Subgroups — C₅×#83972 #14439201

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 588 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, complemented
2	C₅×#5832	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#942	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#909	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5190	C₂	1	2	yes	maximal, complemented
8	C₅×#5183	C₂	1	2	yes	maximal, complemented
9	C₅×#5175	C₂	1	2	yes	maximal, complemented
10	C₅×#5167	C₂	1	2	yes	maximal, complemented
11	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3152	—	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	C₂×C₅×#235	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₅×#137	—	2	4	no	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₅×#951	—	2	4	no	—
22	C₅×#947	C₂²	1	1	yes	characteristic
23	C₅×#944	—	2	2	no	—
24	C₅×#944	C₂²	1	2	yes	—
25	C₅×#944	C₂²	1	2	yes	—
26	C₅×#944	C₂²	1	1	yes	characteristic
27	C₂×C₅×#216	C₂²	1	2	yes	—
28	C₂×C₅×#216	C₂²	1	2	yes	—
29	C₅×#942	—	2	4	no	—
30	C₂×C₅×#215	C₂²	1	2	yes	—
31	C₅×#940	C₂²	1	1	yes	characteristic
32	C₅×#939	—	2	2	no	—
33	C₅×#936	C₂²	1	1	yes	characteristic
34	C₂×C₅×#214	C₂²	1	2	yes	—
35	C₄×C₅×#67	—	2	2	no	—
36	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₅×#208	C₂²	1	1	yes	characteristic
39	C₅×#909	—	2	4	no	—
40	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
41	C₂×C₅×#204	C₂²	1	2	yes	—
42	C₅×#815	C₂²	1	2	yes	—
43	C₅×C₈×Dic₃	C₂²	1	2	yes	—
44	#83972	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	—	3	1	no	—
46	C₂×C₅×#137	—	3	1	no	—
47	C₂×C₅×#137	—	3	1	no	—
48	C₂×C₅×#137	D₃	1	1	yes	characteristic, complemented
49	C₅×#532	—	3	1	no	—
50	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
51	C₅×#497	—	3	2	no	—
52	C₅×#497	—	3	2	no	—
53	C₅×#494	—	3	2	no	—
54	C₅×#492	—	3	2	no	—
55	C₄×C₅×M₁₆	—	3	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	1	no	—
59	C₂×C₃×C₅×Q₈	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×#67	—	2	1	no	—
69	C₂×C₅×#67	—	2	2	no	—
70	C₂²×C₅×Dic₃	—	2	1	no	—
71	C₂²×C₅×Dic₃	D₄	1	2	yes	—
72	C₅×#235	—	2	2	no	—
73	C₅×#235	—	2	2	no	—
74	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
75	C₂×C₄×C₅×D₃	—	2	1	no	—
76	C₂×C₅×Dic₆	—	2	2	no	—
77	C₂×C₅×Dic₆	—	2	2	no	—
78	C₂×C₅×Dic₆	—	2	1	no	—
79	C₂×C₅×Dic₆	C₂³	1	2	yes	—
80	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
81	C₃×C₅×Q₁₆	—	2	4	no	—
82	C₃×C₅×SD₁₆	—	2	4	no	—
83	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₅×#217	—	2	2	no	—
86	C₅×#216	—	2	4	no	—
87	C₅×#216	—	2	4	no	—
88	C₅×#215	—	2	4	no	—
89	C₅×#214	—	2	4	no	—
90	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
91	C₅×Dic₃⋊C₄	—	2	4	no	—
92	C₅×Dic₃⋊C₄	—	2	4	no	—
93	C₅×Dic₃⋊C₄	—	2	2	no	—
94	C₄×C₅×Dic₃	D₄	1	2	yes	—
95	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₅×#208	D₄	1	4	yes	complemented
98	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
99	C₅×Dic₁₂	—	2	4	no	—
100	C₅×#204	—	2	4	no	—
101	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
102	#5832	C₂×C₅	1	1	yes	characteristic
103	C₂×#951	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#942	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#909	C₂×C₅	1	1	yes	characteristic, complemented
107	#5190	C₂×C₅	1	2	yes	complemented
108	#5183	C₂×C₅	1	2	yes	complemented
109	#5175	C₂×C₅	1	2	yes	complemented
110	#5167	C₂×C₅	1	2	yes	complemented
111	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
116	C₅×#137	—	2	4	no	—
117	C₅×#137	—	6	4	no	—
118	C₅×#137	—	6	4	no	—
119	C₅×#137	—	6	4	no	—
120	C₂×C₅×Q₁₆	—	3	2	no	—
121	C₂×C₅×Q₁₆	—	3	2	no	—
122	C₂×C₅×Q₁₆	—	3	2	no	—
123	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
124	C₂×C₅×SD₁₆	—	3	2	no	—
125	C₂×C₅×SD₁₆	—	3	2	no	—
126	C₂×C₅×SD₁₆	—	3	2	no	—
127	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
128	C₂×C₅×M₁₆	—	3	1	no	—
129	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
130	C₅×C₄⋊Q₈	—	3	2	no	—
131	C₅×C₄⋊Q₈	—	3	1	no	—
132	C₅×C₄⋊Q₈	—	3	2	no	—
133	C₅×C₄⋊Q₈	—	6	2	no	—
134	C₅×#127	—	3	1	no	—
135	C₅×#124	—	3	1	no	—
136	C₅×#124	—	3	1	no	—
137	C₅×#121	—	6	2	no	—
138	C₄×C₅×D₄	—	6	2	no	—
139	C₂×C₅×C₄⋊C₄	—	6	2	no	—
140	C₂×C₄²×C₅	—	3	1	no	—
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	#3152	—	3	1	no	Sylow
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₅×D₃	—	2	1	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	1	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	4	2	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	2	1	no	—
154	C₃×C₅×D₄	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	4	2	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₅×#67	—	4	2	no	—
164	C₅×#67	—	4	4	no	—
165	C₂×C₅×Dic₃	—	2	4	no	—
166	C₂×C₅×Dic₃	—	2	2	no	—
167	C₂×C₅×Dic₃	—	2	1	no	—
168	C₂×C₅×Dic₃	—	4	2	no	—
169	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
170	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
171	C₅×D₁₂	—	2	1	no	—
172	C₅×D₁₂	—	2	1	no	—
173	C₄×C₅×D₃	—	4	2	no	—
174	C₅×Dic₆	—	2	2	no	—
175	C₅×Dic₆	—	2	1	no	—
176	C₅×Dic₆	—	2	2	no	—
177	C₅×Dic₆	—	2	1	no	—
178	C₅×Dic₆	—	4	2	no	—
179	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
180	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×#235	C₂²×C₅	1	1	yes	characteristic
184	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
185	C₃×#137	—	2	4	no	—
186	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
187	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
188	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
189	#951	—	2	4	no	—
190	#947	C₂²×C₅	1	1	yes	characteristic
191	#944	—	2	2	no	—
192	#944	C₂²×C₅	1	2	yes	—
193	#944	C₂²×C₅	1	2	yes	—
194	#944	C₂²×C₅	1	1	yes	characteristic
195	C₂×#216	C₂²×C₅	1	2	yes	—
196	C₂×#216	C₂²×C₅	1	2	yes	—
197	#942	—	2	4	no	—
198	C₂×#215	C₂²×C₅	1	2	yes	—
199	#940	C₂²×C₅	1	1	yes	characteristic
200	#939	—	2	2	no	—
201	#936	C₂²×C₅	1	1	yes	characteristic
202	C₂×#214	C₂²×C₅	1	2	yes	—
203	C₄×#67	—	2	2	no	—
204	C₂×Dic₃⋊C₄	—	2	2	no	—
205	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
206	C₂×#208	C₂²×C₅	1	1	yes	characteristic
207	#909	—	2	4	no	—
208	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
209	C₂×#204	C₂²×C₅	1	2	yes	—
210	#815	C₂²×C₅	1	2	yes	—
211	C₈×Dic₃	C₂²×C₅	1	2	yes	—
212	C₅×#41	—	2	2	no	—
213	C₅×#41	—	2	2	no	—
214	C₅×#41	—	6	2	no	—
215	C₅×#41	—	6	2	no	—
216	C₂×C₅×Q₈	—	2	1	no	—
217	C₂×C₅×Q₈	—	2	2	no	—
218	C₂×C₅×Q₈	—	2	2	no	—
219	C₂×C₅×Q₈	—	3	1	no	—
220	C₂×C₅×Q₈	—	3	2	no	—
221	C₂×C₅×Q₈	—	6	1	no	—
222	C₂×C₅×Q₈	—	6	2	no	—
223	C₂×C₅×Q₈	—	6	2	no	—
224	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
225	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
226	C₂×C₅×D₄	—	2	1	no	—
227	C₂×C₅×D₄	—	3	1	no	—
228	C₂×C₅×D₄	—	6	2	no	—
229	C₂×C₅×D₄	—	6	1	no	—
230	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	—	2	1	no	—
232	C₂²×C₄×C₅	—	2	1	no	—
233	C₂²×C₄×C₅	—	3	2	no	—
234	C₂²×C₄×C₅	—	6	1	no	—
235	C₂²×C₄×C₅	—	6	1	no	—
236	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₅×Q₁₆	—	2	4	no	—
238	C₅×Q₁₆	—	6	4	no	—
239	C₅×Q₁₆	—	6	4	no	—
240	C₅×Q₁₆	—	6	4	no	—
241	C₅×SD₁₆	—	2	4	no	—
242	C₅×SD₁₆	—	6	4	no	—
243	C₅×SD₁₆	—	6	4	no	—
244	C₅×SD₁₆	—	6	4	no	—
245	C₅×M₁₆	—	3	4	no	—
246	C₅×M₁₆	#67	1	4	yes	complemented
247	C₂×C₅×C₈	—	3	2	no	—
248	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
249	C₅×C₄⋊C₄	—	6	4	no	—
250	C₅×C₄⋊C₄	—	6	4	no	—
251	C₅×C₄⋊C₄	—	6	2	no	—
252	C₅×C₂²⋊C₄	—	6	2	no	—
253	C₅×C₂²⋊C₄	—	6	2	no	—
254	C₄²×C₅	—	3	2	no	—
255	C₄²×C₅	—	3	1	no	—
256	C₄²×C₅	—	3	1	no	—
257	C₂×#137	—	3	1	no	—
258	C₂×#137	—	3	1	no	—
259	C₂×#137	—	3	1	no	—
260	C₂×#137	C₅×D₃	1	1	yes	characteristic, complemented
261	#532	—	3	1	no	—
262	C₂×C₄⋊Q₈	—	3	1	no	—
263	#497	—	3	2	no	—
264	#497	—	3	2	no	—
265	#494	—	3	2	no	—
266	#492	—	3	2	no	—
267	C₄×M₁₆	—	3	1	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	#127	1	2	yes	—
272	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₅×D₃	—	4	1	no	—
274	C₂×C₅×D₃	—	4	2	no	—
275	C₃×C₄×C₅	—	4	1	no	—
276	C₃×C₄×C₅	—	4	2	no	—
277	C₃×C₄×C₅	#127	1	2	yes	—
278	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₅×Dic₃	—	2	2	no	—
281	C₅×Dic₃	—	4	2	no	—
282	C₅×Dic₃	—	4	1	no	—
283	C₅×Dic₃	#137	1	4	yes	complemented
284	C₃×#41	—	2	2	no	—
285	C₃×#41	—	2	2	no	—
286	C₂×C₃×Q₈	—	2	1	no	—
287	C₂×C₃×Q₈	—	2	2	no	—
288	C₂×C₃×Q₈	—	2	2	no	—
289	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
290	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₃×D₄	—	2	1	no	—
292	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	2	1	no	—
295	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
296	C₂×#67	—	2	1	no	—
297	C₂×#67	—	2	2	no	—
298	C₂²×Dic₃	—	2	1	no	—
299	C₂²×Dic₃	C₅×D₄	1	2	yes	—
300	#235	—	2	2	no	—
301	#235	—	2	2	no	—
302	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄×D₃	—	2	1	no	—
304	C₂×Dic₆	—	2	2	no	—
305	C₂×Dic₆	—	2	2	no	—
306	C₂×Dic₆	—	2	1	no	—
307	C₂×Dic₆	C₂³×C₅	1	2	yes	—
308	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
309	C₃×Q₁₆	—	2	4	no	—
310	C₃×SD₁₆	—	2	4	no	—
311	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
312	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
313	#217	—	2	2	no	—
314	#216	—	2	4	no	—
315	#216	—	2	4	no	—
316	#215	—	2	4	no	—
317	#214	—	2	4	no	—
318	(C₂×D₃)⋊C₄	—	2	2	no	—
319	Dic₃⋊C₄	—	2	4	no	—
320	Dic₃⋊C₄	—	2	4	no	—
321	Dic₃⋊C₄	—	2	2	no	—
322	C₄×Dic₃	C₅×D₄	1	2	yes	—
323	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
324	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
325	#208	C₅×D₄	1	4	yes	complemented
326	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
327	Dic₁₂	—	2	4	no	—
328	#204	—	2	4	no	—
329	C₂³×C₅	—	2	1	no	—
330	C₂³×C₅	—	6	1	no	—
331	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
332	C₅×Q₈	—	2	2	no	—
333	C₅×Q₈	—	2	1	no	—
334	C₅×Q₈	—	2	2	no	—
335	C₅×Q₈	—	2	1	no	—
336	C₅×Q₈	—	4	2	no	—
337	C₅×Q₈	—	6	2	no	—
338	C₅×Q₈	—	6	1	no	—
339	C₅×Q₈	—	6	2	no	—
340	C₅×Q₈	—	6	1	no	—
341	C₅×Q₈	—	12	2	no	—
342	C₅×D₄	—	2	1	no	—
343	C₅×D₄	—	2	1	no	—
344	C₅×D₄	—	4	2	no	—
345	C₅×D₄	—	6	1	no	—
346	C₅×D₄	—	6	1	no	—
347	C₅×D₄	—	12	4	no	—
348	C₅×D₄	—	12	2	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	3	2	no	—
352	C₂×C₄×C₅	—	3	2	no	—
353	C₂×C₄×C₅	—	4	2	no	—
354	C₂×C₄×C₅	—	4	2	no	—
355	C₂×C₄×C₅	—	6	4	no	—
356	C₂×C₄×C₅	—	6	1	no	—
357	C₂×C₄×C₅	—	6	2	no	—
358	C₂×C₄×C₅	—	12	2	no	—
359	C₂×C₄×C₅	—	12	2	no	—
360	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
361	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
362	C₂×C₄×C₅	C₂×#67	1	2	yes	—
363	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
364	C₅×C₈	—	3	4	no	—
365	C₅×C₈	C₂×#67	1	4	yes	—
366	C₂×#41	—	3	1	no	—
367	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
368	C₂²×Q₈	—	3	1	no	—
369	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
370	#137	—	2	4	no	—
371	#137	—	6	4	no	—
372	#137	—	6	4	no	—
373	#137	—	6	4	no	—
374	C₂×Q₁₆	—	3	2	no	—
375	C₂×Q₁₆	—	3	2	no	—
376	C₂×Q₁₆	—	3	2	no	—
377	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
378	C₂×SD₁₆	—	3	2	no	—
379	C₂×SD₁₆	—	3	2	no	—
380	C₂×SD₁₆	—	3	2	no	—
381	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
382	C₂×M₁₆	—	3	1	no	—
383	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
384	C₄⋊Q₈	—	3	2	no	—
385	C₄⋊Q₈	—	3	2	no	—
386	C₄⋊Q₈	—	3	1	no	—
387	C₄⋊Q₈	—	6	2	no	—
388	#127	—	3	1	no	—
389	#124	—	3	1	no	—
390	#124	—	3	1	no	—
391	#121	—	6	2	no	—
392	C₄×D₄	—	6	2	no	—
393	C₂×C₄⋊C₄	—	6	2	no	—
394	C₂×C₄²	—	3	1	no	—
395	#97	—	3	2	no	—
396	C₄×C₈	—	3	2	no	—
397	C₂×C₃×C₅	—	2	2	no	—
398	C₂×C₃×C₅	—	8	1	no	—
399	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
400	C₂×C₃×C₅	C₂×#137	1	2	yes	—
401	C₅×D₃	—	8	1	no	—
402	C₂³×C₃	—	2	1	no	—
403	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂²×D₃	—	2	1	no	—
405	C₃×Q₈	—	2	2	no	—
406	C₃×Q₈	—	2	1	no	—
407	C₃×Q₈	—	2	2	no	—
408	C₃×Q₈	—	2	1	no	—
409	C₃×Q₈	—	4	2	no	—
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	—	2	1	no	—
412	C₃×D₄	—	4	2	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	4	2	no	—
416	C₂×C₃×C₄	—	4	2	no	—
417	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
419	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
421	#67	—	4	2	no	—
422	#67	—	4	4	no	—
423	C₂×Dic₃	—	2	4	no	—
424	C₂×Dic₃	—	2	2	no	—
425	C₂×Dic₃	—	2	1	no	—
426	C₂×Dic₃	—	4	2	no	—
427	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
428	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
429	D₁₂	—	2	1	no	—
430	D₁₂	—	2	1	no	—
431	C₄×D₃	—	4	2	no	—
432	Dic₆	—	2	2	no	—
433	Dic₆	—	2	1	no	—
434	Dic₆	—	2	2	no	—
435	Dic₆	—	2	1	no	—
436	Dic₆	—	4	2	no	—
437	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
438	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	4	2	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	12	2	no	—
443	C₂²×C₅	—	12	1	no	—
444	C₂²×C₅	#940	1	2	yes	—
445	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
446	C₄×C₅	—	3	4	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	2	no	—
449	C₄×C₅	—	6	2	no	—
450	C₄×C₅	—	12	1	no	—
451	C₄×C₅	—	12	2	no	—
452	C₄×C₅	#940	1	2	yes	—
453	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
454	C₄×C₅	C₂²×#67	1	1	yes	characteristic
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	6	2	no	—
458	#41	—	6	2	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	3	1	no	—
463	C₂×Q₈	—	3	2	no	—
464	C₂×Q₈	—	6	1	no	—
465	C₂×Q₈	—	6	2	no	—
466	C₂×Q₈	—	6	2	no	—
467	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	3	1	no	—
471	C₂×D₄	—	6	2	no	—
472	C₂×D₄	—	6	1	no	—
473	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	3	2	no	—
477	C₂²×C₄	—	6	1	no	—
478	C₂²×C₄	—	6	1	no	—
479	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
480	Q₁₆	—	2	4	no	—
481	Q₁₆	—	6	4	no	—
482	Q₁₆	—	6	4	no	—
483	Q₁₆	—	6	4	no	—
484	SD₁₆	—	2	4	no	—
485	SD₁₆	—	6	4	no	—
486	SD₁₆	—	6	4	no	—
487	SD₁₆	—	6	4	no	—
488	M₁₆	—	3	4	no	—
489	M₁₆	C₅×#67	1	4	yes	complemented
490	C₂×C₈	—	3	2	no	—
491	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
492	C₄⋊C₄	—	6	4	no	—
493	C₄⋊C₄	—	6	4	no	—
494	C₄⋊C₄	—	6	2	no	—
495	C₂²⋊C₄	—	6	2	no	—
496	C₂²⋊C₄	—	6	2	no	—
497	C₄²	—	3	2	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	1	no	—
500	C₃×C₅	#3152	1	1	yes	characteristic, complemented, Hall
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	—	4	2	no	—
504	C₂²×C₃	C₅×#127	1	2	yes	—
505	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
506	C₂×D₃	—	4	1	no	—
507	C₂×D₃	—	4	2	no	—
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	—	4	2	no	—
510	C₃×C₄	C₅×#127	1	2	yes	—
511	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
512	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
513	Dic₃	—	2	2	no	—
514	Dic₃	—	4	2	no	—
515	Dic₃	—	4	1	no	—
516	Dic₃	C₅×#137	1	4	yes	complemented
517	C₂×C₅	—	2	2	no	—
518	C₂×C₅	—	8	1	no	—
519	C₂×C₅	—	24	1	no	—
520	C₂×C₅	D₃×#137	1	2	yes	—
521	C₂×C₅	C₂×#940	1	1	yes	characteristic
522	C₂³	—	2	1	no	—
523	C₂³	—	6	1	no	—
524	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	2	1	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	6	2	no	—
531	Q₈	—	6	1	no	—
532	Q₈	—	6	2	no	—
533	Q₈	—	6	1	no	—
534	Q₈	—	12	2	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	4	2	no	—
538	D₄	—	6	1	no	—
539	D₄	—	6	1	no	—
540	D₄	—	12	4	no	—
541	D₄	—	12	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	3	2	no	—
545	C₂×C₄	—	3	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	6	4	no	—
549	C₂×C₄	—	6	1	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	12	2	no	—
552	C₂×C₄	—	12	2	no	—
553	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
554	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
555	C₂×C₄	C₂×C₅×#67	1	2	yes	—
556	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
557	C₈	—	3	4	no	—
558	C₈	C₂×C₅×#67	1	4	yes	—
559	C₂×C₃	—	2	2	no	—
560	C₂×C₃	—	8	1	no	—
561	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
562	C₂×C₃	C₂×C₅×#137	1	2	yes	—
563	D₃	—	8	1	no	—
564	C₅	#83972	1	1	yes	characteristic, direct product factor, Sylow
565	C₂²	—	2	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	12	2	no	—
569	C₂²	—	12	1	no	—
570	C₂²	C₅×#940	1	2	yes	—
571	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
572	C₄	—	3	4	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	6	2	no	—
576	C₄	—	12	1	no	—
577	C₄	—	12	2	no	—
578	C₄	C₅×#940	1	2	yes	—
579	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
580	C₄	C₂²×C₅×#67	1	1	yes	characteristic
581	C₃	C₅×#3152	1	1	yes	characteristic, complemented, Sylow
582	C₂	—	2	2	no	—
583	C₂	—	8	1	no	—
584	C₂	—	24	1	no	—
585	C₂	C₅×D₃×#137	1	2	yes	—
586	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5832	C₂
hypercenter	C₂×C₅×#137	D₃
hypocenter	C₃	C₅×#3152
LCS	G ▷ C₂×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
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₅×#951	C₂	semidirect
4. C₂×C₅×#944	C₂	semidirect
5. C₂×C₅×#942	C₂	semidirect
6. C₂×C₅×#909	C₂	semidirect
7. C₅×#5190	C₂	semidirect
8. C₅×#5183	C₂	semidirect
9. C₅×#5175	C₂	semidirect
10. C₅×#5167	C₂	semidirect
11. C₅×Dic₃×M₁₆	C₂	semidirect
44. #83972	C₅	direct (N × H)
48. C₂×C₅×#137	D₃	semidirect
83. C₃×C₅×M₁₆	D₄	semidirect
97. C₅×#208	D₄	semidirect
101. C₂×C₃×#137	C₂×C₅	semidirect
103. C₂×#951	C₂×C₅	semidirect
104. C₂×#944	C₂×C₅	semidirect
105. C₂×#942	C₂×C₅	semidirect
106. C₂×#909	C₂×C₅	semidirect
107. #5190	C₂×C₅	semidirect
108. #5183	C₂×C₅	semidirect
109. #5175	C₂×C₅	semidirect
110. #5167	C₂×C₅	semidirect
111. Dic₃×M₁₆	C₂×C₅	semidirect
246. C₅×M₁₆	#67	semidirect
260. C₂×#137	C₅×D₃	semidirect
283. C₅×Dic₃	#137	semidirect
311. C₃×M₁₆	C₅×D₄	semidirect
325. #208	C₅×D₄	semidirect
489. M₁₆	C₅×#67	semidirect
500. C₃×C₅	#3152	semidirect
516. Dic₃	C₅×#137	semidirect
564. C₅	#83972	direct (N × H)
581. C₃	C₅×#3152	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×#5832	2
C₂×C₅×#951	2
C₂×C₅×#944	2
C₂×C₅×#942	2
C₂×C₅×#909	2
C₅×#5190	2
C₅×#5183	2
C₅×#5175	2
C₅×#5167	2
C₅×Dic₃×M₁₆	2
C₅×#3152	3
#83972	5

Subgroups — C5×#83972 #14439201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83972 #14439201