Subgroups — C₂×C₅×#5694 #14483415

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5694	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#894	C₂	1	2	yes	maximal
7	C₂×C₅×#892	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#890	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#552	—	3	1	no	maximal, Hall
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₅×#125	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
37	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
38	C₅×#898	C₂²	1	16	yes	complemented
39	C₅×#897	C₂²	1	8	yes	complemented
40	C₅×#897	C₂²	1	8	yes	complemented
41	C₅×#894	C₂²	1	16	yes	—
42	C₅×#892	C₂²	1	16	yes	complemented
43	C₅×#892	C₂²	1	8	yes	complemented
44	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
45	C₅×#890	C₂²	1	16	yes	complemented
46	C₄×C₅×D₁₂	C₂²	1	8	yes	—
47	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
48	C₂×#5694	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#552	—	3	16	no	—
50	C₂×C₅×#126	—	3	2	no	—
51	C₂×C₅×#125	—	3	2	no	—
52	C₂×C₅×#125	D₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#123	—	3	2	no	—
54	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
55	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
56	C₂×C₄×C₅×Q₈	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₅×#117	—	3	1	no	—
59	C₂×C₅×#117	—	3	2	no	—
60	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
61	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
69	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₅×D₁₂	—	2	4	no	—
73	C₂×C₅×D₁₂	C₂³	1	4	yes	—
74	C₂×C₄×C₅×D₃	—	2	8	no	—
75	C₂×C₄×C₅×D₃	—	2	4	no	—
76	C₂×C₄×C₅×D₃	—	2	4	no	—
77	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
78	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
79	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
80	C₂×C₅×Dic₆	—	2	4	no	—
81	C₂×C₅×Dic₆	C₂³	1	4	yes	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
86	C₃×C₄²×C₅	C₂³	1	4	yes	—
87	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
88	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
89	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
90	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
91	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
92	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
93	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
94	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
95	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
96	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
97	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
98	C₄×C₅×Dic₃	C₂³	1	8	yes	—
99	C₄×C₅×Dic₃	C₂³	1	8	yes	—
100	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
101	#5694	C₂×C₅	1	16	yes	direct product factor
102	C₂×#898	C₂×C₅	1	2	yes	complemented
103	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#894	C₂×C₅	1	2	yes	—
106	C₂×#892	C₂×C₅	1	2	yes	complemented
107	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#890	C₂×C₅	1	2	yes	complemented
110	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
111	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂²×C₅×Q₈	—	3	1	no	—
113	C₂²×C₅×D₄	—	3	1	no	—
114	C₂³×C₄×C₅	—	3	2	no	—
115	C₂³×C₄×C₅	—	3	1	no	—
116	C₂³×C₄×C₅	—	3	1	no	—
117	C₅×#126	—	3	16	no	—
118	C₅×#125	—	3	16	no	—
119	C₅×#125	C₂×D₃	1	8	yes	complemented
120	C₅×#123	—	3	16	no	—
121	C₅×C₂²⋊Q₈	—	3	8	no	—
122	C₅×C₂²⋊Q₈	—	3	8	no	—
123	C₄×C₅×Q₈	—	3	8	no	—
124	C₄×C₅×D₄	—	3	8	no	—
125	C₅×#117	—	3	8	no	—
126	C₅×#117	—	3	16	no	—
127	C₂×C₅×C₄⋊C₄	—	3	2	no	—
128	C₂×C₅×C₄⋊C₄	—	3	2	no	—
129	C₂×C₅×C₄⋊C₄	—	3	1	no	—
130	C₂×C₅×C₄⋊C₄	—	3	2	no	—
131	C₂×C₅×C₄⋊C₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	—	3	2	no	—
133	C₂×C₅×C₄⋊C₄	—	3	8	no	—
134	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
137	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
138	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
139	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
141	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
143	C₂×C₄²×C₅	—	3	2	no	—
144	C₂×C₄²×C₅	—	3	2	no	—
145	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
146	C₂×#552	—	3	1	no	Sylow
147	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
148	C₂²×C₅×D₃	—	2	2	no	—
149	C₂²×C₅×D₃	—	2	2	no	—
150	C₂²×C₅×D₃	—	2	2	no	—
151	C₂²×C₅×D₃	—	2	2	no	—
152	C₂²×C₅×D₃	—	2	2	no	—
153	C₂²×C₅×D₃	#41	1	4	yes	—
154	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
155	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
156	C₂×C₃×C₄×C₅	—	2	4	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	4	no	—
160	C₂×C₃×C₄×C₅	#41	1	4	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
166	C₂×C₅×Dic₃	—	2	4	no	—
167	C₂×C₅×Dic₃	—	2	2	no	—
168	C₂×C₅×Dic₃	—	2	2	no	—
169	C₂×C₅×Dic₃	—	2	4	no	—
170	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
171	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
174	C₅×D₁₂	—	2	8	no	—
175	C₄×C₅×D₃	—	2	16	no	—
176	C₄×C₅×D₃	—	2	8	no	—
177	C₄×C₅×D₃	—	2	8	no	—
178	C₅×Dic₆	—	2	8	no	—
179	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
180	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
181	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
183	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
184	C₃×#125	C₂²×C₅	1	8	yes	complemented
185	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
189	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
190	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
198	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
199	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
201	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
202	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
203	#898	C₂²×C₅	1	16	yes	complemented
204	#897	C₂²×C₅	1	8	yes	complemented
205	#897	C₂²×C₅	1	8	yes	complemented
206	#894	C₂²×C₅	1	16	yes	—
207	#892	C₂²×C₅	1	16	yes	complemented
208	#892	C₂²×C₅	1	8	yes	complemented
209	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
210	#890	C₂²×C₅	1	16	yes	complemented
211	C₄×D₁₂	C₂²×C₅	1	8	yes	—
212	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
213	C₂⁴×C₅	—	3	1	no	—
214	C₂⁴×C₅	—	3	1	no	—
215	C₂×C₅×Q₈	—	3	4	no	—
216	C₂×C₅×Q₈	—	6	4	no	—
217	C₂×C₅×D₄	—	3	4	no	—
218	C₂×C₅×D₄	—	6	4	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	2	no	—
221	C₂²×C₄×C₅	—	3	2	no	—
222	C₂²×C₄×C₅	—	3	1	no	—
223	C₂²×C₄×C₅	—	3	8	no	—
224	C₂²×C₄×C₅	—	3	4	no	—
225	C₂²×C₄×C₅	—	3	4	no	—
226	C₂²×C₄×C₅	—	6	8	no	—
227	C₂²×C₄×C₅	—	6	4	no	—
228	C₂²×C₄×C₅	—	6	4	no	—
229	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
231	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
233	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
234	C₅×C₄⋊C₄	—	3	4	no	—
235	C₅×C₄⋊C₄	—	3	8	no	—
236	C₅×C₄⋊C₄	—	3	8	no	—
237	C₅×C₄⋊C₄	—	3	4	no	—
238	C₅×C₄⋊C₄	—	3	8	no	—
239	C₅×C₄⋊C₄	—	3	8	no	—
240	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
241	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
242	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
243	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
244	C₅×C₂²⋊C₄	—	3	4	no	—
245	C₅×C₂²⋊C₄	—	3	8	no	—
246	C₅×C₂²⋊C₄	—	3	8	no	—
247	C₅×C₂²⋊C₄	—	3	4	no	—
248	C₅×C₂²⋊C₄	—	3	8	no	—
249	C₄²×C₅	—	3	8	no	—
250	C₄²×C₅	—	3	8	no	—
251	C₄²×C₅	C₂²×D₃	1	4	yes	—
252	#552	—	3	16	no	—
253	C₂×#126	—	3	2	no	—
254	C₂×#125	—	3	2	no	—
255	C₂×#125	C₅×D₃	1	1	yes	characteristic, complemented
256	C₂×#123	—	3	2	no	—
257	C₂×C₂²⋊Q₈	—	3	1	no	—
258	C₂×C₂²⋊Q₈	—	3	1	no	—
259	C₂×C₄×Q₈	—	3	1	no	—
260	C₂×C₄×D₄	—	3	1	no	—
261	C₂×#117	—	3	1	no	—
262	C₂×#117	—	3	2	no	—
263	C₂²×C₄⋊C₄	—	3	1	no	—
264	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
265	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
266	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
267	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
268	C₂×C₅×D₃	—	2	8	no	—
269	C₂×C₅×D₃	—	2	2	no	—
270	C₂×C₅×D₃	—	2	2	no	—
271	C₂×C₅×D₃	—	2	2	no	—
272	C₂×C₅×D₃	—	2	2	no	—
273	C₂×C₅×D₃	—	2	2	no	—
274	C₂×C₅×D₃	—	4	4	no	—
275	C₂×C₅×D₃	C₂×#41	1	4	yes	—
276	C₃×C₄×C₅	—	2	4	no	—
277	C₃×C₄×C₅	—	2	2	no	—
278	C₃×C₄×C₅	—	2	2	no	—
279	C₃×C₄×C₅	—	2	4	no	—
280	C₃×C₄×C₅	C₂×#41	1	4	yes	—
281	C₅×Dic₃	—	2	4	no	—
282	C₅×Dic₃	—	2	2	no	—
283	C₅×Dic₃	—	2	2	no	—
284	C₅×Dic₃	—	2	4	no	—
285	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
286	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
289	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
291	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
292	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
293	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
294	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
295	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
296	C₂×D₁₂	—	2	4	no	—
297	C₂×D₁₂	C₂³×C₅	1	4	yes	—
298	C₂×C₄×D₃	—	2	8	no	—
299	C₂×C₄×D₃	—	2	4	no	—
300	C₂×C₄×D₃	—	2	4	no	—
301	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
302	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
303	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
304	C₂×Dic₆	—	2	4	no	—
305	C₂×Dic₆	C₂³×C₅	1	4	yes	—
306	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
307	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
308	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
309	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
310	C₃×C₄²	C₂³×C₅	1	4	yes	—
311	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
312	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
313	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
314	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
315	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
316	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
317	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
318	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
319	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
320	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
321	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
322	C₄×Dic₃	C₂³×C₅	1	8	yes	—
323	C₄×Dic₃	C₂³×C₅	1	8	yes	—
324	C₂³×C₅	—	3	4	no	—
325	C₂³×C₅	—	3	2	no	—
326	C₂³×C₅	—	3	2	no	—
327	C₂³×C₅	—	6	2	no	—
328	C₂³×C₅	—	6	2	no	—
329	C₂³×C₅	—	6	2	no	—
330	C₂³×C₅	—	6	2	no	—
331	C₂³×C₅	—	6	2	no	—
332	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×Q₈	—	6	8	no	—
334	C₅×D₄	—	6	8	no	—
335	C₂×C₄×C₅	—	2	4	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	3	2	no	—
340	C₂×C₄×C₅	—	3	4	no	—
341	C₂×C₄×C₅	—	3	4	no	—
342	C₂×C₄×C₅	—	3	2	no	—
343	C₂×C₄×C₅	—	6	16	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	—	6	4	no	—
347	C₂×C₄×C₅	—	6	4	no	—
348	C₂×C₄×C₅	—	6	8	no	—
349	C₂×C₄×C₅	—	6	8	no	—
350	C₂×C₄×C₅	#239	1	4	yes	—
351	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
352	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
353	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
354	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
355	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
356	C₂²×Q₈	—	3	1	no	—
357	C₂²×D₄	—	3	1	no	—
358	C₂³×C₄	—	3	2	no	—
359	C₂³×C₄	—	3	1	no	—
360	C₂³×C₄	—	3	1	no	—
361	#126	—	3	16	no	—
362	#125	—	3	16	no	—
363	#125	C₂×C₅×D₃	1	8	yes	complemented
364	#123	—	3	16	no	—
365	C₂²⋊Q₈	—	3	8	no	—
366	C₂²⋊Q₈	—	3	8	no	—
367	C₄×Q₈	—	3	8	no	—
368	C₄×D₄	—	3	8	no	—
369	#117	—	3	8	no	—
370	#117	—	3	16	no	—
371	C₂×C₄⋊C₄	—	3	1	no	—
372	C₂×C₄⋊C₄	—	3	2	no	—
373	C₂×C₄⋊C₄	—	3	2	no	—
374	C₂×C₄⋊C₄	—	3	1	no	—
375	C₂×C₄⋊C₄	—	3	2	no	—
376	C₂×C₄⋊C₄	—	3	2	no	—
377	C₂×C₄⋊C₄	—	3	8	no	—
378	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
382	C₂×C₂²⋊C₄	—	3	1	no	—
383	C₂×C₂²⋊C₄	—	3	2	no	—
384	C₂×C₂²⋊C₄	—	3	2	no	—
385	C₂×C₂²⋊C₄	—	3	1	no	—
386	C₂×C₂²⋊C₄	—	3	2	no	—
387	C₂×C₄²	—	3	2	no	—
388	C₂×C₄²	—	3	2	no	—
389	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
390	C₂×C₃×C₅	#552	1	4	yes	complemented
391	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
392	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
393	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
394	C₅×D₃	—	2	4	no	—
395	C₅×D₃	—	4	2	no	—
396	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
397	C₂²×D₃	—	2	2	no	—
398	C₂²×D₃	—	2	2	no	—
399	C₂²×D₃	—	2	2	no	—
400	C₂²×D₃	—	2	2	no	—
401	C₂²×D₃	—	2	2	no	—
402	C₂²×D₃	C₅×#41	1	4	yes	—
403	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
404	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
405	C₂×C₃×C₄	—	2	4	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	C₅×#41	1	4	yes	—
410	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
411	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
412	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
413	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
415	C₂×Dic₃	—	2	4	no	—
416	C₂×Dic₃	—	2	2	no	—
417	C₂×Dic₃	—	2	2	no	—
418	C₂×Dic₃	—	2	4	no	—
419	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
420	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
421	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
422	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
423	D₁₂	—	2	8	no	—
424	C₄×D₃	—	2	16	no	—
425	C₄×D₃	—	2	8	no	—
426	C₄×D₃	—	2	8	no	—
427	Dic₆	—	2	8	no	—
428	C₂²×C₅	—	3	4	no	—
429	C₂²×C₅	—	6	8	no	—
430	C₂²×C₅	—	6	2	no	—
431	C₂²×C₅	—	6	2	no	—
432	C₂²×C₅	—	6	2	no	—
433	C₂²×C₅	—	6	2	no	—
434	C₂²×C₅	—	6	2	no	—
435	C₂²×C₅	—	12	4	no	—
436	C₂²×C₅	C₂×#239	1	2	yes	—
437	C₂²×C₅	D₃×#41	1	2	yes	—
438	C₂²×C₅	#1010	1	2	yes	—
439	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
440	C₄×C₅	—	2	4	no	—
441	C₄×C₅	—	2	2	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	4	no	—
444	C₄×C₅	—	6	2	no	—
445	C₄×C₅	—	6	2	no	—
446	C₄×C₅	—	6	4	no	—
447	C₄×C₅	—	6	4	no	—
448	C₄×C₅	C₂×#239	1	4	yes	—
449	C₂⁴	—	3	1	no	—
450	C₂⁴	—	3	1	no	—
451	C₂×Q₈	—	3	4	no	—
452	C₂×Q₈	—	6	4	no	—
453	C₂×D₄	—	3	4	no	—
454	C₂×D₄	—	6	4	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	2	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	8	no	—
460	C₂²×C₄	—	3	4	no	—
461	C₂²×C₄	—	3	4	no	—
462	C₂²×C₄	—	6	8	no	—
463	C₂²×C₄	—	6	4	no	—
464	C₂²×C₄	—	6	4	no	—
465	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
467	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
469	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₄⋊C₄	—	3	4	no	—
471	C₄⋊C₄	—	3	8	no	—
472	C₄⋊C₄	—	3	8	no	—
473	C₄⋊C₄	—	3	4	no	—
474	C₄⋊C₄	—	3	8	no	—
475	C₄⋊C₄	—	3	8	no	—
476	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
477	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
478	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
479	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
480	C₂²⋊C₄	—	3	4	no	—
481	C₂²⋊C₄	—	3	8	no	—
482	C₂²⋊C₄	—	3	8	no	—
483	C₂²⋊C₄	—	3	4	no	—
484	C₂²⋊C₄	—	3	8	no	—
485	C₄²	—	3	8	no	—
486	C₄²	—	3	8	no	—
487	C₄²	C₂²×C₅×D₃	1	4	yes	—
488	C₃×C₅	C₂×#552	1	1	yes	characteristic, complemented, Hall
489	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
490	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
491	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
492	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
493	C₂×D₃	—	2	8	no	—
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	2	2	no	—
496	C₂×D₃	—	2	2	no	—
497	C₂×D₃	—	2	2	no	—
498	C₂×D₃	—	2	2	no	—
499	C₂×D₃	—	4	4	no	—
500	C₂×D₃	C₂×C₅×#41	1	4	yes	—
501	C₃×C₄	—	2	4	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	2	4	no	—
505	C₃×C₄	C₂×C₅×#41	1	4	yes	—
506	Dic₃	—	2	4	no	—
507	Dic₃	—	2	2	no	—
508	Dic₃	—	2	2	no	—
509	Dic₃	—	2	4	no	—
510	C₂×C₅	—	6	4	no	—
511	C₂×C₅	—	12	2	no	—
512	C₂×C₅	#5694	1	4	yes	direct product factor
513	C₂×C₅	C₂²×#239	1	1	yes	characteristic
514	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
515	C₂×C₅	C₂×#1010	1	1	yes	characteristic
516	C₂³	—	3	4	no	—
517	C₂³	—	3	2	no	—
518	C₂³	—	3	2	no	—
519	C₂³	—	6	2	no	—
520	C₂³	—	6	2	no	—
521	C₂³	—	6	2	no	—
522	C₂³	—	6	2	no	—
523	C₂³	—	6	2	no	—
524	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
525	Q₈	—	6	8	no	—
526	D₄	—	6	8	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	3	2	no	—
532	C₂×C₄	—	3	4	no	—
533	C₂×C₄	—	3	4	no	—
534	C₂×C₄	—	3	2	no	—
535	C₂×C₄	—	6	16	no	—
536	C₂×C₄	—	6	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	4	no	—
539	C₂×C₄	—	6	4	no	—
540	C₂×C₄	—	6	8	no	—
541	C₂×C₄	—	6	8	no	—
542	C₂×C₄	C₅×#239	1	4	yes	—
543	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
544	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
545	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
546	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
547	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
548	C₂×C₃	C₅×#552	1	4	yes	complemented
549	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
550	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
551	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
552	D₃	—	2	4	no	—
553	D₃	—	4	2	no	—
554	C₅	C₂×#5694	1	1	yes	characteristic, direct product factor, Sylow
555	C₂²	—	3	4	no	—
556	C₂²	—	6	8	no	—
557	C₂²	—	6	2	no	—
558	C₂²	—	6	2	no	—
559	C₂²	—	6	2	no	—
560	C₂²	—	6	2	no	—
561	C₂²	—	6	2	no	—
562	C₂²	—	12	4	no	—
563	C₂²	C₂×C₅×#239	1	2	yes	—
564	C₂²	C₅×D₃×#41	1	2	yes	—
565	C₂²	C₅×#1010	1	2	yes	—
566	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
567	C₄	—	2	4	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	4	no	—
571	C₄	—	6	2	no	—
572	C₄	—	6	2	no	—
573	C₄	—	6	4	no	—
574	C₄	—	6	4	no	—
575	C₄	C₂×C₅×#239	1	4	yes	—
576	C₃	C₂×C₅×#552	1	1	yes	characteristic, complemented, Sylow
577	C₂	—	6	4	no	—
578	C₂	—	12	2	no	—
579	C₂	C₅×#5694	1	4	yes	direct product factor
580	C₂	C₂²×C₅×#239	1	1	yes	characteristic
581	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
582	C₂	C₂×C₅×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×#125	D₃
hypocenter	C₃	C₂×C₅×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₅×#5694	C₂	direct (N × H)
3. C₂×C₅×#898	C₂	semidirect
4. C₂×C₅×#897	C₂	semidirect
5. C₂×C₅×#897	C₂	semidirect
7. C₂×C₅×#892	C₂	semidirect
8. C₂×C₅×#892	C₂	semidirect
9. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
10. C₂×C₅×#890	C₂	semidirect
12. C₂×C₄×C₅×Dic₆	C₂	semidirect
19. C₃×C₅×#125	C₂²	semidirect
38. C₅×#898	C₂²	semidirect
39. C₅×#897	C₂²	semidirect
40. C₅×#897	C₂²	semidirect
42. C₅×#892	C₂²	semidirect
43. C₅×#892	C₂²	semidirect
44. C₅×D₃×C₄⋊C₄	C₂²	semidirect
45. C₅×#890	C₂²	semidirect
47. C₄×C₅×Dic₆	C₂²	semidirect
48. C₂×#5694	C₅	direct (N × H)
52. C₂×C₅×#125	D₃	semidirect
100. C₂×C₃×#125	C₂×C₅	semidirect
101. #5694	C₂×C₅	direct (N × H)
102. C₂×#898	C₂×C₅	semidirect
103. C₂×#897	C₂×C₅	semidirect
104. C₂×#897	C₂×C₅	semidirect
106. C₂×#892	C₂×C₅	semidirect
107. C₂×#892	C₂×C₅	semidirect
108. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
109. C₂×#890	C₂×C₅	semidirect
111. C₂×C₄×Dic₆	C₂×C₅	semidirect
119. C₅×#125	C₂×D₃	semidirect
184. C₃×#125	C₂²×C₅	semidirect
203. #898	C₂²×C₅	semidirect
204. #897	C₂²×C₅	semidirect
205. #897	C₂²×C₅	semidirect
207. #892	C₂²×C₅	semidirect
208. #892	C₂²×C₅	semidirect
209. D₃×C₄⋊C₄	C₂²×C₅	semidirect
210. #890	C₂²×C₅	semidirect
212. C₄×Dic₆	C₂²×C₅	semidirect
255. C₂×#125	C₅×D₃	semidirect
363. #125	C₂×C₅×D₃	semidirect
390. C₂×C₃×C₅	#552	semidirect
488. C₃×C₅	C₂×#552	semidirect
512. C₂×C₅	#5694	direct (N × H)
548. C₂×C₃	C₅×#552	semidirect
554. C₅	C₂×#5694	direct (N × H)
576. C₃	C₂×C₅×#552	semidirect
579. C₂	C₅×#5694	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#125	2
C₅×#5694	2
C₂×C₅×#898	2
C₂×C₅×#897	2
C₂×C₅×#894	2
C₂×C₅×#892	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#890	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#552	3
C₂×#5694	5

Subgroups — C2×C5×#5694 #14483415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5694 #14483415