₅×#127	2
C₃×#66032	2
C₃×D₅×#125	2
C₃×#65997	2
C₃×D₅×#123	2
C₃×#65953	2
C₃×#65949	2
C₃×D₅×#121	2
C₃×#65896	2
C₃×C₄×D₄×D₅	2
C₃×#65869	2
C₃×D₅×#117	2
D₅×#540	3
C₂×C₃×#540	5

Subgroups — C3×D5×#540 #14481077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#540 #14481077