Subgroups — C₅×#80427 #14426229

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#916	C₂	1	2	yes	maximal, complemented
2	C₅×#5725	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5165	C₂	1	2	yes	maximal, complemented
6	C₅×#5090	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4804	C₂	1	2	yes	maximal, complemented
11	C₅×#4798	C₂	1	2	yes	maximal, complemented
12	C₅×#3035	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	2	yes	—
14	C₂×C₅×#237	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₅×#947	C₂²	1	2	yes	—
19	C₂×C₅×#216	C₂²	1	2	yes	—
20	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#213	C₂²	1	2	yes	—
22	C₄×C₅×#67	—	2	1	no	—
23	C₂×C₄×C₅×Dic₃	—	2	1	no	—
24	C₅×#916	—	2	8	no	—
25	C₂×C₅×#204	C₂²	1	2	yes	—
26	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
27	C₅×#895	—	2	1	no	—
28	C₅×#895	—	2	1	no	—
29	C₅×#893	—	2	1	no	—
30	C₅×#893	—	2	1	no	—
31	C₅×#892	C₂²	1	1	yes	characteristic
32	C₅×#887	C₂²	1	1	yes	characteristic
33	C₅×#67⋊C₄	—	2	1	no	—
34	C₅×#877	—	2	1	no	—
35	C₅×#874	C₂²	1	1	yes	characteristic
36	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
37	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×#103	C₂²	1	2	yes	—
40	C₅×#835	C₂²	1	2	yes	—
41	C₅×#821	C₂²	1	2	yes	—
42	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
43	C₅×#809	C₂²	1	2	yes	—
44	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
45	#80427	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×#135	—	3	2	no	—
47	C₅×#532	—	3	1	no	—
48	C₄×C₅×#41	—	3	1	no	—
49	C₅×#464	—	3	2	no	—
50	C₅×#463	—	3	2	no	—
51	C₅×#462	—	3	1	no	—
52	C₅×#461	D₃	1	1	yes	characteristic, complemented
53	C₅×#460	—	3	1	no	—
54	C₅×#459	—	3	1	no	—
55	C₂×C₅×C₄⋊C₈	—	3	1	no	—
56	C₅×#416	—	3	2	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂×C₅×#67	—	2	1	no	—
61	C₂²×C₅×Dic₃	—	2	1	no	—
62	C₂²×C₅×Dic₃	—	2	1	no	—
63	C₅×#239	—	2	4	no	—
64	C₅×#239	—	2	4	no	—
65	C₅×#237	—	2	2	no	—
66	C₅×#237	D₄	1	4	yes	complemented
67	C₂×C₅×D₁₂	—	2	2	no	—
68	C₂×C₅×D₁₂	—	2	1	no	—
69	C₂×C₅×D₁₂	—	2	1	no	—
70	C₂×C₅×D₁₂	C₂³	1	2	yes	—
71	C₂×C₄×C₅×D₃	—	2	2	no	—
72	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
76	C₃×C₅×SD₁₆	—	2	4	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₅×#217	—	2	1	no	—
84	C₅×#216	—	2	4	no	—
85	C₅×#213	—	2	4	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
88	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
89	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
90	C₅×Dic₃⋊C₄	—	2	1	no	—
91	C₅×Dic₃⋊C₄	—	2	1	no	—
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
96	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
99	C₅×#204	—	2	4	no	—
100	C₅×D₃×C₈	—	2	4	no	—
101	C₂×#916	C₂×C₅	1	2	yes	complemented
102	#5725	C₂×C₅	1	1	yes	characteristic, complemented
103	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
105	#5165	C₂×C₅	1	2	yes	complemented
106	#5090	C₂×C₅	1	1	yes	characteristic, complemented
107	#5015	C₂×C₅	1	1	yes	characteristic, complemented
108	#4848	C₂×C₅	1	1	yes	characteristic, complemented
109	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
110	#4804	C₂×C₅	1	2	yes	complemented
111	#4798	C₂×C₅	1	2	yes	complemented
112	C₂×C₅×#41	—	3	2	no	—
113	C₂×C₅×#41	—	3	1	no	—
114	C₅×#135	—	6	8	no	—
115	C₂×C₅×Q₁₆	—	3	2	no	—
116	C₂×C₅×SD₁₆	—	3	2	no	—
117	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
118	C₂×C₅×D₈	—	3	2	no	—
119	C₂²×C₅×C₈	—	3	2	no	—
120	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
121	C₅×#127	—	3	1	no	—
122	C₅×#124	—	3	2	no	—
123	C₅×#121	—	6	1	no	—
124	C₅×#121	—	6	1	no	—
125	C₄×C₅×Q₈	—	3	1	no	—
126	C₄×C₅×Q₈	—	3	1	no	—
127	C₄×C₅×D₄	—	3	1	no	—
128	C₄×C₅×D₄	—	6	1	no	—
129	C₄×C₅×D₄	—	6	1	no	—
130	C₄×C₅×D₄	—	6	1	no	—
131	C₄×C₅×D₄	—	6	1	no	—
132	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
133	C₅×#117	—	3	1	no	—
134	C₅×#117	—	6	1	no	—
135	C₂×C₄²×C₅	—	3	1	no	—
136	C₂×C₄²×C₅	—	6	1	no	—
137	C₅×C₄⋊C₈	—	3	2	no	—
138	C₅×C₄⋊C₈	—	3	1	no	—
139	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
140	C₅×#103	—	3	2	no	—
141	C₅×#103	C₂×D₃	1	2	yes	—
142	C₅×#102	—	3	2	no	—
143	C₅×#102	—	3	2	no	—
144	#3035	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂²×C₅×D₃	—	2	2	no	—
147	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
148	C₃×C₅×Q₈	—	2	2	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×D₄	—	2	1	no	—
151	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	4	2	no	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₅×#67	—	2	4	no	—
159	C₂×C₅×Dic₃	—	2	1	no	—
160	C₂×C₅×Dic₃	—	2	4	no	—
161	C₂×C₅×Dic₃	—	2	1	no	—
162	C₂×C₅×Dic₃	—	4	2	no	—
163	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
166	C₅×D₁₂	—	2	2	no	—
167	C₅×D₁₂	—	2	2	no	—
168	C₅×D₁₂	—	4	2	no	—
169	C₅×D₁₂	—	4	4	no	—
170	C₅×D₁₂	—	4	2	no	—
171	C₄×C₅×D₃	—	2	2	no	—
172	C₄×C₅×D₃	—	4	1	no	—
173	C₄×C₅×D₃	—	4	4	no	—
174	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
175	C₄×C₅×D₃	#41	1	2	yes	—
176	C₅×Dic₆	—	2	1	no	—
177	C₅×Dic₆	C₂×D₄	1	2	yes	—
178	C₃×C₅×C₈	—	2	2	no	—
179	C₅×C₃⋊C₈	—	2	2	no	—
180	C₂×#239	C₂²×C₅	1	2	yes	—
181	C₂×#237	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
183	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
184	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
185	#947	C₂²×C₅	1	2	yes	—
186	C₂×#216	C₂²×C₅	1	2	yes	—
187	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
188	C₂×#213	C₂²×C₅	1	2	yes	—
189	C₄×#67	—	2	1	no	—
190	C₂×C₄×Dic₃	—	2	1	no	—
191	#916	—	2	8	no	—
192	C₂×#204	C₂²×C₅	1	2	yes	—
193	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
194	#895	—	2	1	no	—
195	#895	—	2	1	no	—
196	#893	—	2	1	no	—
197	#893	—	2	1	no	—
198	#892	C₂²×C₅	1	1	yes	characteristic
199	#887	C₂²×C₅	1	1	yes	characteristic
200	#67⋊C₄	—	2	1	no	—
201	#877	—	2	1	no	—
202	#874	C₂²×C₅	1	1	yes	characteristic
203	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
204	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
205	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₃×#103	C₂²×C₅	1	2	yes	—
207	#835	C₂²×C₅	1	2	yes	—
208	#821	C₂²×C₅	1	2	yes	—
209	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
210	#809	C₂²×C₅	1	2	yes	—
211	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
212	C₅×#41	—	3	4	no	—
213	C₅×#41	—	6	2	no	—
214	C₅×#41	—	6	4	no	—
215	C₅×#41	—	6	4	no	—
216	C₂×C₅×Q₈	—	3	1	no	—
217	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
218	C₂×C₅×D₄	—	3	2	no	—
219	C₂×C₅×D₄	—	6	2	no	—
220	C₂×C₅×D₄	—	6	1	no	—
221	C₂×C₅×D₄	—	6	1	no	—
222	C₂×C₅×D₄	—	6	1	no	—
223	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	3	1	no	—
228	C₂²×C₄×C₅	—	6	2	no	—
229	C₂²×C₄×C₅	—	6	1	no	—
230	C₂²×C₄×C₅	—	6	1	no	—
231	C₅×Q₁₆	—	6	4	no	—
232	C₅×SD₁₆	—	2	4	no	—
233	C₅×SD₁₆	—	6	4	no	—
234	C₅×D₈	—	6	4	no	—
235	C₂×C₅×C₈	—	3	2	no	—
236	C₂×C₅×C₈	—	6	4	no	—
237	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	3	1	no	—
241	C₅×C₄⋊C₄	—	6	1	no	—
242	C₅×C₄⋊C₄	—	6	1	no	—
243	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	6	2	no	—
246	C₅×C₂²⋊C₄	—	6	2	no	—
247	C₅×C₂²⋊C₄	—	6	1	no	—
248	C₅×C₂²⋊C₄	—	6	1	no	—
249	C₄²×C₅	—	3	1	no	—
250	C₄²×C₅	—	3	1	no	—
251	C₄²×C₅	—	3	1	no	—
252	C₄²×C₅	—	6	1	no	—
253	C₄²×C₅	—	6	1	no	—
254	C₄²×C₅	—	6	1	no	—
255	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
256	C₂×#135	—	3	2	no	—
257	#532	—	3	1	no	—
258	C₄×#41	—	3	1	no	—
259	#464	—	3	2	no	—
260	#463	—	3	2	no	—
261	#462	—	3	1	no	—
262	#461	C₅×D₃	1	1	yes	characteristic, complemented
263	#460	—	3	1	no	—
264	#459	—	3	1	no	—
265	C₂×C₄⋊C₈	—	3	1	no	—
266	#416	—	3	2	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	4	1	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₅×D₃	—	2	1	no	—
272	C₂×C₅×D₃	—	2	1	no	—
273	C₂×C₅×D₃	—	4	2	no	—
274	C₂×C₅×D₃	—	4	2	no	—
275	C₂×C₅×D₃	—	4	2	no	—
276	C₂×C₅×D₃	#121	1	2	yes	—
277	C₃×C₄×C₅	—	2	1	no	—
278	C₃×C₄×C₅	—	4	2	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	#135	1	2	yes	complemented
281	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
283	C₅×Dic₃	—	2	2	no	—
284	C₅×Dic₃	—	2	1	no	—
285	C₅×Dic₃	—	2	1	no	—
286	C₅×Dic₃	—	4	1	no	—
287	C₅×Dic₃	#121	1	2	yes	—
288	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
289	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	—	2	1	no	—
291	C₂×#67	—	2	1	no	—
292	C₂²×Dic₃	—	2	1	no	—
293	C₂²×Dic₃	—	2	1	no	—
294	#239	—	2	4	no	—
295	#239	—	2	4	no	—
296	#237	—	2	2	no	—
297	#237	C₅×D₄	1	4	yes	complemented
298	C₂×D₁₂	—	2	2	no	—
299	C₂×D₁₂	—	2	1	no	—
300	C₂×D₁₂	—	2	1	no	—
301	C₂×D₁₂	C₂³×C₅	1	2	yes	—
302	C₂×C₄×D₃	—	2	2	no	—
303	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
304	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
305	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
306	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
307	C₃×SD₁₆	—	2	4	no	—
308	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
309	C₃×C₄⋊C₄	—	2	1	no	—
310	C₃×C₄⋊C₄	—	2	1	no	—
311	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
312	C₃×C₂²⋊C₄	—	2	1	no	—
313	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
314	#217	—	2	1	no	—
315	#216	—	2	4	no	—
316	#213	—	2	4	no	—
317	(C₂×D₃)⋊C₄	—	2	1	no	—
318	(C₂×D₃)⋊C₄	—	2	2	no	—
319	(C₂×D₃)⋊C₄	—	2	2	no	—
320	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
321	Dic₃⋊C₄	—	2	1	no	—
322	Dic₃⋊C₄	—	2	1	no	—
323	C₄×Dic₃	—	2	1	no	—
324	C₄×Dic₃	—	2	1	no	—
325	C₄×Dic₃	—	2	1	no	—
326	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
327	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
328	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
329	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
330	#204	—	2	4	no	—
331	D₃×C₈	—	2	4	no	—
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	—	3	1	no	—
334	C₂³×C₅	—	6	2	no	—
335	C₅×Q₈	—	2	2	no	—
336	C₅×Q₈	—	2	2	no	—
337	C₅×Q₈	—	3	2	no	—
338	C₅×Q₈	—	6	1	no	—
339	C₅×D₄	—	2	1	no	—
340	C₅×D₄	—	6	4	no	—
341	C₅×D₄	—	6	2	no	—
342	C₅×D₄	—	6	2	no	—
343	C₅×D₄	—	12	2	no	—
344	C₅×D₄	—	12	4	no	—
345	C₅×D₄	—	12	2	no	—
346	C₅×D₄	D₃×D₄	1	2	yes	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	3	1	no	—
350	C₂×C₄×C₅	—	3	2	no	—
351	C₂×C₄×C₅	—	3	2	no	—
352	C₂×C₄×C₅	—	3	1	no	—
353	C₂×C₄×C₅	—	3	1	no	—
354	C₂×C₄×C₅	—	4	2	no	—
355	C₂×C₄×C₅	—	6	4	no	—
356	C₂×C₄×C₅	—	6	1	no	—
357	C₂×C₄×C₅	—	6	2	no	—
358	C₂×C₄×C₅	—	6	1	no	—
359	C₂×C₄×C₅	—	12	1	no	—
360	C₂×C₄×C₅	—	12	4	no	—
361	C₂×C₄×C₅	—	12	2	no	—
362	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
363	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
365	C₅×C₈	—	2	2	no	—
366	C₅×C₈	—	6	2	no	—
367	C₂×#41	—	3	2	no	—
368	C₂×#41	—	3	1	no	—
369	#135	—	6	8	no	—
370	C₂×Q₁₆	—	3	2	no	—
371	C₂×SD₁₆	—	3	2	no	—
372	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
373	C₂×D₈	—	3	2	no	—
374	C₂²×C₈	—	3	2	no	—
375	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
376	#127	—	3	1	no	—
377	#124	—	3	2	no	—
378	#121	—	6	1	no	—
379	#121	—	6	1	no	—
380	C₄×Q₈	—	3	1	no	—
381	C₄×Q₈	—	3	1	no	—
382	C₄×D₄	—	3	1	no	—
383	C₄×D₄	—	6	1	no	—
384	C₄×D₄	—	6	1	no	—
385	C₄×D₄	—	6	1	no	—
386	C₄×D₄	—	6	1	no	—
387	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
388	#117	—	3	1	no	—
389	#117	—	6	1	no	—
390	C₂×C₄²	—	3	1	no	—
391	C₂×C₄²	—	6	1	no	—
392	C₄⋊C₈	—	3	2	no	—
393	C₄⋊C₈	—	3	1	no	—
394	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
395	#103	—	3	2	no	—
396	#103	C₂×C₅×D₃	1	2	yes	—
397	#102	—	3	2	no	—
398	#102	—	3	2	no	—
399	C₂×C₃×C₅	—	4	2	no	—
400	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
401	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
402	C₂×C₃×C₅	#575	1	1	yes	characteristic
403	C₅×D₃	—	2	2	no	—
404	C₅×D₃	—	8	2	no	—
405	C₂³×C₃	—	2	1	no	—
406	C₂²×D₃	—	2	2	no	—
407	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
408	C₃×Q₈	—	2	2	no	—
409	C₃×Q₈	—	2	2	no	—
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	4	2	no	—
415	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
418	#67	—	2	4	no	—
419	C₂×Dic₃	—	2	1	no	—
420	C₂×Dic₃	—	2	4	no	—
421	C₂×Dic₃	—	2	1	no	—
422	C₂×Dic₃	—	4	2	no	—
423	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
426	D₁₂	—	2	2	no	—
427	D₁₂	—	2	2	no	—
428	D₁₂	—	4	2	no	—
429	D₁₂	—	4	4	no	—
430	D₁₂	—	4	2	no	—
431	C₄×D₃	—	2	2	no	—
432	C₄×D₃	—	4	1	no	—
433	C₄×D₃	—	4	4	no	—
434	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
435	C₄×D₃	C₅×#41	1	2	yes	—
436	Dic₆	—	2	1	no	—
437	Dic₆	C₂×C₅×D₄	1	2	yes	—
438	C₃×C₈	—	2	2	no	—
439	C₃⋊C₈	—	2	2	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	3	2	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	6	1	no	—
445	C₂²×C₅	—	6	1	no	—
446	C₂²×C₅	—	12	2	no	—
447	C₂²×C₅	—	12	2	no	—
448	C₂²×C₅	—	12	2	no	—
449	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	3	2	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	6	1	no	—
455	C₄×C₅	—	6	1	no	—
456	C₄×C₅	—	6	2	no	—
457	C₄×C₅	—	12	1	no	—
458	C₄×C₅	#916	1	2	yes	complemented
459	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
460	C₄×C₅	D₃×#41	1	1	yes	characteristic
461	#41	—	3	4	no	—
462	#41	—	6	2	no	—
463	#41	—	6	4	no	—
464	#41	—	6	4	no	—
465	C₂×Q₈	—	3	1	no	—
466	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
467	C₂×D₄	—	3	2	no	—
468	C₂×D₄	—	6	2	no	—
469	C₂×D₄	—	6	1	no	—
470	C₂×D₄	—	6	1	no	—
471	C₂×D₄	—	6	1	no	—
472	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₂²×C₄	—	3	1	no	—
476	C₂²×C₄	—	3	1	no	—
477	C₂²×C₄	—	6	2	no	—
478	C₂²×C₄	—	6	1	no	—
479	C₂²×C₄	—	6	1	no	—
480	Q₁₆	—	6	4	no	—
481	SD₁₆	—	2	4	no	—
482	SD₁₆	—	6	4	no	—
483	D₈	—	6	4	no	—
484	C₂×C₈	—	3	2	no	—
485	C₂×C₈	—	6	4	no	—
486	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₄⋊C₄	—	6	1	no	—
491	C₄⋊C₄	—	6	1	no	—
492	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	6	2	no	—
495	C₂²⋊C₄	—	6	2	no	—
496	C₂²⋊C₄	—	6	1	no	—
497	C₂²⋊C₄	—	6	1	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	1	no	—
500	C₄²	—	3	1	no	—
501	C₄²	—	6	1	no	—
502	C₄²	—	6	1	no	—
503	C₄²	—	6	1	no	—
504	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
505	C₃×C₅	#3035	1	1	yes	characteristic, complemented, Hall
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	4	1	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
510	C₂×D₃	—	2	1	no	—
511	C₂×D₃	—	2	1	no	—
512	C₂×D₃	—	4	2	no	—
513	C₂×D₃	—	4	2	no	—
514	C₂×D₃	—	4	2	no	—
515	C₂×D₃	C₅×#121	1	2	yes	—
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	4	2	no	—
518	C₃×C₄	—	4	1	no	—
519	C₃×C₄	C₅×#135	1	2	yes	complemented
520	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
521	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
522	Dic₃	—	2	2	no	—
523	Dic₃	—	2	1	no	—
524	Dic₃	—	2	1	no	—
525	Dic₃	—	4	1	no	—
526	Dic₃	C₅×#121	1	2	yes	—
527	C₂×C₅	—	4	2	no	—
528	C₂×C₅	—	6	2	no	—
529	C₂×C₅	—	24	2	no	—
530	C₂×C₅	D₃×#121	1	1	yes	characteristic
531	C₂×C₅	C₂×#916	1	1	yes	characteristic
532	C₂×C₅	#5777	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	3	1	no	—
535	C₂³	—	6	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	3	2	no	—
539	Q₈	—	6	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	6	4	no	—
542	D₄	—	6	2	no	—
543	D₄	—	6	2	no	—
544	D₄	—	12	2	no	—
545	D₄	—	12	4	no	—
546	D₄	—	12	2	no	—
547	D₄	C₅×D₃×D₄	1	2	yes	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	3	1	no	—
551	C₂×C₄	—	3	2	no	—
552	C₂×C₄	—	3	2	no	—
553	C₂×C₄	—	3	1	no	—
554	C₂×C₄	—	3	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	6	4	no	—
557	C₂×C₄	—	6	1	no	—
558	C₂×C₄	—	6	2	no	—
559	C₂×C₄	—	6	1	no	—
560	C₂×C₄	—	12	1	no	—
561	C₂×C₄	—	12	4	no	—
562	C₂×C₄	—	12	2	no	—
563	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
564	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	6	2	no	—
568	C₂×C₃	—	4	2	no	—
569	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
570	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
571	C₂×C₃	C₅×#575	1	1	yes	characteristic
572	D₃	—	2	2	no	—
573	D₃	—	8	2	no	—
574	C₅	#80427	1	1	yes	characteristic, direct product factor, Sylow
575	C₂²	—	2	2	no	—
576	C₂²	—	3	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	6	1	no	—
580	C₂²	—	6	1	no	—
581	C₂²	—	12	2	no	—
582	C₂²	—	12	2	no	—
583	C₂²	—	12	2	no	—
584	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	3	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	6	1	no	—
590	C₄	—	6	1	no	—
591	C₄	—	6	2	no	—
592	C₄	—	12	1	no	—
593	C₄	C₅×#916	1	2	yes	complemented
594	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
595	C₄	C₅×D₃×#41	1	1	yes	characteristic
596	C₃	C₅×#3035	1	1	yes	characteristic, complemented, Sylow
597	C₂	—	4	2	no	—
598	C₂	—	6	2	no	—
599	C₂	—	24	2	no	—
600	C₂	C₅×D₃×#121	1	1	yes	characteristic
601	C₂	C₂×C₅×#916	1	1	yes	characteristic
602	C₂	C₅×#5777	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×#461	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#461	D₃
hypocenter	C₃	C₅×#3035
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#461

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#916	C₂	semidirect
2. C₅×#5725	C₂	semidirect
3. C₄×C₅×#237	C₂	semidirect
4. C₃×C₅×#461	C₂	semidirect
5. C₅×#5165	C₂	semidirect
6. C₅×#5090	C₂	semidirect
7. C₅×#5015	C₂	semidirect
8. C₅×#4848	C₂	semidirect
9. C₅×D₃×C₄⋊C₈	C₂	semidirect
10. C₅×#4804	C₂	semidirect
11. C₅×#4798	C₂	semidirect
45. #80427	C₅	direct (N × H)
52. C₅×#461	D₃	semidirect
66. C₅×#237	D₄	semidirect
101. C₂×#916	C₂×C₅	semidirect
102. #5725	C₂×C₅	semidirect
103. C₄×#237	C₂×C₅	semidirect
104. C₃×#461	C₂×C₅	semidirect
105. #5165	C₂×C₅	semidirect
106. #5090	C₂×C₅	semidirect
107. #5015	C₂×C₅	semidirect
108. #4848	C₂×C₅	semidirect
109. D₃×C₄⋊C₈	C₂×C₅	semidirect
110. #4804	C₂×C₅	semidirect
111. #4798	C₂×C₅	semidirect
262. #461	C₅×D₃	semidirect
280. C₃×C₄×C₅	#135	semidirect
297. #237	C₅×D₄	semidirect
458. C₄×C₅	#916	semidirect
505. C₃×C₅	#3035	semidirect
519. C₃×C₄	C₅×#135	semidirect
574. C₅	#80427	direct (N × H)
593. C₄	C₅×#916	semidirect
596. C₃	C₅×#3035	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#916	2
C₅×#5725	2
C₄×C₅×#237	2
C₃×C₅×#461	2
C₅×#5165	2
C₅×#5090	2
C₅×#5015	2
C₅×#4848	2
C₅×D₃×C₄⋊C₈	2
C₅×#4804	2
C₅×#4798	2
C₅×#3035	3
#80427	5

Subgroups — C5×#80427 #14426229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80427 #14426229