Subgroups — C₅×#83483 #14458452

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₅×#5543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5218	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
5	C₅×#5075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5070	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5041	C₂	1	2	yes	maximal, complemented
8	C₅×#5034	C₂	1	2	yes	maximal, complemented
9	C₄×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5008	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3295	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×D₄	—	2	1	no	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₃×C₅×#121	—	2	1	no	—
17	C₃×C₅×#121	C₂²	1	2	yes	—
18	C₃×C₅×#120	—	2	2	no	—
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₅×D₄×Dic₃	—	2	1	no	—
22	C₂×C₅×#214	C₂²	1	1	yes	characteristic
23	C₂×C₅×#214	C₂²	1	2	yes	complemented
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
25	C₅×#924	C₂²	1	2	yes	complemented
26	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
27	C₅×#890	—	2	1	no	—
28	C₅×#878	—	2	2	no	—
29	C₅×#869	C₂²	1	1	yes	characteristic, complemented
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₅×#832	C₂²	1	1	yes	characteristic
32	C₅×#832	C₂²	1	2	yes	—
33	C₅×#832	C₂²	1	2	yes	complemented
34	C₅×#832	C₂²	1	2	yes	complemented
35	C₅×#832	C₂²	1	2	yes	complemented
36	C₅×#830	C₂²	1	2	yes	complemented
37	C₅×#810	C₂²	1	1	yes	characteristic, complemented
38	C₅×#808	C₂²	1	2	yes	complemented
39	C₅×#808	C₂²	1	1	yes	characteristic, complemented
40	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	#83483	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#554	—	3	1	no	—
44	C₅×D₄²	D₃	1	1	yes	characteristic
45	C₅×#486	—	3	1	no	—
46	C₅×#481	—	3	2	no	—
47	C₅×#476	—	3	1	no	—
48	C₅×#465	—	3	2	no	—
49	C₅×#460	—	3	1	no	—
50	C₅×#450	—	3	2	no	—
51	C₄×C₅×SD₁₆	—	3	1	no	—
52	C₅×C₈×D₄	—	3	1	no	—
53	C₂×C₅×#102	—	3	2	no	—
54	C₂⁴×C₃×C₅	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	2	4	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	4	2	no	—
61	C₂×C₃×C₅×D₄	—	4	4	no	—
62	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₅×Dic₃	—	2	2	no	—
68	C₂×C₅×Dic₆	—	2	1	no	—
69	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#217	—	2	2	no	—
77	C₅×#214	—	2	2	no	—
78	C₅×#214	—	4	2	no	—
79	C₅×C₄⋊Dic₃	—	2	1	no	—
80	C₅×C₄⋊Dic₃	—	2	2	no	—
81	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
83	C₅×Dic₃⋊C₄	—	2	1	no	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₄×C₅×Dic₃	—	2	1	no	—
86	C₂×C₅×C₃⋊C₈	—	4	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
89	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₃×D₄²	C₂×C₅	1	1	yes	characteristic
91	#5543	C₂×C₅	1	1	yes	characteristic, complemented
92	#5218	C₂×C₅	1	2	yes	complemented
93	C₂×#832	C₂×C₅	1	2	yes	complemented
94	#5075	C₂×C₅	1	1	yes	characteristic, complemented
95	#5070	C₂×C₅	1	1	yes	characteristic, complemented
96	#5041	C₂×C₅	1	2	yes	complemented
97	#5034	C₂×C₅	1	2	yes	complemented
98	C₄×#214	C₂×C₅	1	1	yes	characteristic, complemented
99	D₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
100	#5008	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×C₅×D₄	—	2	1	no	—
102	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
103	C₂×C₅×SD₁₆	—	3	1	no	—
104	C₂×C₅×SD₁₆	—	3	2	no	—
105	C₂²×C₅×C₈	—	3	2	no	—
106	C₅×C₄⋊Q₈	—	3	1	no	—
107	C₅×#127	C₂×D₃	1	1	yes	characteristic
108	C₅×#125	—	6	1	no	—
109	C₅×C₂²⋊Q₈	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	6	2	no	—
111	C₅×#121	—	2	1	no	—
112	C₅×#121	C₂×D₃	1	2	yes	—
113	C₅×#120	—	2	2	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×D₄	—	6	1	no	—
116	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
117	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×#106	—	3	2	no	—
121	C₅×C₄⋊C₈	—	3	1	no	—
122	C₅×#103	—	3	1	no	—
123	C₅×#102	—	3	1	no	—
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×#102	—	3	2	no	—
128	C₅×C₂²⋊C₈	—	3	2	no	—
129	C₄×C₅×C₈	—	3	1	no	—
130	#3295	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	—	4	4	no	—
134	C₂³×C₃×C₅	—	4	4	no	—
135	C₂³×C₃×C₅	—	8	2	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	1	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	4	4	no	—
141	C₃×C₅×D₄	—	4	4	no	—
142	C₃×C₅×D₄	—	4	2	no	—
143	C₃×C₅×D₄	—	8	1	no	—
144	C₃×C₅×D₄	SD₁₆	1	4	yes	complemented
145	C₃×C₅×D₄	#41	1	2	yes	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	4	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×C₅×Dic₃	—	2	1	no	—
155	C₂×C₅×Dic₃	—	2	1	no	—
156	C₂×C₅×Dic₃	—	2	2	no	—
157	C₂×C₅×Dic₃	—	8	2	no	—
158	C₅×Dic₆	—	2	1	no	—
159	C₅×Dic₆	—	2	1	no	—
160	C₅×Dic₆	—	8	1	no	—
161	C₅×C₃⋊C₈	—	2	1	no	—
162	C₅×C₃⋊C₈	—	2	1	no	—
163	C₅×C₃⋊C₈	—	2	2	no	—
164	C₂²×C₃×D₄	—	2	1	no	—
165	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
166	C₃×#127	C₂²×C₅	1	1	yes	characteristic
167	C₃×#121	—	2	1	no	—
168	C₃×#121	C₂²×C₅	1	2	yes	—
169	C₃×#120	—	2	2	no	—
170	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
172	D₄×Dic₃	—	2	1	no	—
173	C₂×#214	C₂²×C₅	1	1	yes	characteristic
174	C₂×#214	C₂²×C₅	1	2	yes	complemented
175	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
176	#924	C₂²×C₅	1	2	yes	complemented
177	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
178	#890	—	2	1	no	—
179	#878	—	2	2	no	—
180	#869	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
182	#832	C₂²×C₅	1	1	yes	characteristic
183	#832	C₂²×C₅	1	2	yes	—
184	#832	C₂²×C₅	1	2	yes	complemented
185	#832	C₂²×C₅	1	2	yes	complemented
186	#832	C₂²×C₅	1	2	yes	complemented
187	#830	C₂²×C₅	1	2	yes	complemented
188	#810	C₂²×C₅	1	1	yes	characteristic, complemented
189	#808	C₂²×C₅	1	2	yes	complemented
190	#808	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂⁴×C₅	—	2	2	no	—
194	C₂×C₅×Q₈	—	3	1	no	—
195	C₂×C₅×Q₈	—	6	1	no	—
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	—	2	2	no	—
198	C₂×C₅×D₄	—	2	2	no	—
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	—	4	2	no	—
202	C₂×C₅×D₄	—	4	4	no	—
203	C₂×C₅×D₄	#67	1	1	yes	characteristic
204	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
205	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	—	6	2	no	—
208	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
209	C₅×SD₁₆	—	6	2	no	—
210	C₅×SD₁₆	—	12	2	no	—
211	C₂×C₅×C₈	—	3	1	no	—
212	C₂×C₅×C₈	—	3	2	no	—
213	C₂×C₅×C₈	—	3	1	no	—
214	C₂×C₅×C₈	—	12	2	no	—
215	C₅×C₄⋊C₄	—	3	1	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	6	2	no	—
218	C₅×C₄⋊C₄	—	6	1	no	—
219	C₅×C₄⋊C₄	—	6	1	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	—	6	2	no	—
226	C₅×C₂²⋊C₄	#67	1	2	yes	—
227	C₄²×C₅	—	6	1	no	—
228	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
229	#554	—	3	1	no	—
230	D₄²	C₅×D₃	1	1	yes	characteristic
231	#486	—	3	1	no	—
232	#481	—	3	2	no	—
233	#476	—	3	1	no	—
234	#465	—	3	2	no	—
235	#460	—	3	1	no	—
236	#450	—	3	2	no	—
237	C₄×SD₁₆	—	3	1	no	—
238	C₈×D₄	—	3	1	no	—
239	C₂×#102	—	3	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	4	2	no	—
247	C₂²×C₃×C₅	—	4	2	no	—
248	C₂²×C₃×C₅	—	8	8	no	—
249	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
255	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
256	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
257	C₅×Dic₃	—	4	1	no	—
258	C₅×Dic₃	—	4	2	no	—
259	C₅×Dic₃	—	4	1	no	—
260	C₂⁴×C₃	—	2	2	no	—
261	C₂×C₃×D₄	—	2	4	no	—
262	C₂×C₃×D₄	—	2	2	no	—
263	C₂×C₃×D₄	—	2	2	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	2	1	no	—
266	C₂×C₃×D₄	—	4	2	no	—
267	C₂×C₃×D₄	—	4	4	no	—
268	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
270	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
271	C₂²×C₃×C₄	—	2	1	no	—
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×Dic₃	—	2	2	no	—
274	C₂×Dic₆	—	2	1	no	—
275	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	—	2	1	no	—
279	C₃×C₂²⋊C₄	—	2	2	no	—
280	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
281	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
282	#217	—	2	2	no	—
283	#214	—	2	2	no	—
284	#214	—	4	2	no	—
285	C₄⋊Dic₃	—	2	1	no	—
286	C₄⋊Dic₃	—	2	2	no	—
287	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
288	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
289	Dic₃⋊C₄	—	2	1	no	—
290	Dic₃⋊C₄	—	2	2	no	—
291	C₄×Dic₃	—	2	1	no	—
292	C₂×C₃⋊C₈	—	4	2	no	—
293	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	4	4	no	—
299	C₂³×C₅	—	4	4	no	—
300	C₂³×C₅	—	8	2	no	—
301	C₂³×C₅	C₂×#67	1	2	yes	—
302	C₅×Q₈	—	6	1	no	—
303	C₅×Q₈	—	6	1	no	—
304	C₅×Q₈	—	24	1	no	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	2	1	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	4	4	no	—
309	C₅×D₄	—	4	4	no	—
310	C₅×D₄	—	4	2	no	—
311	C₅×D₄	—	8	1	no	—
312	C₅×D₄	#214	1	4	yes	complemented
313	C₅×D₄	#237	1	2	yes	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	4	2	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	1	no	—
320	C₂×C₄×C₅	—	6	2	no	—
321	C₂×C₄×C₅	—	24	2	no	—
322	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×#67	1	2	yes	—
324	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
326	C₅×C₈	—	6	1	no	—
327	C₅×C₈	—	6	1	no	—
328	C₅×C₈	—	6	2	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
331	C₂×SD₁₆	—	3	1	no	—
332	C₂×SD₁₆	—	3	2	no	—
333	C₂²×C₈	—	3	2	no	—
334	C₄⋊Q₈	—	3	1	no	—
335	#127	C₂×C₅×D₃	1	1	yes	characteristic
336	#125	—	6	1	no	—
337	C₂²⋊Q₈	—	3	2	no	—
338	C₂²⋊Q₈	—	6	2	no	—
339	#121	—	2	1	no	—
340	#121	C₂×C₅×D₃	1	2	yes	—
341	#120	—	2	2	no	—
342	C₄×Q₈	—	3	1	no	—
343	C₄×D₄	—	6	1	no	—
344	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
345	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	3	2	no	—
347	#106	—	3	1	no	—
348	#106	—	3	2	no	—
349	C₄⋊C₈	—	3	1	no	—
350	#103	—	3	1	no	—
351	#102	—	3	1	no	—
352	#102	—	3	2	no	—
353	#102	—	3	2	no	—
354	#102	—	3	2	no	—
355	#102	—	3	2	no	—
356	C₂²⋊C₈	—	3	2	no	—
357	C₄×C₈	—	3	1	no	—
358	C₂×C₃×C₅	—	2	4	no	—
359	C₂×C₃×C₅	—	4	2	no	—
360	C₂×C₃×C₅	—	8	2	no	—
361	C₂×C₃×C₅	#546	1	1	yes	characteristic
362	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
363	C₂×C₃×C₅	#576	1	1	yes	characteristic
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	2	no	—
366	C₂³×C₃	—	4	4	no	—
367	C₂³×C₃	—	4	4	no	—
368	C₂³×C₃	—	8	2	no	—
369	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	2	1	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	4	4	no	—
374	C₃×D₄	—	4	4	no	—
375	C₃×D₄	—	4	2	no	—
376	C₃×D₄	—	8	1	no	—
377	C₃×D₄	C₅×SD₁₆	1	4	yes	complemented
378	C₃×D₄	C₅×#41	1	2	yes	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
387	C₂×Dic₃	—	2	1	no	—
388	C₂×Dic₃	—	2	1	no	—
389	C₂×Dic₃	—	2	2	no	—
390	C₂×Dic₃	—	8	2	no	—
391	Dic₆	—	2	1	no	—
392	Dic₆	—	2	1	no	—
393	Dic₆	—	8	1	no	—
394	C₃⋊C₈	—	2	1	no	—
395	C₃⋊C₈	—	2	1	no	—
396	C₃⋊C₈	—	2	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	8	8	no	—
406	C₂²×C₅	C₂×#214	1	4	yes	—
407	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	12	1	no	—
412	C₄×C₅	—	12	1	no	—
413	C₄×C₅	—	12	2	no	—
414	C₄×C₅	C₂×#214	1	2	yes	—
415	C₄×C₅	C₂×#237	1	1	yes	characteristic
416	C₄×C₅	#1004	1	1	yes	characteristic
417	C₂⁴	—	2	2	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	6	1	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	C₅×#67	1	1	yes	characteristic
428	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
429	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	6	2	no	—
432	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
433	SD₁₆	—	6	2	no	—
434	SD₁₆	—	12	2	no	—
435	C₂×C₈	—	3	1	no	—
436	C₂×C₈	—	3	1	no	—
437	C₂×C₈	—	3	2	no	—
438	C₂×C₈	—	12	2	no	—
439	C₄⋊C₄	—	3	1	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	6	2	no	—
442	C₄⋊C₄	—	6	1	no	—
443	C₄⋊C₄	—	6	1	no	—
444	C₄⋊C₄	—	6	2	no	—
445	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
446	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	6	2	no	—
450	C₂²⋊C₄	C₅×#67	1	2	yes	—
451	C₄²	—	6	1	no	—
452	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₃×C₅	#3295	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	—	4	1	no	—
459	C₂²×C₃	—	4	2	no	—
460	C₂²×C₃	—	4	2	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	8	8	no	—
463	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	—
464	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₃×C₄	—	2	2	no	—
466	C₃×C₄	—	2	1	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
469	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
470	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
471	Dic₃	—	4	1	no	—
472	Dic₃	—	4	2	no	—
473	Dic₃	—	4	1	no	—
474	C₂×C₅	—	2	4	no	—
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	—	8	2	no	—
477	C₂×C₅	C₂²×#214	1	1	yes	characteristic
478	C₂×C₅	#5806	1	1	yes	characteristic
479	C₂×C₅	#5835	1	1	yes	characteristic
480	C₂³	—	2	1	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	8	2	no	—
485	C₂³	C₂×C₅×#67	1	2	yes	—
486	Q₈	—	6	1	no	—
487	Q₈	—	6	1	no	—
488	Q₈	—	24	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	1	no	—
491	D₄	—	2	2	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	8	1	no	—
496	D₄	C₅×#214	1	4	yes	complemented
497	D₄	C₅×#237	1	2	yes	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	6	1	no	—
503	C₂×C₄	—	6	1	no	—
504	C₂×C₄	—	6	2	no	—
505	C₂×C₄	—	24	2	no	—
506	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
507	C₂×C₄	C₂×C₅×#67	1	2	yes	—
508	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
509	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
510	C₈	—	6	1	no	—
511	C₈	—	6	1	no	—
512	C₈	—	6	2	no	—
513	C₂×C₃	—	2	4	no	—
514	C₂×C₃	—	4	2	no	—
515	C₂×C₃	—	8	2	no	—
516	C₂×C₃	C₅×#546	1	1	yes	characteristic
517	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
518	C₂×C₃	C₅×#576	1	1	yes	characteristic
519	C₅	#83483	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	8	8	no	—
529	C₂²	C₂×C₅×#214	1	4	yes	—
530	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
531	C₄	—	2	2	no	—
532	C₄	—	2	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	12	1	no	—
535	C₄	—	12	1	no	—
536	C₄	—	12	2	no	—
537	C₄	C₂×C₅×#214	1	2	yes	—
538	C₄	C₂×C₅×#237	1	1	yes	characteristic
539	C₄	C₅×#1004	1	1	yes	characteristic
540	C₃	C₅×#3295	1	1	yes	characteristic, complemented, Sylow
541	C₂	—	2	4	no	—
542	C₂	—	4	2	no	—
543	C₂	—	8	2	no	—
544	C₂	C₂²×C₅×#214	1	1	yes	characteristic
545	C₂	C₅×#5806	1	1	yes	characteristic
546	C₂	C₅×#5835	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₃×C₅×D₄²	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×D₄²	D₃
hypocenter	C₃	C₅×#3295
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×D₄²

Complements

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

N	H ≅ G/N	type
2. C₅×#5543	C₂	semidirect
3. C₅×#5218	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5075	C₂	semidirect
6. C₅×#5070	C₂	semidirect
7. C₅×#5041	C₂	semidirect
8. C₅×#5034	C₂	semidirect
9. C₄×C₅×#214	C₂	semidirect
10. C₅×D₄×C₃⋊C₈	C₂	semidirect
11. C₅×#5008	C₂	semidirect
23. C₂×C₅×#214	C₂²	semidirect
24. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
25. C₅×#924	C₂²	semidirect
26. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
29. C₅×#869	C₂²	semidirect
30. C₄×C₅×Dic₆	C₂²	semidirect
33. C₅×#832	C₂²	semidirect
34. C₅×#832	C₂²	semidirect
35. C₅×#832	C₂²	semidirect
36. C₅×#830	C₂²	semidirect
37. C₅×#810	C₂²	semidirect
38. C₅×#808	C₂²	semidirect
39. C₅×#808	C₂²	semidirect
40. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
41. C₄×C₅×C₃⋊C₈	C₂²	semidirect
42. #83483	C₅	direct (N × H)
91. #5543	C₂×C₅	semidirect
92. #5218	C₂×C₅	semidirect
93. C₂×#832	C₂×C₅	semidirect
94. #5075	C₂×C₅	semidirect
95. #5070	C₂×C₅	semidirect
96. #5041	C₂×C₅	semidirect
97. #5034	C₂×C₅	semidirect
98. C₄×#214	C₂×C₅	semidirect
99. D₄×C₃⋊C₈	C₂×C₅	semidirect
100. #5008	C₂×C₅	semidirect
144. C₃×C₅×D₄	SD₁₆	semidirect
174. C₂×#214	C₂²×C₅	semidirect
175. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
176. #924	C₂²×C₅	semidirect
177. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
180. #869	C₂²×C₅	semidirect
181. C₄×Dic₆	C₂²×C₅	semidirect
184. #832	C₂²×C₅	semidirect
185. #832	C₂²×C₅	semidirect
186. #832	C₂²×C₅	semidirect
187. #830	C₂²×C₅	semidirect
188. #810	C₂²×C₅	semidirect
189. #808	C₂²×C₅	semidirect
190. #808	C₂²×C₅	semidirect
191. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
192. C₄×C₃⋊C₈	C₂²×C₅	semidirect
312. C₅×D₄	#214	semidirect
377. C₃×D₄	C₅×SD₁₆	semidirect
453. C₃×C₅	#3295	semidirect
496. D₄	C₅×#214	semidirect
519. C₅	#83483	direct (N × H)
540. C₃	C₅×#3295	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₄²	2
C₅×#5543	2
C₅×#5218	2
C₂×C₅×#832	2
C₅×#5075	2
C₅×#5070	2
C₅×#5041	2
C₅×#5034	2
C₄×C₅×#214	2
C₅×D₄×C₃⋊C₈	2
C₅×#5008	2
C₅×#3295	3
#83483	5

Subgroups — C5×#83483 #14458452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83483 #14458452