Subgroups — C₅×#79720 #14417528

Order 1920.

912 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×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#5572	C₂	1	2	yes	maximal
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5030	C₂	1	2	yes	maximal, complemented
6	C₅×#4880	C₂	1	1	yes	maximal, characteristic
7	C₅×#4873	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4802	C₂	1	2	yes	maximal
9	C₅×#4789	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4689	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×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#818	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×#808	C₂²	1	2	yes	—
40	C₅×#803	C₂²	1	1	yes	characteristic
41	#79720	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	2	no	—
45	C₅×#441	—	3	2	no	—
46	C₄×C₅×Q₁₆	—	3	1	no	—
47	C₄×C₅×Q₁₆	—	3	1	no	—
48	C₄×C₅×Q₁₆	—	3	1	no	—
49	C₄×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
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	1	yes	characteristic
70	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
71	C₅×C₄⋊Dic₃	—	2	2	no	—
72	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₅×Dic₃⋊C₄	—	2	2	no	—
74	C₅×Dic₃⋊C₄	—	2	2	no	—
75	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
76	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	—	2	2	no	—
78	C₄×C₅×Dic₃	—	2	2	no	—
79	C₄×C₅×Dic₃	—	2	2	no	—
80	C₄×C₅×Dic₃	—	2	2	no	—
81	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×Dic₁₂	C₂×C₄	1	4	yes	—
85	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
86	C₅×D₃×C₈	C₂×C₄	1	4	yes	—
87	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic
88	#5572	C₂×C₅	1	2	yes	—
89	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
90	Dic₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	#5030	C₂×C₅	1	2	yes	complemented
92	#4880	C₂×C₅	1	1	yes	characteristic
93	#4873	C₂×C₅	1	1	yes	characteristic, complemented
94	#4802	C₂×C₅	1	2	yes	—
95	#4789	C₂×C₅	1	2	yes	complemented
96	C₄×Dic₁₂	C₂×C₅	1	1	yes	characteristic, complemented
97	#4689	C₂×C₅	1	1	yes	characteristic
98	C₂²×C₅×Q₈	—	3	2	no	—
99	C₂×C₅×Q₁₆	—	3	2	no	—
100	C₂×C₅×Q₁₆	—	3	8	no	—
101	C₂×C₅×Q₁₆	—	3	1	no	—
102	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₄×C₅×Q₈	—	3	2	no	—
106	C₄×C₅×Q₈	—	3	2	no	—
107	C₄×C₅×Q₈	—	3	2	no	—
108	C₄×C₅×Q₈	—	6	2	no	—
109	C₄×C₅×Q₈	—	6	2	no	—
110	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
111	C₅×#117	—	3	1	no	—
112	C₅×#117	—	3	2	no	—
113	C₅×#117	—	6	2	no	—
114	C₅×#117	—	6	2	no	—
115	C₅×#107	—	3	1	no	—
116	C₅×#107	C₂×D₃	1	1	yes	characteristic
117	C₅×#106	—	3	2	no	—
118	C₅×#103	—	3	2	no	—
119	C₅×#103	—	3	2	no	—
120	C₅×#103	—	3	2	no	—
121	C₅×#103	C₂×D₃	1	2	yes	—
122	C₅×#97	—	3	1	no	—
123	C₅×#97	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
126	#2950	—	3	1	no	Sylow
127	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₅×Dic₃	—	2	2	no	—
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
140	C₄×C₅×D₃	—	2	8	no	—
141	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₄×C₅×D₃	#41	1	2	yes	—
143	C₅×Dic₆	—	2	2	no	—
144	C₅×Dic₆	—	2	8	no	—
145	C₅×Dic₆	C₂²×C₄	1	4	yes	—
146	C₃×C₅×C₈	—	2	1	no	—
147	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₅×C₃⋊C₈	—	2	1	no	—
149	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
151	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
152	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
153	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
154	C₂×#216	C₂²×C₅	1	2	yes	—
155	D₃×Q₁₆	C₄×C₅	1	8	yes	complemented
156	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
157	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
158	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
159	#892	—	2	2	no	—
160	#892	C₂²×C₅	1	2	yes	—
161	#887	—	2	2	no	—
162	#887	C₂²×C₅	1	2	yes	—
163	#872	—	2	2	no	—
164	#872	C₂²×C₅	1	1	yes	characteristic
165	C₄×Dic₆	—	2	2	no	—
166	C₄×Dic₆	C₂²×C₅	1	2	yes	—
167	C₃×#107	C₂²×C₅	1	1	yes	characteristic
168	C₃×#103	C₂²×C₅	1	2	yes	—
169	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
170	#835	C₂²×C₅	1	2	yes	—
171	#818	C₂²×C₅	1	1	yes	characteristic
172	#816	C₂²×C₅	1	2	yes	—
173	#815	C₂²×C₅	1	1	yes	characteristic
174	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
175	#810	C₂²×C₅	1	2	yes	—
176	#808	C₂²×C₅	1	2	yes	—
177	#803	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₅×Q₈	—	3	8	no	—
179	C₂×C₅×Q₈	—	3	2	no	—
180	C₂×C₅×Q₈	—	6	2	no	—
181	C₂×C₅×Q₈	—	6	4	no	—
182	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	6	2	no	—
185	C₅×Q₁₆	—	3	8	no	—
186	C₅×Q₁₆	—	3	4	no	—
187	C₅×Q₁₆	C₄×D₃	1	4	yes	—
188	C₅×M₁₆	—	6	2	no	—
189	C₂×C₅×C₈	—	3	1	no	—
190	C₂×C₅×C₈	—	3	4	no	—
191	C₂×C₅×C₈	—	3	1	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	3	1	no	—
196	C₅×C₄⋊C₄	—	3	1	no	—
197	C₅×C₄⋊C₄	—	3	2	no	—
198	C₅×C₄⋊C₄	—	6	2	no	—
199	C₅×C₄⋊C₄	—	6	2	no	—
200	C₅×C₄⋊C₄	—	6	2	no	—
201	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
202	C₅×C₂²⋊C₄	—	3	1	no	—
203	C₅×C₂²⋊C₄	—	3	1	no	—
204	C₅×C₂²⋊C₄	—	6	2	no	—
205	C₄²×C₅	—	2	2	no	—
206	C₄²×C₅	—	3	1	no	—
207	C₄²×C₅	—	6	2	no	—
208	C₄²×C₅	—	6	2	no	—
209	C₄²×C₅	—	6	2	no	—
210	C₄²×C₅	—	6	2	no	—
211	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₂²×Q₁₆	—	3	1	no	—
213	#519	—	3	2	no	—
214	#441	—	3	2	no	—
215	#441	—	3	2	no	—
216	C₄×Q₁₆	—	3	1	no	—
217	C₄×Q₁₆	—	3	1	no	—
218	C₄×Q₁₆	—	3	1	no	—
219	C₄×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
220	#427	—	3	1	no	—
221	#419	—	3	2	no	—
222	#405	—	3	1	no	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	1	no	—
225	C₂×C₅×D₃	—	2	1	no	—
226	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
227	C₃×C₄×C₅	—	2	4	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	1	no	—
230	C₃×C₄×C₅	—	4	2	no	—
231	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₅×Dic₃	—	2	4	no	—
234	C₅×Dic₃	—	2	1	no	—
235	C₅×Dic₃	—	2	1	no	—
236	C₅×Dic₃	—	4	2	no	—
237	C₅×Dic₃	C₄×D₄	1	2	yes	—
238	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
239	D₃×Q₈	—	2	4	no	—
240	D₃×Q₈	C₂×C₄×C₅	1	8	yes	—
241	C₂×C₄×D₃	—	2	2	no	—
242	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
243	C₂×Dic₆	—	2	2	no	—
244	C₂×Dic₆	C₂³×C₅	1	2	yes	—
245	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	—
246	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
250	C₃×C₄²	—	2	2	no	—
251	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
252	#216	C₂×C₄×C₅	1	8	yes	—
253	(C₂×D₃)⋊C₄	—	2	2	no	—
254	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
255	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
256	C₄⋊Dic₃	—	2	2	no	—
257	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
258	Dic₃⋊C₄	—	2	2	no	—
259	Dic₃⋊C₄	—	2	2	no	—
260	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
261	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
262	C₄×Dic₃	—	2	2	no	—
263	C₄×Dic₃	—	2	2	no	—
264	C₄×Dic₃	—	2	2	no	—
265	C₄×Dic₃	—	2	2	no	—
266	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
269	Dic₁₂	C₂×C₄×C₅	1	4	yes	—
270	ΓL(1,𝔽₂₅)	—	2	2	no	—
271	D₃×C₈	C₂×C₄×C₅	1	4	yes	—
272	C₂³×C₅	—	3	1	no	—
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	—	3	4	no	—
275	C₅×Q₈	—	6	8	no	—
276	C₅×Q₈	—	6	2	no	—
277	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	3	1	no	—
281	C₂×C₄×C₅	—	3	2	no	—
282	C₂×C₄×C₅	—	3	2	no	—
283	C₂×C₄×C₅	—	3	1	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	6	8	no	—
286	C₂×C₄×C₅	—	6	2	no	—
287	C₂×C₄×C₅	—	6	2	no	—
288	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
291	C₅×C₈	—	2	1	no	—
292	C₅×C₈	—	3	2	no	—
293	C₅×C₈	—	6	1	no	—
294	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
295	C₂²×Q₈	—	3	2	no	—
296	C₂×Q₁₆	—	3	2	no	—
297	C₂×Q₁₆	—	3	8	no	—
298	C₂×Q₁₆	—	3	1	no	—
299	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
300	C₂×M₁₆	—	3	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₄×Q₈	—	3	2	no	—
303	C₄×Q₈	—	3	2	no	—
304	C₄×Q₈	—	3	2	no	—
305	C₄×Q₈	—	6	2	no	—
306	C₄×Q₈	—	6	2	no	—
307	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
308	#117	—	3	1	no	—
309	#117	—	3	2	no	—
310	#117	—	6	2	no	—
311	#117	—	6	2	no	—
312	#107	—	3	1	no	—
313	#107	C₂×C₅×D₃	1	1	yes	characteristic
314	#106	—	3	2	no	—
315	#103	—	3	2	no	—
316	#103	—	3	2	no	—
317	#103	—	3	2	no	—
318	#103	C₂×C₅×D₃	1	2	yes	—
319	#97	—	3	1	no	—
320	#97	—	3	1	no	—
321	C₄×C₈	—	3	1	no	—
322	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×C₅	#578	1	1	yes	characteristic
325	C₂×C₃×C₅	#578	1	1	yes	characteristic
326	C₅×D₃	—	2	2	no	—
327	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
335	C₂×Dic₃	—	2	2	no	—
336	C₂×Dic₃	—	2	2	no	—
337	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
340	C₄×D₃	—	2	8	no	—
341	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
342	C₄×D₃	C₅×#41	1	2	yes	—
343	Dic₆	—	2	2	no	—
344	Dic₆	—	2	8	no	—
345	Dic₆	C₂²×C₄×C₅	1	4	yes	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
348	C₃⋊C₈	—	2	1	no	—
349	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
350	C₂²×C₅	—	3	2	no	—
351	C₂²×C₅	—	6	1	no	—
352	C₂²×C₅	—	6	1	no	—
353	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	4	no	—
357	C₄×C₅	—	3	2	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	—	6	1	no	—
360	C₄×C₅	—	6	1	no	—
361	C₄×C₅	—	6	4	no	—
362	C₄×C₅	—	12	2	no	—
363	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
364	C₄×C₅	D₃×#41	1	1	yes	characteristic
365	C₂×Q₈	—	3	8	no	—
366	C₂×Q₈	—	3	2	no	—
367	C₂×Q₈	—	6	2	no	—
368	C₂×Q₈	—	6	4	no	—
369	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	6	2	no	—
372	Q₁₆	—	3	8	no	—
373	Q₁₆	—	3	4	no	—
374	Q₁₆	C₄×C₅×D₃	1	4	yes	—
375	M₁₆	—	6	2	no	—
376	C₂×C₈	—	3	1	no	—
377	C₂×C₈	—	3	4	no	—
378	C₂×C₈	—	3	1	no	—
379	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
380	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	3	1	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	—	6	2	no	—
386	C₄⋊C₄	—	6	2	no	—
387	C₄⋊C₄	—	6	2	no	—
388	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
389	C₂²⋊C₄	—	3	1	no	—
390	C₂²⋊C₄	—	3	1	no	—
391	C₂²⋊C₄	—	6	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	6	2	no	—
395	C₄²	—	6	2	no	—
396	C₄²	—	6	2	no	—
397	C₄²	—	6	2	no	—
398	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₃×C₅	#2950	1	1	yes	characteristic, complemented, Hall
400	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	—	2	1	no	—
403	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
404	C₃×C₄	—	2	4	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
409	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
410	Dic₃	—	2	4	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	—	2	1	no	—
413	Dic₃	—	4	2	no	—
414	Dic₃	C₄×C₅×D₄	1	2	yes	—
415	C₂×C₅	—	6	2	no	—
416	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
417	C₂×C₅	#5766	1	1	yes	characteristic
418	C₂×C₅	#5771	1	1	yes	characteristic
419	C₂³	—	3	1	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	3	4	no	—
422	Q₈	—	6	8	no	—
423	Q₈	—	6	2	no	—
424	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	1	no	—
431	C₂×C₄	—	3	1	no	—
432	C₂×C₄	—	6	8	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
436	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	3	2	no	—
440	C₈	—	6	1	no	—
441	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
442	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
443	C₂×C₃	C₅×#578	1	1	yes	characteristic
444	C₂×C₃	C₅×#578	1	1	yes	characteristic
445	D₃	—	2	2	no	—
446	C₅	#79720	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	3	2	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	4	no	—
454	C₄	—	3	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	6	1	no	—
457	C₄	—	6	1	no	—
458	C₄	—	6	4	no	—
459	C₄	—	12	2	no	—
460	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
461	C₄	C₅×D₃×#41	1	1	yes	characteristic
462	C₃	C₅×#2950	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	2	no	—
464	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
465	C₂	C₅×#5766	1	1	yes	characteristic
466	C₂	C₅×#5771	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#2950
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×Dic₃×Q₁₆	C₂	semidirect
5. C₅×#5030	C₂	semidirect
7. C₅×#4873	C₂	semidirect
9. C₅×#4789	C₂	semidirect
10. C₄×C₅×Dic₁₂	C₂	semidirect
18. C₅×D₃×Q₁₆	C₄	semidirect
41. #79720	C₅	direct (N × H)
49. C₄×C₅×Q₁₆	D₃	semidirect
89. C₃×C₄×Q₁₆	C₂×C₅	semidirect
90. Dic₃×Q₁₆	C₂×C₅	semidirect
91. #5030	C₂×C₅	semidirect
93. #4873	C₂×C₅	semidirect
95. #4789	C₂×C₅	semidirect
96. C₄×Dic₁₂	C₂×C₅	semidirect
155. D₃×Q₁₆	C₄×C₅	semidirect
219. C₄×Q₁₆	C₅×D₃	semidirect
399. C₃×C₅	#2950	semidirect
446. C₅	#79720	direct (N × H)
462. 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×C₄×C₅×Q₁₆	2
C₅×Dic₃×Q₁₆	2
C₅×#5030	2
C₅×#4880	2
C₅×#4873	2
C₅×#4802	2
C₅×#4789	2
C₄×C₅×Dic₁₂	2
C₅×#4689	2
C₅×#2950	3
#79720	5

Subgroups — C5×#79720 #14417528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79720 #14417528