Subgroups — C₅×#83903 #14438883

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#950	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5191	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5183	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5175	C₂	1	2	yes	maximal, complemented
8	C₅×#5168	C₂	1	2	yes	maximal, complemented
9	C₅×#5155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3147	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₅×#235	C₂²	1	2	yes	—
15	C₃×C₅×#135	—	2	4	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₅×#950	—	2	8	no	—
21	C₅×#947	C₂²	1	2	yes	—
22	C₅×#944	C₂²	1	2	yes	—
23	C₂×C₅×#216	C₂²	1	2	yes	—
24	C₂×C₅×#215	C₂²	1	2	yes	—
25	C₅×#940	C₂²	1	2	yes	—
26	C₅×#939	—	2	4	no	—
27	C₅×#936	C₂²	1	2	yes	—
28	C₂×C₅×#214	C₂²	1	2	yes	—
29	C₂×C₅×#213	C₂²	1	2	yes	—
30	C₄×C₅×#67	—	2	4	no	—
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
34	C₅×#904	—	2	4	no	—
35	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×#204	C₂²	1	2	yes	—
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
40	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
41	#83903	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#135	—	3	2	no	—
43	C₂×C₅×#135	—	3	1	no	—
44	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
45	C₅×#532	—	3	2	no	—
46	C₅×#495	—	3	1	no	—
47	C₅×#495	—	3	2	no	—
48	C₅×#495	—	3	1	no	—
49	C₅×#494	—	3	1	no	—
50	C₅×#493	—	3	1	no	—
51	C₅×#492	—	3	2	no	—
52	C₂×C₄×C₅×C₈	—	3	1	no	—
53	C₃×C₅×#41	—	2	4	no	—
54	C₃×C₅×#41	—	2	4	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₅×#67	—	2	2	no	—
61	C₂×C₅×#67	—	2	4	no	—
62	C₂²×C₅×Dic₃	D₄	1	2	yes	—
63	C₅×#235	—	2	4	no	—
64	C₅×#235	—	2	4	no	—
65	C₂×C₅×D₁₂	C₂³	1	2	yes	—
66	C₂×C₄×C₅×D₃	—	2	2	no	—
67	C₂×C₅×Dic₆	C₂³	1	2	yes	—
68	C₃×C₅×Q₁₆	—	2	2	no	—
69	C₃×C₅×SD₁₆	—	2	4	no	—
70	C₃×C₅×D₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₅×#217	—	2	4	no	—
75	C₅×#216	—	2	4	no	—
76	C₅×#215	—	2	4	no	—
77	C₅×#214	—	2	4	no	—
78	C₅×#213	—	2	4	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
80	C₅×Dic₃⋊C₄	—	2	4	no	—
81	C₄×C₅×Dic₃	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×Dic₁₂	—	2	2	no	—
88	C₅×D₂₄	—	2	2	no	—
89	C₅×#204	—	2	4	no	—
90	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
91	#5832	C₂×C₅	1	2	yes	complemented
92	C₂×#950	C₂×C₅	1	2	yes	complemented
93	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
94	#5191	C₂×C₅	1	1	yes	characteristic, complemented
95	#5183	C₂×C₅	1	1	yes	characteristic, complemented
96	#5175	C₂×C₅	1	2	yes	complemented
97	#5168	C₂×C₅	1	2	yes	complemented
98	#5155	C₂×C₅	1	1	yes	characteristic, complemented
99	#5151	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×#41	—	3	2	no	—
102	C₂×C₅×#41	C₂×D₃	1	2	yes	—
103	C₅×#135	—	2	4	no	—
104	C₅×#135	—	6	8	no	—
105	C₅×#135	—	6	4	no	—
106	C₂×C₅×Q₁₆	—	3	2	no	—
107	C₂×C₅×Q₁₆	—	3	1	no	—
108	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
109	C₂×C₅×SD₁₆	—	3	2	no	—
110	C₂×C₅×SD₁₆	—	3	2	no	—
111	C₂×C₅×SD₁₆	—	3	2	no	—
112	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
113	C₂×C₅×D₈	—	3	2	no	—
114	C₂×C₅×D₈	—	3	1	no	—
115	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₅×C₈	—	3	1	no	—
117	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	C₅×C₄⋊Q₈	—	3	2	no	—
119	C₅×#127	—	3	2	no	—
120	C₅×#124	—	3	2	no	—
121	C₅×#124	—	3	2	no	—
122	C₅×#121	—	6	4	no	—
123	C₄×C₅×D₄	—	6	4	no	—
124	C₂×C₄²×C₅	—	3	1	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	C₄×C₅×C₈	—	3	1	no	—
128	C₄×C₅×C₈	—	3	1	no	—
129	#3147	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₅×D₃	—	2	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	4	4	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	4	4	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₅×#67	—	4	4	no	—
145	C₅×#67	—	4	8	no	—
146	C₂×C₅×Dic₃	—	2	4	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
149	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
150	C₅×D₁₂	—	2	2	no	—
151	C₅×D₁₂	—	2	2	no	—
152	C₄×C₅×D₃	—	4	4	no	—
153	C₅×Dic₆	—	2	2	no	—
154	C₅×Dic₆	—	2	2	no	—
155	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
158	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
160	C₂×#235	C₂²×C₅	1	2	yes	—
161	C₃×#135	—	2	4	no	—
162	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
164	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
166	#950	—	2	8	no	—
167	#947	C₂²×C₅	1	2	yes	—
168	#944	C₂²×C₅	1	2	yes	—
169	C₂×#216	C₂²×C₅	1	2	yes	—
170	C₂×#215	C₂²×C₅	1	2	yes	—
171	#940	C₂²×C₅	1	2	yes	—
172	#939	—	2	4	no	—
173	#936	C₂²×C₅	1	2	yes	—
174	C₂×#214	C₂²×C₅	1	2	yes	—
175	C₂×#213	C₂²×C₅	1	2	yes	—
176	C₄×#67	—	2	4	no	—
177	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
179	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
180	#904	—	2	4	no	—
181	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
182	C₂×#204	C₂²×C₅	1	2	yes	—
183	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
184	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
185	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
186	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
187	C₅×#41	—	2	4	no	—
188	C₅×#41	—	2	4	no	—
189	C₅×#41	—	6	4	no	—
190	C₅×#41	—	6	4	no	—
191	C₂×C₅×Q₈	—	3	2	no	—
192	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	—	3	2	no	—
195	C₂×C₅×D₄	—	6	4	no	—
196	C₂×C₅×D₄	—	6	2	no	—
197	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
198	C₂²×C₄×C₅	—	2	2	no	—
199	C₂²×C₄×C₅	—	3	2	no	—
200	C₂²×C₄×C₅	—	6	2	no	—
201	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₅×Q₁₆	—	2	2	no	—
203	C₅×Q₁₆	—	6	4	no	—
204	C₅×Q₁₆	—	6	2	no	—
205	C₅×SD₁₆	—	2	4	no	—
206	C₅×SD₁₆	—	6	4	no	—
207	C₅×SD₁₆	—	6	4	no	—
208	C₅×SD₁₆	—	6	4	no	—
209	C₅×D₈	—	2	2	no	—
210	C₅×D₈	—	6	4	no	—
211	C₅×D₈	—	6	2	no	—
212	C₂×C₅×C₈	—	3	4	no	—
213	C₂×C₅×C₈	—	3	1	no	—
214	C₂×C₅×C₈	—	3	1	no	—
215	C₂×C₅×C₈	#67	1	4	yes	complemented
216	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₅×C₄⋊C₄	—	6	4	no	—
219	C₅×C₂²⋊C₄	—	6	4	no	—
220	C₅×C₂²⋊C₄	—	6	4	no	—
221	C₄²×C₅	—	3	2	no	—
222	C₄²×C₅	—	3	1	no	—
223	C₄²×C₅	—	3	1	no	—
224	C₂×#135	—	3	2	no	—
225	C₂×#135	—	3	1	no	—
226	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
227	#532	—	3	2	no	—
228	#495	—	3	1	no	—
229	#495	—	3	2	no	—
230	#495	—	3	1	no	—
231	#494	—	3	1	no	—
232	#493	—	3	1	no	—
233	#492	—	3	2	no	—
234	C₂×C₄×C₈	—	3	1	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	4	no	—
238	C₂²×C₃×C₅	#127	1	2	yes	—
239	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₅×D₃	—	4	2	no	—
241	C₂×C₅×D₃	—	4	4	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	#127	1	2	yes	—
244	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₅×Dic₃	—	2	2	no	—
247	C₅×Dic₃	—	4	2	no	—
248	C₅×Dic₃	#135	1	4	yes	complemented
249	C₃×#41	—	2	4	no	—
250	C₃×#41	—	2	4	no	—
251	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃×D₄	—	2	2	no	—
253	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×#67	—	2	2	no	—
257	C₂×#67	—	2	4	no	—
258	C₂²×Dic₃	C₅×D₄	1	2	yes	—
259	#235	—	2	4	no	—
260	#235	—	2	4	no	—
261	C₂×D₁₂	C₂³×C₅	1	2	yes	—
262	C₂×C₄×D₃	—	2	2	no	—
263	C₂×Dic₆	C₂³×C₅	1	2	yes	—
264	C₃×Q₁₆	—	2	2	no	—
265	C₃×SD₁₆	—	2	4	no	—
266	C₃×D₈	—	2	2	no	—
267	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
268	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
270	#217	—	2	4	no	—
271	#216	—	2	4	no	—
272	#215	—	2	4	no	—
273	#214	—	2	4	no	—
274	#213	—	2	4	no	—
275	(C₂×D₃)⋊C₄	—	2	4	no	—
276	Dic₃⋊C₄	—	2	4	no	—
277	C₄×Dic₃	C₅×D₄	1	2	yes	—
278	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
279	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
281	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
283	Dic₁₂	—	2	2	no	—
284	D₂₄	—	2	2	no	—
285	#204	—	2	4	no	—
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	—	6	2	no	—
288	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
289	C₅×Q₈	—	2	2	no	—
290	C₅×Q₈	—	2	2	no	—
291	C₅×Q₈	—	6	2	no	—
292	C₅×Q₈	—	6	2	no	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	4	4	no	—
296	C₅×D₄	—	6	2	no	—
297	C₅×D₄	—	6	2	no	—
298	C₅×D₄	—	12	8	no	—
299	C₅×D₄	—	12	4	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	3	2	no	—
302	C₂×C₄×C₅	—	3	2	no	—
303	C₂×C₄×C₅	—	4	4	no	—
304	C₂×C₄×C₅	—	6	4	no	—
305	C₂×C₄×C₅	—	6	2	no	—
306	C₂×C₄×C₅	—	12	4	no	—
307	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
308	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×#67	1	2	yes	—
310	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
311	C₅×C₈	—	3	2	no	—
312	C₅×C₈	—	3	2	no	—
313	C₅×C₈	C₂×#67	1	2	yes	—
314	C₅×C₈	C₂×#67	1	2	yes	—
315	C₂×#41	—	3	2	no	—
316	C₂×#41	C₂×C₅×D₃	1	2	yes	—
317	#135	—	2	4	no	—
318	#135	—	6	8	no	—
319	#135	—	6	4	no	—
320	C₂×Q₁₆	—	3	2	no	—
321	C₂×Q₁₆	—	3	1	no	—
322	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
323	C₂×SD₁₆	—	3	2	no	—
324	C₂×SD₁₆	—	3	2	no	—
325	C₂×SD₁₆	—	3	2	no	—
326	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
327	C₂×D₈	—	3	2	no	—
328	C₂×D₈	—	3	1	no	—
329	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
330	C₂²×C₈	—	3	1	no	—
331	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
332	C₄⋊Q₈	—	3	2	no	—
333	#127	—	3	2	no	—
334	#124	—	3	2	no	—
335	#124	—	3	2	no	—
336	#121	—	6	4	no	—
337	C₄×D₄	—	6	4	no	—
338	C₂×C₄²	—	3	1	no	—
339	C₄×C₈	—	3	1	no	—
340	C₄×C₈	—	3	1	no	—
341	C₄×C₈	—	3	1	no	—
342	C₄×C₈	—	3	1	no	—
343	C₂×C₃×C₅	—	2	2	no	—
344	C₂×C₃×C₅	—	8	2	no	—
345	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
346	C₂×C₃×C₅	C₂×#135	1	2	yes	—
347	C₅×D₃	—	8	2	no	—
348	C₂³×C₃	—	2	2	no	—
349	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂²×D₃	—	2	2	no	—
351	C₃×Q₈	—	2	2	no	—
352	C₃×Q₈	—	2	2	no	—
353	C₃×D₄	—	2	2	no	—
354	C₃×D₄	—	2	2	no	—
355	C₃×D₄	—	4	4	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	4	4	no	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
360	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
361	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
362	#67	—	4	4	no	—
363	#67	—	4	8	no	—
364	C₂×Dic₃	—	2	4	no	—
365	C₂×Dic₃	—	2	2	no	—
366	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
367	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
368	D₁₂	—	2	2	no	—
369	D₁₂	—	2	2	no	—
370	C₄×D₃	—	4	4	no	—
371	Dic₆	—	2	2	no	—
372	Dic₆	—	2	2	no	—
373	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
374	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
375	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
376	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	4	4	no	—
379	C₂²×C₅	—	4	2	no	—
380	C₂²×C₅	—	12	4	no	—
381	C₂²×C₅	—	12	2	no	—
382	C₂²×C₅	#940	1	2	yes	—
383	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
384	C₄×C₅	—	3	4	no	—
385	C₄×C₅	—	4	2	no	—
386	C₄×C₅	—	6	2	no	—
387	C₄×C₅	—	12	2	no	—
388	C₄×C₅	#940	1	2	yes	—
389	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
390	C₄×C₅	C₂²×#67	1	1	yes	characteristic
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	6	4	no	—
394	#41	—	6	4	no	—
395	C₂×Q₈	—	3	2	no	—
396	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	3	2	no	—
399	C₂×D₄	—	6	4	no	—
400	C₂×D₄	—	6	2	no	—
401	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	3	2	no	—
404	C₂²×C₄	—	6	2	no	—
405	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
406	Q₁₆	—	2	2	no	—
407	Q₁₆	—	6	4	no	—
408	Q₁₆	—	6	2	no	—
409	SD₁₆	—	2	4	no	—
410	SD₁₆	—	6	4	no	—
411	SD₁₆	—	6	4	no	—
412	SD₁₆	—	6	4	no	—
413	D₈	—	2	2	no	—
414	D₈	—	6	4	no	—
415	D₈	—	6	2	no	—
416	C₂×C₈	—	3	4	no	—
417	C₂×C₈	—	3	1	no	—
418	C₂×C₈	—	3	1	no	—
419	C₂×C₈	C₅×#67	1	4	yes	complemented
420	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₄⋊C₄	—	6	4	no	—
423	C₂²⋊C₄	—	6	4	no	—
424	C₂²⋊C₄	—	6	4	no	—
425	C₄²	—	3	2	no	—
426	C₄²	—	3	1	no	—
427	C₄²	—	3	1	no	—
428	C₃×C₅	#3147	1	1	yes	characteristic, complemented, Hall
429	C₂²×C₃	—	2	2	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	4	no	—
432	C₂²×C₃	C₅×#127	1	2	yes	—
433	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
434	C₂×D₃	—	4	2	no	—
435	C₂×D₃	—	4	4	no	—
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	C₅×#127	1	2	yes	—
438	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
439	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
440	Dic₃	—	2	2	no	—
441	Dic₃	—	4	2	no	—
442	Dic₃	C₅×#135	1	4	yes	complemented
443	C₂×C₅	—	2	2	no	—
444	C₂×C₅	—	8	2	no	—
445	C₂×C₅	—	24	2	no	—
446	C₂×C₅	D₃×#135	1	2	yes	—
447	C₂×C₅	C₂×#940	1	1	yes	characteristic
448	C₂³	—	2	2	no	—
449	C₂³	—	6	2	no	—
450	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	6	2	no	—
454	Q₈	—	6	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	6	2	no	—
459	D₄	—	6	2	no	—
460	D₄	—	12	8	no	—
461	D₄	—	12	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	3	2	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	6	4	no	—
467	C₂×C₄	—	6	2	no	—
468	C₂×C₄	—	12	4	no	—
469	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
470	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
471	C₂×C₄	C₂×C₅×#67	1	2	yes	—
472	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
473	C₈	—	3	2	no	—
474	C₈	—	3	2	no	—
475	C₈	C₂×C₅×#67	1	2	yes	—
476	C₈	C₂×C₅×#67	1	2	yes	—
477	C₂×C₃	—	2	2	no	—
478	C₂×C₃	—	8	2	no	—
479	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
480	C₂×C₃	C₂×C₅×#135	1	2	yes	—
481	D₃	—	8	2	no	—
482	C₅	#83903	1	1	yes	characteristic, direct product factor, Sylow
483	C₂²	—	2	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	12	4	no	—
487	C₂²	—	12	2	no	—
488	C₂²	C₅×#940	1	2	yes	—
489	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
490	C₄	—	3	4	no	—
491	C₄	—	4	2	no	—
492	C₄	—	6	2	no	—
493	C₄	—	12	2	no	—
494	C₄	C₅×#940	1	2	yes	—
495	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
496	C₄	C₂²×C₅×#67	1	1	yes	characteristic
497	C₃	C₅×#3147	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	2	2	no	—
499	C₂	—	8	2	no	—
500	C₂	—	24	2	no	—
501	C₂	C₅×D₃×#135	1	2	yes	—
502	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₅×#3147
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₅×#5832	C₂	semidirect
3. C₂×C₅×#950	C₂	semidirect
4. C₂×C₅×#904	C₂	semidirect
5. C₅×#5191	C₂	semidirect
6. C₅×#5183	C₂	semidirect
7. C₅×#5175	C₂	semidirect
8. C₅×#5168	C₂	semidirect
9. C₅×#5155	C₂	semidirect
10. C₅×#5151	C₂	semidirect
11. C₂×C₅×C₈×Dic₃	C₂	semidirect
41. #83903	C₅	direct (N × H)
44. C₂×C₅×#135	D₃	semidirect
71. C₂×C₃×C₅×C₈	D₄	semidirect
84. C₂×C₅×C₃⋊C₈	D₄	semidirect
90. C₂×C₃×#135	C₂×C₅	semidirect
91. #5832	C₂×C₅	semidirect
92. C₂×#950	C₂×C₅	semidirect
93. C₂×#904	C₂×C₅	semidirect
94. #5191	C₂×C₅	semidirect
95. #5183	C₂×C₅	semidirect
96. #5175	C₂×C₅	semidirect
97. #5168	C₂×C₅	semidirect
98. #5155	C₂×C₅	semidirect
99. #5151	C₂×C₅	semidirect
100. C₂×C₈×Dic₃	C₂×C₅	semidirect
215. C₂×C₅×C₈	#67	semidirect
226. C₂×#135	C₅×D₃	semidirect
248. C₅×Dic₃	#135	semidirect
267. C₂×C₃×C₈	C₅×D₄	semidirect
280. C₂×C₃⋊C₈	C₅×D₄	semidirect
419. C₂×C₈	C₅×#67	semidirect
428. C₃×C₅	#3147	semidirect
442. Dic₃	C₅×#135	semidirect
482. C₅	#83903	direct (N × H)
497. C₃	C₅×#3147	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×#135	2
C₅×#5832	2
C₂×C₅×#950	2
C₂×C₅×#904	2
C₅×#5191	2
C₅×#5183	2
C₅×#5175	2
C₅×#5168	2
C₅×#5155	2
C₅×#5151	2
C₂×C₅×C₈×Dic₃	2
C₅×#3147	3
#83903	5

Subgroups — C5×#83903 #14438883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83903 #14438883