Subgroups — C₅×#79831 #14417534

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#5572	C₂	1	2	yes	maximal
3	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5184	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#216	C₂	1	2	yes	maximal, complemented
6	C₅×#4860	C₂	1	1	yes	maximal, characteristic
7	C₅×#4853	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4802	C₂	1	2	yes	maximal
9	C₅×#4790	C₂	1	2	yes	maximal, complemented
10	C₅×#4716	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4708	C₂	1	1	yes	maximal, characteristic
12	C₅×#2950	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#216	C₂²	1	2	yes	—
18	C₅×D₃×Q₁₆	C₄	1	8	yes	complemented
19	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₅×#892	—	2	2	no	—
23	C₅×#892	C₂²	1	2	yes	—
24	C₅×#887	—	2	2	no	—
25	C₅×#887	C₂²	1	2	yes	—
26	C₅×#872	—	2	2	no	—
27	C₅×#872	C₂²	1	1	yes	characteristic
28	C₄×C₅×Dic₆	—	2	2	no	—
29	C₄×C₅×Dic₆	C₂²	1	2	yes	—
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#817	C₂²	1	1	yes	characteristic
35	C₅×#816	C₂²	1	2	yes	—
36	C₅×#815	C₂²	1	1	yes	characteristic
37	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₅×#810	C₂²	1	2	yes	—
39	C₅×#807	C₂²	1	2	yes	—
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	#79831	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×Q₁₆	—	3	1	no	—
43	C₅×#519	—	3	2	no	—
44	C₅×#441	—	3	1	no	—
45	C₅×#441	—	3	1	no	—
46	C₅×#441	—	3	1	no	—
47	C₅×#441	D₃	1	1	yes	characteristic, complemented
48	C₄×C₅×Q₁₆	—	3	2	no	—
49	C₄×C₅×Q₁₆	—	3	2	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#419	—	3	2	no	—
52	C₅×#405	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₅×D₃×Q₈	—	2	4	no	—
55	C₅×D₃×Q₈	C₂×C₄	1	8	yes	—
56	C₂×C₄×C₅×D₃	—	2	2	no	—
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₅×Dic₆	—	2	2	no	—
59	C₂×C₅×Dic₆	C₂³	1	2	yes	—
60	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₄²×C₅	—	2	2	no	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₅×#216	C₂×C₄	1	8	yes	—
68	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
69	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
70	C₅×C₄⋊Dic₃	—	2	2	no	—
71	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
72	C₅×Dic₃⋊C₄	—	2	2	no	—
73	C₅×Dic₃⋊C₄	—	2	2	no	—
74	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
75	C₄×C₅×Dic₃	—	2	2	no	—
76	C₄×C₅×Dic₃	—	2	2	no	—
77	C₄×C₅×Dic₃	—	2	2	no	—
78	C₄×C₅×Dic₃	—	2	2	no	—
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×Dic₁₂	C₂×C₄	1	4	yes	—
83	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
84	C₅×D₃×C₈	C₂×C₄	1	4	yes	—
85	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic
86	#5572	C₂×C₅	1	2	yes	—
87	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
88	#5184	C₂×C₅	1	1	yes	characteristic, complemented
89	C₄×#216	C₂×C₅	1	2	yes	complemented
90	#4860	C₂×C₅	1	1	yes	characteristic
91	#4853	C₂×C₅	1	1	yes	characteristic, complemented
92	#4802	C₂×C₅	1	2	yes	—
93	#4790	C₂×C₅	1	2	yes	complemented
94	#4716	C₂×C₅	1	1	yes	characteristic, complemented
95	#4708	C₂×C₅	1	1	yes	characteristic
96	C₂²×C₅×Q₈	—	3	2	no	—
97	C₂×C₅×Q₁₆	—	3	2	no	—
98	C₂×C₅×Q₁₆	—	3	8	no	—
99	C₂×C₅×Q₁₆	—	3	1	no	—
100	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×M₁₆	—	3	1	no	—
102	C₂²×C₅×C₈	—	3	1	no	—
103	C₄×C₅×Q₈	—	3	2	no	—
104	C₄×C₅×Q₈	—	3	2	no	—
105	C₄×C₅×Q₈	—	3	2	no	—
106	C₄×C₅×Q₈	—	6	2	no	—
107	C₄×C₅×Q₈	—	6	2	no	—
108	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
109	C₅×#117	—	3	1	no	—
110	C₅×#117	—	3	2	no	—
111	C₅×#117	—	6	2	no	—
112	C₅×#117	—	6	2	no	—
113	C₅×#107	—	3	2	no	—
114	C₅×#106	—	3	1	no	—
115	C₅×#106	C₂×D₃	1	1	yes	characteristic
116	C₅×#103	—	3	2	no	—
117	C₅×#103	—	3	2	no	—
118	C₅×#103	—	3	2	no	—
119	C₅×#103	C₂×D₃	1	2	yes	—
120	C₅×#97	—	3	1	no	—
121	C₅×#97	C₂×D₃	1	1	yes	characteristic
122	C₄×C₅×C₈	—	3	1	no	—
123	C₄×C₅×C₈	—	3	1	no	—
124	#2950	—	3	1	no	Sylow
125	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×C₅×Dic₃	—	2	2	no	—
133	C₂×C₅×Dic₃	—	2	2	no	—
134	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
135	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
136	C₄×C₅×D₃	—	2	8	no	—
137	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
138	C₄×C₅×D₃	#41	1	2	yes	—
139	C₅×Dic₆	—	2	2	no	—
140	C₅×Dic₆	—	2	8	no	—
141	C₅×Dic₆	C₂²×C₄	1	4	yes	—
142	C₃×C₅×C₈	—	2	1	no	—
143	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
144	C₅×C₃⋊C₈	—	2	1	no	—
145	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
147	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
148	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
149	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
150	C₂×#216	C₂²×C₅	1	2	yes	—
151	D₃×Q₁₆	C₄×C₅	1	8	yes	complemented
152	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
153	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
154	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
155	#892	—	2	2	no	—
156	#892	C₂²×C₅	1	2	yes	—
157	#887	—	2	2	no	—
158	#887	C₂²×C₅	1	2	yes	—
159	#872	—	2	2	no	—
160	#872	C₂²×C₅	1	1	yes	characteristic
161	C₄×Dic₆	—	2	2	no	—
162	C₄×Dic₆	C₂²×C₅	1	2	yes	—
163	C₃×#106	C₂²×C₅	1	1	yes	characteristic
164	C₃×#103	C₂²×C₅	1	2	yes	—
165	C₃×#97	C₂²×C₅	1	1	yes	characteristic
166	#835	C₂²×C₅	1	2	yes	—
167	#817	C₂²×C₅	1	1	yes	characteristic
168	#816	C₂²×C₅	1	2	yes	—
169	#815	C₂²×C₅	1	1	yes	characteristic
170	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
171	#810	C₂²×C₅	1	2	yes	—
172	#807	C₂²×C₅	1	2	yes	—
173	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₅×Q₈	—	3	8	no	—
175	C₂×C₅×Q₈	—	3	2	no	—
176	C₂×C₅×Q₈	—	6	2	no	—
177	C₂×C₅×Q₈	—	6	4	no	—
178	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
179	C₂²×C₄×C₅	—	3	1	no	—
180	C₂²×C₄×C₅	—	6	2	no	—
181	C₅×Q₁₆	—	3	8	no	—
182	C₅×Q₁₆	—	3	4	no	—
183	C₅×Q₁₆	C₄×D₃	1	4	yes	—
184	C₅×M₁₆	—	6	2	no	—
185	C₂×C₅×C₈	—	3	1	no	—
186	C₂×C₅×C₈	—	3	4	no	—
187	C₂×C₅×C₈	—	3	1	no	—
188	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	3	2	no	—
192	C₅×C₄⋊C₄	—	3	2	no	—
193	C₅×C₄⋊C₄	—	6	2	no	—
194	C₅×C₄⋊C₄	—	6	2	no	—
195	C₅×C₄⋊C₄	—	6	2	no	—
196	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
197	C₅×C₂²⋊C₄	—	3	2	no	—
198	C₅×C₂²⋊C₄	—	6	2	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	3	1	no	—
201	C₄²×C₅	—	6	2	no	—
202	C₄²×C₅	—	6	2	no	—
203	C₄²×C₅	—	6	2	no	—
204	C₄²×C₅	—	6	2	no	—
205	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₂²×Q₁₆	—	3	1	no	—
207	#519	—	3	2	no	—
208	#441	—	3	1	no	—
209	#441	—	3	1	no	—
210	#441	—	3	1	no	—
211	#441	C₅×D₃	1	1	yes	characteristic, complemented
212	C₄×Q₁₆	—	3	2	no	—
213	C₄×Q₁₆	—	3	2	no	—
214	#427	—	3	1	no	—
215	#419	—	3	2	no	—
216	#405	—	3	1	no	—
217	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₅×D₃	—	2	2	no	—
219	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₅×Dic₃	—	2	4	no	—
226	C₅×Dic₃	—	2	2	no	—
227	C₅×Dic₃	—	4	2	no	—
228	C₅×Dic₃	C₄×D₄	1	2	yes	—
229	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
230	D₃×Q₈	—	2	4	no	—
231	D₃×Q₈	C₂×C₄×C₅	1	8	yes	—
232	C₂×C₄×D₃	—	2	2	no	—
233	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
234	C₂×Dic₆	—	2	2	no	—
235	C₂×Dic₆	C₂³×C₅	1	2	yes	—
236	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	—
237	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
243	#216	C₂×C₄×C₅	1	8	yes	—
244	(C₂×D₃)⋊C₄	—	2	2	no	—
245	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
246	C₄⋊Dic₃	—	2	2	no	—
247	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
248	Dic₃⋊C₄	—	2	2	no	—
249	Dic₃⋊C₄	—	2	2	no	—
250	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
251	C₄×Dic₃	—	2	2	no	—
252	C₄×Dic₃	—	2	2	no	—
253	C₄×Dic₃	—	2	2	no	—
254	C₄×Dic₃	—	2	2	no	—
255	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
258	Dic₁₂	C₂×C₄×C₅	1	4	yes	—
259	ΓL(1,𝔽₂₅)	—	2	2	no	—
260	D₃×C₈	C₂×C₄×C₅	1	4	yes	—
261	C₂³×C₅	—	3	1	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	3	4	no	—
264	C₅×Q₈	—	6	8	no	—
265	C₅×Q₈	—	6	2	no	—
266	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	3	1	no	—
270	C₂×C₄×C₅	—	3	2	no	—
271	C₂×C₄×C₅	—	3	2	no	—
272	C₂×C₄×C₅	—	3	2	no	—
273	C₂×C₄×C₅	—	6	8	no	—
274	C₂×C₄×C₅	—	6	2	no	—
275	C₂×C₄×C₅	—	6	2	no	—
276	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
277	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
278	C₅×C₈	—	2	1	no	—
279	C₅×C₈	—	3	2	no	—
280	C₅×C₈	—	6	1	no	—
281	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
282	C₂²×Q₈	—	3	2	no	—
283	C₂×Q₁₆	—	3	2	no	—
284	C₂×Q₁₆	—	3	8	no	—
285	C₂×Q₁₆	—	3	1	no	—
286	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
287	C₂×M₁₆	—	3	1	no	—
288	C₂²×C₈	—	3	1	no	—
289	C₄×Q₈	—	3	2	no	—
290	C₄×Q₈	—	3	2	no	—
291	C₄×Q₈	—	3	2	no	—
292	C₄×Q₈	—	6	2	no	—
293	C₄×Q₈	—	6	2	no	—
294	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
295	#117	—	3	1	no	—
296	#117	—	3	2	no	—
297	#117	—	6	2	no	—
298	#117	—	6	2	no	—
299	#107	—	3	2	no	—
300	#106	—	3	1	no	—
301	#106	C₂×C₅×D₃	1	1	yes	characteristic
302	#103	—	3	2	no	—
303	#103	—	3	2	no	—
304	#103	—	3	2	no	—
305	#103	C₂×C₅×D₃	1	2	yes	—
306	#97	—	3	1	no	—
307	#97	C₂×C₅×D₃	1	1	yes	characteristic
308	C₄×C₈	—	3	1	no	—
309	C₄×C₈	—	3	1	no	—
310	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂×C₃×C₅	#578	1	2	yes	—
312	C₅×D₃	—	2	2	no	—
313	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
314	C₃×Q₈	—	2	2	no	—
315	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	C₂×Dic₃	—	2	2	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
323	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
324	C₄×D₃	—	2	8	no	—
325	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
326	C₄×D₃	C₅×#41	1	2	yes	—
327	Dic₆	—	2	2	no	—
328	Dic₆	—	2	8	no	—
329	Dic₆	C₂²×C₄×C₅	1	4	yes	—
330	C₃×C₈	—	2	1	no	—
331	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
332	C₃⋊C₈	—	2	1	no	—
333	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
334	C₂²×C₅	—	3	2	no	—
335	C₂²×C₅	—	6	2	no	—
336	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	3	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₄×C₅	—	6	2	no	—
342	C₄×C₅	—	6	4	no	—
343	C₄×C₅	—	12	2	no	—
344	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
345	C₄×C₅	D₃×#41	1	1	yes	characteristic
346	C₂×Q₈	—	3	8	no	—
347	C₂×Q₈	—	3	2	no	—
348	C₂×Q₈	—	6	2	no	—
349	C₂×Q₈	—	6	4	no	—
350	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
351	C₂²×C₄	—	3	1	no	—
352	C₂²×C₄	—	6	2	no	—
353	Q₁₆	—	3	8	no	—
354	Q₁₆	—	3	4	no	—
355	Q₁₆	C₄×C₅×D₃	1	4	yes	—
356	M₁₆	—	6	2	no	—
357	C₂×C₈	—	3	1	no	—
358	C₂×C₈	—	3	4	no	—
359	C₂×C₈	—	3	1	no	—
360	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
361	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	3	2	no	—
364	C₄⋊C₄	—	3	2	no	—
365	C₄⋊C₄	—	6	2	no	—
366	C₄⋊C₄	—	6	2	no	—
367	C₄⋊C₄	—	6	2	no	—
368	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
369	C₂²⋊C₄	—	3	2	no	—
370	C₂²⋊C₄	—	6	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	3	1	no	—
373	C₄²	—	6	2	no	—
374	C₄²	—	6	2	no	—
375	C₄²	—	6	2	no	—
376	C₄²	—	6	2	no	—
377	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
378	C₃×C₅	#2950	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
386	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	Dic₃	—	2	4	no	—
388	Dic₃	—	2	2	no	—
389	Dic₃	—	4	2	no	—
390	Dic₃	C₄×C₅×D₄	1	2	yes	—
391	C₂×C₅	—	6	2	no	—
392	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
393	C₂×C₅	#5779	1	2	yes	—
394	C₂³	—	3	1	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	3	4	no	—
397	Q₈	—	6	8	no	—
398	Q₈	—	6	2	no	—
399	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	3	1	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	2	no	—
406	C₂×C₄	—	6	8	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
410	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	3	2	no	—
413	C₈	—	6	1	no	—
414	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
415	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
416	C₂×C₃	C₅×#578	1	2	yes	—
417	D₃	—	2	2	no	—
418	C₅	#79831	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	3	2	no	—
420	C₂²	—	6	2	no	—
421	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	3	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	6	2	no	—
427	C₄	—	6	4	no	—
428	C₄	—	12	2	no	—
429	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
430	C₄	C₅×D₃×#41	1	1	yes	characteristic
431	C₃	C₅×#2950	1	1	yes	characteristic, complemented, Sylow
432	C₂	—	6	2	no	—
433	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
434	C₂	C₅×#5779	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#441	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#441	D₃
hypocenter	C₃	C₅×#2950
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#441

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#441	C₂	semidirect
4. C₅×#5184	C₂	semidirect
5. C₄×C₅×#216	C₂	semidirect
7. C₅×#4853	C₂	semidirect
9. C₅×#4790	C₂	semidirect
10. C₅×#4716	C₂	semidirect
18. C₅×D₃×Q₁₆	C₄	semidirect
41. #79831	C₅	direct (N × H)
47. C₅×#441	D₃	semidirect
87. C₃×#441	C₂×C₅	semidirect
88. #5184	C₂×C₅	semidirect
89. C₄×#216	C₂×C₅	semidirect
91. #4853	C₂×C₅	semidirect
93. #4790	C₂×C₅	semidirect
94. #4716	C₂×C₅	semidirect
151. D₃×Q₁₆	C₄×C₅	semidirect
211. #441	C₅×D₃	semidirect
378. C₃×C₅	#2950	semidirect
418. C₅	#79831	direct (N × H)
431. C₃	C₅×#2950	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×Q₁₆	2
C₅×#5572	2
C₃×C₅×#441	2
C₅×#5184	2
C₄×C₅×#216	2
C₅×#4860	2
C₅×#4853	2
C₅×#4802	2
C₅×#4790	2
C₅×#4716	2
C₅×#4708	2
C₅×#2950	3
#79831	5

Subgroups — C5×#79831 #14417534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79831 #14417534