Subgroups — C₅×#83975 #14439645

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 576 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×#5825	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic
4	C₅×#5816	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#216	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×#5168	C₂	1	2	yes	maximal, complemented
10	C₅×#5167	C₂	1	2	yes	maximal, complemented
11	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3156	—	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×#950	—	2	4	no	—
22	C₅×#947	C₂²	1	2	yes	—
23	C₅×#946	—	2	2	no	—
24	C₅×#944	C₂²	1	2	yes	—
25	C₅×#944	C₂²	1	2	yes	—
26	C₂×C₅×#216	—	2	4	no	—
27	C₂×C₅×#216	C₂²	1	2	yes	—
28	C₂×C₅×#216	C₂²	1	2	yes	—
29	C₂×C₅×#216	C₂²	1	1	yes	characteristic
30	C₂×C₅×#215	C₂²	1	1	yes	characteristic
31	C₅×#936	C₂²	1	2	yes	—
32	C₅×#935	—	2	2	no	—
33	C₂×C₅×#214	C₂²	1	1	yes	characteristic
34	C₂×C₅×#213	C₂²	1	1	yes	characteristic
35	C₅×#929	—	2	2	no	—
36	C₅×#926	C₂²	1	1	yes	characteristic
37	C₅×#924	—	2	2	no	—
38	C₂²×C₅×C₃⋊C₈	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	#83975	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	—	3	1	no	—
46	C₂×C₅×#137	D₃	1	1	yes	characteristic, complemented
47	C₂×C₅×#135	—	3	1	no	—
48	C₂²×C₅×Q₁₆	—	3	1	no	—
49	C₅×#536	—	3	1	no	—
50	C₅×#536	—	3	1	no	—
51	C₅×#497	—	3	2	no	—
52	C₅×#497	—	3	2	no	—
53	C₅×#495	—	3	2	no	—
54	C₅×#494	—	3	2	no	—
55	C₅×#405	—	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	1	yes	characteristic
62	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
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	C₂²×C₅×Dic₃	—	2	1	no	—
70	C₅×#235	—	2	2	no	—
71	C₅×#235	—	2	2	no	—
72	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	—	2	1	no	—
74	C₂×C₅×Dic₆	—	2	2	no	—
75	C₂×C₅×Dic₆	—	2	2	no	—
76	C₂×C₅×Dic₆	—	2	1	no	—
77	C₂×C₅×Dic₆	C₂³	1	2	yes	—
78	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
79	C₃×C₅×Q₁₆	—	2	4	no	—
80	C₃×C₅×SD₁₆	—	2	4	no	—
81	C₃×C₅×M₁₆	D₄	1	4	yes	—
82	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
83	C₅×#217	—	2	4	no	—
84	C₅×#217	D₄	1	2	yes	—
85	C₅×#216	—	2	4	no	—
86	C₅×#216	—	2	4	no	—
87	C₅×#216	—	2	2	no	—
88	C₅×#215	—	2	2	no	—
89	C₅×#214	—	2	2	no	—
90	C₅×#213	—	2	2	no	—
91	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
92	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
93	C₅×Dic₃⋊C₄	—	2	4	no	—
94	C₅×Dic₃⋊C₄	—	2	4	no	—
95	C₄×C₅×Dic₃	C₂³	1	2	yes	—
96	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	—
97	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×Dic₁₂	—	2	4	no	—
100	C₅×#204	—	2	4	no	—
101	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
102	#5825	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#950	C₂×C₅	1	1	yes	characteristic
104	#5816	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂²×#216	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	#5168	C₂×C₅	1	2	yes	complemented
110	#5167	C₂×C₅	1	2	yes	complemented
111	#5122	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×#135	—	6	4	no	—
119	C₂×C₅×Q₁₆	—	3	1	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	—	6	4	no	—
124	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
125	C₂×C₅×SD₁₆	—	3	1	no	—
126	C₂×C₅×SD₁₆	—	3	1	no	—
127	C₂×C₅×SD₁₆	—	3	2	no	—
128	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
129	C₂×C₅×D₈	—	3	1	no	—
130	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
131	C₂²×C₅×C₈	—	3	1	no	—
132	C₅×C₄⋊Q₈	—	3	2	no	—
133	C₅×C₄⋊Q₈	—	3	2	no	—
134	C₅×#124	—	3	2	no	—
135	C₅×#124	—	3	2	no	—
136	C₅×#123	—	6	2	no	—
137	C₅×#123	—	6	2	no	—
138	C₅×C₂²⋊Q₈	—	6	2	no	—
139	C₅×C₂²⋊Q₈	—	6	2	no	—
140	C₅×#117	—	3	1	no	—
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	#3156	—	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	1	no	—
148	C₃×C₅×Q₈	—	2	2	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	1	no	—
156	C₂×C₃×C₄×C₅	—	2	2	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	C₂×C₅×Dic₃	—	2	1	no	—
165	C₂×C₅×Dic₃	—	2	2	no	—
166	C₂×C₅×Dic₃	—	4	2	no	—
167	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
168	C₅×D₁₂	—	2	1	no	—
169	C₅×D₁₂	—	2	1	no	—
170	C₄×C₅×D₃	—	4	2	no	—
171	C₅×Dic₆	—	2	2	no	—
172	C₅×Dic₆	—	2	1	no	—
173	C₅×Dic₆	—	2	1	no	—
174	C₅×Dic₆	—	2	2	no	—
175	C₅×Dic₆	—	4	2	no	—
176	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
177	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
178	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
179	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
180	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
181	C₂×#235	C₂²×C₅	1	1	yes	characteristic
182	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
183	C₃×#137	—	2	4	no	—
184	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
185	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
186	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
187	#950	—	2	4	no	—
188	#947	C₂²×C₅	1	2	yes	—
189	#946	—	2	2	no	—
190	#944	C₂²×C₅	1	2	yes	—
191	#944	C₂²×C₅	1	2	yes	—
192	C₂×#216	—	2	4	no	—
193	C₂×#216	C₂²×C₅	1	2	yes	—
194	C₂×#216	C₂²×C₅	1	2	yes	—
195	C₂×#216	C₂²×C₅	1	1	yes	characteristic
196	C₂×#215	C₂²×C₅	1	1	yes	characteristic
197	#936	C₂²×C₅	1	2	yes	—
198	#935	—	2	2	no	—
199	C₂×#214	C₂²×C₅	1	1	yes	characteristic
200	C₂×#213	C₂²×C₅	1	1	yes	characteristic
201	#929	—	2	2	no	—
202	#926	C₂²×C₅	1	1	yes	characteristic
203	#924	—	2	2	no	—
204	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	#909	—	2	4	no	—
206	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
207	C₂×#204	C₂²×C₅	1	2	yes	—
208	#815	C₂²×C₅	1	2	yes	—
209	C₈×Dic₃	C₂²×C₅	1	2	yes	—
210	C₅×#41	—	2	2	no	—
211	C₅×#41	—	2	2	no	—
212	C₅×#41	—	6	2	no	—
213	C₅×#41	—	6	2	no	—
214	C₂×C₅×Q₈	—	2	1	no	—
215	C₂×C₅×Q₈	—	2	2	no	—
216	C₂×C₅×Q₈	—	2	2	no	—
217	C₂×C₅×Q₈	—	3	2	no	—
218	C₂×C₅×Q₈	—	3	1	no	—
219	C₂×C₅×Q₈	—	6	1	no	—
220	C₂×C₅×Q₈	—	6	2	no	—
221	C₂×C₅×Q₈	—	6	2	no	—
222	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
223	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₅×D₄	—	2	1	no	—
225	C₂×C₅×D₄	—	3	1	no	—
226	C₂×C₅×D₄	—	6	1	no	—
227	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	—	2	1	no	—
230	C₂²×C₄×C₅	—	6	1	no	—
231	C₂²×C₄×C₅	—	6	1	no	—
232	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₅×Q₁₆	—	2	4	no	—
234	C₅×Q₁₆	—	6	4	no	—
235	C₅×Q₁₆	—	6	4	no	—
236	C₅×Q₁₆	—	6	2	no	—
237	C₅×Q₁₆	—	6	4	no	—
238	C₅×SD₁₆	—	2	4	no	—
239	C₅×SD₁₆	—	6	2	no	—
240	C₅×SD₁₆	—	6	2	no	—
241	C₅×SD₁₆	—	6	4	no	—
242	C₅×D₈	—	6	2	no	—
243	C₅×M₁₆	#67	1	4	yes	—
244	C₂×C₅×C₈	—	3	4	no	—
245	C₂×C₅×C₈	—	3	1	no	—
246	C₂×C₅×C₈	—	3	1	no	—
247	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
248	C₅×C₄⋊C₄	—	3	2	no	—
249	C₅×C₄⋊C₄	—	6	4	no	—
250	C₅×C₄⋊C₄	—	6	4	no	—
251	C₅×C₂²⋊C₄	—	3	2	no	—
252	C₅×C₂²⋊C₄	—	6	4	no	—
253	C₅×C₂²⋊C₄	—	6	4	no	—
254	C₄²×C₅	—	3	2	no	—
255	C₂×#137	—	3	1	no	—
256	C₂×#137	C₅×D₃	1	1	yes	characteristic, complemented
257	C₂×#135	—	3	1	no	—
258	C₂²×Q₁₆	—	3	1	no	—
259	#536	—	3	1	no	—
260	#536	—	3	1	no	—
261	#497	—	3	2	no	—
262	#497	—	3	2	no	—
263	#495	—	3	2	no	—
264	#494	—	3	2	no	—
265	#405	—	3	1	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	4	1	no	—
268	C₂²×C₃×C₅	—	4	2	no	—
269	C₂²×C₃×C₅	#127	1	2	yes	—
270	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₅×D₃	—	4	1	no	—
272	C₂×C₅×D₃	—	4	2	no	—
273	C₃×C₄×C₅	—	4	1	no	—
274	C₃×C₄×C₅	—	4	2	no	—
275	C₃×C₄×C₅	#127	1	2	yes	—
276	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₅×Dic₃	—	2	4	no	—
279	C₅×Dic₃	—	4	2	no	—
280	C₅×Dic₃	—	4	1	no	—
281	C₃×#41	—	2	2	no	—
282	C₃×#41	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	1	no	—
284	C₂×C₃×Q₈	—	2	2	no	—
285	C₂×C₃×Q₈	—	2	2	no	—
286	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	—	2	1	no	—
291	C₂²×C₃×C₄	—	2	1	no	—
292	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
293	C₂×#67	—	2	1	no	—
294	C₂²×Dic₃	—	2	1	no	—
295	#235	—	2	2	no	—
296	#235	—	2	2	no	—
297	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
298	C₂×C₄×D₃	—	2	1	no	—
299	C₂×Dic₆	—	2	2	no	—
300	C₂×Dic₆	—	2	2	no	—
301	C₂×Dic₆	—	2	1	no	—
302	C₂×Dic₆	C₂³×C₅	1	2	yes	—
303	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
304	C₃×Q₁₆	—	2	4	no	—
305	C₃×SD₁₆	—	2	4	no	—
306	C₃×M₁₆	C₅×D₄	1	4	yes	—
307	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
308	#217	—	2	4	no	—
309	#217	C₅×D₄	1	2	yes	—
310	#216	—	2	4	no	—
311	#216	—	2	4	no	—
312	#216	—	2	2	no	—
313	#215	—	2	2	no	—
314	#214	—	2	2	no	—
315	#213	—	2	2	no	—
316	(C₂×D₃)⋊C₄	—	2	4	no	—
317	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
318	Dic₃⋊C₄	—	2	4	no	—
319	Dic₃⋊C₄	—	2	4	no	—
320	C₄×Dic₃	C₂³×C₅	1	2	yes	—
321	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	—
322	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
323	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
324	Dic₁₂	—	2	4	no	—
325	#204	—	2	4	no	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	6	1	no	—
328	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
329	C₅×Q₈	—	2	1	no	—
330	C₅×Q₈	—	2	2	no	—
331	C₅×Q₈	—	2	2	no	—
332	C₅×Q₈	—	2	1	no	—
333	C₅×Q₈	—	4	2	no	—
334	C₅×Q₈	—	6	1	no	—
335	C₅×Q₈	—	6	2	no	—
336	C₅×Q₈	—	6	2	no	—
337	C₅×Q₈	—	6	1	no	—
338	C₅×Q₈	—	12	2	no	—
339	C₅×D₄	—	2	1	no	—
340	C₅×D₄	—	2	1	no	—
341	C₅×D₄	—	4	2	no	—
342	C₅×D₄	—	6	1	no	—
343	C₅×D₄	—	6	1	no	—
344	C₅×D₄	—	12	2	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	3	4	no	—
348	C₂×C₄×C₅	—	4	2	no	—
349	C₂×C₄×C₅	—	4	2	no	—
350	C₂×C₄×C₅	—	6	2	no	—
351	C₂×C₄×C₅	—	6	1	no	—
352	C₂×C₄×C₅	—	12	2	no	—
353	C₂×C₄×C₅	—	12	2	no	—
354	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
355	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
356	C₂×C₄×C₅	C₂×#67	1	2	yes	—
357	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
358	C₅×C₈	—	3	2	no	—
359	C₅×C₈	—	3	2	no	—
360	C₅×C₈	C₂×#67	1	4	yes	—
361	C₂×#41	—	3	1	no	—
362	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
363	C₂²×Q₈	—	3	1	no	—
364	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
365	#137	—	2	4	no	—
366	#137	—	6	4	no	—
367	#135	—	6	4	no	—
368	C₂×Q₁₆	—	3	2	no	—
369	C₂×Q₁₆	—	3	2	no	—
370	C₂×Q₁₆	—	3	1	no	—
371	C₂×Q₁₆	—	3	2	no	—
372	C₂×Q₁₆	—	6	4	no	—
373	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
374	C₂×SD₁₆	—	3	1	no	—
375	C₂×SD₁₆	—	3	1	no	—
376	C₂×SD₁₆	—	3	2	no	—
377	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
378	C₂×D₈	—	3	1	no	—
379	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
380	C₂²×C₈	—	3	1	no	—
381	C₄⋊Q₈	—	3	2	no	—
382	C₄⋊Q₈	—	3	2	no	—
383	#124	—	3	2	no	—
384	#124	—	3	2	no	—
385	#123	—	6	2	no	—
386	#123	—	6	2	no	—
387	C₂²⋊Q₈	—	6	2	no	—
388	C₂²⋊Q₈	—	6	2	no	—
389	#117	—	3	1	no	—
390	#97	—	3	2	no	—
391	C₄×C₈	—	3	2	no	—
392	C₂×C₃×C₅	—	2	2	no	—
393	C₂×C₃×C₅	—	8	1	no	—
394	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
395	C₂×C₃×C₅	#578	1	2	yes	—
396	C₅×D₃	—	8	1	no	—
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂²×D₃	—	2	1	no	—
400	C₃×Q₈	—	2	1	no	—
401	C₃×Q₈	—	2	2	no	—
402	C₃×Q₈	—	2	2	no	—
403	C₃×Q₈	—	2	1	no	—
404	C₃×Q₈	—	4	2	no	—
405	C₃×D₄	—	2	1	no	—
406	C₃×D₄	—	2	1	no	—
407	C₃×D₄	—	4	2	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	4	2	no	—
412	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
414	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
415	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
416	#67	—	4	2	no	—
417	C₂×Dic₃	—	2	1	no	—
418	C₂×Dic₃	—	2	2	no	—
419	C₂×Dic₃	—	4	2	no	—
420	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
421	D₁₂	—	2	1	no	—
422	D₁₂	—	2	1	no	—
423	C₄×D₃	—	4	2	no	—
424	Dic₆	—	2	2	no	—
425	Dic₆	—	2	1	no	—
426	Dic₆	—	2	1	no	—
427	Dic₆	—	2	2	no	—
428	Dic₆	—	4	2	no	—
429	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
430	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
431	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	4	2	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	12	2	no	—
436	C₂²×C₅	—	12	1	no	—
437	C₂²×C₅	#940	1	2	yes	—
438	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	2	no	—
441	C₄×C₅	—	6	4	no	—
442	C₄×C₅	—	12	1	no	—
443	C₄×C₅	—	12	2	no	—
444	C₄×C₅	#940	1	2	yes	—
445	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
446	C₄×C₅	C₂²×#67	1	1	yes	characteristic
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	6	2	no	—
450	#41	—	6	2	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	3	2	no	—
455	C₂×Q₈	—	3	1	no	—
456	C₂×Q₈	—	6	1	no	—
457	C₂×Q₈	—	6	2	no	—
458	C₂×Q₈	—	6	2	no	—
459	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
460	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	3	1	no	—
463	C₂×D₄	—	6	1	no	—
464	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	6	1	no	—
468	C₂²×C₄	—	6	1	no	—
469	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
470	Q₁₆	—	2	4	no	—
471	Q₁₆	—	6	4	no	—
472	Q₁₆	—	6	4	no	—
473	Q₁₆	—	6	2	no	—
474	Q₁₆	—	6	4	no	—
475	SD₁₆	—	2	4	no	—
476	SD₁₆	—	6	2	no	—
477	SD₁₆	—	6	2	no	—
478	SD₁₆	—	6	4	no	—
479	D₈	—	6	2	no	—
480	M₁₆	C₅×#67	1	4	yes	—
481	C₂×C₈	—	3	4	no	—
482	C₂×C₈	—	3	1	no	—
483	C₂×C₈	—	3	1	no	—
484	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
485	C₄⋊C₄	—	3	2	no	—
486	C₄⋊C₄	—	6	4	no	—
487	C₄⋊C₄	—	6	4	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	6	4	no	—
490	C₂²⋊C₄	—	6	4	no	—
491	C₄²	—	3	2	no	—
492	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	C₅×#127	1	2	yes	—
497	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₂×D₃	—	4	1	no	—
499	C₂×D₃	—	4	2	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	—	4	2	no	—
502	C₃×C₄	C₅×#127	1	2	yes	—
503	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
504	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
505	Dic₃	—	2	4	no	—
506	Dic₃	—	4	2	no	—
507	Dic₃	—	4	1	no	—
508	C₂×C₅	—	2	2	no	—
509	C₂×C₅	—	8	1	no	—
510	C₂×C₅	—	24	1	no	—
511	C₂×C₅	#5779	1	2	yes	—
512	C₂×C₅	C₂×#940	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	6	1	no	—
515	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
516	Q₈	—	2	1	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	6	1	no	—
522	Q₈	—	6	2	no	—
523	Q₈	—	6	2	no	—
524	Q₈	—	6	1	no	—
525	Q₈	—	12	2	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	4	2	no	—
529	D₄	—	6	1	no	—
530	D₄	—	6	1	no	—
531	D₄	—	12	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	3	4	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	1	no	—
539	C₂×C₄	—	12	2	no	—
540	C₂×C₄	—	12	2	no	—
541	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
542	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
543	C₂×C₄	C₂×C₅×#67	1	2	yes	—
544	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
545	C₈	—	3	2	no	—
546	C₈	—	3	2	no	—
547	C₈	C₂×C₅×#67	1	4	yes	—
548	C₂×C₃	—	2	2	no	—
549	C₂×C₃	—	8	1	no	—
550	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
551	C₂×C₃	C₅×#578	1	2	yes	—
552	D₃	—	8	1	no	—
553	C₅	#83975	1	1	yes	characteristic, direct product factor, Sylow
554	C₂²	—	2	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	12	2	no	—
558	C₂²	—	12	1	no	—
559	C₂²	C₅×#940	1	2	yes	—
560	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
561	C₄	—	4	1	no	—
562	C₄	—	4	2	no	—
563	C₄	—	6	4	no	—
564	C₄	—	12	1	no	—
565	C₄	—	12	2	no	—
566	C₄	C₅×#940	1	2	yes	—
567	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
568	C₄	C₂²×C₅×#67	1	1	yes	characteristic
569	C₃	C₅×#3156	1	1	yes	characteristic, complemented, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	8	1	no	—
572	C₂	—	24	1	no	—
573	C₂	C₅×#5779	1	2	yes	—
574	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	C₂×C₅×#950	C₂
hypercenter	C₂×C₅×#137	D₃
hypocenter	C₃	C₅×#3156
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
2. C₅×#5825	C₂	semidirect
4. C₅×#5816	C₂	semidirect
5. C₂²×C₅×#216	C₂	semidirect
6. C₂×C₅×#909	C₂	semidirect
7. C₅×#5190	C₂	semidirect
8. C₅×#5183	C₂	semidirect
9. C₅×#5168	C₂	semidirect
10. C₅×#5167	C₂	semidirect
11. C₅×#5122	C₂	semidirect
44. #83975	C₅	direct (N × H)
46. C₂×C₅×#137	D₃	semidirect
101. C₂×C₃×#137	C₂×C₅	semidirect
102. #5825	C₂×C₅	semidirect
104. #5816	C₂×C₅	semidirect
105. C₂²×#216	C₂×C₅	semidirect
106. C₂×#909	C₂×C₅	semidirect
107. #5190	C₂×C₅	semidirect
108. #5183	C₂×C₅	semidirect
109. #5168	C₂×C₅	semidirect
110. #5167	C₂×C₅	semidirect
111. #5122	C₂×C₅	semidirect
256. C₂×#137	C₅×D₃	semidirect
492. C₃×C₅	#3156	semidirect
553. C₅	#83975	direct (N × H)
569. C₃	C₅×#3156	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×#5825	2
C₂×C₅×#950	2
C₅×#5816	2
C₂²×C₅×#216	2
C₂×C₅×#909	2
C₅×#5190	2
C₅×#5183	2
C₅×#5168	2
C₅×#5167	2
C₅×#5122	2
C₅×#3156	3
#83975	5

Subgroups — C5×#83975 #14439645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83975 #14439645