Subgroups — C₅×D₃×#578 #14510118

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#578	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5838	C₂	1	2	yes	maximal, complemented
4	C₅×#5779	C₂	1	6	yes	maximal, complemented
5	C₅×D₃×#137	C₂	1	6	yes	maximal, complemented
6	C₅×#5771	C₂	1	3	yes	maximal, complemented
7	C₅×D₃×#135	C₂	1	3	yes	maximal, complemented
8	C₅×#5766	C₂	1	3	yes	maximal, complemented
9	C₂×C₅×D₃×Q₁₆	C₂	1	3	yes	maximal, complemented
10	C₅×#5753	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#578	—	3	1	no	maximal, Hall
13	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	complemented
14	C₅×#1010	—	2	6	no	—
15	C₅×#1010	C₂²	1	6	yes	complemented
16	C₅×#1010	C₂²	1	2	yes	complemented
17	C₅×D₃×#41	—	2	6	no	—
18	C₅×D₃×#41	C₂²	1	6	yes	—
19	C₅×D₃×#41	C₂²	1	1	yes	characteristic
20	C₅×#1007	—	2	2	no	—
21	C₅×#1007	C₂²	1	6	yes	complemented
22	C₂×C₅×D₃×Q₈	—	2	2	no	—
23	C₂×C₅×D₃×Q₈	C₂²	1	6	yes	—
24	C₃×C₅×#137	C₂²	1	6	yes	complemented
25	C₃×C₅×#135	C₂²	1	3	yes	complemented
26	C₂×C₃×C₅×Q₁₆	C₂²	1	3	yes	complemented
27	C₃×C₅×#131	C₂²	1	1	yes	characteristic, complemented
28	C₅×#951	C₂²	1	6	yes	complemented
29	C₅×#950	C₂²	1	6	yes	complemented
30	C₅×#948	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#216	C₂²	1	6	yes	complemented
32	C₅×#942	C₂²	1	6	yes	complemented
33	C₅×#919	C₂²	1	3	yes	complemented
34	C₅×#918	C₂²	1	12	yes	complemented
35	C₅×D₃×Q₁₆	C₂²	1	3	yes	—
36	C₅×D₃×Q₁₆	C₂²	1	6	yes	—
37	C₅×D₃×Q₁₆	C₂²	1	6	yes	complemented
38	C₅×D₃×Q₁₆	C₂²	1	6	yes	complemented
39	C₅×#916	C₂²	1	6	yes	complemented
40	C₅×#915	C₂²	1	12	yes	complemented
41	C₅×D₃×SD₁₆	C₂²	1	6	yes	—
42	C₅×#912	C₂²	1	3	yes	complemented
43	C₅×D₃×D₈	C₂²	1	1	yes	characteristic
44	C₅×#909	C₂²	1	6	yes	complemented
45	C₅×#907	C₂²	1	3	yes	complemented
46	C₅×D₃×M₁₆	C₂²	1	3	yes	—
47	C₂×C₅×Dic₁₂	C₂²	1	3	yes	complemented
48	C₅×#904	C₂²	1	3	yes	complemented
49	C₅×#901	C₂²	1	3	yes	complemented
50	C₂×C₅×D₃×C₈	C₂²	1	3	yes	—
51	D₃×#578	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₂×C₅×2₋¹⁺⁴	—	3	2	no	—
53	C₅×#578	—	3	2	no	—
54	C₅×#578	—	3	6	no	—
55	C₅×#578	—	3	3	no	—
56	C₅×#578	—	3	3	no	—
57	C₅×#578	—	3	1	no	—
58	C₅×#578	D₃	1	1	yes	characteristic, direct product factor
59	C₂×C₅×#137	—	3	6	no	—
60	C₂×C₅×#135	—	3	3	no	—
61	C₂²×C₅×Q₁₆	—	3	3	no	—
62	C₂×C₅×#131	—	3	1	no	—
63	C₃×C₅×#41	—	2	6	no	—
64	C₃×C₅×#41	C₂³	1	6	yes	—
65	C₃×C₅×#41	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×Q₈	—	2	2	no	—
67	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	—
68	C₅×#239	—	2	6	no	—
69	C₅×#239	D₄	1	1	yes	characteristic
70	C₅×#239	C₂³	1	6	yes	—
71	C₅×D₃×Q₈	—	2	2	no	—
72	C₅×D₃×Q₈	—	2	6	no	—
73	C₅×D₃×Q₈	—	2	6	no	—
74	C₅×D₃×Q₈	—	2	6	no	—
75	C₅×D₃×Q₈	D₄	1	1	yes	characteristic
76	C₅×D₃×Q₈	C₂³	1	6	yes	—
77	C₅×D₃×Q₈	C₂³	1	12	yes	—
78	C₅×#237	—	2	6	no	—
79	C₅×#237	—	2	12	no	—
80	C₅×#237	—	2	6	no	—
81	C₅×#237	D₄	1	3	yes	—
82	C₅×#237	C₂³	1	6	yes	—
83	C₅×D₃×D₄	—	2	6	no	—
84	C₅×D₃×D₄	D₄	1	3	yes	—
85	C₅×D₃×D₄	C₂³	1	2	yes	—
86	C₅×#235	—	2	12	no	—
87	C₅×#235	—	2	6	no	—
88	C₅×#235	—	2	6	no	—
89	C₅×#235	C₂³	1	3	yes	—
90	C₅×#235	C₂³	1	6	yes	—
91	C₂×C₄×C₅×D₃	—	2	6	no	—
92	C₂×C₄×C₅×D₃	—	2	6	no	—
93	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
94	C₂×C₅×Dic₆	—	2	6	no	—
95	C₂×C₅×Dic₆	—	2	6	no	—
96	C₂×C₅×Dic₆	C₂³	1	6	yes	—
97	C₃×C₅×Q₁₆	C₂³	1	3	yes	—
98	C₃×C₅×Q₁₆	C₂³	1	6	yes	—
99	C₃×C₅×SD₁₆	C₂³	1	6	yes	—
100	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
101	C₃×C₅×M₁₆	C₂³	1	3	yes	—
102	C₂×C₃×C₅×C₈	C₂³	1	3	yes	—
103	C₅×#216	C₂³	1	12	yes	—
104	C₅×#216	C₂³	1	6	yes	—
105	C₅×#215	C₂³	1	6	yes	—
106	C₅×#214	C₂³	1	6	yes	—
107	C₅×#213	C₂³	1	2	yes	—
108	C₅×#208	C₂³	1	3	yes	—
109	C₂×C₅×C₃⋊C₈	C₂³	1	3	yes	—
110	C₅×Dic₁₂	C₂³	1	3	yes	—
111	C₅×Dic₁₂	C₂³	1	6	yes	—
112	C₅×D₂₄	C₂³	1	1	yes	characteristic
113	C₅×#204	C₂³	1	6	yes	—
114	C₅×ΓL(1,𝔽₂₅)	C₂³	1	6	yes	—
115	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
116	C₅×D₃×C₈	C₂³	1	3	yes	—
117	C₅×D₃×C₈	C₂³	1	3	yes	—
118	C₅×D₃×C₈	C₂³	1	3	yes	—
119	D₃×2₋¹⁺⁴	C₂×C₅	1	2	yes	complemented
120	C₃×#578	C₂×C₅	1	1	yes	characteristic, complemented
121	#5838	C₂×C₅	1	2	yes	complemented
122	#5779	C₂×C₅	1	6	yes	complemented
123	D₃×#137	C₂×C₅	1	6	yes	complemented
124	#5771	C₂×C₅	1	3	yes	complemented
125	D₃×#135	C₂×C₅	1	3	yes	complemented
126	#5766	C₂×C₅	1	3	yes	complemented
127	C₂×D₃×Q₁₆	C₂×C₅	1	3	yes	complemented
128	#5753	C₂×C₅	1	1	yes	characteristic, complemented
129	D₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
130	C₅×2₋¹⁺⁴	—	3	6	no	—
131	C₅×2₋¹⁺⁴	—	3	2	no	—
132	C₅×2₋¹⁺⁴	—	3	6	no	—
133	C₅×2₋¹⁺⁴	—	6	2	no	—
134	C₅×2₋¹⁺⁴	—	6	6	no	—
135	C₅×2₋¹⁺⁴	C₂×D₃	1	2	yes	complemented
136	C₂×C₅×#41	—	3	1	no	—
137	C₂×C₅×#41	—	3	6	no	—
138	C₂×C₅×#41	—	6	6	no	—
139	C₂²×C₅×Q₈	—	3	6	no	—
140	C₂²×C₅×Q₈	—	6	2	no	—
141	C₅×#137	—	3	6	no	—
142	C₅×#137	—	3	6	no	—
143	C₅×#137	—	3	12	no	—
144	C₅×#137	—	3	12	no	—
145	C₅×#137	—	3	6	no	—
146	C₅×#137	C₂×D₃	1	6	yes	complemented
147	C₅×#135	—	3	6	no	—
148	C₅×#135	—	3	3	no	—
149	C₅×#135	—	3	6	no	—
150	C₅×#135	—	3	3	no	—
151	C₅×#135	—	3	3	no	—
152	C₅×#135	C₂×D₃	1	3	yes	complemented
153	C₂×C₅×Q₁₆	—	3	6	no	—
154	C₂×C₅×Q₁₆	—	3	3	no	—
155	C₂×C₅×Q₁₆	—	3	6	no	—
156	C₂×C₅×Q₁₆	—	3	6	no	—
157	C₂×C₅×Q₁₆	—	3	6	no	—
158	C₂×C₅×Q₁₆	—	3	3	no	—
159	C₂×C₅×Q₁₆	C₂×D₃	1	3	yes	complemented
160	C₂×C₅×SD₁₆	—	3	6	no	—
161	C₂×C₅×D₈	—	3	1	no	—
162	C₅×#131	—	3	1	no	—
163	C₅×#131	—	3	3	no	—
164	C₅×#131	—	3	3	no	—
165	C₅×#131	C₂×D₃	1	1	yes	characteristic, complemented
166	C₂×C₅×M₁₆	—	3	3	no	—
167	C₂²×C₅×C₈	—	3	3	no	—
168	C₂×#578	—	3	1	no	Sylow
169	C₂²×C₅×D₃	—	2	2	no	—
170	C₂²×C₅×D₃	C₂×D₄	1	3	yes	—
171	C₃×C₅×Q₈	—	2	6	no	—
172	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
173	C₃×C₅×Q₈	C₂⁴	1	6	yes	—
174	C₃×C₅×D₄	—	2	6	no	—
175	C₃×C₅×D₄	C₂×D₄	1	3	yes	—
176	C₃×C₅×D₄	C₂⁴	1	2	yes	—
177	C₂×C₃×C₄×C₅	—	2	6	no	—
178	C₂×C₃×C₄×C₅	—	2	6	no	—
179	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
180	C₅×#67	—	2	6	no	—
181	C₅×#67	—	2	6	no	—
182	C₅×#67	—	2	2	no	—
183	C₅×#67	C₂×D₄	1	6	yes	—
184	C₂×C₅×Dic₃	—	2	6	no	—
185	C₂×C₅×Dic₃	—	2	6	no	—
186	C₂×C₅×Dic₃	C₂×D₄	1	3	yes	—
187	C₅×D₁₂	—	2	6	no	—
188	C₅×D₁₂	C₂×D₄	1	3	yes	—
189	C₅×D₁₂	C₂⁴	1	2	yes	—
190	C₄×C₅×D₃	—	2	6	no	—
191	C₄×C₅×D₃	—	2	12	no	—
192	C₄×C₅×D₃	—	2	6	no	—
193	C₄×C₅×D₃	—	2	6	no	—
194	C₄×C₅×D₃	C₂×D₄	1	3	yes	—
195	C₄×C₅×D₃	C₂×D₄	1	3	yes	—
196	C₄×C₅×D₃	C₂⁴	1	1	yes	characteristic
197	C₄×C₅×D₃	C₂⁴	1	3	yes	—
198	C₅×Dic₆	—	2	6	no	—
199	C₅×Dic₆	—	2	6	no	—
200	C₅×Dic₆	—	2	12	no	—
201	C₅×Dic₆	C₂×D₄	1	3	yes	—
202	C₅×Dic₆	C₂⁴	1	6	yes	—
203	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
204	C₃×C₅×C₈	C₂⁴	1	3	yes	—
205	C₅×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
206	C₅×C₃⋊C₈	C₂⁴	1	3	yes	—
207	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	complemented
208	#1010	—	2	6	no	—
209	#1010	C₂²×C₅	1	6	yes	complemented
210	#1010	C₂²×C₅	1	2	yes	complemented
211	D₃×#41	—	2	6	no	—
212	D₃×#41	C₂²×C₅	1	6	yes	—
213	D₃×#41	C₂²×C₅	1	1	yes	characteristic
214	#1007	—	2	2	no	—
215	#1007	C₂²×C₅	1	6	yes	complemented
216	C₂×D₃×Q₈	—	2	2	no	—
217	C₂×D₃×Q₈	C₂²×C₅	1	6	yes	—
218	C₃×#137	C₂²×C₅	1	6	yes	complemented
219	C₃×#135	C₂²×C₅	1	3	yes	complemented
220	C₂×C₃×Q₁₆	C₂²×C₅	1	3	yes	complemented
221	C₃×#131	C₂²×C₅	1	1	yes	characteristic, complemented
222	#951	C₂²×C₅	1	6	yes	complemented
223	#950	C₂²×C₅	1	6	yes	complemented
224	#948	C₂²×C₅	1	1	yes	characteristic, complemented
225	C₂×#216	C₂²×C₅	1	6	yes	complemented
226	#942	C₂²×C₅	1	6	yes	complemented
227	#919	C₂²×C₅	1	3	yes	complemented
228	#918	C₂²×C₅	1	12	yes	complemented
229	D₃×Q₁₆	C₂²×C₅	1	3	yes	—
230	D₃×Q₁₆	C₂²×C₅	1	6	yes	—
231	D₃×Q₁₆	C₂²×C₅	1	6	yes	complemented
232	D₃×Q₁₆	C₂²×C₅	1	6	yes	complemented
233	#916	C₂²×C₅	1	6	yes	complemented
234	#915	C₂²×C₅	1	12	yes	complemented
235	D₃×SD₁₆	C₂²×C₅	1	6	yes	—
236	#912	C₂²×C₅	1	3	yes	complemented
237	D₃×D₈	C₂²×C₅	1	1	yes	characteristic
238	#909	C₂²×C₅	1	6	yes	complemented
239	#907	C₂²×C₅	1	3	yes	complemented
240	D₃×M₁₆	C₂²×C₅	1	3	yes	—
241	C₂×Dic₁₂	C₂²×C₅	1	3	yes	complemented
242	#904	C₂²×C₅	1	3	yes	complemented
243	#901	C₂²×C₅	1	3	yes	complemented
244	C₂×D₃×C₈	C₂²×C₅	1	3	yes	—
245	C₅×#41	—	2	6	no	—
246	C₅×#41	—	3	1	no	—
247	C₅×#41	—	3	3	no	—
248	C₅×#41	—	3	3	no	—
249	C₅×#41	—	3	6	no	—
250	C₅×#41	—	3	6	no	—
251	C₅×#41	—	3	6	no	—
252	C₅×#41	—	6	6	no	—
253	C₅×#41	—	6	12	no	—
254	C₅×#41	—	6	6	no	—
255	C₅×#41	—	6	6	no	—
256	C₅×#41	—	6	12	no	—
257	C₅×#41	—	6	6	no	—
258	C₅×#41	—	6	6	no	—
259	C₅×#41	C₂²×D₃	1	6	yes	—
260	C₅×#41	C₂²×D₃	1	1	yes	characteristic
261	C₂×C₅×Q₈	—	2	2	no	—
262	C₂×C₅×Q₈	—	3	1	no	—
263	C₂×C₅×Q₈	—	3	6	no	—
264	C₂×C₅×Q₈	—	3	12	no	—
265	C₂×C₅×Q₈	—	3	6	no	—
266	C₂×C₅×Q₈	—	6	6	no	—
267	C₂×C₅×Q₈	—	6	6	no	—
268	C₂×C₅×Q₈	—	6	6	no	—
269	C₂×C₅×Q₈	—	6	6	no	—
270	C₂×C₅×Q₈	—	6	6	no	—
271	C₂×C₅×Q₈	—	6	2	no	—
272	C₂×C₅×Q₈	C₂²×D₃	1	6	yes	—
273	C₂×C₅×D₄	—	3	3	no	—
274	C₂×C₅×D₄	—	3	2	no	—
275	C₂×C₅×D₄	—	6	6	no	—
276	C₂²×C₄×C₅	—	3	3	no	—
277	C₂²×C₄×C₅	—	6	6	no	—
278	C₂²×C₄×C₅	—	6	6	no	—
279	C₅×Q₁₆	—	3	6	no	—
280	C₅×Q₁₆	—	3	12	no	—
281	C₅×Q₁₆	—	3	3	no	—
282	C₅×Q₁₆	—	3	6	no	—
283	C₅×Q₁₆	C₂²×D₃	1	3	yes	—
284	C₅×Q₁₆	C₂²×D₃	1	6	yes	—
285	C₅×SD₁₆	—	3	6	no	—
286	C₅×SD₁₆	—	3	6	no	—
287	C₅×SD₁₆	—	3	6	no	—
288	C₅×SD₁₆	C₂²×D₃	1	6	yes	—
289	C₅×D₈	—	3	2	no	—
290	C₅×D₈	—	3	1	no	—
291	C₅×D₈	C₂²×D₃	1	1	yes	characteristic
292	C₅×M₁₆	—	3	3	no	—
293	C₅×M₁₆	—	3	6	no	—
294	C₅×M₁₆	C₂²×D₃	1	3	yes	—
295	C₂×C₅×C₈	—	3	3	no	—
296	C₂×C₅×C₈	—	3	1	no	—
297	C₂×C₅×C₈	—	3	3	no	—
298	C₂×C₅×C₈	—	3	3	no	—
299	C₂×C₅×C₈	—	3	3	no	—
300	C₂×C₅×C₈	C₂²×D₃	1	3	yes	—
301	C₂×2₋¹⁺⁴	—	3	2	no	—
302	#578	—	3	2	no	—
303	#578	—	3	6	no	—
304	#578	—	3	3	no	—
305	#578	—	3	3	no	—
306	#578	—	3	1	no	—
307	#578	C₅×D₃	1	1	yes	characteristic, direct product factor
308	C₂×#137	—	3	6	no	—
309	C₂×#135	—	3	3	no	—
310	C₂²×Q₁₆	—	3	3	no	—
311	C₂×#131	—	3	1	no	—
312	C₂²×C₃×C₅	—	2	2	no	—
313	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
314	C₂×C₅×D₃	—	2	6	no	—
315	C₂×C₅×D₃	—	2	2	no	—
316	C₂×C₅×D₃	—	4	4	no	—
317	C₂×C₅×D₃	C₂²×D₄	1	3	yes	—
318	C₂×C₅×D₃	C₂²×D₄	1	1	yes	characteristic
319	C₃×C₄×C₅	—	2	6	no	—
320	C₃×C₄×C₅	C₂²×D₄	1	3	yes	—
321	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
322	C₅×Dic₃	—	2	6	no	—
323	C₅×Dic₃	C₂²×D₄	1	1	yes	characteristic
324	C₅×Dic₃	C₂²×D₄	1	3	yes	—
325	C₃×#41	—	2	6	no	—
326	C₃×#41	C₂³×C₅	1	6	yes	—
327	C₃×#41	C₂³×C₅	1	1	yes	characteristic
328	C₂×C₃×Q₈	—	2	2	no	—
329	C₂×C₃×Q₈	C₂³×C₅	1	6	yes	—
330	#239	—	2	6	no	—
331	#239	C₅×D₄	1	1	yes	characteristic
332	#239	C₂³×C₅	1	6	yes	—
333	D₃×Q₈	—	2	2	no	—
334	D₃×Q₈	—	2	6	no	—
335	D₃×Q₈	—	2	6	no	—
336	D₃×Q₈	—	2	6	no	—
337	D₃×Q₈	C₅×D₄	1	1	yes	characteristic
338	D₃×Q₈	C₂³×C₅	1	6	yes	—
339	D₃×Q₈	C₂³×C₅	1	12	yes	—
340	#237	—	2	6	no	—
341	#237	—	2	12	no	—
342	#237	—	2	6	no	—
343	#237	C₅×D₄	1	3	yes	—
344	#237	C₂³×C₅	1	6	yes	—
345	D₃×D₄	—	2	6	no	—
346	D₃×D₄	C₅×D₄	1	3	yes	—
347	D₃×D₄	C₂³×C₅	1	2	yes	—
348	#235	—	2	12	no	—
349	#235	—	2	6	no	—
350	#235	—	2	6	no	—
351	#235	C₂³×C₅	1	3	yes	—
352	#235	C₂³×C₅	1	6	yes	—
353	C₂×C₄×D₃	—	2	6	no	—
354	C₂×C₄×D₃	—	2	6	no	—
355	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
356	C₂×Dic₆	—	2	6	no	—
357	C₂×Dic₆	—	2	6	no	—
358	C₂×Dic₆	C₂³×C₅	1	6	yes	—
359	C₃×Q₁₆	C₂³×C₅	1	3	yes	—
360	C₃×Q₁₆	C₂³×C₅	1	6	yes	—
361	C₃×SD₁₆	C₂³×C₅	1	6	yes	—
362	C₃×D₈	C₂³×C₅	1	1	yes	characteristic
363	C₃×M₁₆	C₂³×C₅	1	3	yes	—
364	C₂×C₃×C₈	C₂³×C₅	1	3	yes	—
365	#216	C₂³×C₅	1	12	yes	—
366	#216	C₂³×C₅	1	6	yes	—
367	#215	C₂³×C₅	1	6	yes	—
368	#214	C₂³×C₅	1	6	yes	—
369	#213	C₂³×C₅	1	2	yes	—
370	#208	C₂³×C₅	1	3	yes	—
371	C₂×C₃⋊C₈	C₂³×C₅	1	3	yes	—
372	Dic₁₂	C₂³×C₅	1	3	yes	—
373	Dic₁₂	C₂³×C₅	1	6	yes	—
374	D₂₄	C₂³×C₅	1	1	yes	characteristic
375	#204	C₂³×C₅	1	6	yes	—
376	ΓL(1,𝔽₂₅)	C₂³×C₅	1	6	yes	—
377	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	D₃×C₈	C₂³×C₅	1	3	yes	—
379	D₃×C₈	C₂³×C₅	1	3	yes	—
380	D₃×C₈	C₂³×C₅	1	3	yes	—
381	C₂³×C₅	—	3	3	no	—
382	C₂³×C₅	—	6	2	no	—
383	C₅×Q₈	—	2	6	no	—
384	C₅×Q₈	—	3	3	no	—
385	C₅×Q₈	—	3	6	no	—
386	C₅×Q₈	—	6	6	no	—
387	C₅×Q₈	—	6	12	no	—
388	C₅×Q₈	—	6	6	no	—
389	C₅×Q₈	D₃×D₄	1	1	yes	characteristic
390	C₅×Q₈	C₂³×D₃	1	6	yes	—
391	C₅×D₄	—	2	6	no	—
392	C₅×D₄	—	3	6	no	—
393	C₅×D₄	—	3	3	no	—
394	C₅×D₄	—	3	2	no	—
395	C₅×D₄	—	6	6	no	—
396	C₅×D₄	—	6	2	no	—
397	C₅×D₄	—	6	6	no	—
398	C₅×D₄	—	6	6	no	—
399	C₅×D₄	D₃×D₄	1	3	yes	—
400	C₅×D₄	C₂³×D₃	1	2	yes	—
401	C₂×C₄×C₅	—	2	6	no	—
402	C₂×C₄×C₅	—	2	6	no	—
403	C₂×C₄×C₅	—	3	3	no	—
404	C₂×C₄×C₅	—	3	3	no	—
405	C₂×C₄×C₅	—	3	3	no	—
406	C₂×C₄×C₅	—	3	1	no	—
407	C₂×C₄×C₅	—	3	3	no	—
408	C₂×C₄×C₅	—	6	6	no	—
409	C₂×C₄×C₅	—	6	6	no	—
410	C₂×C₄×C₅	—	6	12	no	—
411	C₂×C₄×C₅	—	6	6	no	—
412	C₂×C₄×C₅	—	6	6	no	—
413	C₂×C₄×C₅	—	6	6	no	—
414	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
415	C₅×C₈	—	3	1	no	—
416	C₅×C₈	—	3	3	no	—
417	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
418	C₅×C₈	C₂³×D₃	1	3	yes	—
419	2₋¹⁺⁴	—	3	6	no	—
420	2₋¹⁺⁴	—	3	2	no	—
421	2₋¹⁺⁴	—	3	6	no	—
422	2₋¹⁺⁴	—	6	2	no	—
423	2₋¹⁺⁴	—	6	6	no	—
424	2₋¹⁺⁴	C₂×C₅×D₃	1	2	yes	complemented
425	C₂×#41	—	3	1	no	—
426	C₂×#41	—	3	6	no	—
427	C₂×#41	—	6	6	no	—
428	C₂²×Q₈	—	3	6	no	—
429	C₂²×Q₈	—	6	2	no	—
430	#137	—	3	6	no	—
431	#137	—	3	6	no	—
432	#137	—	3	12	no	—
433	#137	—	3	12	no	—
434	#137	—	3	6	no	—
435	#137	C₂×C₅×D₃	1	6	yes	complemented
436	#135	—	3	6	no	—
437	#135	—	3	3	no	—
438	#135	—	3	6	no	—
439	#135	—	3	3	no	—
440	#135	—	3	3	no	—
441	#135	C₂×C₅×D₃	1	3	yes	complemented
442	C₂×Q₁₆	—	3	6	no	—
443	C₂×Q₁₆	—	3	3	no	—
444	C₂×Q₁₆	—	3	6	no	—
445	C₂×Q₁₆	—	3	6	no	—
446	C₂×Q₁₆	—	3	6	no	—
447	C₂×Q₁₆	—	3	3	no	—
448	C₂×Q₁₆	C₂×C₅×D₃	1	3	yes	complemented
449	C₂×SD₁₆	—	3	6	no	—
450	C₂×D₈	—	3	1	no	—
451	#131	—	3	1	no	—
452	#131	—	3	3	no	—
453	#131	—	3	3	no	—
454	#131	C₂×C₅×D₃	1	1	yes	characteristic, complemented
455	C₂×M₁₆	—	3	3	no	—
456	C₂²×C₈	—	3	3	no	—
457	C₂×C₃×C₅	—	2	3	no	—
458	C₂×C₃×C₅	—	4	2	no	—
459	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
460	C₅×D₃	—	2	3	no	—
461	C₅×D₃	—	4	2	no	—
462	C₅×D₃	#578	1	2	yes	direct product factor
463	C₂²×D₃	—	2	2	no	—
464	C₂²×D₃	C₂×C₅×D₄	1	3	yes	—
465	C₃×Q₈	—	2	6	no	—
466	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
467	C₃×Q₈	C₂⁴×C₅	1	6	yes	—
468	C₃×D₄	—	2	6	no	—
469	C₃×D₄	C₂×C₅×D₄	1	3	yes	—
470	C₃×D₄	C₂⁴×C₅	1	2	yes	—
471	C₂×C₃×C₄	—	2	6	no	—
472	C₂×C₃×C₄	—	2	6	no	—
473	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
474	#67	—	2	6	no	—
475	#67	—	2	6	no	—
476	#67	—	2	2	no	—
477	#67	C₂×C₅×D₄	1	6	yes	—
478	C₂×Dic₃	—	2	6	no	—
479	C₂×Dic₃	—	2	6	no	—
480	C₂×Dic₃	C₂×C₅×D₄	1	3	yes	—
481	D₁₂	—	2	6	no	—
482	D₁₂	C₂×C₅×D₄	1	3	yes	—
483	D₁₂	C₂⁴×C₅	1	2	yes	—
484	C₄×D₃	—	2	6	no	—
485	C₄×D₃	—	2	12	no	—
486	C₄×D₃	—	2	6	no	—
487	C₄×D₃	—	2	6	no	—
488	C₄×D₃	C₂×C₅×D₄	1	3	yes	—
489	C₄×D₃	C₂×C₅×D₄	1	3	yes	—
490	C₄×D₃	C₂⁴×C₅	1	1	yes	characteristic
491	C₄×D₃	C₂⁴×C₅	1	3	yes	—
492	Dic₆	—	2	6	no	—
493	Dic₆	—	2	6	no	—
494	Dic₆	—	2	12	no	—
495	Dic₆	C₂×C₅×D₄	1	3	yes	—
496	Dic₆	C₂⁴×C₅	1	6	yes	—
497	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
498	C₃×C₈	C₂⁴×C₅	1	3	yes	—
499	C₃⋊C₈	C₂⁴×C₅	1	1	yes	characteristic
500	C₃⋊C₈	C₂⁴×C₅	1	3	yes	—
501	C₂²×C₅	—	2	2	no	—
502	C₂²×C₅	—	3	1	no	—
503	C₂²×C₅	—	3	3	no	—
504	C₂²×C₅	—	6	6	no	—
505	C₂²×C₅	—	6	2	no	—
506	C₂²×C₅	—	12	4	no	—
507	C₂²×C₅	C₂×D₃×D₄	1	3	yes	—
508	C₄×C₅	—	2	6	no	—
509	C₄×C₅	—	3	1	no	—
510	C₄×C₅	—	3	3	no	—
511	C₄×C₅	—	6	6	no	—
512	C₄×C₅	C₂×D₃×D₄	1	3	yes	—
513	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
514	#41	—	2	6	no	—
515	#41	—	3	1	no	—
516	#41	—	3	3	no	—
517	#41	—	3	3	no	—
518	#41	—	3	6	no	—
519	#41	—	3	6	no	—
520	#41	—	3	6	no	—
521	#41	—	6	6	no	—
522	#41	—	6	12	no	—
523	#41	—	6	6	no	—
524	#41	—	6	6	no	—
525	#41	—	6	12	no	—
526	#41	—	6	6	no	—
527	#41	—	6	6	no	—
528	#41	C₂²×C₅×D₃	1	6	yes	—
529	#41	C₂²×C₅×D₃	1	1	yes	characteristic
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	3	1	no	—
532	C₂×Q₈	—	3	6	no	—
533	C₂×Q₈	—	3	12	no	—
534	C₂×Q₈	—	3	6	no	—
535	C₂×Q₈	—	6	6	no	—
536	C₂×Q₈	—	6	6	no	—
537	C₂×Q₈	—	6	6	no	—
538	C₂×Q₈	—	6	6	no	—
539	C₂×Q₈	—	6	6	no	—
540	C₂×Q₈	—	6	2	no	—
541	C₂×Q₈	C₂²×C₅×D₃	1	6	yes	—
542	C₂×D₄	—	3	3	no	—
543	C₂×D₄	—	3	2	no	—
544	C₂×D₄	—	6	6	no	—
545	C₂²×C₄	—	3	3	no	—
546	C₂²×C₄	—	6	6	no	—
547	C₂²×C₄	—	6	6	no	—
548	Q₁₆	—	3	6	no	—
549	Q₁₆	—	3	12	no	—
550	Q₁₆	—	3	3	no	—
551	Q₁₆	—	3	6	no	—
552	Q₁₆	C₂²×C₅×D₃	1	3	yes	—
553	Q₁₆	C₂²×C₅×D₃	1	6	yes	—
554	SD₁₆	—	3	6	no	—
555	SD₁₆	—	3	6	no	—
556	SD₁₆	—	3	6	no	—
557	SD₁₆	C₂²×C₅×D₃	1	6	yes	—
558	D₈	—	3	2	no	—
559	D₈	—	3	1	no	—
560	D₈	C₂²×C₅×D₃	1	1	yes	characteristic
561	M₁₆	—	3	3	no	—
562	M₁₆	—	3	6	no	—
563	M₁₆	C₂²×C₅×D₃	1	3	yes	—
564	C₂×C₈	—	3	3	no	—
565	C₂×C₈	—	3	1	no	—
566	C₂×C₈	—	3	3	no	—
567	C₂×C₈	—	3	3	no	—
568	C₂×C₈	—	3	3	no	—
569	C₂×C₈	C₂²×C₅×D₃	1	3	yes	—
570	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
571	C₂²×C₃	—	2	2	no	—
572	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
573	C₂×D₃	—	2	6	no	—
574	C₂×D₃	—	2	2	no	—
575	C₂×D₃	—	4	4	no	—
576	C₂×D₃	C₂²×C₅×D₄	1	3	yes	—
577	C₂×D₃	C₂²×C₅×D₄	1	1	yes	characteristic
578	C₃×C₄	—	2	6	no	—
579	C₃×C₄	C₂²×C₅×D₄	1	3	yes	—
580	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
581	Dic₃	—	2	6	no	—
582	Dic₃	C₂²×C₅×D₄	1	1	yes	characteristic
583	Dic₃	C₂²×C₅×D₄	1	3	yes	—
584	C₂×C₅	—	2	3	no	—
585	C₂×C₅	—	3	2	no	—
586	C₂×C₅	—	4	2	no	—
587	C₂×C₅	—	6	3	no	—
588	C₂×C₅	—	12	2	no	—
589	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
590	C₂³	—	3	3	no	—
591	C₂³	—	6	2	no	—
592	Q₈	—	2	6	no	—
593	Q₈	—	3	3	no	—
594	Q₈	—	3	6	no	—
595	Q₈	—	6	6	no	—
596	Q₈	—	6	12	no	—
597	Q₈	—	6	6	no	—
598	Q₈	C₅×D₃×D₄	1	1	yes	characteristic
599	Q₈	C₂³×C₅×D₃	1	6	yes	—
600	D₄	—	2	6	no	—
601	D₄	—	3	6	no	—
602	D₄	—	3	3	no	—
603	D₄	—	3	2	no	—
604	D₄	—	6	6	no	—
605	D₄	—	6	2	no	—
606	D₄	—	6	6	no	—
607	D₄	—	6	6	no	—
608	D₄	C₅×D₃×D₄	1	3	yes	—
609	D₄	C₂³×C₅×D₃	1	2	yes	—
610	C₂×C₄	—	2	6	no	—
611	C₂×C₄	—	2	6	no	—
612	C₂×C₄	—	3	3	no	—
613	C₂×C₄	—	3	3	no	—
614	C₂×C₄	—	3	3	no	—
615	C₂×C₄	—	3	1	no	—
616	C₂×C₄	—	3	3	no	—
617	C₂×C₄	—	6	6	no	—
618	C₂×C₄	—	6	6	no	—
619	C₂×C₄	—	6	12	no	—
620	C₂×C₄	—	6	6	no	—
621	C₂×C₄	—	6	6	no	—
622	C₂×C₄	—	6	6	no	—
623	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
624	C₈	—	3	1	no	—
625	C₈	—	3	3	no	—
626	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
627	C₈	C₂³×C₅×D₃	1	3	yes	—
628	C₂×C₃	—	2	3	no	—
629	C₂×C₃	—	4	2	no	—
630	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
631	D₃	—	2	3	no	—
632	D₃	—	4	2	no	—
633	D₃	C₅×#578	1	2	yes	direct product factor
634	C₅	D₃×#578	1	1	yes	characteristic, direct product factor, Sylow
635	C₂²	—	2	2	no	—
636	C₂²	—	3	1	no	—
637	C₂²	—	3	3	no	—
638	C₂²	—	6	6	no	—
639	C₂²	—	6	2	no	—
640	C₂²	—	12	4	no	—
641	C₂²	C₂×C₅×D₃×D₄	1	3	yes	—
642	C₄	—	2	6	no	—
643	C₄	—	3	1	no	—
644	C₄	—	3	3	no	—
645	C₄	—	6	6	no	—
646	C₄	C₂×C₅×D₃×D₄	1	3	yes	—
647	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
648	C₃	C₂×C₅×#578	1	1	yes	characteristic, complemented, Sylow
649	C₂	—	2	3	no	—
650	C₂	—	3	2	no	—
651	C₂	—	4	2	no	—
652	C₂	—	6	3	no	—
653	C₂	—	12	2	no	—
654	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#578	C₂
socle	C₂×C₃×C₅	C₂³×D₄
hypercenter	C₅×#578	D₃
hypocenter	C₃	C₂×C₅×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41 ◁ C₅×#578

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×2₋¹⁺⁴	C₂	semidirect
2. C₃×C₅×#578	C₂	semidirect
3. C₅×#5838	C₂	semidirect
4. C₅×#5779	C₂	semidirect
5. C₅×D₃×#137	C₂	semidirect
6. C₅×#5771	C₂	semidirect
7. C₅×D₃×#135	C₂	semidirect
8. C₅×#5766	C₂	semidirect
9. C₂×C₅×D₃×Q₁₆	C₂	semidirect
10. C₅×#5753	C₂	semidirect
11. C₅×D₃×#131	C₂	semidirect
13. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
15. C₅×#1010	C₂²	semidirect
16. C₅×#1010	C₂²	semidirect
21. C₅×#1007	C₂²	semidirect
24. C₃×C₅×#137	C₂²	semidirect
25. C₃×C₅×#135	C₂²	semidirect
26. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
27. C₃×C₅×#131	C₂²	semidirect
28. C₅×#951	C₂²	semidirect
29. C₅×#950	C₂²	semidirect
30. C₅×#948	C₂²	semidirect
31. C₂×C₅×#216	C₂²	semidirect
32. C₅×#942	C₂²	semidirect
33. C₅×#919	C₂²	semidirect
34. C₅×#918	C₂²	semidirect
37. C₅×D₃×Q₁₆	C₂²	semidirect
38. C₅×D₃×Q₁₆	C₂²	semidirect
39. C₅×#916	C₂²	semidirect
40. C₅×#915	C₂²	semidirect
42. C₅×#912	C₂²	semidirect
44. C₅×#909	C₂²	semidirect
45. C₅×#907	C₂²	semidirect
47. C₂×C₅×Dic₁₂	C₂²	semidirect
48. C₅×#904	C₂²	semidirect
49. C₅×#901	C₂²	semidirect
51. D₃×#578	C₅	direct (N × H)
58. C₅×#578	D₃	direct (N × H)
119. D₃×2₋¹⁺⁴	C₂×C₅	semidirect
120. C₃×#578	C₂×C₅	semidirect
121. #5838	C₂×C₅	semidirect
122. #5779	C₂×C₅	semidirect
123. D₃×#137	C₂×C₅	semidirect
124. #5771	C₂×C₅	semidirect
125. D₃×#135	C₂×C₅	semidirect
126. #5766	C₂×C₅	semidirect
127. C₂×D₃×Q₁₆	C₂×C₅	semidirect
128. #5753	C₂×C₅	semidirect
129. D₃×#131	C₂×C₅	semidirect
135. C₅×2₋¹⁺⁴	C₂×D₃	semidirect
146. C₅×#137	C₂×D₃	semidirect
152. C₅×#135	C₂×D₃	semidirect
159. C₂×C₅×Q₁₆	C₂×D₃	semidirect
165. C₅×#131	C₂×D₃	semidirect
207. C₃×2₋¹⁺⁴	C₂²×C₅	semidirect
209. #1010	C₂²×C₅	semidirect
210. #1010	C₂²×C₅	semidirect
215. #1007	C₂²×C₅	semidirect
218. C₃×#137	C₂²×C₅	semidirect
219. C₃×#135	C₂²×C₅	semidirect
220. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
221. C₃×#131	C₂²×C₅	semidirect
222. #951	C₂²×C₅	semidirect
223. #950	C₂²×C₅	semidirect
224. #948	C₂²×C₅	semidirect
225. C₂×#216	C₂²×C₅	semidirect
226. #942	C₂²×C₅	semidirect
227. #919	C₂²×C₅	semidirect
228. #918	C₂²×C₅	semidirect
231. D₃×Q₁₆	C₂²×C₅	semidirect
232. D₃×Q₁₆	C₂²×C₅	semidirect
233. #916	C₂²×C₅	semidirect
234. #915	C₂²×C₅	semidirect
236. #912	C₂²×C₅	semidirect
238. #909	C₂²×C₅	semidirect
239. #907	C₂²×C₅	semidirect
241. C₂×Dic₁₂	C₂²×C₅	semidirect
242. #904	C₂²×C₅	semidirect
243. #901	C₂²×C₅	semidirect
307. #578	C₅×D₃	direct (N × H)
424. 2₋¹⁺⁴	C₂×C₅×D₃	semidirect
435. #137	C₂×C₅×D₃	semidirect
441. #135	C₂×C₅×D₃	semidirect
448. C₂×Q₁₆	C₂×C₅×D₃	semidirect
454. #131	C₂×C₅×D₃	semidirect
462. C₅×D₃	#578	direct (N × H)
570. C₃×C₅	C₂×#578	semidirect
633. D₃	C₅×#578	direct (N × H)
634. C₅	D₃×#578	direct (N × H)
648. C₃	C₂×C₅×#578	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×2₋¹⁺⁴	2
C₃×C₅×#578	2
C₅×#5838	2
C₅×#5779	2
C₅×D₃×#137	2
C₅×#5771	2
C₅×D₃×#135	2
C₅×#5766	2
C₂×C₅×D₃×Q₁₆	2
C₅×#5753	2
C₅×D₃×#131	2
C₂×C₅×#578	3
D₃×#578	5

Subgroups — C5×D3×#578 #14510118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#578 #14510118