Subgroups — C₅×#83965 #14417177

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic
2	C₅×#5827	C₂	1	1	yes	maximal, characteristic
3	C₅×#5812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5184	C₂	1	2	yes	maximal, complemented
7	C₅×Dic₃×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#5164	C₂	1	2	yes	maximal, complemented
9	C₅×Dic₃×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2947	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#137	C₄	1	8	yes	complemented
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₅×Q₈×Dic₃	—	2	1	no	—
20	C₅×Q₈×Dic₃	—	2	1	no	—
21	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
22	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
23	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
24	C₅×D₄×Dic₃	—	2	2	no	—
25	C₅×D₄×Dic₃	C₂²	1	2	yes	—
26	C₅×#926	—	2	2	no	—
27	C₅×#926	—	2	1	no	—
28	C₅×#926	C₂²	1	1	yes	characteristic
29	C₅×#926	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#835	C₂²	1	2	yes	—
35	C₅×#835	C₂²	1	1	yes	characteristic
36	C₅×#835	C₂²	1	1	yes	characteristic
37	C₅×#832	C₂²	1	1	yes	characteristic
38	C₅×#832	C₂²	1	1	yes	characteristic
39	C₅×#818	C₂²	1	2	yes	—
40	C₅×#817	C₂²	1	2	yes	—
41	C₅×#815	C₂²	1	2	yes	—
42	C₅×C₈×Dic₃	C₂²	1	2	yes	—
43	#83965	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×#137	D₃	1	1	yes	characteristic
45	C₅×#520	—	3	1	no	—
46	C₅×#519	—	3	1	no	—
47	C₅×#441	—	3	2	no	—
48	C₅×#440	—	3	2	no	—
49	C₄×C₅×Q₁₆	—	3	2	no	—
50	C₄×C₅×SD₁₆	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#416	—	3	1	no	—
53	C₂×C₅×#103	—	3	1	no	—
54	C₅×#405	—	3	1	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	C₂×C₄	1	4	yes	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Dic₃	—	2	1	no	—
68	C₂²×C₅×Dic₃	—	2	2	no	—
69	C₃×C₅×Q₁₆	C₂×C₄	1	8	yes	complemented
70	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
71	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₅×#217	—	2	1	no	—
74	C₅×#217	—	2	2	no	—
75	C₅×#217	D₄	1	2	yes	—
76	C₅×C₄⋊Dic₃	—	2	1	no	—
77	C₅×C₄⋊Dic₃	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	2	2	no	—
79	C₅×C₄⋊Dic₃	—	2	2	no	—
80	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
81	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
82	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
85	C₄×C₅×Dic₃	—	2	1	no	—
86	C₄×C₅×Dic₃	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	2	no	—
88	C₄×C₅×Dic₃	—	2	2	no	—
89	C₄×C₅×Dic₃	C₂³	1	2	yes	—
90	C₂×C₅×C₃⋊C₈	—	2	2	no	—
91	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic
94	#5827	C₂×C₅	1	1	yes	characteristic
95	#5812	C₂×C₅	1	1	yes	characteristic, complemented
96	#5233	C₂×C₅	1	1	yes	characteristic
97	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
98	#5184	C₂×C₅	1	2	yes	complemented
99	Dic₃×Q₁₆	C₂×C₅	1	2	yes	complemented
100	#5164	C₂×C₅	1	2	yes	complemented
101	Dic₃×SD₁₆	C₂×C₅	1	2	yes	complemented
102	#5122	C₂×C₅	1	1	yes	characteristic, complemented
103	#5121	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
106	C₅×#137	Dic₃	1	8	yes	complemented
107	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
108	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
109	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
110	C₂²×C₅×C₈	—	3	1	no	—
111	C₄×C₅×Q₈	—	3	2	no	—
112	C₄×C₅×Q₈	—	3	2	no	—
113	C₄×C₅×Q₈	—	3	2	no	—
114	C₄×C₅×Q₈	—	6	1	no	—
115	C₄×C₅×Q₈	—	6	1	no	—
116	C₄×C₅×D₄	—	3	2	no	—
117	C₄×C₅×D₄	—	6	2	no	—
118	C₅×#117	—	3	1	no	—
119	C₅×#117	—	3	1	no	—
120	C₅×#117	—	6	2	no	—
121	C₅×#117	—	6	1	no	—
122	C₂×C₅×C₄⋊C₄	—	3	1	no	—
123	C₂×C₅×C₄⋊C₄	—	6	1	no	—
124	C₅×#107	—	3	2	no	—
125	C₅×#106	—	3	2	no	—
126	C₅×#103	—	3	2	no	—
127	C₅×#103	—	3	2	no	—
128	C₅×#103	—	3	1	no	—
129	C₅×#103	—	3	1	no	—
130	C₅×#102	—	3	1	no	—
131	C₅×#102	—	3	1	no	—
132	C₅×#97	—	3	2	no	—
133	C₄×C₅×C₈	—	3	2	no	—
134	#2947	—	3	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₅×Q₈	—	2	4	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
141	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	4	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×C₅×Dic₃	—	2	1	no	—
154	C₂×C₅×Dic₃	—	2	1	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	8	2	no	—
157	C₂×C₅×Dic₃	—	8	1	no	—
158	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
159	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
160	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
161	C₅×C₃⋊C₈	—	2	1	no	—
162	C₅×C₃⋊C₈	—	2	1	no	—
163	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₃×#137	C₄×C₅	1	8	yes	complemented
166	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
168	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
169	Q₈×Dic₃	—	2	1	no	—
170	Q₈×Dic₃	—	2	1	no	—
171	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
172	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
173	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
174	D₄×Dic₃	—	2	2	no	—
175	D₄×Dic₃	C₂²×C₅	1	2	yes	—
176	#926	—	2	2	no	—
177	#926	—	2	1	no	—
178	#926	C₂²×C₅	1	1	yes	characteristic
179	#926	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄⋊Dic₃	—	2	1	no	—
181	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
183	#835	C₂²×C₅	1	2	yes	—
184	#835	C₂²×C₅	1	2	yes	—
185	#835	C₂²×C₅	1	1	yes	characteristic
186	#835	C₂²×C₅	1	1	yes	characteristic
187	#832	C₂²×C₅	1	1	yes	characteristic
188	#832	C₂²×C₅	1	1	yes	characteristic
189	#818	C₂²×C₅	1	2	yes	—
190	#817	C₂²×C₅	1	2	yes	—
191	#815	C₂²×C₅	1	2	yes	—
192	C₈×Dic₃	C₂²×C₅	1	2	yes	—
193	C₅×#41	—	2	2	no	—
194	C₅×#41	C₂×Dic₃	1	4	yes	—
195	C₂×C₅×Q₈	—	2	1	no	—
196	C₂×C₅×Q₈	—	2	2	no	—
197	C₂×C₅×Q₈	C₂×Dic₃	1	4	yes	complemented
198	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
199	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	6	2	no	—
205	C₂²×C₄×C₅	—	6	1	no	—
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×Q₁₆	C₂×Dic₃	1	8	yes	complemented
208	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
209	C₅×M₁₆	C₂×Dic₃	1	4	yes	complemented
210	C₂×C₅×C₈	—	3	1	no	—
211	C₂×C₅×C₈	—	3	1	no	—
212	C₂×C₅×C₈	—	6	2	no	—
213	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
214	C₅×C₄⋊C₄	—	3	1	no	—
215	C₅×C₄⋊C₄	—	3	1	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	3	1	no	—
218	C₅×C₄⋊C₄	—	3	1	no	—
219	C₅×C₄⋊C₄	—	6	2	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	—	6	2	no	—
222	C₅×C₄⋊C₄	—	6	1	no	—
223	C₅×C₂²⋊C₄	—	3	2	no	—
224	C₅×C₂²⋊C₄	—	6	2	no	—
225	C₅×C₂²⋊C₄	—	6	1	no	—
226	C₄²×C₅	—	3	2	no	—
227	C₄²×C₅	—	6	2	no	—
228	C₄²×C₅	—	6	2	no	—
229	C₄²×C₅	—	6	2	no	—
230	C₄²×C₅	—	6	1	no	—
231	C₂×#137	C₅×D₃	1	1	yes	characteristic
232	#520	—	3	1	no	—
233	#519	—	3	1	no	—
234	#441	—	3	2	no	—
235	#440	—	3	2	no	—
236	C₄×Q₁₆	—	3	2	no	—
237	C₄×SD₁₆	—	3	2	no	—
238	#428	—	3	1	no	—
239	#416	—	3	1	no	—
240	C₂×#103	—	3	1	no	—
241	#405	—	3	1	no	—
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
252	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
253	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
254	C₅×Dic₃	—	2	2	no	—
255	C₅×Dic₃	—	2	2	no	—
256	C₅×Dic₃	—	4	1	no	—
257	C₅×Dic₃	—	4	2	no	—
258	C₅×Dic₃	—	4	1	no	—
259	C₃×#41	—	2	2	no	—
260	C₃×#41	C₂×C₄×C₅	1	4	yes	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×Q₈	—	2	2	no	—
263	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
264	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
265	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
271	C₂²×Dic₃	—	2	1	no	—
272	C₂²×Dic₃	—	2	2	no	—
273	C₃×Q₁₆	C₂×C₄×C₅	1	8	yes	complemented
274	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
275	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
276	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
277	#217	—	2	1	no	—
278	#217	—	2	2	no	—
279	#217	C₅×D₄	1	2	yes	—
280	C₄⋊Dic₃	—	2	1	no	—
281	C₄⋊Dic₃	—	2	2	no	—
282	C₄⋊Dic₃	—	2	2	no	—
283	C₄⋊Dic₃	—	2	2	no	—
284	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
285	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
286	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
287	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
288	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₄×Dic₃	—	2	1	no	—
290	C₄×Dic₃	—	2	2	no	—
291	C₄×Dic₃	—	2	2	no	—
292	C₄×Dic₃	—	2	2	no	—
293	C₄×Dic₃	C₂³×C₅	1	2	yes	—
294	C₂×C₃⋊C₈	—	2	2	no	—
295	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
299	C₅×Q₈	—	2	4	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	2	1	no	—
302	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
303	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
304	C₅×D₄	—	2	4	no	—
305	C₅×D₄	—	2	1	no	—
306	C₅×D₄	C₂²×Dic₃	1	2	yes	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	4	no	—
311	C₂×C₄×C₅	—	3	2	no	—
312	C₂×C₄×C₅	—	3	2	no	—
313	C₂×C₄×C₅	—	6	1	no	—
314	C₂×C₄×C₅	—	6	1	no	—
315	C₂×C₄×C₅	—	6	2	no	—
316	C₂×C₄×C₅	—	24	2	no	—
317	C₂×C₄×C₅	—	24	1	no	—
318	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	#237	1	2	yes	—
320	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
321	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
322	C₅×C₈	—	6	1	no	—
323	C₅×C₈	—	6	1	no	—
324	C₅×C₈	C₂²×Dic₃	1	4	yes	—
325	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
327	#137	C₅×Dic₃	1	8	yes	complemented
328	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
329	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
330	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂²×C₈	—	3	1	no	—
332	C₄×Q₈	—	3	2	no	—
333	C₄×Q₈	—	3	2	no	—
334	C₄×Q₈	—	3	2	no	—
335	C₄×Q₈	—	6	1	no	—
336	C₄×Q₈	—	6	1	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	6	2	no	—
339	#117	—	3	1	no	—
340	#117	—	3	1	no	—
341	#117	—	6	2	no	—
342	#117	—	6	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	6	1	no	—
345	#107	—	3	2	no	—
346	#106	—	3	2	no	—
347	#103	—	3	2	no	—
348	#103	—	3	2	no	—
349	#103	—	3	1	no	—
350	#103	—	3	1	no	—
351	#102	—	3	1	no	—
352	#102	—	3	1	no	—
353	#97	—	3	2	no	—
354	C₄×C₈	—	3	2	no	—
355	C₂×C₃×C₅	—	2	2	no	—
356	C₂×C₃×C₅	—	4	2	no	—
357	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
358	C₂×C₃×C₅	#577	1	1	yes	characteristic
359	C₂×C₃×C₅	#578	1	1	yes	characteristic
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
362	C₃×Q₈	—	2	4	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	2	1	no	—
365	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
366	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂×C₃×C₄	C₅×#41	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
378	C₂×Dic₃	—	2	1	no	—
379	C₂×Dic₃	—	2	1	no	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	8	2	no	—
382	C₂×Dic₃	—	8	1	no	—
383	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
384	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
385	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
386	C₃⋊C₈	—	2	1	no	—
387	C₃⋊C₈	—	2	1	no	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	4	1	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	D₄×Dic₃	1	2	yes	—
394	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	4	no	—
397	C₄×C₅	—	6	2	no	—
398	C₄×C₅	—	6	2	no	—
399	C₄×C₅	—	12	1	no	—
400	C₄×C₅	—	12	2	no	—
401	C₄×C₅	—	12	1	no	—
402	C₄×C₅	D₄×Dic₃	1	2	yes	—
403	C₄×C₅	C₂×#237	1	1	yes	characteristic
404	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
405	#41	—	2	2	no	—
406	#41	C₂×C₅×Dic₃	1	4	yes	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	C₂×C₅×Dic₃	1	4	yes	complemented
410	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
411	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	6	2	no	—
417	C₂²×C₄	—	6	1	no	—
418	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	Q₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
420	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
421	M₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
422	C₂×C₈	—	3	1	no	—
423	C₂×C₈	—	3	1	no	—
424	C₂×C₈	—	6	2	no	—
425	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
426	C₄⋊C₄	—	3	1	no	—
427	C₄⋊C₄	—	3	1	no	—
428	C₄⋊C₄	—	3	1	no	—
429	C₄⋊C₄	—	3	1	no	—
430	C₄⋊C₄	—	3	2	no	—
431	C₄⋊C₄	—	6	2	no	—
432	C₄⋊C₄	—	6	2	no	—
433	C₄⋊C₄	—	6	2	no	—
434	C₄⋊C₄	—	6	1	no	—
435	C₂²⋊C₄	—	3	2	no	—
436	C₂²⋊C₄	—	6	2	no	—
437	C₂²⋊C₄	—	6	1	no	—
438	C₄²	—	3	2	no	—
439	C₄²	—	6	2	no	—
440	C₄²	—	6	2	no	—
441	C₄²	—	6	2	no	—
442	C₄²	—	6	1	no	—
443	C₃×C₅	#2947	1	1	yes	characteristic, complemented, Hall
444	C₂²×C₃	—	2	1	no	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	4	1	no	—
448	C₂²×C₃	—	4	1	no	—
449	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
450	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	4	no	—
453	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
454	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
455	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
456	Dic₃	—	2	2	no	—
457	Dic₃	—	2	2	no	—
458	Dic₃	—	4	1	no	—
459	Dic₃	—	4	2	no	—
460	Dic₃	—	4	1	no	—
461	C₂×C₅	—	2	2	no	—
462	C₂×C₅	—	4	2	no	—
463	C₂×C₅	#5778	1	1	yes	characteristic
464	C₂×C₅	#5779	1	1	yes	characteristic
465	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
466	C₂³	—	2	1	no	—
467	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
468	Q₈	—	2	4	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	1	no	—
471	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
472	Q₈	C₂²×C₅×Dic₃	1	2	yes	—
473	D₄	—	2	4	no	—
474	D₄	—	2	1	no	—
475	D₄	C₂²×C₅×Dic₃	1	2	yes	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	3	2	no	—
481	C₂×C₄	—	3	2	no	—
482	C₂×C₄	—	6	1	no	—
483	C₂×C₄	—	6	1	no	—
484	C₂×C₄	—	6	2	no	—
485	C₂×C₄	—	24	2	no	—
486	C₂×C₄	—	24	1	no	—
487	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
488	C₂×C₄	C₅×#237	1	2	yes	—
489	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
490	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
491	C₈	—	6	1	no	—
492	C₈	—	6	1	no	—
493	C₈	C₂²×C₅×Dic₃	1	4	yes	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	4	2	no	—
496	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
497	C₂×C₃	C₅×#577	1	1	yes	characteristic
498	C₂×C₃	C₅×#578	1	1	yes	characteristic
499	C₅	#83965	1	1	yes	characteristic, direct product factor, Sylow
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	C₅×D₄×Dic₃	1	2	yes	—
506	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	4	no	—
509	C₄	—	6	2	no	—
510	C₄	—	6	2	no	—
511	C₄	—	12	2	no	—
512	C₄	—	12	1	no	—
513	C₄	—	12	1	no	—
514	C₄	C₅×D₄×Dic₃	1	2	yes	—
515	C₄	C₂×C₅×#237	1	1	yes	characteristic
516	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
517	C₃	C₅×#2947	1	1	yes	characteristic, complemented, Sylow
518	C₂	—	2	2	no	—
519	C₂	—	4	2	no	—
520	C₂	C₅×#5778	1	1	yes	characteristic
521	C₂	C₅×#5779	1	1	yes	characteristic
522	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#137	D₃
hypocenter	C₃	C₅×#2947
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#137

Complements

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

N	H ≅ G/N	type
3. C₅×#5812	C₂	semidirect
5. C₂×C₅×#835	C₂	semidirect
6. C₅×#5184	C₂	semidirect
7. C₅×Dic₃×Q₁₆	C₂	semidirect
8. C₅×#5164	C₂	semidirect
9. C₅×Dic₃×SD₁₆	C₂	semidirect
10. C₅×#5122	C₂	semidirect
11. C₅×#5121	C₂	semidirect
15. C₃×C₅×#137	C₄	semidirect
43. #83965	C₅	direct (N × H)
59. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
69. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₃×C₅×SD₁₆	C₂×C₄	semidirect
71. C₃×C₅×M₁₆	C₂×C₄	semidirect
95. #5812	C₂×C₅	semidirect
97. C₂×#835	C₂×C₅	semidirect
98. #5184	C₂×C₅	semidirect
99. Dic₃×Q₁₆	C₂×C₅	semidirect
100. #5164	C₂×C₅	semidirect
101. Dic₃×SD₁₆	C₂×C₅	semidirect
102. #5122	C₂×C₅	semidirect
103. #5121	C₂×C₅	semidirect
106. C₅×#137	Dic₃	semidirect
165. C₃×#137	C₄×C₅	semidirect
197. C₂×C₅×Q₈	C₂×Dic₃	semidirect
207. C₅×Q₁₆	C₂×Dic₃	semidirect
208. C₅×SD₁₆	C₂×Dic₃	semidirect
209. C₅×M₁₆	C₂×Dic₃	semidirect
263. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
273. C₃×Q₁₆	C₂×C₄×C₅	semidirect
274. C₃×SD₁₆	C₂×C₄×C₅	semidirect
275. C₃×M₁₆	C₂×C₄×C₅	semidirect
327. #137	C₅×Dic₃	semidirect
409. C₂×Q₈	C₂×C₅×Dic₃	semidirect
419. Q₁₆	C₂×C₅×Dic₃	semidirect
420. SD₁₆	C₂×C₅×Dic₃	semidirect
421. M₁₆	C₂×C₅×Dic₃	semidirect
443. C₃×C₅	#2947	semidirect
499. C₅	#83965	direct (N × H)
517. C₃	C₅×#2947	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#137	2
C₅×#5827	2
C₅×#5812	2
C₅×#5233	2
C₂×C₅×#835	2
C₅×#5184	2
C₅×Dic₃×Q₁₆	2
C₅×#5164	2
C₅×Dic₃×SD₁₆	2
C₅×#5122	2
C₅×#5121	2
C₅×#2947	3
#83965	5

Subgroups — C5×#83965 #14417177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83965 #14417177