Subgroups — C₂×C₅×#5597 #14480560

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#237	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5597	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#537	—	3	1	no	maximal, Hall
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	C₂²	1	2	yes	—
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×#67	C₂²	1	2	yes	—
18	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
19	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#237	—	2	16	no	—
22	C₂×C₅×#237	C₂²	1	16	yes	complemented
23	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
25	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
26	C₃×C₅×#121	C₂²	1	8	yes	complemented
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×#217	C₂²	1	2	yes	—
30	C₅×#939	C₂²	1	16	yes	complemented
31	C₅×#939	C₂²	1	16	yes	complemented
32	C₅×#930	C₂²	1	8	yes	complemented
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	complemented
40	C₅×#896	C₂²	1	16	yes	complemented
41	C₅×#884	C₂²	1	16	yes	complemented
42	C₅×#878	C₂²	1	16	yes	complemented
43	C₂×#5597	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂²×C₅×#41	—	3	2	no	—
45	C₅×#537	—	3	16	no	—
46	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
47	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
48	C₂×C₅×#121	—	3	2	no	—
49	C₂×C₅×#121	—	3	2	no	—
50	C₂×C₅×#121	—	3	1	no	—
51	C₂×C₅×#121	—	3	2	no	—
52	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
53	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
54	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
55	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
56	C₂³×C₅×D₃	C₂³	1	2	yes	—
57	C₂×C₃×C₅×D₄	—	2	8	no	—
58	C₂×C₃×C₅×D₄	—	4	2	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
60	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	—	4	2	no	—
62	C₂²×C₃×C₄×C₅	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	4	yes	—
66	C₂×C₅×#67	—	2	8	no	—
67	C₂×C₅×#67	—	2	8	no	—
68	C₂×C₅×#67	—	4	4	no	—
69	C₂×C₅×#67	C₂³	1	8	yes	—
70	C₂×C₅×#67	C₂³	1	8	yes	—
71	C₂×C₅×#67	C₂³	1	8	yes	—
72	C₂²×C₅×Dic₃	—	2	8	no	—
73	C₂²×C₅×Dic₃	—	4	2	no	—
74	C₂²×C₅×Dic₃	D₄	1	8	yes	complemented
75	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
76	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
77	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
78	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
79	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
80	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
81	C₅×#237	—	2	64	no	—
82	C₂×C₅×D₁₂	—	4	2	no	—
83	C₂×C₅×D₁₂	C₂³	1	4	yes	—
84	C₂×C₄×C₅×D₃	—	2	8	no	—
85	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
86	C₂×C₅×Dic₆	—	2	8	no	—
87	C₂×C₅×Dic₆	C₂³	1	8	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₅×#217	C₂³	1	8	yes	—
91	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
93	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
94	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
95	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
96	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
97	C₂²×#237	C₂×C₅	1	2	yes	complemented
98	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×#939	C₂×C₅	1	2	yes	complemented
100	C₂×#939	C₂×C₅	1	2	yes	complemented
101	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
103	#5597	C₂×C₅	1	16	yes	direct product factor
104	C₂×#896	C₂×C₅	1	2	yes	complemented
105	C₂×#884	C₂×C₅	1	2	yes	complemented
106	C₂×#878	C₂×C₅	1	2	yes	complemented
107	C₂×C₅×#41	—	3	16	no	—
108	C₂×C₅×#41	—	6	16	no	—
109	C₂²×C₅×Q₈	—	3	2	no	—
110	C₂²×C₅×D₄	—	3	2	no	—
111	C₂²×C₅×D₄	—	3	2	no	—
112	C₂²×C₅×D₄	—	3	2	no	—
113	C₂²×C₅×D₄	—	3	1	no	—
114	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
115	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
116	C₂³×C₄×C₅	—	3	1	no	—
117	C₂³×C₄×C₅	—	3	2	no	—
118	C₂³×C₄×C₅	—	3	1	no	—
119	C₂³×C₄×C₅	—	3	2	no	—
120	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
121	C₅×C₂²⋊Q₈	—	3	16	no	—
122	C₅×C₂²⋊Q₈	—	3	16	no	—
123	C₅×#121	—	3	16	no	—
124	C₅×#121	—	3	16	no	—
125	C₅×#121	—	3	8	no	—
126	C₅×#121	—	3	16	no	—
127	C₅×#121	C₂×D₃	1	8	yes	complemented
128	C₂×C₅×C₄⋊C₄	—	3	2	no	—
129	C₂×C₅×C₄⋊C₄	—	3	2	no	—
130	C₂×C₅×C₄⋊C₄	—	3	2	no	—
131	C₂×C₅×C₄⋊C₄	—	3	8	no	—
132	C₂×C₅×C₄⋊C₄	—	3	1	no	—
133	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
135	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
136	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
137	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
138	C₂×#537	—	3	1	no	Sylow
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	4	no	—
142	C₂³×C₃×C₅	—	2	4	no	—
143	C₂³×C₃×C₅	—	2	4	no	—
144	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
145	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
146	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
147	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
148	C₂²×C₅×D₃	—	2	4	no	—
149	C₂²×C₅×D₃	—	2	4	no	—
150	C₂²×C₅×D₃	—	2	4	no	—
151	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
152	C₃×C₅×D₄	—	2	16	no	—
153	C₃×C₅×D₄	—	4	4	no	—
154	C₂×C₃×C₄×C₅	—	2	4	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	4	4	no	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
161	C₅×#67	—	2	16	no	—
162	C₅×#67	—	2	16	no	—
163	C₅×#67	—	4	8	no	—
164	C₂×C₅×Dic₃	—	2	4	no	—
165	C₂×C₅×Dic₃	—	2	4	no	—
166	C₂×C₅×Dic₃	—	2	16	no	—
167	C₂×C₅×Dic₃	—	4	4	no	—
168	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
169	C₂×C₅×Dic₃	C₂×D₄	1	16	yes	complemented
170	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
171	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
173	C₅×D₁₂	—	4	4	no	—
174	C₄×C₅×D₃	—	2	16	no	—
175	C₅×Dic₆	—	2	16	no	—
176	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
177	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
178	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
179	C₂²×#67	C₂²×C₅	1	2	yes	—
180	C₂²×#67	C₂²×C₅	1	2	yes	—
181	C₂²×#67	C₂²×C₅	1	2	yes	—
182	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
183	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
184	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
185	C₂×#237	—	2	16	no	—
186	C₂×#237	C₂²×C₅	1	16	yes	complemented
187	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
188	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
189	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
190	C₃×#121	C₂²×C₅	1	8	yes	complemented
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×#217	C₂²×C₅	1	2	yes	—
194	#939	C₂²×C₅	1	16	yes	complemented
195	#939	C₂²×C₅	1	16	yes	complemented
196	#930	C₂²×C₅	1	8	yes	complemented
197	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
200	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
201	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
202	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
203	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	complemented
204	#896	C₂²×C₅	1	16	yes	complemented
205	#884	C₂²×C₅	1	16	yes	complemented
206	#878	C₂²×C₅	1	16	yes	complemented
207	C₂⁴×C₅	—	3	2	no	—
208	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
209	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₅×#41	—	6	64	no	—
211	C₂×C₅×Q₈	—	3	8	no	—
212	C₂×C₅×Q₈	—	6	8	no	—
213	C₂×C₅×D₄	—	2	8	no	—
214	C₂×C₅×D₄	—	3	8	no	—
215	C₂×C₅×D₄	—	3	8	no	—
216	C₂×C₅×D₄	—	3	8	no	—
217	C₂×C₅×D₄	—	3	4	no	—
218	C₂×C₅×D₄	—	4	2	no	—
219	C₂×C₅×D₄	—	6	8	no	—
220	C₂×C₅×D₄	—	6	8	no	—
221	C₂×C₅×D₄	—	12	2	no	—
222	C₂×C₅×D₄	—	12	4	no	—
223	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
224	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
225	C₂²×C₄×C₅	—	3	8	no	—
226	C₂²×C₄×C₅	—	3	4	no	—
227	C₂²×C₄×C₅	—	3	2	no	—
228	C₂²×C₄×C₅	—	3	8	no	—
229	C₂²×C₄×C₅	—	3	2	no	—
230	C₂²×C₄×C₅	—	3	2	no	—
231	C₂²×C₄×C₅	—	3	4	no	—
232	C₂²×C₄×C₅	—	3	8	no	—
233	C₂²×C₄×C₅	—	4	2	no	—
234	C₂²×C₄×C₅	—	6	8	no	—
235	C₂²×C₄×C₅	—	6	8	no	—
236	C₂²×C₄×C₅	—	12	2	no	—
237	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
239	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
241	C₅×C₄⋊C₄	—	3	8	no	—
242	C₅×C₄⋊C₄	—	3	8	no	—
243	C₅×C₄⋊C₄	—	3	8	no	—
244	C₅×C₄⋊C₄	—	3	4	no	—
245	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
246	C₅×C₂²⋊C₄	—	3	8	no	—
247	C₅×C₂²⋊C₄	—	3	8	no	—
248	C₅×C₂²⋊C₄	—	3	8	no	—
249	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
250	C₂²×#41	—	3	2	no	—
251	#537	—	3	16	no	—
252	C₂×C₂²⋊Q₈	—	3	2	no	—
253	C₂×C₂²⋊Q₈	—	3	2	no	—
254	C₂×#121	—	3	2	no	—
255	C₂×#121	—	3	2	no	—
256	C₂×#121	—	3	1	no	—
257	C₂×#121	—	3	2	no	—
258	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
259	C₂²×C₄⋊C₄	—	3	1	no	—
260	C₂²×C₃×C₅	—	2	8	no	—
261	C₂²×C₃×C₅	—	2	2	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	—	2	4	no	—
264	C₂²×C₃×C₅	—	2	4	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	4	8	no	—
267	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
268	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
269	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
270	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
271	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
272	C₂×C₅×D₃	—	2	4	no	—
273	C₂×C₅×D₃	—	2	4	no	—
274	C₂×C₅×D₃	—	2	4	no	—
275	C₂×C₅×D₃	—	4	8	no	—
276	C₃×C₄×C₅	—	2	4	no	—
277	C₃×C₄×C₅	—	2	2	no	—
278	C₃×C₄×C₅	—	2	2	no	—
279	C₅×Dic₃	—	2	4	no	—
280	C₅×Dic₃	—	2	4	no	—
281	C₅×Dic₃	C₂²×D₄	1	8	yes	—
282	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
283	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
284	C₂³×D₃	C₂³×C₅	1	2	yes	—
285	C₂×C₃×D₄	—	2	8	no	—
286	C₂×C₃×D₄	—	4	2	no	—
287	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
288	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
289	C₂²×C₃×C₄	—	4	2	no	—
290	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
293	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
294	C₂×#67	—	2	8	no	—
295	C₂×#67	—	2	8	no	—
296	C₂×#67	—	4	4	no	—
297	C₂×#67	C₂³×C₅	1	8	yes	—
298	C₂×#67	C₂³×C₅	1	8	yes	—
299	C₂×#67	C₂³×C₅	1	8	yes	—
300	C₂²×Dic₃	—	2	8	no	—
301	C₂²×Dic₃	—	4	2	no	—
302	C₂²×Dic₃	C₅×D₄	1	8	yes	complemented
303	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
304	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
305	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
306	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
307	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
308	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
309	#237	—	2	64	no	—
310	C₂×D₁₂	—	4	2	no	—
311	C₂×D₁₂	C₂³×C₅	1	4	yes	—
312	C₂×C₄×D₃	—	2	8	no	—
313	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
314	C₂×Dic₆	—	2	8	no	—
315	C₂×Dic₆	C₂³×C₅	1	8	yes	—
316	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
317	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
318	#217	C₂³×C₅	1	8	yes	—
319	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
320	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
321	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
322	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
323	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
324	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
325	C₂³×C₅	—	2	2	no	—
326	C₂³×C₅	—	2	2	no	—
327	C₂³×C₅	—	2	4	no	—
328	C₂³×C₅	—	2	4	no	—
329	C₂³×C₅	—	2	4	no	—
330	C₂³×C₅	—	3	4	no	—
331	C₂³×C₅	—	6	4	no	—
332	C₂³×C₅	—	6	4	no	—
333	C₂³×C₅	—	6	4	no	—
334	C₂³×C₅	D₃×D₄	1	4	yes	—
335	C₂³×C₅	C₂³×D₃	1	4	yes	—
336	C₂³×C₅	C₂³×D₃	1	2	yes	—
337	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
338	C₅×Q₈	—	6	16	no	—
339	C₅×D₄	—	2	16	no	—
340	C₅×D₄	—	4	4	no	—
341	C₅×D₄	—	6	16	no	—
342	C₅×D₄	—	6	16	no	—
343	C₅×D₄	—	12	4	no	—
344	C₅×D₄	—	12	8	no	—
345	C₂×C₄×C₅	—	2	4	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	3	8	no	—
349	C₂×C₄×C₅	—	3	16	no	—
350	C₂×C₄×C₅	—	3	4	no	—
351	C₂×C₄×C₅	—	3	4	no	—
352	C₂×C₄×C₅	—	3	4	no	—
353	C₂×C₄×C₅	—	4	4	no	—
354	C₂×C₄×C₅	—	6	16	no	—
355	C₂×C₄×C₅	—	6	16	no	—
356	C₂×C₄×C₅	—	6	4	no	—
357	C₂×C₄×C₅	—	6	4	no	—
358	C₂×C₄×C₅	—	12	4	no	—
359	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
360	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
361	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
362	C₂×#41	—	3	16	no	—
363	C₂×#41	—	6	16	no	—
364	C₂²×Q₈	—	3	2	no	—
365	C₂²×D₄	—	3	2	no	—
366	C₂²×D₄	—	3	2	no	—
367	C₂²×D₄	—	3	2	no	—
368	C₂²×D₄	—	3	1	no	—
369	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
370	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
371	C₂³×C₄	—	3	1	no	—
372	C₂³×C₄	—	3	2	no	—
373	C₂³×C₄	—	3	1	no	—
374	C₂³×C₄	—	3	2	no	—
375	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
376	C₂²⋊Q₈	—	3	16	no	—
377	C₂²⋊Q₈	—	3	16	no	—
378	#121	—	3	16	no	—
379	#121	—	3	16	no	—
380	#121	—	3	8	no	—
381	#121	—	3	16	no	—
382	#121	C₂×C₅×D₃	1	8	yes	complemented
383	C₂×C₄⋊C₄	—	3	2	no	—
384	C₂×C₄⋊C₄	—	3	2	no	—
385	C₂×C₄⋊C₄	—	3	8	no	—
386	C₂×C₄⋊C₄	—	3	2	no	—
387	C₂×C₄⋊C₄	—	3	1	no	—
388	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	3	2	no	—
390	C₂×C₂²⋊C₄	—	3	2	no	—
391	C₂×C₂²⋊C₄	—	3	2	no	—
392	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
393	C₂×C₃×C₅	—	2	4	no	—
394	C₂×C₃×C₅	—	4	4	no	—
395	C₂×C₃×C₅	#537	1	4	yes	complemented
396	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
397	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
399	C₅×D₃	—	4	4	no	—
400	C₂³×C₃	—	2	2	no	—
401	C₂³×C₃	—	2	2	no	—
402	C₂³×C₃	—	2	4	no	—
403	C₂³×C₃	—	2	4	no	—
404	C₂³×C₃	—	2	4	no	—
405	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
406	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
407	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
408	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
409	C₂²×D₃	—	2	4	no	—
410	C₂²×D₃	—	2	4	no	—
411	C₂²×D₃	—	2	4	no	—
412	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
413	C₃×D₄	—	2	16	no	—
414	C₃×D₄	—	4	4	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	4	4	no	—
419	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
420	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
421	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
422	#67	—	2	16	no	—
423	#67	—	2	16	no	—
424	#67	—	4	8	no	—
425	C₂×Dic₃	—	2	4	no	—
426	C₂×Dic₃	—	2	4	no	—
427	C₂×Dic₃	—	2	16	no	—
428	C₂×Dic₃	—	4	4	no	—
429	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
430	C₂×Dic₃	C₂×C₅×D₄	1	16	yes	complemented
431	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
432	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
433	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
434	D₁₂	—	4	4	no	—
435	C₄×D₃	—	2	16	no	—
436	Dic₆	—	2	16	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	2	8	no	—
440	C₂²×C₅	—	2	4	no	—
441	C₂²×C₅	—	2	4	no	—
442	C₂²×C₅	—	2	4	no	—
443	C₂²×C₅	—	4	8	no	—
444	C₂²×C₅	—	6	4	no	—
445	C₂²×C₅	—	6	4	no	—
446	C₂²×C₅	—	6	4	no	—
447	C₂²×C₅	—	12	8	no	—
448	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
449	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
450	C₂²×C₅	#1004	1	2	yes	—
451	C₂²×C₅	#1010	1	2	yes	—
452	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
453	C₄×C₅	—	2	4	no	—
454	C₄×C₅	—	2	2	no	—
455	C₄×C₅	—	2	2	no	—
456	C₄×C₅	—	3	8	no	—
457	C₄×C₅	—	6	4	no	—
458	C₄×C₅	—	6	4	no	—
459	C₂⁴	—	3	2	no	—
460	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
461	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
462	#41	—	6	64	no	—
463	C₂×Q₈	—	3	8	no	—
464	C₂×Q₈	—	6	8	no	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	3	8	no	—
467	C₂×D₄	—	3	8	no	—
468	C₂×D₄	—	3	8	no	—
469	C₂×D₄	—	3	4	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	6	8	no	—
472	C₂×D₄	—	6	8	no	—
473	C₂×D₄	—	12	2	no	—
474	C₂×D₄	—	12	4	no	—
475	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
476	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
477	C₂²×C₄	—	3	8	no	—
478	C₂²×C₄	—	3	2	no	—
479	C₂²×C₄	—	3	4	no	—
480	C₂²×C₄	—	3	2	no	—
481	C₂²×C₄	—	3	2	no	—
482	C₂²×C₄	—	3	8	no	—
483	C₂²×C₄	—	3	4	no	—
484	C₂²×C₄	—	3	8	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	6	8	no	—
487	C₂²×C₄	—	6	8	no	—
488	C₂²×C₄	—	12	2	no	—
489	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
491	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
492	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
493	C₄⋊C₄	—	3	8	no	—
494	C₄⋊C₄	—	3	8	no	—
495	C₄⋊C₄	—	3	8	no	—
496	C₄⋊C₄	—	3	4	no	—
497	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
498	C₂²⋊C₄	—	3	8	no	—
499	C₂²⋊C₄	—	3	8	no	—
500	C₂²⋊C₄	—	3	8	no	—
501	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
502	C₃×C₅	C₂×#537	1	1	yes	characteristic, complemented, Hall
503	C₂²×C₃	—	2	8	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	4	no	—
507	C₂²×C₃	—	2	4	no	—
508	C₂²×C₃	—	2	4	no	—
509	C₂²×C₃	—	4	8	no	—
510	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
511	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
512	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
513	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
514	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
515	C₂×D₃	—	2	4	no	—
516	C₂×D₃	—	2	4	no	—
517	C₂×D₃	—	2	4	no	—
518	C₂×D₃	—	4	8	no	—
519	C₃×C₄	—	2	4	no	—
520	C₃×C₄	—	2	2	no	—
521	C₃×C₄	—	2	2	no	—
522	Dic₃	—	2	4	no	—
523	Dic₃	—	2	4	no	—
524	Dic₃	C₂²×C₅×D₄	1	8	yes	—
525	C₂×C₅	—	2	4	no	—
526	C₂×C₅	—	4	4	no	—
527	C₂×C₅	—	12	4	no	—
528	C₂×C₅	#5597	1	4	yes	direct product factor
529	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
530	C₂×C₅	C₂×#1004	1	1	yes	characteristic
531	C₂×C₅	C₂×#1010	1	1	yes	characteristic
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	3	4	no	—
538	C₂³	—	6	4	no	—
539	C₂³	—	6	4	no	—
540	C₂³	—	6	4	no	—
541	C₂³	C₅×D₃×D₄	1	4	yes	—
542	C₂³	C₂³×C₅×D₃	1	4	yes	—
543	C₂³	C₂³×C₅×D₃	1	2	yes	—
544	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
545	Q₈	—	6	16	no	—
546	D₄	—	2	16	no	—
547	D₄	—	4	4	no	—
548	D₄	—	6	16	no	—
549	D₄	—	6	16	no	—
550	D₄	—	12	4	no	—
551	D₄	—	12	8	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	3	8	no	—
556	C₂×C₄	—	3	16	no	—
557	C₂×C₄	—	3	4	no	—
558	C₂×C₄	—	3	4	no	—
559	C₂×C₄	—	3	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	6	16	no	—
562	C₂×C₄	—	6	16	no	—
563	C₂×C₄	—	6	4	no	—
564	C₂×C₄	—	6	4	no	—
565	C₂×C₄	—	12	4	no	—
566	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
567	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
568	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
569	C₂×C₃	—	2	4	no	—
570	C₂×C₃	—	4	4	no	—
571	C₂×C₃	C₅×#537	1	4	yes	complemented
572	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
573	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
575	D₃	—	4	4	no	—
576	C₅	C₂×#5597	1	1	yes	characteristic, direct product factor, Sylow
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	6	4	no	—
585	C₂²	—	6	4	no	—
586	C₂²	—	6	4	no	—
587	C₂²	—	12	8	no	—
588	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
589	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
590	C₂²	C₅×#1004	1	2	yes	—
591	C₂²	C₅×#1010	1	2	yes	—
592	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
593	C₄	—	2	4	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	3	8	no	—
597	C₄	—	6	4	no	—
598	C₄	—	6	4	no	—
599	C₃	C₂×C₅×#537	1	1	yes	characteristic, complemented, Sylow
600	C₂	—	2	4	no	—
601	C₂	—	4	4	no	—
602	C₂	—	12	4	no	—
603	C₂	C₅×#5597	1	4	yes	direct product factor
604	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
605	C₂	C₂×C₅×#1004	1	1	yes	characteristic
606	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×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#537
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#237	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₅×#939	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂×C₅×#930	C₂	semidirect
6. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
7. C₅×#5597	C₂	direct (N × H)
8. C₂×C₅×#896	C₂	semidirect
9. C₂×C₅×#884	C₂	semidirect
10. C₂×C₅×#878	C₂	semidirect
22. C₂×C₅×#237	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
30. C₅×#939	C₂²	semidirect
31. C₅×#939	C₂²	semidirect
32. C₅×#930	C₂²	semidirect
39. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
40. C₅×#896	C₂²	semidirect
41. C₅×#884	C₂²	semidirect
42. C₅×#878	C₂²	semidirect
43. C₂×#5597	C₅	direct (N × H)
52. C₂×C₅×#121	D₃	semidirect
74. C₂²×C₅×Dic₃	D₄	semidirect
97. C₂²×#237	C₂×C₅	semidirect
98. C₂×C₃×#121	C₂×C₅	semidirect
99. C₂×#939	C₂×C₅	semidirect
100. C₂×#939	C₂×C₅	semidirect
101. C₂×#930	C₂×C₅	semidirect
102. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
103. #5597	C₂×C₅	direct (N × H)
104. C₂×#896	C₂×C₅	semidirect
105. C₂×#884	C₂×C₅	semidirect
106. C₂×#878	C₂×C₅	semidirect
127. C₅×#121	C₂×D₃	semidirect
169. C₂×C₅×Dic₃	C₂×D₄	semidirect
186. C₂×#237	C₂²×C₅	semidirect
190. C₃×#121	C₂²×C₅	semidirect
194. #939	C₂²×C₅	semidirect
195. #939	C₂²×C₅	semidirect
196. #930	C₂²×C₅	semidirect
203. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
204. #896	C₂²×C₅	semidirect
205. #884	C₂²×C₅	semidirect
206. #878	C₂²×C₅	semidirect
258. C₂×#121	C₅×D₃	semidirect
302. C₂²×Dic₃	C₅×D₄	semidirect
382. #121	C₂×C₅×D₃	semidirect
395. C₂×C₃×C₅	#537	semidirect
430. C₂×Dic₃	C₂×C₅×D₄	semidirect
502. C₃×C₅	C₂×#537	semidirect
528. C₂×C₅	#5597	direct (N × H)
571. C₂×C₃	C₅×#537	semidirect
576. C₅	C₂×#5597	direct (N × H)
599. C₃	C₂×C₅×#537	semidirect
603. C₂	C₅×#5597	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#237	2
C₂×C₃×C₅×#121	2
C₂×C₅×#939	2
C₂×C₅×#930	2
C₂²×C₅×Dic₃⋊C₄	2
C₅×#5597	2
C₂×C₅×#896	2
C₂×C₅×#884	2
C₂×C₅×#878	2
C₂×C₅×#537	3
C₂×#5597	5

Subgroups — C2×C5×#5597 #14480560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5597 #14480560