Subgroups — C₅×#81577 #14458449

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5730	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5717	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4778	C₂	1	2	yes	maximal, complemented
7	C₅×#4777	C₂	1	2	yes	maximal, complemented
8	C₅×#4776	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3295	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	—	2	1	no	—
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₅×#946	—	2	2	no	—
18	C₅×#938	—	2	1	no	—
19	C₅×#938	C₂²	1	2	yes	—
20	C₅×#937	—	2	2	no	—
21	C₂×C₅×#214	C₂²	1	2	yes	complemented
22	C₂×C₅×#204	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
24	C₅×#897	C₂²	1	2	yes	complemented
25	C₅×#893	—	2	1	no	—
26	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
27	C₅×#890	—	2	1	no	—
28	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#102	C₂²	1	2	yes	complemented
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₅×#832	C₂²	1	2	yes	complemented
35	C₅×#821	C₂²	1	1	yes	characteristic
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
37	C₅×#817	C₂²	1	1	yes	characteristic, complemented
38	C₅×#816	C₂²	1	1	yes	characteristic, complemented
39	C₅×#809	C₂²	1	2	yes	—
40	C₅×#808	C₂²	1	2	yes	complemented
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
42	#81577	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#554	—	3	1	no	—
44	C₅×D₄²	—	3	1	no	—
45	C₅×#486	D₃	1	1	yes	characteristic, complemented
46	C₅×#481	—	3	2	no	—
47	C₅×#476	—	3	1	no	—
48	C₅×#465	—	3	2	no	—
49	C₅×#460	—	3	1	no	—
50	C₅×#450	—	3	2	no	—
51	C₄×C₅×SD₁₆	—	3	1	no	—
52	C₅×C₈×D₄	—	3	1	no	—
53	C₂×C₅×#102	—	3	2	no	—
54	C₂³×C₅×D₃	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂×C₅×#67	—	2	2	no	—
60	C₂×C₅×#67	—	2	2	no	—
61	C₅×D₃×D₄	—	2	4	no	—
62	C₅×D₃×D₄	—	4	2	no	—
63	C₅×D₃×D₄	—	4	4	no	—
64	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
65	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
69	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#217	—	2	2	no	—
76	C₅×#214	—	4	2	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
79	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
80	C₅×C₄⋊Dic₃	—	2	2	no	—
81	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
82	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×Dic₃⋊C₄	—	2	1	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₄×C₅×Dic₃	—	2	1	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₅×#204	—	2	2	no	—
89	C₅×D₃×C₈	—	4	2	no	—
90	#5730	C₂×C₅	1	1	yes	characteristic, complemented
91	#5717	C₂×C₅	1	1	yes	characteristic
92	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
93	#5084	C₂×C₅	1	1	yes	characteristic, complemented
94	#5075	C₂×C₅	1	1	yes	characteristic, complemented
95	#4778	C₂×C₅	1	2	yes	complemented
96	#4777	C₂×C₅	1	2	yes	complemented
97	#4776	C₂×C₅	1	2	yes	complemented
98	D₃×#102	C₂×C₅	1	2	yes	complemented
99	C₄×#204	C₂×C₅	1	1	yes	characteristic, complemented
100	C₈×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×C₅×D₄	—	3	2	no	—
102	C₂²×C₅×D₄	—	6	1	no	—
103	C₂×C₅×SD₁₆	—	3	2	no	—
104	C₂×C₅×SD₁₆	—	3	1	no	—
105	C₂²×C₅×C₈	—	3	2	no	—
106	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
107	C₅×#127	C₂×D₃	1	1	yes	characteristic
108	C₅×#125	—	6	1	no	—
109	C₅×C₂²⋊Q₈	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	6	2	no	—
111	C₅×#121	—	3	2	no	—
112	C₅×#121	—	6	1	no	—
113	C₅×#120	—	6	2	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	6	1	no	—
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×#106	—	3	2	no	—
121	C₅×C₄⋊C₈	—	3	1	no	—
122	C₅×#103	—	3	1	no	—
123	C₅×#102	—	3	2	no	—
124	C₅×#102	—	3	1	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	C₂×D₃	1	2	yes	complemented
127	C₅×#102	C₂×D₃	1	2	yes	complemented
128	C₅×C₂²⋊C₈	—	3	2	no	—
129	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
130	#3295	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂²×C₅×D₃	—	2	1	no	—
133	C₂²×C₅×D₃	—	4	4	no	—
134	C₂²×C₅×D₃	—	4	4	no	—
135	C₂²×C₅×D₃	—	8	2	no	—
136	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
137	C₃×C₅×Q₈	—	8	1	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	4	2	no	—
141	C₃×C₅×D₄	—	8	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₅×#67	—	4	4	no	—
147	C₅×#67	—	4	4	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	—	2	1	no	—
151	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
152	C₅×D₁₂	—	2	1	no	—
153	C₅×D₁₂	SD₁₆	1	4	yes	complemented
154	C₅×D₁₂	#41	1	2	yes	—
155	C₄×C₅×D₃	—	2	2	no	—
156	C₄×C₅×D₃	—	2	2	no	—
157	C₄×C₅×D₃	—	4	2	no	—
158	C₄×C₅×D₃	—	8	2	no	—
159	C₅×Dic₆	—	2	1	no	—
160	C₅×Dic₆	—	2	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	—	2	1	no	—
163	C₅×C₃⋊C₈	—	2	2	no	—
164	C₂×D₃×D₄	—	2	1	no	—
165	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
166	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
167	C₃×#127	C₂²×C₅	1	1	yes	characteristic
168	#946	—	2	2	no	—
169	#938	—	2	1	no	—
170	#938	C₂²×C₅	1	2	yes	—
171	#937	—	2	2	no	—
172	C₂×#214	C₂²×C₅	1	2	yes	complemented
173	C₂×#204	C₂²×C₅	1	1	yes	characteristic
174	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
175	#897	C₂²×C₅	1	2	yes	complemented
176	#893	—	2	1	no	—
177	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
178	#890	—	2	1	no	—
179	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
180	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
181	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₃×#102	C₂²×C₅	1	2	yes	complemented
183	C₃×#102	C₂²×C₅	1	2	yes	complemented
184	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
185	#832	C₂²×C₅	1	2	yes	complemented
186	#821	C₂²×C₅	1	1	yes	characteristic
187	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	complemented
188	#817	C₂²×C₅	1	1	yes	characteristic, complemented
189	#816	C₂²×C₅	1	1	yes	characteristic, complemented
190	#809	C₂²×C₅	1	2	yes	—
191	#808	C₂²×C₅	1	2	yes	complemented
192	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂⁴×C₅	—	6	2	no	—
194	C₂×C₅×Q₈	—	2	1	no	—
195	C₂×C₅×Q₈	—	3	1	no	—
196	C₂×C₅×D₄	—	2	1	no	—
197	C₂×C₅×D₄	—	2	1	no	—
198	C₂×C₅×D₄	—	3	1	no	—
199	C₂×C₅×D₄	—	3	1	no	—
200	C₂×C₅×D₄	—	6	2	no	—
201	C₂×C₅×D₄	—	6	4	no	—
202	C₂×C₅×D₄	—	6	2	no	—
203	C₂×C₅×D₄	—	12	2	no	—
204	C₂×C₅×D₄	—	12	4	no	—
205	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
206	C₂²×C₄×C₅	—	3	2	no	—
207	C₂²×C₄×C₅	—	6	2	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₅×SD₁₆	—	6	2	no	—
210	C₅×SD₁₆	—	12	2	no	—
211	C₂×C₅×C₈	—	3	2	no	—
212	C₂×C₅×C₈	—	12	2	no	—
213	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	3	1	no	—
217	C₅×C₄⋊C₄	—	3	1	no	—
218	C₅×C₄⋊C₄	—	3	1	no	—
219	C₅×C₄⋊C₄	—	6	2	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	—	6	1	no	—
222	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
223	C₅×C₂²⋊C₄	—	3	2	no	—
224	C₅×C₂²⋊C₄	—	6	2	no	—
225	C₅×C₂²⋊C₄	—	6	2	no	—
226	C₅×C₂²⋊C₄	—	6	1	no	—
227	C₄²×C₅	—	6	1	no	—
228	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
229	#554	—	3	1	no	—
230	D₄²	—	3	1	no	—
231	#486	C₅×D₃	1	1	yes	characteristic, complemented
232	#481	—	3	2	no	—
233	#476	—	3	1	no	—
234	#465	—	3	2	no	—
235	#460	—	3	1	no	—
236	#450	—	3	2	no	—
237	C₄×SD₁₆	—	3	1	no	—
238	C₈×D₄	—	3	1	no	—
239	C₂×#102	—	3	2	no	—
240	C₂²×C₃×C₅	—	4	2	no	—
241	C₂²×C₃×C₅	—	4	2	no	—
242	C₂²×C₃×C₅	—	4	2	no	—
243	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₅×D₃	—	2	2	no	—
245	C₂×C₅×D₃	—	2	2	no	—
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	4	1	no	—
248	C₂×C₅×D₃	—	4	1	no	—
249	C₂×C₅×D₃	—	8	8	no	—
250	C₂×C₅×D₃	C₂×SD₁₆	1	4	yes	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
254	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
255	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
256	C₅×Dic₃	—	2	2	no	—
257	C₅×Dic₃	—	4	1	no	—
258	C₅×Dic₃	—	4	1	no	—
259	C₅×Dic₃	—	4	1	no	—
260	C₂³×D₃	—	2	2	no	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
265	C₂×#67	—	2	2	no	—
266	C₂×#67	—	2	2	no	—
267	D₃×D₄	—	2	4	no	—
268	D₃×D₄	—	4	2	no	—
269	D₃×D₄	—	4	4	no	—
270	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
271	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄×D₃	—	2	1	no	—
273	C₂×C₄×D₃	—	2	2	no	—
274	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
275	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
278	C₃×C₄⋊C₄	—	2	1	no	—
279	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
280	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
281	#217	—	2	2	no	—
282	#214	—	4	2	no	—
283	(C₂×D₃)⋊C₄	—	2	2	no	—
284	(C₂×D₃)⋊C₄	—	2	1	no	—
285	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
286	C₄⋊Dic₃	—	2	2	no	—
287	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
288	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
290	Dic₃⋊C₄	—	2	1	no	—
291	Dic₃⋊C₄	—	2	2	no	—
292	C₄×Dic₃	—	2	1	no	—
293	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
294	#204	—	2	2	no	—
295	D₃×C₈	—	4	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	3	2	no	—
298	C₂³×C₅	—	6	1	no	—
299	C₂³×C₅	—	12	4	no	—
300	C₂³×C₅	—	12	4	no	—
301	C₂³×C₅	—	24	2	no	—
302	C₅×Q₈	—	6	1	no	—
303	C₅×Q₈	—	6	1	no	—
304	C₅×Q₈	—	8	1	no	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	3	4	no	—
308	C₅×D₄	—	3	2	no	—
309	C₅×D₄	—	4	2	no	—
310	C₅×D₄	—	6	1	no	—
311	C₅×D₄	—	8	1	no	—
312	C₅×D₄	—	12	4	no	—
313	C₅×D₄	—	12	4	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	3	2	no	—
316	C₂×C₄×C₅	—	6	2	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	1	no	—
320	C₂×C₄×C₅	—	6	1	no	—
321	C₂×C₄×C₅	—	12	2	no	—
322	C₂×C₄×C₅	—	24	2	no	—
323	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	C₅×C₈	—	6	2	no	—
329	C₂²×D₄	—	3	2	no	—
330	C₂²×D₄	—	6	1	no	—
331	C₂×SD₁₆	—	3	2	no	—
332	C₂×SD₁₆	—	3	1	no	—
333	C₂²×C₈	—	3	2	no	—
334	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
335	#127	C₂×C₅×D₃	1	1	yes	characteristic
336	#125	—	6	1	no	—
337	C₂²⋊Q₈	—	3	2	no	—
338	C₂²⋊Q₈	—	6	2	no	—
339	#121	—	3	2	no	—
340	#121	—	6	1	no	—
341	#120	—	6	2	no	—
342	C₄×Q₈	—	3	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	—	3	1	no	—
345	C₄×D₄	—	6	1	no	—
346	C₂×C₄⋊C₄	—	3	2	no	—
347	#106	—	3	1	no	—
348	#106	—	3	2	no	—
349	C₄⋊C₈	—	3	1	no	—
350	#103	—	3	1	no	—
351	#102	—	3	2	no	—
352	#102	—	3	1	no	—
353	#102	—	3	2	no	—
354	#102	C₂×C₅×D₃	1	2	yes	complemented
355	#102	C₂×C₅×D₃	1	2	yes	complemented
356	C₂²⋊C₈	—	3	2	no	—
357	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
358	C₂×C₃×C₅	—	8	2	no	—
359	C₂×C₃×C₅	#546	1	1	yes	characteristic
360	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
361	C₂×C₃×C₅	#576	1	1	yes	characteristic
362	C₅×D₃	—	2	4	no	—
363	C₅×D₃	—	4	2	no	—
364	C₂³×C₃	—	2	2	no	—
365	C₂²×D₃	—	2	1	no	—
366	C₂²×D₃	—	4	4	no	—
367	C₂²×D₃	—	4	4	no	—
368	C₂²×D₃	—	8	2	no	—
369	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
370	C₃×Q₈	—	8	1	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	4	2	no	—
374	C₃×D₄	—	8	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
379	#67	—	4	4	no	—
380	#67	—	4	4	no	—
381	C₂×Dic₃	—	2	1	no	—
382	C₂×Dic₃	—	2	1	no	—
383	C₂×Dic₃	—	2	1	no	—
384	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
385	D₁₂	—	2	1	no	—
386	D₁₂	C₅×SD₁₆	1	4	yes	complemented
387	D₁₂	C₅×#41	1	2	yes	—
388	C₄×D₃	—	2	2	no	—
389	C₄×D₃	—	2	2	no	—
390	C₄×D₃	—	4	2	no	—
391	C₄×D₃	—	8	2	no	—
392	Dic₆	—	2	1	no	—
393	Dic₆	—	2	1	no	—
394	C₃×C₈	—	2	1	no	—
395	C₃×C₈	—	2	1	no	—
396	C₃⋊C₈	—	2	2	no	—
397	C₂²×C₅	—	3	4	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	4	2	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	6	2	no	—
402	C₂²×C₅	—	6	2	no	—
403	C₂²×C₅	—	6	2	no	—
404	C₂²×C₅	—	12	1	no	—
405	C₂²×C₅	—	12	1	no	—
406	C₂²×C₅	—	24	8	no	—
407	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	—	6	2	no	—
411	C₄×C₅	—	12	1	no	—
412	C₄×C₅	—	12	1	no	—
413	C₄×C₅	—	12	1	no	—
414	C₄×C₅	D₃×SD₁₆	1	2	yes	—
415	C₄×C₅	D₃×#41	1	1	yes	characteristic
416	C₄×C₅	#1009	1	1	yes	characteristic
417	C₂⁴	—	6	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	3	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	1	no	—
424	C₂×D₄	—	6	2	no	—
425	C₂×D₄	—	6	4	no	—
426	C₂×D₄	—	6	2	no	—
427	C₂×D₄	—	12	2	no	—
428	C₂×D₄	—	12	4	no	—
429	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	6	2	no	—
432	C₂²×C₄	—	6	1	no	—
433	SD₁₆	—	6	2	no	—
434	SD₁₆	—	12	2	no	—
435	C₂×C₈	—	3	2	no	—
436	C₂×C₈	—	12	2	no	—
437	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
438	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	3	1	no	—
441	C₄⋊C₄	—	3	1	no	—
442	C₄⋊C₄	—	3	1	no	—
443	C₄⋊C₄	—	6	2	no	—
444	C₄⋊C₄	—	6	2	no	—
445	C₄⋊C₄	—	6	1	no	—
446	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
447	C₂²⋊C₄	—	3	2	no	—
448	C₂²⋊C₄	—	6	2	no	—
449	C₂²⋊C₄	—	6	2	no	—
450	C₂²⋊C₄	—	6	1	no	—
451	C₄²	—	6	1	no	—
452	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₃×C₅	#3295	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	4	2	no	—
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	—	4	2	no	—
457	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×D₃	—	2	2	no	—
459	C₂×D₃	—	2	2	no	—
460	C₂×D₃	—	2	2	no	—
461	C₂×D₃	—	4	1	no	—
462	C₂×D₃	—	4	1	no	—
463	C₂×D₃	—	8	8	no	—
464	C₂×D₃	C₂×C₅×SD₁₆	1	4	yes	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	4	2	no	—
467	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
468	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
469	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
470	Dic₃	—	2	2	no	—
471	Dic₃	—	4	1	no	—
472	Dic₃	—	4	1	no	—
473	Dic₃	—	4	1	no	—
474	C₂×C₅	—	6	4	no	—
475	C₂×C₅	—	8	2	no	—
476	C₂×C₅	—	12	2	no	—
477	C₂×C₅	#5676	1	1	yes	characteristic
478	C₂×C₅	#5757	1	1	yes	characteristic
479	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	3	2	no	—
482	C₂³	—	6	1	no	—
483	C₂³	—	12	4	no	—
484	C₂³	—	12	4	no	—
485	C₂³	—	24	2	no	—
486	Q₈	—	6	1	no	—
487	Q₈	—	6	1	no	—
488	Q₈	—	8	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	3	4	no	—
492	D₄	—	3	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	6	1	no	—
495	D₄	—	8	1	no	—
496	D₄	—	12	4	no	—
497	D₄	—	12	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	3	2	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	6	2	no	—
502	C₂×C₄	—	6	1	no	—
503	C₂×C₄	—	6	1	no	—
504	C₂×C₄	—	6	1	no	—
505	C₂×C₄	—	12	2	no	—
506	C₂×C₄	—	24	2	no	—
507	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
508	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	6	2	no	—
513	C₂×C₃	—	8	2	no	—
514	C₂×C₃	C₅×#546	1	1	yes	characteristic
515	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
516	C₂×C₃	C₅×#576	1	1	yes	characteristic
517	D₃	—	2	4	no	—
518	D₃	—	4	2	no	—
519	C₅	#81577	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	3	4	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	6	2	no	—
525	C₂²	—	6	2	no	—
526	C₂²	—	6	2	no	—
527	C₂²	—	12	1	no	—
528	C₂²	—	12	1	no	—
529	C₂²	—	24	8	no	—
530	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	6	2	no	—
534	C₄	—	12	1	no	—
535	C₄	—	12	1	no	—
536	C₄	—	12	1	no	—
537	C₄	C₅×D₃×SD₁₆	1	2	yes	—
538	C₄	C₅×D₃×#41	1	1	yes	characteristic
539	C₄	C₅×#1009	1	1	yes	characteristic
540	C₃	C₅×#3295	1	1	yes	characteristic, complemented, Sylow
541	C₂	—	6	4	no	—
542	C₂	—	8	2	no	—
543	C₂	—	12	2	no	—
544	C₂	C₅×#5676	1	1	yes	characteristic
545	C₂	C₅×#5757	1	1	yes	characteristic
546	C₂	C₂×C₅×D₃×SD₁₆	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	C₃×C₅×#486	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5717	C₂
hypercenter	C₅×#486	D₃
hypocenter	C₃	C₅×#3295
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#486

Complements

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

N	H ≅ G/N	type
1. C₅×#5730	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#5075	C₂	semidirect
6. C₅×#4778	C₂	semidirect
7. C₅×#4777	C₂	semidirect
8. C₅×#4776	C₂	semidirect
9. C₅×D₃×#102	C₂	semidirect
10. C₄×C₅×#204	C₂	semidirect
11. C₅×C₈×D₁₂	C₂	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₅×#214	C₂²	semidirect
23. C₂×C₅×D₃×C₈	C₂²	semidirect
24. C₅×#897	C₂²	semidirect
26. C₅×D₃×C₄⋊C₄	C₂²	semidirect
30. C₄×C₅×Dic₆	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#102	C₂²	semidirect
33. C₃×C₄×C₅×C₈	C₂²	semidirect
34. C₅×#832	C₂²	semidirect
36. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
37. C₅×#817	C₂²	semidirect
38. C₅×#816	C₂²	semidirect
40. C₅×#808	C₂²	semidirect
41. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
42. #81577	C₅	direct (N × H)
45. C₅×#486	D₃	semidirect
90. #5730	C₂×C₅	semidirect
92. C₃×#486	C₂×C₅	semidirect
93. #5084	C₂×C₅	semidirect
94. #5075	C₂×C₅	semidirect
95. #4778	C₂×C₅	semidirect
96. #4777	C₂×C₅	semidirect
97. #4776	C₂×C₅	semidirect
98. D₃×#102	C₂×C₅	semidirect
99. C₄×#204	C₂×C₅	semidirect
100. C₈×D₁₂	C₂×C₅	semidirect
106. C₅×C₄⋊Q₈	C₂×D₃	semidirect
126. C₅×#102	C₂×D₃	semidirect
127. C₅×#102	C₂×D₃	semidirect
129. C₄×C₅×C₈	C₂×D₃	semidirect
153. C₅×D₁₂	SD₁₆	semidirect
166. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
172. C₂×#214	C₂²×C₅	semidirect
174. C₂×D₃×C₈	C₂²×C₅	semidirect
175. #897	C₂²×C₅	semidirect
177. D₃×C₄⋊C₄	C₂²×C₅	semidirect
181. C₄×Dic₆	C₂²×C₅	semidirect
182. C₃×#102	C₂²×C₅	semidirect
183. C₃×#102	C₂²×C₅	semidirect
184. C₃×C₄×C₈	C₂²×C₅	semidirect
185. #832	C₂²×C₅	semidirect
187. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
188. #817	C₂²×C₅	semidirect
189. #816	C₂²×C₅	semidirect
191. #808	C₂²×C₅	semidirect
192. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
231. #486	C₅×D₃	semidirect
334. C₄⋊Q₈	C₂×C₅×D₃	semidirect
354. #102	C₂×C₅×D₃	semidirect
355. #102	C₂×C₅×D₃	semidirect
357. C₄×C₈	C₂×C₅×D₃	semidirect
386. D₁₂	C₅×SD₁₆	semidirect
453. C₃×C₅	#3295	semidirect
519. C₅	#81577	direct (N × H)
540. C₃	C₅×#3295	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5730	2
C₅×#5717	2
C₃×C₅×#486	2
C₅×#5084	2
C₅×#5075	2
C₅×#4778	2
C₅×#4777	2
C₅×#4776	2
C₅×D₃×#102	2
C₄×C₅×#204	2
C₅×C₈×D₁₂	2
C₅×#3295	3
#81577	5

Subgroups — C5×#81577 #14458449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81577 #14458449