Subgroups — C₅×D₃×#540 #14481076

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	C₅×#5719	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5697	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5663	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#123	C₂	1	4	yes	maximal, complemented
8	C₅×#5619	C₂	1	2	yes	maximal, complemented
9	C₅×#5615	C₂	1	4	yes	maximal, complemented
10	C₅×D₃×#121	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
12	C₅×#5562	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
14	C₅×#5535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#540	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
18	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
19	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	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	C₅×#940	C₂²	1	4	yes	complemented
30	C₅×#940	C₂²	1	2	yes	complemented
31	C₅×#939	C₂²	1	4	yes	complemented
32	C₅×#939	C₂²	1	4	yes	complemented
33	C₅×#939	C₂²	1	4	yes	complemented
34	C₅×#938	C₂²	1	2	yes	complemented
35	C₅×#938	C₂²	1	4	yes	complemented
36	C₅×#935	C₂²	1	4	yes	complemented
37	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
38	C₅×#930	C₂²	1	4	yes	complemented
39	C₅×#930	C₂²	1	2	yes	complemented
40	C₅×#929	C₂²	1	4	yes	complemented
41	C₄×C₅×#67	C₂²	1	4	yes	complemented
42	C₅×#926	C₂²	1	1	yes	characteristic, complemented
43	C₅×#895	C₂²	1	4	yes	complemented
44	C₅×#895	C₂²	1	2	yes	complemented
45	C₅×#894	C₂²	1	4	yes	complemented
46	C₅×#894	C₂²	1	4	yes	complemented
47	C₅×#893	C₂²	1	2	yes	complemented
48	C₅×#892	C₂²	1	2	yes	complemented
49	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
51	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
52	C₅×#890	C₂²	1	2	yes	complemented
53	C₅×#889	C₂²	1	4	yes	complemented
54	C₅×#886	C₂²	1	4	yes	complemented
55	C₅×#884	C₂²	1	4	yes	complemented
56	C₅×#884	C₂²	1	4	yes	complemented
57	C₅×#884	C₂²	1	4	yes	complemented
58	C₅×#883	C₂²	1	4	yes	complemented
59	C₅×#883	C₂²	1	4	yes	complemented
60	C₅×#67⋊C₄	C₂²	1	4	yes	complemented
61	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
62	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₅×#877	C₂²	1	2	yes	complemented
65	C₅×#874	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
67	C₅×#872	C₂²	1	1	yes	characteristic, complemented
68	C₅×#872	C₂²	1	1	yes	characteristic, complemented
69	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
70	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
71	C₅×#870	C₂²	1	1	yes	characteristic, complemented
72	D₃×#540	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
73	C₅×#540	—	3	1	no	—
74	C₅×#540	—	3	1	no	—
75	C₅×#540	—	3	4	no	—
76	C₅×#540	—	3	4	no	—
77	C₅×#540	—	3	2	no	—
78	C₅×#540	—	3	2	no	—
79	C₅×#540	—	3	1	no	—
80	C₅×#540	D₃	1	1	yes	characteristic, direct product factor
81	C₂×C₅×#127	—	3	1	no	—
82	C₂×C₅×#125	—	3	1	no	—
83	C₂×C₅×#123	—	3	4	no	—
84	C₂×C₅×#121	—	3	4	no	—
85	C₂×C₅×#121	—	3	2	no	—
86	C₂×C₄×C₅×D₄	—	3	2	no	—
87	C₂×C₅×#117	—	3	1	no	—
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂³×C₅×D₃	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×C₅×#67	C₂³	1	4	yes	—
96	C₂×C₅×#67	C₂³	1	4	yes	—
97	C₂×C₅×#67	C₂³	1	4	yes	—
98	C₂×C₅×#67	C₂³	1	4	yes	—
99	C₂×C₅×#67	C₂³	1	4	yes	—
100	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
102	C₅×D₃×D₄	—	2	8	no	—
103	C₅×D₃×D₄	—	4	8	no	—
104	C₅×D₃×D₄	—	4	8	no	—
105	C₂×C₅×D₁₂	C₂³	1	2	yes	—
106	C₂×C₅×D₁₂	C₂³	1	4	yes	—
107	C₂×C₅×D₁₂	C₂³	1	4	yes	—
108	C₂×C₄×C₅×D₃	—	2	4	no	—
109	C₂×C₄×C₅×D₃	—	4	8	no	—
110	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
111	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
112	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
114	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
115	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
116	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
117	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
118	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
119	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
120	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	2	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	C₅×#217	C₂³	1	2	yes	—
128	C₅×#217	C₂³	1	4	yes	—
129	C₅×#217	C₂³	1	4	yes	—
130	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
131	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
132	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
133	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
134	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
135	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
137	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
138	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
139	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
140	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
141	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
142	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
145	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
146	C₄×C₅×Dic₃	C₂³	1	2	yes	—
147	C₄×C₅×Dic₃	C₂³	1	2	yes	—
148	C₃×#540	C₂×C₅	1	1	yes	characteristic, complemented
149	#5719	C₂×C₅	1	1	yes	characteristic, complemented
150	D₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
151	#5697	C₂×C₅	1	1	yes	characteristic, complemented
152	D₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
153	#5663	C₂×C₅	1	4	yes	complemented
154	D₃×#123	C₂×C₅	1	4	yes	complemented
155	#5619	C₂×C₅	1	2	yes	complemented
156	#5615	C₂×C₅	1	4	yes	complemented
157	D₃×#121	C₂×C₅	1	2	yes	complemented
158	D₃×#121	C₂×C₅	1	4	yes	complemented
159	#5562	C₂×C₅	1	2	yes	complemented
160	C₄×D₃×D₄	C₂×C₅	1	2	yes	complemented
161	#5535	C₂×C₅	1	1	yes	characteristic, complemented
162	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂²×C₅×D₄	—	3	2	no	—
164	C₂²×C₅×D₄	—	3	4	no	—
165	C₂²×C₅×D₄	—	3	4	no	—
166	C₂³×C₄×C₅	—	3	1	no	—
167	C₂³×C₄×C₅	—	3	4	no	—
168	C₅×#127	—	3	4	no	—
169	C₅×#127	—	3	2	no	—
170	C₅×#127	—	3	1	no	—
171	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
172	C₅×#125	—	3	4	no	—
173	C₅×#125	—	3	2	no	—
174	C₅×#125	—	3	1	no	—
175	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
176	C₅×#123	—	3	4	no	—
177	C₅×#123	—	3	4	no	—
178	C₅×#123	—	3	4	no	—
179	C₅×#123	—	3	4	no	—
180	C₅×#123	—	3	4	no	—
181	C₅×#123	—	3	4	no	—
182	C₅×#123	—	3	4	no	—
183	C₅×#123	C₂×D₃	1	4	yes	complemented
184	C₅×#121	—	3	4	no	—
185	C₅×#121	—	3	2	no	—
186	C₅×#121	—	3	4	no	—
187	C₅×#121	—	3	4	no	—
188	C₅×#121	—	3	4	no	—
189	C₅×#121	—	3	4	no	—
190	C₅×#121	—	3	2	no	—
191	C₅×#121	—	3	4	no	—
192	C₅×#121	—	3	2	no	—
193	C₅×#121	—	3	4	no	—
194	C₅×#121	—	3	4	no	—
195	C₅×#121	—	3	4	no	—
196	C₅×#121	C₂×D₃	1	4	yes	complemented
197	C₅×#121	C₂×D₃	1	2	yes	complemented
198	C₄×C₅×D₄	—	3	2	no	—
199	C₄×C₅×D₄	—	3	4	no	—
200	C₄×C₅×D₄	—	3	2	no	—
201	C₄×C₅×D₄	—	3	4	no	—
202	C₄×C₅×D₄	—	3	2	no	—
203	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
204	C₅×#117	—	3	1	no	—
205	C₅×#117	—	3	2	no	—
206	C₅×#117	—	3	2	no	—
207	C₅×#117	—	3	1	no	—
208	C₅×#117	—	3	1	no	—
209	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
210	C₂×C₅×C₄⋊C₄	—	3	2	no	—
211	C₂×C₅×C₄⋊C₄	—	3	2	no	—
212	C₂×C₅×C₄⋊C₄	—	3	4	no	—
213	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
214	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
215	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
216	C₂×C₄²×C₅	—	3	1	no	—
217	C₂×C₄²×C₅	—	3	1	no	—
218	C₂×#540	—	3	1	no	Sylow
219	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
220	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
221	C₂²×C₅×D₃	—	2	2	no	—
222	C₂²×C₅×D₃	—	2	8	no	—
223	C₂²×C₅×D₃	—	2	8	no	—
224	C₂²×C₅×D₃	—	2	4	no	—
225	C₂²×C₅×D₃	—	2	8	no	—
226	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
228	C₂²×C₅×D₃	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	C₅×#67	—	2	8	no	—
240	C₅×#67	—	4	4	no	—
241	C₅×#67	—	4	4	no	—
242	C₅×#67	—	4	4	no	—
243	C₅×#67	—	4	4	no	—
244	C₂×C₅×Dic₃	—	2	2	no	—
245	C₂×C₅×Dic₃	—	4	4	no	—
246	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
247	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
248	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
249	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
251	C₅×D₁₂	—	2	4	no	—
252	C₅×D₁₂	—	4	4	no	—
253	C₅×D₁₂	—	4	4	no	—
254	C₄×C₅×D₃	—	2	2	no	—
255	C₄×C₅×D₃	—	2	4	no	—
256	C₄×C₅×D₃	—	2	8	no	—
257	C₄×C₅×D₃	—	2	4	no	—
258	C₄×C₅×D₃	—	2	2	no	—
259	C₄×C₅×D₃	—	2	2	no	—
260	C₄×C₅×D₃	—	4	4	no	—
261	C₄×C₅×D₃	—	4	4	no	—
262	C₄×C₅×D₃	#41	1	4	yes	—
263	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
264	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
265	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
266	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
267	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
268	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₃×#123	C₂²×C₅	1	4	yes	complemented
271	C₃×#121	C₂²×C₅	1	4	yes	complemented
272	C₃×#121	C₂²×C₅	1	2	yes	complemented
273	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
274	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
275	#940	C₂²×C₅	1	4	yes	complemented
276	#940	C₂²×C₅	1	2	yes	complemented
277	#939	C₂²×C₅	1	4	yes	complemented
278	#939	C₂²×C₅	1	4	yes	complemented
279	#939	C₂²×C₅	1	4	yes	complemented
280	#938	C₂²×C₅	1	2	yes	complemented
281	#938	C₂²×C₅	1	4	yes	complemented
282	#935	C₂²×C₅	1	4	yes	complemented
283	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
284	#930	C₂²×C₅	1	4	yes	complemented
285	#930	C₂²×C₅	1	2	yes	complemented
286	#929	C₂²×C₅	1	4	yes	complemented
287	C₄×#67	C₂²×C₅	1	4	yes	complemented
288	#926	C₂²×C₅	1	1	yes	characteristic, complemented
289	#895	C₂²×C₅	1	4	yes	complemented
290	#895	C₂²×C₅	1	2	yes	complemented
291	#894	C₂²×C₅	1	4	yes	complemented
292	#894	C₂²×C₅	1	4	yes	complemented
293	#893	C₂²×C₅	1	2	yes	complemented
294	#892	C₂²×C₅	1	2	yes	complemented
295	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
296	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
297	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
298	#890	C₂²×C₅	1	2	yes	complemented
299	#889	C₂²×C₅	1	4	yes	complemented
300	#886	C₂²×C₅	1	4	yes	complemented
301	#884	C₂²×C₅	1	4	yes	complemented
302	#884	C₂²×C₅	1	4	yes	complemented
303	#884	C₂²×C₅	1	4	yes	complemented
304	#883	C₂²×C₅	1	4	yes	complemented
305	#883	C₂²×C₅	1	4	yes	complemented
306	#67⋊C₄	C₂²×C₅	1	4	yes	complemented
307	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
308	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
309	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
310	#877	C₂²×C₅	1	2	yes	complemented
311	#874	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
313	#872	C₂²×C₅	1	1	yes	characteristic, complemented
314	#872	C₂²×C₅	1	1	yes	characteristic, complemented
315	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
316	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
317	#870	C₂²×C₅	1	1	yes	characteristic, complemented
318	C₂⁴×C₅	—	3	1	no	—
319	C₂⁴×C₅	—	3	4	no	—
320	C₂×C₅×D₄	—	3	4	no	—
321	C₂×C₅×D₄	—	3	4	no	—
322	C₂×C₅×D₄	—	3	4	no	—
323	C₂×C₅×D₄	—	3	4	no	—
324	C₂×C₅×D₄	—	3	4	no	—
325	C₂×C₅×D₄	—	3	2	no	—
326	C₂×C₅×D₄	—	3	4	no	—
327	C₂×C₅×D₄	—	3	4	no	—
328	C₂×C₅×D₄	—	6	8	no	—
329	C₂×C₅×D₄	—	12	8	no	—
330	C₂×C₅×D₄	—	12	8	no	—
331	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
332	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
333	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
334	C₂²×C₄×C₅	—	3	1	no	—
335	C₂²×C₄×C₅	—	3	1	no	—
336	C₂²×C₄×C₅	—	3	4	no	—
337	C₂²×C₄×C₅	—	3	2	no	—
338	C₂²×C₄×C₅	—	3	2	no	—
339	C₂²×C₄×C₅	—	3	1	no	—
340	C₂²×C₄×C₅	—	3	4	no	—
341	C₂²×C₄×C₅	—	3	1	no	—
342	C₂²×C₄×C₅	—	3	1	no	—
343	C₂²×C₄×C₅	—	3	4	no	—
344	C₂²×C₄×C₅	—	3	4	no	—
345	C₂²×C₄×C₅	—	6	4	no	—
346	C₂²×C₄×C₅	—	12	8	no	—
347	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
348	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
349	C₅×C₄⋊C₄	—	3	2	no	—
350	C₅×C₄⋊C₄	—	3	2	no	—
351	C₅×C₄⋊C₄	—	3	2	no	—
352	C₅×C₄⋊C₄	—	3	4	no	—
353	C₅×C₄⋊C₄	—	3	2	no	—
354	C₅×C₄⋊C₄	—	3	4	no	—
355	C₅×C₄⋊C₄	—	3	4	no	—
356	C₅×C₄⋊C₄	—	3	4	no	—
357	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
358	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
359	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
360	C₅×C₂²⋊C₄	—	3	2	no	—
361	C₅×C₂²⋊C₄	—	3	4	no	—
362	C₅×C₂²⋊C₄	—	3	4	no	—
363	C₅×C₂²⋊C₄	—	3	2	no	—
364	C₅×C₂²⋊C₄	—	3	2	no	—
365	C₅×C₂²⋊C₄	—	3	4	no	—
366	C₅×C₂²⋊C₄	—	3	4	no	—
367	C₅×C₂²⋊C₄	—	3	4	no	—
368	C₅×C₂²⋊C₄	—	3	4	no	—
369	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
370	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
371	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
372	C₄²×C₅	—	3	2	no	—
373	C₄²×C₅	—	3	1	no	—
374	C₄²×C₅	—	3	2	no	—
375	C₄²×C₅	—	3	1	no	—
376	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
377	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
378	#540	—	3	1	no	—
379	#540	—	3	1	no	—
380	#540	—	3	4	no	—
381	#540	—	3	4	no	—
382	#540	—	3	2	no	—
383	#540	—	3	2	no	—
384	#540	—	3	1	no	—
385	#540	C₅×D₃	1	1	yes	characteristic, direct product factor
386	C₂×#127	—	3	1	no	—
387	C₂×#125	—	3	1	no	—
388	C₂×#123	—	3	4	no	—
389	C₂×#121	—	3	4	no	—
390	C₂×#121	—	3	2	no	—
391	C₂×C₄×D₄	—	3	2	no	—
392	C₂×#117	—	3	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×C₅×D₃	—	2	1	no	—
400	C₂×C₅×D₃	—	2	4	no	—
401	C₂×C₅×D₃	—	2	4	no	—
402	C₂×C₅×D₃	—	2	2	no	—
403	C₂×C₅×D₃	—	2	4	no	—
404	C₂×C₅×D₃	—	4	4	no	—
405	C₂×C₅×D₃	—	4	16	no	—
406	C₂×C₅×D₃	C₂×#41	1	2	yes	—
407	C₂×C₅×D₃	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	C₅×Dic₃	—	2	1	no	—
414	C₅×Dic₃	—	2	2	no	—
415	C₅×Dic₃	—	2	4	no	—
416	C₅×Dic₃	—	2	2	no	—
417	C₅×Dic₃	C₂×#41	1	2	yes	—
418	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
419	C₂³×D₃	C₂³×C₅	1	4	yes	—
420	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
421	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
422	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
423	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
425	C₂×#67	C₂³×C₅	1	4	yes	—
426	C₂×#67	C₂³×C₅	1	4	yes	—
427	C₂×#67	C₂³×C₅	1	4	yes	—
428	C₂×#67	C₂³×C₅	1	4	yes	—
429	C₂×#67	C₂³×C₅	1	4	yes	—
430	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
431	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
432	D₃×D₄	—	2	8	no	—
433	D₃×D₄	—	4	8	no	—
434	D₃×D₄	—	4	8	no	—
435	C₂×D₁₂	C₂³×C₅	1	2	yes	—
436	C₂×D₁₂	C₂³×C₅	1	4	yes	—
437	C₂×D₁₂	C₂³×C₅	1	4	yes	—
438	C₂×C₄×D₃	—	2	4	no	—
439	C₂×C₄×D₃	—	4	8	no	—
440	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
441	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
442	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
444	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
445	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
447	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
448	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
449	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
450	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
451	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
452	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
453	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
454	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
455	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
457	#217	C₂³×C₅	1	2	yes	—
458	#217	C₂³×C₅	1	4	yes	—
459	#217	C₂³×C₅	1	4	yes	—
460	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
461	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
462	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
463	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
464	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
465	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
466	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
467	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
468	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
469	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
470	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
471	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
472	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
473	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
474	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
475	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
476	C₄×Dic₃	C₂³×C₅	1	2	yes	—
477	C₄×Dic₃	C₂³×C₅	1	2	yes	—
478	C₂³×C₅	—	3	1	no	—
479	C₂³×C₅	—	3	1	no	—
480	C₂³×C₅	—	3	4	no	—
481	C₂³×C₅	—	6	2	no	—
482	C₂³×C₅	—	6	8	no	—
483	C₂³×C₅	—	6	8	no	—
484	C₂³×C₅	—	6	4	no	—
485	C₂³×C₅	—	6	8	no	—
486	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
487	C₂³×C₅	C₂³×D₃	1	4	yes	—
488	C₅×D₄	—	2	4	no	—
489	C₅×D₄	—	4	4	no	—
490	C₅×D₄	—	4	4	no	—
491	C₅×D₄	—	6	8	no	—
492	C₅×D₄	—	6	4	no	—
493	C₅×D₄	—	12	4	no	—
494	C₅×D₄	—	12	4	no	—
495	C₅×D₄	—	12	4	no	—
496	C₅×D₄	—	12	4	no	—
497	C₅×D₄	—	12	4	no	—
498	C₅×D₄	—	12	4	no	—
499	C₂×C₄×C₅	—	2	2	no	—
500	C₂×C₄×C₅	—	3	1	no	—
501	C₂×C₄×C₅	—	3	4	no	—
502	C₂×C₄×C₅	—	3	2	no	—
503	C₂×C₄×C₅	—	3	2	no	—
504	C₂×C₄×C₅	—	3	1	no	—
505	C₂×C₄×C₅	—	3	4	no	—
506	C₂×C₄×C₅	—	4	4	no	—
507	C₂×C₄×C₅	—	6	2	no	—
508	C₂×C₄×C₅	—	6	2	no	—
509	C₂×C₄×C₅	—	6	4	no	—
510	C₂×C₄×C₅	—	6	8	no	—
511	C₂×C₄×C₅	—	6	4	no	—
512	C₂×C₄×C₅	—	6	2	no	—
513	C₂×C₄×C₅	—	6	2	no	—
514	C₂×C₄×C₅	—	12	4	no	—
515	C₂×C₄×C₅	—	12	4	no	—
516	C₂×C₄×C₅	—	12	4	no	—
517	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
518	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
519	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
520	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
521	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
522	C₂²×D₄	—	3	2	no	—
523	C₂²×D₄	—	3	4	no	—
524	C₂²×D₄	—	3	4	no	—
525	C₂³×C₄	—	3	1	no	—
526	C₂³×C₄	—	3	4	no	—
527	#127	—	3	4	no	—
528	#127	—	3	2	no	—
529	#127	—	3	1	no	—
530	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
531	#125	—	3	4	no	—
532	#125	—	3	2	no	—
533	#125	—	3	1	no	—
534	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
535	#123	—	3	4	no	—
536	#123	—	3	4	no	—
537	#123	—	3	4	no	—
538	#123	—	3	4	no	—
539	#123	—	3	4	no	—
540	#123	—	3	4	no	—
541	#123	—	3	4	no	—
542	#123	C₂×C₅×D₃	1	4	yes	complemented
543	#121	—	3	4	no	—
544	#121	—	3	2	no	—
545	#121	—	3	4	no	—
546	#121	—	3	4	no	—
547	#121	—	3	4	no	—
548	#121	—	3	4	no	—
549	#121	—	3	2	no	—
550	#121	—	3	4	no	—
551	#121	—	3	2	no	—
552	#121	—	3	4	no	—
553	#121	—	3	4	no	—
554	#121	—	3	4	no	—
555	#121	C₂×C₅×D₃	1	4	yes	complemented
556	#121	C₂×C₅×D₃	1	2	yes	complemented
557	C₄×D₄	—	3	2	no	—
558	C₄×D₄	—	3	4	no	—
559	C₄×D₄	—	3	2	no	—
560	C₄×D₄	—	3	4	no	—
561	C₄×D₄	—	3	2	no	—
562	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
563	#117	—	3	1	no	—
564	#117	—	3	2	no	—
565	#117	—	3	2	no	—
566	#117	—	3	1	no	—
567	#117	—	3	1	no	—
568	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	C₂×C₄⋊C₄	—	3	2	no	—
570	C₂×C₄⋊C₄	—	3	2	no	—
571	C₂×C₄⋊C₄	—	3	4	no	—
572	C₂×C₂²⋊C₄	—	3	2	no	—
573	C₂×C₂²⋊C₄	—	3	4	no	—
574	C₂×C₂²⋊C₄	—	3	4	no	—
575	C₂×C₄²	—	3	1	no	—
576	C₂×C₄²	—	3	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	C₅×D₃	—	4	1	no	—
582	C₅×D₃	—	4	4	no	—
583	C₅×D₃	#540	1	4	yes	direct product factor
584	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
585	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
586	C₂²×D₃	—	2	2	no	—
587	C₂²×D₃	—	2	8	no	—
588	C₂²×D₃	—	2	8	no	—
589	C₂²×D₃	—	2	4	no	—
590	C₂²×D₃	—	2	8	no	—
591	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
592	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
593	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
594	C₃×D₄	—	2	4	no	—
595	C₃×D₄	—	4	4	no	—
596	C₃×D₄	—	4	4	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	4	4	no	—
599	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
600	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
601	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
602	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
603	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
604	#67	—	2	8	no	—
605	#67	—	4	4	no	—
606	#67	—	4	4	no	—
607	#67	—	4	4	no	—
608	#67	—	4	4	no	—
609	C₂×Dic₃	—	2	2	no	—
610	C₂×Dic₃	—	4	4	no	—
611	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
612	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
613	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
614	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
615	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
616	D₁₂	—	2	4	no	—
617	D₁₂	—	4	4	no	—
618	D₁₂	—	4	4	no	—
619	C₄×D₃	—	2	2	no	—
620	C₄×D₃	—	2	4	no	—
621	C₄×D₃	—	2	8	no	—
622	C₄×D₃	—	2	4	no	—
623	C₄×D₃	—	2	2	no	—
624	C₄×D₃	—	2	2	no	—
625	C₄×D₃	—	4	4	no	—
626	C₄×D₃	—	4	4	no	—
627	C₄×D₃	C₅×#41	1	4	yes	—
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	—	3	2	no	—
634	C₂²×C₅	—	3	4	no	—
635	C₂²×C₅	—	6	1	no	—
636	C₂²×C₅	—	6	4	no	—
637	C₂²×C₅	—	6	4	no	—
638	C₂²×C₅	—	6	2	no	—
639	C₂²×C₅	—	6	4	no	—
640	C₂²×C₅	—	12	4	no	—
641	C₂²×C₅	—	12	16	no	—
642	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
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	—	3	2	no	—
648	C₄×C₅	—	6	1	no	—
649	C₄×C₅	—	6	2	no	—
650	C₄×C₅	—	6	4	no	—
651	C₄×C₅	—	6	2	no	—
652	C₄×C₅	D₃×#41	1	2	yes	—
653	C₂⁴	—	3	1	no	—
654	C₂⁴	—	3	4	no	—
655	C₂×D₄	—	3	4	no	—
656	C₂×D₄	—	3	4	no	—
657	C₂×D₄	—	3	4	no	—
658	C₂×D₄	—	3	4	no	—
659	C₂×D₄	—	3	4	no	—
660	C₂×D₄	—	3	2	no	—
661	C₂×D₄	—	3	4	no	—
662	C₂×D₄	—	3	4	no	—
663	C₂×D₄	—	6	8	no	—
664	C₂×D₄	—	12	8	no	—
665	C₂×D₄	—	12	8	no	—
666	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
667	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
668	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
669	C₂²×C₄	—	3	1	no	—
670	C₂²×C₄	—	3	1	no	—
671	C₂²×C₄	—	3	4	no	—
672	C₂²×C₄	—	3	2	no	—
673	C₂²×C₄	—	3	2	no	—
674	C₂²×C₄	—	3	1	no	—
675	C₂²×C₄	—	3	4	no	—
676	C₂²×C₄	—	3	1	no	—
677	C₂²×C₄	—	3	1	no	—
678	C₂²×C₄	—	3	4	no	—
679	C₂²×C₄	—	3	4	no	—
680	C₂²×C₄	—	6	4	no	—
681	C₂²×C₄	—	12	8	no	—
682	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
683	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
684	C₄⋊C₄	—	3	2	no	—
685	C₄⋊C₄	—	3	2	no	—
686	C₄⋊C₄	—	3	2	no	—
687	C₄⋊C₄	—	3	4	no	—
688	C₄⋊C₄	—	3	2	no	—
689	C₄⋊C₄	—	3	4	no	—
690	C₄⋊C₄	—	3	4	no	—
691	C₄⋊C₄	—	3	4	no	—
692	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
693	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
694	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
695	C₂²⋊C₄	—	3	2	no	—
696	C₂²⋊C₄	—	3	4	no	—
697	C₂²⋊C₄	—	3	4	no	—
698	C₂²⋊C₄	—	3	2	no	—
699	C₂²⋊C₄	—	3	2	no	—
700	C₂²⋊C₄	—	3	4	no	—
701	C₂²⋊C₄	—	3	4	no	—
702	C₂²⋊C₄	—	3	4	no	—
703	C₂²⋊C₄	—	3	4	no	—
704	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
705	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
706	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
707	C₄²	—	3	2	no	—
708	C₄²	—	3	1	no	—
709	C₄²	—	3	2	no	—
710	C₄²	—	3	1	no	—
711	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₄²	C₂²×C₅×D₃	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	C₂⁵×C₅	1	1	yes	characteristic
720	C₂×D₃	—	2	1	no	—
721	C₂×D₃	—	2	4	no	—
722	C₂×D₃	—	2	4	no	—
723	C₂×D₃	—	2	2	no	—
724	C₂×D₃	—	2	4	no	—
725	C₂×D₃	—	4	4	no	—
726	C₂×D₃	—	4	16	no	—
727	C₂×D₃	C₂×C₅×#41	1	2	yes	—
728	C₂×D₃	C₅×H(5,𝔽₂)	1	4	yes	—
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	C₂×C₅×#41	1	2	yes	—
734	Dic₃	—	2	1	no	—
735	Dic₃	—	2	2	no	—
736	Dic₃	—	2	4	no	—
737	Dic₃	—	2	2	no	—
738	Dic₃	C₂×C₅×#41	1	2	yes	—
739	C₂×C₅	—	3	4	no	—
740	C₂×C₅	—	4	1	no	—
741	C₂×C₅	—	4	4	no	—
742	C₂×C₅	—	12	1	no	—
743	C₂×C₅	—	12	4	no	—
744	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
745	C₂×C₅	D₃×H(5,𝔽₂)	1	2	yes	—
746	C₂³	—	3	1	no	—
747	C₂³	—	3	1	no	—
748	C₂³	—	3	4	no	—
749	C₂³	—	6	2	no	—
750	C₂³	—	6	8	no	—
751	C₂³	—	6	8	no	—
752	C₂³	—	6	4	no	—
753	C₂³	—	6	8	no	—
754	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
755	C₂³	C₂³×C₅×D₃	1	4	yes	—
756	D₄	—	2	4	no	—
757	D₄	—	4	4	no	—
758	D₄	—	4	4	no	—
759	D₄	—	6	8	no	—
760	D₄	—	6	4	no	—
761	D₄	—	12	4	no	—
762	D₄	—	12	4	no	—
763	D₄	—	12	4	no	—
764	D₄	—	12	4	no	—
765	D₄	—	12	4	no	—
766	D₄	—	12	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	3	1	no	—
769	C₂×C₄	—	3	4	no	—
770	C₂×C₄	—	3	2	no	—
771	C₂×C₄	—	3	2	no	—
772	C₂×C₄	—	3	1	no	—
773	C₂×C₄	—	3	4	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	6	2	no	—
776	C₂×C₄	—	6	2	no	—
777	C₂×C₄	—	6	4	no	—
778	C₂×C₄	—	6	8	no	—
779	C₂×C₄	—	6	4	no	—
780	C₂×C₄	—	6	2	no	—
781	C₂×C₄	—	6	2	no	—
782	C₂×C₄	—	12	4	no	—
783	C₂×C₄	—	12	4	no	—
784	C₂×C₄	—	12	4	no	—
785	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
786	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
787	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
788	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
789	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
790	C₂×C₃	—	4	1	no	—
791	C₂×C₃	—	4	4	no	—
792	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
793	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
794	D₃	—	4	1	no	—
795	D₃	—	4	4	no	—
796	D₃	C₅×#540	1	4	yes	direct product factor
797	C₅	D₃×#540	1	1	yes	characteristic, direct product factor, 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	—	3	2	no	—
804	C₂²	—	3	4	no	—
805	C₂²	—	6	1	no	—
806	C₂²	—	6	4	no	—
807	C₂²	—	6	4	no	—
808	C₂²	—	6	2	no	—
809	C₂²	—	6	4	no	—
810	C₂²	—	12	4	no	—
811	C₂²	—	12	16	no	—
812	C₂²	C₂⁴×C₅×D₃	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	—	3	2	no	—
818	C₄	—	6	1	no	—
819	C₄	—	6	2	no	—
820	C₄	—	6	4	no	—
821	C₄	—	6	2	no	—
822	C₄	C₅×D₃×#41	1	2	yes	—
823	C₃	C₂×C₅×#540	1	1	yes	characteristic, complemented, Sylow
824	C₂	—	3	4	no	—
825	C₂	—	4	1	no	—
826	C₂	—	4	4	no	—
827	C₂	—	12	1	no	—
828	C₂	—	12	4	no	—
829	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
830	C₂	C₅×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#540	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#540	D₃
hypocenter	C₃	C₂×C₅×#540
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#540

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#540	C₂	semidirect
2. C₅×#5719	C₂	semidirect
3. C₅×D₃×#127	C₂	semidirect
4. C₅×#5697	C₂	semidirect
5. C₅×D₃×#125	C₂	semidirect
6. C₅×#5663	C₂	semidirect
7. C₅×D₃×#123	C₂	semidirect
8. C₅×#5619	C₂	semidirect
9. C₅×#5615	C₂	semidirect
10. C₅×D₃×#121	C₂	semidirect
11. C₅×D₃×#121	C₂	semidirect
12. C₅×#5562	C₂	semidirect
13. C₄×C₅×D₃×D₄	C₂	semidirect
14. C₅×#5535	C₂	semidirect
15. C₅×D₃×#117	C₂	semidirect
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. C₅×#940	C₂²	semidirect
30. C₅×#940	C₂²	semidirect
31. C₅×#939	C₂²	semidirect
32. C₅×#939	C₂²	semidirect
33. C₅×#939	C₂²	semidirect
34. C₅×#938	C₂²	semidirect
35. C₅×#938	C₂²	semidirect
36. C₅×#935	C₂²	semidirect
37. C₅×D₄×Dic₃	C₂²	semidirect
38. C₅×#930	C₂²	semidirect
39. C₅×#930	C₂²	semidirect
40. C₅×#929	C₂²	semidirect
41. C₄×C₅×#67	C₂²	semidirect
42. C₅×#926	C₂²	semidirect
43. C₅×#895	C₂²	semidirect
44. C₅×#895	C₂²	semidirect
45. C₅×#894	C₂²	semidirect
46. C₅×#894	C₂²	semidirect
47. C₅×#893	C₂²	semidirect
48. C₅×#892	C₂²	semidirect
52. C₅×#890	C₂²	semidirect
53. C₅×#889	C₂²	semidirect
54. C₅×#886	C₂²	semidirect
55. C₅×#884	C₂²	semidirect
56. C₅×#884	C₂²	semidirect
57. C₅×#884	C₂²	semidirect
58. C₅×#883	C₂²	semidirect
59. C₅×#883	C₂²	semidirect
60. C₅×#67⋊C₄	C₂²	semidirect
64. C₅×#877	C₂²	semidirect
65. C₅×#874	C₂²	semidirect
66. C₄×C₅×D₁₂	C₂²	semidirect
67. C₅×#872	C₂²	semidirect
68. C₅×#872	C₂²	semidirect
71. C₅×#870	C₂²	semidirect
72. D₃×#540	C₅	direct (N × H)
80. C₅×#540	D₃	direct (N × H)
148. C₃×#540	C₂×C₅	semidirect
149. #5719	C₂×C₅	semidirect
150. D₃×#127	C₂×C₅	semidirect
151. #5697	C₂×C₅	semidirect
152. D₃×#125	C₂×C₅	semidirect
153. #5663	C₂×C₅	semidirect
154. D₃×#123	C₂×C₅	semidirect
155. #5619	C₂×C₅	semidirect
156. #5615	C₂×C₅	semidirect
157. D₃×#121	C₂×C₅	semidirect
158. D₃×#121	C₂×C₅	semidirect
159. #5562	C₂×C₅	semidirect
160. C₄×D₃×D₄	C₂×C₅	semidirect
161. #5535	C₂×C₅	semidirect
162. D₃×#117	C₂×C₅	semidirect
171. C₅×#127	C₂×D₃	semidirect
175. C₅×#125	C₂×D₃	semidirect
183. C₅×#123	C₂×D₃	semidirect
196. C₅×#121	C₂×D₃	semidirect
197. C₅×#121	C₂×D₃	semidirect
203. C₄×C₅×D₄	C₂×D₃	semidirect
209. C₅×#117	C₂×D₃	semidirect
268. C₃×#127	C₂²×C₅	semidirect
269. C₃×#125	C₂²×C₅	semidirect
270. C₃×#123	C₂²×C₅	semidirect
271. C₃×#121	C₂²×C₅	semidirect
272. C₃×#121	C₂²×C₅	semidirect
273. C₃×C₄×D₄	C₂²×C₅	semidirect
274. C₃×#117	C₂²×C₅	semidirect
275. #940	C₂²×C₅	semidirect
276. #940	C₂²×C₅	semidirect
277. #939	C₂²×C₅	semidirect
278. #939	C₂²×C₅	semidirect
279. #939	C₂²×C₅	semidirect
280. #938	C₂²×C₅	semidirect
281. #938	C₂²×C₅	semidirect
282. #935	C₂²×C₅	semidirect
283. D₄×Dic₃	C₂²×C₅	semidirect
284. #930	C₂²×C₅	semidirect
285. #930	C₂²×C₅	semidirect
286. #929	C₂²×C₅	semidirect
287. C₄×#67	C₂²×C₅	semidirect
288. #926	C₂²×C₅	semidirect
289. #895	C₂²×C₅	semidirect
290. #895	C₂²×C₅	semidirect
291. #894	C₂²×C₅	semidirect
292. #894	C₂²×C₅	semidirect
293. #893	C₂²×C₅	semidirect
294. #892	C₂²×C₅	semidirect
298. #890	C₂²×C₅	semidirect
299. #889	C₂²×C₅	semidirect
300. #886	C₂²×C₅	semidirect
301. #884	C₂²×C₅	semidirect
302. #884	C₂²×C₅	semidirect
303. #884	C₂²×C₅	semidirect
304. #883	C₂²×C₅	semidirect
305. #883	C₂²×C₅	semidirect
306. #67⋊C₄	C₂²×C₅	semidirect
310. #877	C₂²×C₅	semidirect
311. #874	C₂²×C₅	semidirect
312. C₄×D₁₂	C₂²×C₅	semidirect
313. #872	C₂²×C₅	semidirect
314. #872	C₂²×C₅	semidirect
317. #870	C₂²×C₅	semidirect
385. #540	C₅×D₃	direct (N × H)
530. #127	C₂×C₅×D₃	semidirect
534. #125	C₂×C₅×D₃	semidirect
542. #123	C₂×C₅×D₃	semidirect
555. #121	C₂×C₅×D₃	semidirect
556. #121	C₂×C₅×D₃	semidirect
562. C₄×D₄	C₂×C₅×D₃	semidirect
568. #117	C₂×C₅×D₃	semidirect
583. C₅×D₃	#540	direct (N × H)
713. C₃×C₅	C₂×#540	semidirect
796. D₃	C₅×#540	direct (N × H)
797. C₅	D₃×#540	direct (N × H)
823. C₃	C₂×C₅×#540	semidirect

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
C₅×#5719	2
C₅×D₃×#127	2
C₅×#5697	2
C₅×D₃×#125	2
C₅×#5663	2
C₅×D₃×#123	2
C₅×#5619	2
C₅×#5615	2
C₅×D₃×#121	2
C₅×#5562	2
C₄×C₅×D₃×D₄	2
C₅×#5535	2
C₅×D₃×#117	2
C₂×C₅×#540	3
D₃×#540	5

Subgroups — C5×D3×#540 #14481076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#540 #14481076