Subgroups — C₅×#83904 #14439072

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 468 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×#5190	C₂	1	2	yes	maximal, complemented
6	C₅×#5176	C₂	1	2	yes	maximal, complemented
7	C₅×#5167	C₂	1	2	yes	maximal, complemented
8	C₅×#5154	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3150	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂×C₅×#235	C₂²	1	2	yes	—
13	C₃×C₅×#135	—	2	4	no	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₅×#950	—	2	8	no	—
19	C₅×#947	C₂²	1	2	yes	—
20	C₅×#944	C₂²	1	2	yes	—
21	C₂×C₅×#216	C₂²	1	2	yes	—
22	C₂×C₅×#215	C₂²	1	2	yes	—
23	C₅×#940	C₂²	1	2	yes	—
24	C₅×#939	—	2	4	no	—
25	C₅×#936	C₂²	1	2	yes	—
26	C₂×C₅×#214	C₂²	1	2	yes	—
27	C₂×C₅×#213	C₂²	1	2	yes	—
28	C₄×C₅×#67	—	2	4	no	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
32	C₅×#904	—	2	4	no	—
33	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×#204	C₂²	1	2	yes	—
35	C₅×#815	C₂²	1	2	yes	—
36	C₅×#815	C₂²	1	2	yes	—
37	#83904	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₅×#135	—	3	2	no	—
39	C₂×C₅×#135	—	3	1	no	—
40	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
41	C₅×#532	—	3	2	no	—
42	C₅×#497	—	3	2	no	—
43	C₅×#497	—	3	2	no	—
44	C₅×#496	—	3	2	no	—
45	C₅×#496	—	3	2	no	—
46	C₂×C₅×#97	—	3	1	no	—
47	C₃×C₅×#41	—	2	4	no	—
48	C₃×C₅×#41	—	2	4	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×#67	—	2	2	no	—
55	C₂×C₅×#67	—	2	4	no	—
56	C₂²×C₅×Dic₃	D₄	1	2	yes	—
57	C₅×#235	—	2	4	no	—
58	C₅×#235	—	2	4	no	—
59	C₂×C₅×D₁₂	C₂³	1	2	yes	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₅×Dic₆	C₂³	1	2	yes	—
62	C₃×C₅×Q₁₆	—	2	2	no	—
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₃×C₅×D₈	—	2	2	no	—
65	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₅×#217	—	2	4	no	—
69	C₅×#216	—	2	4	no	—
70	C₅×#215	—	2	4	no	—
71	C₅×#214	—	2	4	no	—
72	C₅×#213	—	2	4	no	—
73	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
74	C₅×Dic₃⋊C₄	—	2	4	no	—
75	C₄×C₅×Dic₃	D₄	1	2	yes	—
76	C₄×C₅×Dic₃	C₂³	1	2	yes	—
77	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
78	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
79	C₅×Dic₁₂	—	2	2	no	—
80	C₅×D₂₄	—	2	2	no	—
81	C₅×#204	—	2	4	no	—
82	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
83	#5832	C₂×C₅	1	2	yes	complemented
84	C₂×#950	C₂×C₅	1	2	yes	complemented
85	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
86	#5190	C₂×C₅	1	2	yes	complemented
87	#5176	C₂×C₅	1	2	yes	complemented
88	#5167	C₂×C₅	1	2	yes	complemented
89	#5154	C₂×C₅	1	2	yes	complemented
90	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₅×#41	—	3	2	no	—
92	C₂×C₅×#41	C₂×D₃	1	2	yes	—
93	C₅×#135	—	2	4	no	—
94	C₅×#135	—	6	8	no	—
95	C₅×#135	—	6	4	no	—
96	C₂×C₅×Q₁₆	—	3	2	no	—
97	C₂×C₅×Q₁₆	—	3	1	no	—
98	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
99	C₂×C₅×SD₁₆	—	3	2	no	—
100	C₂×C₅×SD₁₆	—	3	2	no	—
101	C₂×C₅×SD₁₆	—	3	2	no	—
102	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
103	C₂×C₅×D₈	—	3	2	no	—
104	C₂×C₅×D₈	—	3	1	no	—
105	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₅×C₈	—	3	1	no	—
107	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
108	C₅×C₄⋊Q₈	—	3	2	no	—
109	C₅×#127	—	3	2	no	—
110	C₅×#124	—	3	2	no	—
111	C₅×#124	—	3	2	no	—
112	C₅×#121	—	6	4	no	—
113	C₄×C₅×D₄	—	6	4	no	—
114	C₂×C₄²×C₅	—	3	1	no	—
115	C₅×#97	—	3	2	no	—
116	C₅×#97	—	3	2	no	—
117	#3150	—	3	1	no	Sylow
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₅×D₃	—	2	2	no	—
121	C₃×C₅×Q₈	—	2	2	no	—
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	—	2	2	no	—
125	C₃×C₅×D₄	—	4	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	4	4	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₅×#67	—	4	8	no	—
133	C₅×#67	—	4	4	no	—
134	C₂×C₅×Dic₃	—	2	2	no	—
135	C₂×C₅×Dic₃	—	4	2	no	—
136	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
137	C₅×D₁₂	—	2	2	no	—
138	C₅×D₁₂	—	2	2	no	—
139	C₄×C₅×D₃	—	4	4	no	—
140	C₅×Dic₆	—	2	2	no	—
141	C₅×Dic₆	—	2	2	no	—
142	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
143	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
145	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
146	C₂×#235	C₂²×C₅	1	2	yes	—
147	C₃×#135	—	2	4	no	—
148	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
150	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
152	#950	—	2	8	no	—
153	#947	C₂²×C₅	1	2	yes	—
154	#944	C₂²×C₅	1	2	yes	—
155	C₂×#216	C₂²×C₅	1	2	yes	—
156	C₂×#215	C₂²×C₅	1	2	yes	—
157	#940	C₂²×C₅	1	2	yes	—
158	#939	—	2	4	no	—
159	#936	C₂²×C₅	1	2	yes	—
160	C₂×#214	C₂²×C₅	1	2	yes	—
161	C₂×#213	C₂²×C₅	1	2	yes	—
162	C₄×#67	—	2	4	no	—
163	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
166	#904	—	2	4	no	—
167	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×#204	C₂²×C₅	1	2	yes	—
169	#815	C₂²×C₅	1	2	yes	—
170	#815	C₂²×C₅	1	2	yes	—
171	C₅×#41	—	2	4	no	—
172	C₅×#41	—	2	4	no	—
173	C₅×#41	—	6	4	no	—
174	C₅×#41	—	6	4	no	—
175	C₂×C₅×Q₈	—	3	2	no	—
176	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
177	C₂×C₅×D₄	—	2	2	no	—
178	C₂×C₅×D₄	—	3	2	no	—
179	C₂×C₅×D₄	—	6	4	no	—
180	C₂×C₅×D₄	—	6	2	no	—
181	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	—	3	2	no	—
184	C₂²×C₄×C₅	—	6	2	no	—
185	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
186	C₅×Q₁₆	—	2	2	no	—
187	C₅×Q₁₆	—	6	4	no	—
188	C₅×Q₁₆	—	6	2	no	—
189	C₅×SD₁₆	—	2	4	no	—
190	C₅×SD₁₆	—	6	4	no	—
191	C₅×SD₁₆	—	6	4	no	—
192	C₅×SD₁₆	—	6	4	no	—
193	C₅×D₈	—	2	2	no	—
194	C₅×D₈	—	6	4	no	—
195	C₅×D₈	—	6	2	no	—
196	C₂×C₅×C₈	—	3	4	no	—
197	C₂×C₅×C₈	—	3	2	no	—
198	C₂×C₅×C₈	#67	1	4	yes	complemented
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
201	C₅×C₄⋊C₄	—	6	4	no	—
202	C₅×C₂²⋊C₄	—	6	4	no	—
203	C₅×C₂²⋊C₄	—	6	4	no	—
204	C₄²×C₅	—	3	2	no	—
205	C₄²×C₅	—	3	2	no	—
206	C₂×#135	—	3	2	no	—
207	C₂×#135	—	3	1	no	—
208	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
209	#532	—	3	2	no	—
210	#497	—	3	2	no	—
211	#497	—	3	2	no	—
212	#496	—	3	2	no	—
213	#496	—	3	2	no	—
214	C₂×#97	—	3	1	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	4	no	—
218	C₂²×C₃×C₅	#127	1	2	yes	—
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₅×D₃	—	4	2	no	—
221	C₂×C₅×D₃	—	4	4	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	#127	1	2	yes	—
224	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₅×Dic₃	—	2	4	no	—
227	C₅×Dic₃	—	4	2	no	—
228	C₃×#41	—	2	4	no	—
229	C₃×#41	—	2	4	no	—
230	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
233	C₂²×C₃×C₄	—	2	2	no	—
234	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
235	C₂×#67	—	2	2	no	—
236	C₂×#67	—	2	4	no	—
237	C₂²×Dic₃	C₅×D₄	1	2	yes	—
238	#235	—	2	4	no	—
239	#235	—	2	4	no	—
240	C₂×D₁₂	C₂³×C₅	1	2	yes	—
241	C₂×C₄×D₃	—	2	2	no	—
242	C₂×Dic₆	C₂³×C₅	1	2	yes	—
243	C₃×Q₁₆	—	2	2	no	—
244	C₃×SD₁₆	—	2	4	no	—
245	C₃×D₈	—	2	2	no	—
246	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
247	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
249	#217	—	2	4	no	—
250	#216	—	2	4	no	—
251	#215	—	2	4	no	—
252	#214	—	2	4	no	—
253	#213	—	2	4	no	—
254	(C₂×D₃)⋊C₄	—	2	4	no	—
255	Dic₃⋊C₄	—	2	4	no	—
256	C₄×Dic₃	C₅×D₄	1	2	yes	—
257	C₄×Dic₃	C₂³×C₅	1	2	yes	—
258	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
259	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
260	Dic₁₂	—	2	2	no	—
261	D₂₄	—	2	2	no	—
262	#204	—	2	4	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	—	6	2	no	—
265	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	—	2	2	no	—
268	C₅×Q₈	—	6	2	no	—
269	C₅×Q₈	—	6	2	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	2	2	no	—
272	C₅×D₄	—	4	4	no	—
273	C₅×D₄	—	6	2	no	—
274	C₅×D₄	—	6	2	no	—
275	C₅×D₄	—	12	8	no	—
276	C₅×D₄	—	12	4	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	3	4	no	—
279	C₂×C₄×C₅	—	4	4	no	—
280	C₂×C₄×C₅	—	6	2	no	—
281	C₂×C₄×C₅	—	12	2	no	—
282	C₂×C₄×C₅	—	12	4	no	—
283	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
284	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×#67	1	2	yes	—
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₅×C₈	—	3	4	no	—
288	C₅×C₈	C₂×#67	1	2	yes	—
289	C₅×C₈	C₂×#67	1	2	yes	—
290	C₂×#41	—	3	2	no	—
291	C₂×#41	C₂×C₅×D₃	1	2	yes	—
292	#135	—	2	4	no	—
293	#135	—	6	8	no	—
294	#135	—	6	4	no	—
295	C₂×Q₁₆	—	3	2	no	—
296	C₂×Q₁₆	—	3	1	no	—
297	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
298	C₂×SD₁₆	—	3	2	no	—
299	C₂×SD₁₆	—	3	2	no	—
300	C₂×SD₁₆	—	3	2	no	—
301	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
302	C₂×D₈	—	3	2	no	—
303	C₂×D₈	—	3	1	no	—
304	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂²×C₈	—	3	1	no	—
306	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
307	C₄⋊Q₈	—	3	2	no	—
308	#127	—	3	2	no	—
309	#124	—	3	2	no	—
310	#124	—	3	2	no	—
311	#121	—	6	4	no	—
312	C₄×D₄	—	6	4	no	—
313	C₂×C₄²	—	3	1	no	—
314	#97	—	3	2	no	—
315	#97	—	3	2	no	—
316	C₂×C₃×C₅	—	2	2	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
319	C₂×C₃×C₅	#575	1	2	yes	—
320	C₅×D₃	—	8	2	no	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂²×D₃	—	2	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×D₄	—	2	2	no	—
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	—	4	4	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	4	4	no	—
331	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
333	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
334	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
335	#67	—	4	8	no	—
336	#67	—	4	4	no	—
337	C₂×Dic₃	—	2	2	no	—
338	C₂×Dic₃	—	4	2	no	—
339	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
340	D₁₂	—	2	2	no	—
341	D₁₂	—	2	2	no	—
342	C₄×D₃	—	4	4	no	—
343	Dic₆	—	2	2	no	—
344	Dic₆	—	2	2	no	—
345	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
346	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
347	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	4	4	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	—	12	4	no	—
352	C₂²×C₅	—	12	2	no	—
353	C₂²×C₅	#940	1	2	yes	—
354	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	—	6	4	no	—
357	C₄×C₅	—	12	2	no	—
358	C₄×C₅	#940	1	2	yes	—
359	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
360	C₄×C₅	C₂²×#67	1	1	yes	characteristic
361	#41	—	2	4	no	—
362	#41	—	2	4	no	—
363	#41	—	6	4	no	—
364	#41	—	6	4	no	—
365	C₂×Q₈	—	3	2	no	—
366	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	3	2	no	—
369	C₂×D₄	—	6	4	no	—
370	C₂×D₄	—	6	2	no	—
371	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	3	2	no	—
374	C₂²×C₄	—	6	2	no	—
375	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
376	Q₁₆	—	2	2	no	—
377	Q₁₆	—	6	4	no	—
378	Q₁₆	—	6	2	no	—
379	SD₁₆	—	2	4	no	—
380	SD₁₆	—	6	4	no	—
381	SD₁₆	—	6	4	no	—
382	SD₁₆	—	6	4	no	—
383	D₈	—	2	2	no	—
384	D₈	—	6	4	no	—
385	D₈	—	6	2	no	—
386	C₂×C₈	—	3	4	no	—
387	C₂×C₈	—	3	2	no	—
388	C₂×C₈	C₅×#67	1	4	yes	complemented
389	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
390	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
391	C₄⋊C₄	—	6	4	no	—
392	C₂²⋊C₄	—	6	4	no	—
393	C₂²⋊C₄	—	6	4	no	—
394	C₄²	—	3	2	no	—
395	C₄²	—	3	2	no	—
396	C₃×C₅	#3150	1	1	yes	characteristic, complemented, Hall
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	4	2	no	—
399	C₂²×C₃	—	4	4	no	—
400	C₂²×C₃	C₅×#127	1	2	yes	—
401	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₂×D₃	—	4	2	no	—
403	C₂×D₃	—	4	4	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	C₅×#127	1	2	yes	—
406	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
407	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
408	Dic₃	—	2	4	no	—
409	Dic₃	—	4	2	no	—
410	C₂×C₅	—	2	2	no	—
411	C₂×C₅	—	8	2	no	—
412	C₂×C₅	—	24	2	no	—
413	C₂×C₅	#5768	1	2	yes	—
414	C₂×C₅	C₂×#940	1	1	yes	characteristic
415	C₂³	—	2	2	no	—
416	C₂³	—	6	2	no	—
417	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	6	2	no	—
421	Q₈	—	6	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	4	no	—
425	D₄	—	6	2	no	—
426	D₄	—	6	2	no	—
427	D₄	—	12	8	no	—
428	D₄	—	12	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	3	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	6	2	no	—
433	C₂×C₄	—	12	2	no	—
434	C₂×C₄	—	12	4	no	—
435	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
436	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
437	C₂×C₄	C₂×C₅×#67	1	2	yes	—
438	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
439	C₈	—	3	4	no	—
440	C₈	C₂×C₅×#67	1	2	yes	—
441	C₈	C₂×C₅×#67	1	2	yes	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	8	2	no	—
444	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
445	C₂×C₃	C₅×#575	1	2	yes	—
446	D₃	—	8	2	no	—
447	C₅	#83904	1	1	yes	characteristic, direct product factor, Sylow
448	C₂²	—	2	2	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	12	4	no	—
452	C₂²	—	12	2	no	—
453	C₂²	C₅×#940	1	2	yes	—
454	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
455	C₄	—	4	2	no	—
456	C₄	—	6	4	no	—
457	C₄	—	12	2	no	—
458	C₄	C₅×#940	1	2	yes	—
459	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
460	C₄	C₂²×C₅×#67	1	1	yes	characteristic
461	C₃	C₅×#3150	1	1	yes	characteristic, complemented, Sylow
462	C₂	—	2	2	no	—
463	C₂	—	8	2	no	—
464	C₂	—	24	2	no	—
465	C₂	C₅×#5768	1	2	yes	—
466	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×#3150
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×#5190	C₂	semidirect
6. C₅×#5176	C₂	semidirect
7. C₅×#5167	C₂	semidirect
8. C₅×#5154	C₂	semidirect
9. C₂×C₅×#815	C₂	semidirect
37. #83904	C₅	direct (N × H)
40. C₂×C₅×#135	D₃	semidirect
65. C₂×C₃×C₅×C₈	D₄	semidirect
77. C₂×C₅×C₃⋊C₈	D₄	semidirect
82. C₂×C₃×#135	C₂×C₅	semidirect
83. #5832	C₂×C₅	semidirect
84. C₂×#950	C₂×C₅	semidirect
85. C₂×#904	C₂×C₅	semidirect
86. #5190	C₂×C₅	semidirect
87. #5176	C₂×C₅	semidirect
88. #5167	C₂×C₅	semidirect
89. #5154	C₂×C₅	semidirect
90. C₂×#815	C₂×C₅	semidirect
198. C₂×C₅×C₈	#67	semidirect
208. C₂×#135	C₅×D₃	semidirect
246. C₂×C₃×C₈	C₅×D₄	semidirect
258. C₂×C₃⋊C₈	C₅×D₄	semidirect
388. C₂×C₈	C₅×#67	semidirect
396. C₃×C₅	#3150	semidirect
447. C₅	#83904	direct (N × H)
461. C₃	C₅×#3150	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×#5190	2
C₅×#5176	2
C₅×#5167	2
C₅×#5154	2
C₂×C₅×#815	2
C₅×#3150	3
#83904	5

Subgroups — C5×#83904 #14439072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83904 #14439072