Subgroups — C₅×D₃×#555 #14483910

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5734	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#124	C₂	1	4	yes	maximal, complemented
5	C₅×#5670	C₂	1	4	yes	maximal, complemented
6	C₅×#5616	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
8	C₅×#5563	C₂	1	2	yes	maximal, complemented
9	C₄×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
10	C₅×#5532	C₂	1	4	yes	maximal, complemented
11	C₅×D₃×#117	C₂	1	4	yes	maximal, complemented
12	C₂×C₅×#555	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#124	C₂²	1	4	yes	complemented
19	C₃×C₅×#121	C₂²	1	4	yes	complemented
20	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
21	C₃×C₅×#117	C₂²	1	4	yes	complemented
22	C₅×#947	C₂²	1	4	yes	complemented
23	C₅×#944	C₂²	1	2	yes	complemented
24	C₅×#939	C₂²	1	8	yes	complemented
25	C₅×#938	C₂²	1	4	yes	complemented
26	C₅×#936	C₂²	1	4	yes	complemented
27	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
28	C₅×#930	C₂²	1	4	yes	complemented
29	C₄×C₅×#67	C₂²	1	4	yes	complemented
30	C₅×#926	C₂²	1	4	yes	complemented
31	C₅×#895	C₂²	1	4	yes	complemented
32	C₅×#893	C₂²	1	2	yes	complemented
33	C₅×#892	C₂²	1	4	yes	complemented
34	C₅×#892	C₂²	1	4	yes	complemented
35	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
36	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₅×#888	C₂²	1	4	yes	complemented
38	C₅×#885	C₂²	1	8	yes	complemented
39	C₅×#885	C₂²	1	8	yes	complemented
40	C₅×#884	C₂²	1	8	yes	complemented
41	C₅×#67⋊C₄	C₂²	1	4	yes	complemented
42	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
43	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	—
44	C₅×#877	C₂²	1	8	yes	complemented
45	C₅×#875	C₂²	1	4	yes	complemented
46	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
47	C₅×#872	C₂²	1	8	yes	complemented
48	C₄²×C₅×D₃	C₂²	1	4	yes	—
49	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
50	C₅×#869	C₂²	1	1	yes	characteristic, complemented
51	D₃×#555	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₅×#555	—	3	1	no	—
53	C₅×#555	—	3	4	no	—
54	C₅×#555	—	3	4	no	—
55	C₅×#555	—	3	2	no	—
56	C₅×#555	—	3	4	no	—
57	C₅×#555	D₃	1	1	yes	characteristic, direct product factor
58	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
59	C₂×C₅×#124	—	3	4	no	—
60	C₂×C₅×#121	—	3	4	no	—
61	C₂×C₄×C₅×D₄	—	3	2	no	—
62	C₂×C₅×#117	—	3	4	no	—
63	C₂³×C₅×D₃	C₂³	1	4	yes	—
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
68	C₂×C₅×#67	C₂³	1	4	yes	—
69	C₂×C₅×#67	C₂³	1	8	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
71	C₅×D₃×Q₈	—	4	4	no	—
72	C₅×D₃×D₄	—	2	8	no	—
73	C₅×D₃×D₄	—	4	8	no	—
74	C₂×C₅×D₁₂	C₂³	1	2	yes	—
75	C₂×C₅×D₁₂	C₂³	1	4	yes	—
76	C₂×C₄×C₅×D₃	—	2	16	no	—
77	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
78	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
80	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
81	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
82	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
83	C₂×C₅×Dic₆	C₂³	1	2	yes	—
84	C₂×C₅×Dic₆	C₂³	1	4	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
87	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₃×C₄²×C₅	C₂³	1	4	yes	—
91	C₅×#217	C₂³	1	8	yes	—
92	C₅×#217	C₂³	1	4	yes	—
93	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
95	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
96	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
97	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
98	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
99	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
100	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
101	C₄×C₅×Dic₃	C₂³	1	8	yes	—
102	C₄×C₅×Dic₃	C₂³	1	4	yes	—
103	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₄×C₅×Dic₃	C₂³	1	2	yes	—
105	C₃×#555	C₂×C₅	1	1	yes	characteristic, complemented
106	#5734	C₂×C₅	1	1	yes	characteristic, complemented
107	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
108	D₃×#124	C₂×C₅	1	4	yes	complemented
109	#5670	C₂×C₅	1	4	yes	complemented
110	#5616	C₂×C₅	1	4	yes	complemented
111	D₃×#121	C₂×C₅	1	4	yes	complemented
112	#5563	C₂×C₅	1	2	yes	complemented
113	C₄×D₃×D₄	C₂×C₅	1	2	yes	complemented
114	#5532	C₂×C₅	1	4	yes	complemented
115	D₃×#117	C₂×C₅	1	4	yes	complemented
116	C₂²×C₅×Q₈	—	3	2	no	—
117	C₂²×C₅×D₄	—	3	2	no	—
118	C₂²×C₅×D₄	—	3	4	no	—
119	C₂³×C₄×C₅	—	3	4	no	—
120	C₅×C₄⋊Q₈	—	3	2	no	—
121	C₅×C₄⋊Q₈	—	3	4	no	—
122	C₅×C₄⋊Q₈	—	3	1	no	—
123	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
124	C₅×#124	—	3	4	no	—
125	C₅×#124	—	3	4	no	—
126	C₅×#124	—	3	8	no	—
127	C₅×#124	—	3	8	no	—
128	C₅×#124	—	3	4	no	—
129	C₅×#124	C₂×D₃	1	4	yes	complemented
130	C₅×#121	—	3	4	no	—
131	C₅×#121	—	3	8	no	—
132	C₅×#121	—	3	4	no	—
133	C₅×#121	—	3	4	no	—
134	C₅×#121	—	3	8	no	—
135	C₅×#121	C₂×D₃	1	4	yes	complemented
136	C₄×C₅×D₄	—	3	2	no	—
137	C₄×C₅×D₄	—	3	4	no	—
138	C₄×C₅×D₄	—	3	2	no	—
139	C₄×C₅×D₄	—	3	4	no	—
140	C₄×C₅×D₄	—	3	2	no	—
141	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
142	C₅×#117	—	3	4	no	—
143	C₅×#117	—	3	4	no	—
144	C₅×#117	—	3	4	no	—
145	C₅×#117	—	3	8	no	—
146	C₅×#117	—	3	8	no	—
147	C₅×#117	C₂×D₃	1	4	yes	complemented
148	C₂×C₅×C₄⋊C₄	—	3	2	no	—
149	C₂×C₅×C₄⋊C₄	—	3	4	no	—
150	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
152	C₂×C₄²×C₅	—	3	4	no	—
153	C₂×C₄²×C₅	—	3	1	no	—
154	C₂×#555	—	3	1	no	Sylow
155	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
156	C₂²×C₅×D₃	—	2	8	no	—
157	C₂²×C₅×D₃	—	2	8	no	—
158	C₂²×C₅×D₃	—	2	8	no	—
159	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
160	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
161	C₃×C₅×Q₈	—	4	2	no	—
162	C₃×C₅×D₄	—	2	4	no	—
163	C₃×C₅×D₄	—	4	4	no	—
164	C₂×C₃×C₄×C₅	—	2	8	no	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
169	C₅×#67	—	2	8	no	—
170	C₅×#67	—	4	8	no	—
171	C₂×C₅×Dic₃	—	2	8	no	—
172	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
174	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
176	C₅×D₁₂	—	2	4	no	—
177	C₅×D₁₂	—	4	4	no	—
178	C₄×C₅×D₃	—	2	8	no	—
179	C₄×C₅×D₃	—	2	8	no	—
180	C₄×C₅×D₃	—	2	2	no	—
181	C₄×C₅×D₃	—	2	8	no	—
182	C₄×C₅×D₃	—	2	8	no	—
183	C₄×C₅×D₃	#41	1	8	yes	—
184	C₅×Dic₆	—	4	4	no	—
185	C₅×Dic₆	—	4	2	no	—
186	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
187	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
188	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
189	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
190	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₃×#124	C₂²×C₅	1	4	yes	complemented
192	C₃×#121	C₂²×C₅	1	4	yes	complemented
193	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
194	C₃×#117	C₂²×C₅	1	4	yes	complemented
195	#947	C₂²×C₅	1	4	yes	complemented
196	#944	C₂²×C₅	1	2	yes	complemented
197	#939	C₂²×C₅	1	8	yes	complemented
198	#938	C₂²×C₅	1	4	yes	complemented
199	#936	C₂²×C₅	1	4	yes	complemented
200	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
201	#930	C₂²×C₅	1	4	yes	complemented
202	C₄×#67	C₂²×C₅	1	4	yes	complemented
203	#926	C₂²×C₅	1	4	yes	complemented
204	#895	C₂²×C₅	1	4	yes	complemented
205	#893	C₂²×C₅	1	2	yes	complemented
206	#892	C₂²×C₅	1	4	yes	complemented
207	#892	C₂²×C₅	1	4	yes	complemented
208	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
209	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
210	#888	C₂²×C₅	1	4	yes	complemented
211	#885	C₂²×C₅	1	8	yes	complemented
212	#885	C₂²×C₅	1	8	yes	complemented
213	#884	C₂²×C₅	1	8	yes	complemented
214	#67⋊C₄	C₂²×C₅	1	4	yes	complemented
215	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
216	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
217	#877	C₂²×C₅	1	8	yes	complemented
218	#875	C₂²×C₅	1	4	yes	complemented
219	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
220	#872	C₂²×C₅	1	8	yes	complemented
221	C₄²×D₃	C₂²×C₅	1	4	yes	—
222	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
223	#869	C₂²×C₅	1	1	yes	characteristic, complemented
224	C₂⁴×C₅	—	3	4	no	—
225	C₂×C₅×Q₈	—	3	4	no	—
226	C₂×C₅×Q₈	—	3	2	no	—
227	C₂×C₅×Q₈	—	12	4	no	—
228	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
229	C₂×C₅×D₄	—	3	4	no	—
230	C₂×C₅×D₄	—	3	8	no	—
231	C₂×C₅×D₄	—	3	2	no	—
232	C₂×C₅×D₄	—	3	4	no	—
233	C₂×C₅×D₄	—	6	8	no	—
234	C₂×C₅×D₄	—	12	8	no	—
235	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
236	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
237	C₂²×C₄×C₅	—	3	2	no	—
238	C₂²×C₄×C₅	—	3	4	no	—
239	C₂²×C₄×C₅	—	3	4	no	—
240	C₂²×C₄×C₅	—	3	1	no	—
241	C₂²×C₄×C₅	—	3	4	no	—
242	C₂²×C₄×C₅	—	3	4	no	—
243	C₂²×C₄×C₅	—	3	4	no	—
244	C₂²×C₄×C₅	—	6	16	no	—
245	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
246	C₅×C₄⋊C₄	—	3	4	no	—
247	C₅×C₄⋊C₄	—	3	2	no	—
248	C₅×C₄⋊C₄	—	3	8	no	—
249	C₅×C₄⋊C₄	—	3	4	no	—
250	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
251	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
252	C₅×C₂²⋊C₄	—	3	8	no	—
253	C₅×C₂²⋊C₄	—	3	4	no	—
254	C₅×C₂²⋊C₄	—	3	8	no	—
255	C₅×C₂²⋊C₄	—	3	8	no	—
256	C₅×C₂²⋊C₄	—	3	4	no	—
257	C₅×C₂²⋊C₄	—	3	4	no	—
258	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
259	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
260	C₄²×C₅	—	3	4	no	—
261	C₄²×C₅	—	3	8	no	—
262	C₄²×C₅	—	3	1	no	—
263	C₄²×C₅	—	3	2	no	—
264	C₄²×C₅	C₂²×D₃	1	4	yes	—
265	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
266	#555	—	3	1	no	—
267	#555	—	3	4	no	—
268	#555	—	3	4	no	—
269	#555	—	3	2	no	—
270	#555	—	3	4	no	—
271	#555	C₅×D₃	1	1	yes	characteristic, direct product factor
272	C₂×C₄⋊Q₈	—	3	1	no	—
273	C₂×#124	—	3	4	no	—
274	C₂×#121	—	3	4	no	—
275	C₂×C₄×D₄	—	3	2	no	—
276	C₂×#117	—	3	4	no	—
277	C₂²×C₃×C₅	—	2	4	no	—
278	C₂²×C₃×C₅	—	2	4	no	—
279	C₂²×C₃×C₅	—	2	4	no	—
280	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
281	C₂×C₅×D₃	—	2	4	no	—
282	C₂×C₅×D₃	—	2	4	no	—
283	C₂×C₅×D₃	—	2	4	no	—
284	C₂×C₅×D₃	—	4	16	no	—
285	C₂×C₅×D₃	C₂×#41	1	4	yes	—
286	C₂×C₅×D₃	H(5,𝔽₂)	1	2	yes	—
287	C₃×C₄×C₅	—	2	4	no	—
288	C₃×C₄×C₅	—	2	1	no	—
289	C₃×C₄×C₅	—	2	4	no	—
290	C₃×C₄×C₅	C₂×#41	1	4	yes	—
291	C₅×Dic₃	—	2	4	no	—
292	C₅×Dic₃	—	2	1	no	—
293	C₅×Dic₃	—	2	4	no	—
294	C₅×Dic₃	C₂×#41	1	4	yes	—
295	C₂³×D₃	C₂³×C₅	1	4	yes	—
296	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
297	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
298	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
299	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
300	C₂×#67	C₂³×C₅	1	4	yes	—
301	C₂×#67	C₂³×C₅	1	8	yes	—
302	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
303	D₃×Q₈	—	4	4	no	—
304	D₃×D₄	—	2	8	no	—
305	D₃×D₄	—	4	8	no	—
306	C₂×D₁₂	C₂³×C₅	1	2	yes	—
307	C₂×D₁₂	C₂³×C₅	1	4	yes	—
308	C₂×C₄×D₃	—	2	16	no	—
309	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
310	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
311	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
312	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
313	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
314	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
315	C₂×Dic₆	C₂³×C₅	1	2	yes	—
316	C₂×Dic₆	C₂³×C₅	1	4	yes	—
317	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
318	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
319	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
320	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
321	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
322	C₃×C₄²	C₂³×C₅	1	4	yes	—
323	#217	C₂³×C₅	1	8	yes	—
324	#217	C₂³×C₅	1	4	yes	—
325	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
326	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
327	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
328	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
329	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
330	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
331	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
332	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
333	C₄×Dic₃	C₂³×C₅	1	8	yes	—
334	C₄×Dic₃	C₂³×C₅	1	4	yes	—
335	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
336	C₄×Dic₃	C₂³×C₅	1	2	yes	—
337	C₂³×C₅	—	3	1	no	—
338	C₂³×C₅	—	3	4	no	—
339	C₂³×C₅	—	6	8	no	—
340	C₂³×C₅	—	6	8	no	—
341	C₂³×C₅	—	6	8	no	—
342	C₂³×C₅	C₂³×D₃	1	4	yes	—
343	C₅×Q₈	—	4	2	no	—
344	C₅×Q₈	—	12	4	no	—
345	C₅×Q₈	—	12	2	no	—
346	C₅×D₄	—	2	4	no	—
347	C₅×D₄	—	4	4	no	—
348	C₅×D₄	—	6	8	no	—
349	C₅×D₄	—	6	4	no	—
350	C₅×D₄	—	12	4	no	—
351	C₅×D₄	—	12	8	no	—
352	C₂×C₄×C₅	—	2	8	no	—
353	C₂×C₄×C₅	—	3	2	no	—
354	C₂×C₄×C₅	—	3	8	no	—
355	C₂×C₄×C₅	—	3	4	no	—
356	C₂×C₄×C₅	—	3	1	no	—
357	C₂×C₄×C₅	—	3	4	no	—
358	C₂×C₄×C₅	—	6	8	no	—
359	C₂×C₄×C₅	—	6	8	no	—
360	C₂×C₄×C₅	—	6	8	no	—
361	C₂×C₄×C₅	—	6	2	no	—
362	C₂×C₄×C₅	—	6	8	no	—
363	C₂×C₄×C₅	—	6	8	no	—
364	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
365	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
367	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
368	C₂²×Q₈	—	3	2	no	—
369	C₂²×D₄	—	3	2	no	—
370	C₂²×D₄	—	3	4	no	—
371	C₂³×C₄	—	3	4	no	—
372	C₄⋊Q₈	—	3	2	no	—
373	C₄⋊Q₈	—	3	4	no	—
374	C₄⋊Q₈	—	3	1	no	—
375	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
376	#124	—	3	4	no	—
377	#124	—	3	4	no	—
378	#124	—	3	8	no	—
379	#124	—	3	8	no	—
380	#124	—	3	4	no	—
381	#124	C₂×C₅×D₃	1	4	yes	complemented
382	#121	—	3	4	no	—
383	#121	—	3	8	no	—
384	#121	—	3	4	no	—
385	#121	—	3	4	no	—
386	#121	—	3	8	no	—
387	#121	C₂×C₅×D₃	1	4	yes	complemented
388	C₄×D₄	—	3	2	no	—
389	C₄×D₄	—	3	4	no	—
390	C₄×D₄	—	3	2	no	—
391	C₄×D₄	—	3	4	no	—
392	C₄×D₄	—	3	2	no	—
393	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
394	#117	—	3	4	no	—
395	#117	—	3	4	no	—
396	#117	—	3	4	no	—
397	#117	—	3	8	no	—
398	#117	—	3	8	no	—
399	#117	C₂×C₅×D₃	1	4	yes	complemented
400	C₂×C₄⋊C₄	—	3	2	no	—
401	C₂×C₄⋊C₄	—	3	4	no	—
402	C₂×C₂²⋊C₄	—	3	8	no	—
403	C₂×C₂²⋊C₄	—	3	4	no	—
404	C₂×C₄²	—	3	4	no	—
405	C₂×C₄²	—	3	1	no	—
406	C₂×C₃×C₅	—	4	4	no	—
407	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
408	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
409	C₅×D₃	—	4	4	no	—
410	C₅×D₃	#555	1	4	yes	direct product factor
411	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
412	C₂²×D₃	—	2	8	no	—
413	C₂²×D₃	—	2	8	no	—
414	C₂²×D₃	—	2	8	no	—
415	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
416	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
417	C₃×Q₈	—	4	2	no	—
418	C₃×D₄	—	2	4	no	—
419	C₃×D₄	—	4	4	no	—
420	C₂×C₃×C₄	—	2	8	no	—
421	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
422	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
423	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
425	#67	—	2	8	no	—
426	#67	—	4	8	no	—
427	C₂×Dic₃	—	2	8	no	—
428	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
429	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
430	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
431	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
432	D₁₂	—	2	4	no	—
433	D₁₂	—	4	4	no	—
434	C₄×D₃	—	2	8	no	—
435	C₄×D₃	—	2	8	no	—
436	C₄×D₃	—	2	2	no	—
437	C₄×D₃	—	2	8	no	—
438	C₄×D₃	—	2	8	no	—
439	C₄×D₃	C₅×#41	1	8	yes	—
440	Dic₆	—	4	4	no	—
441	Dic₆	—	4	2	no	—
442	C₂²×C₅	—	2	4	no	—
443	C₂²×C₅	—	2	4	no	—
444	C₂²×C₅	—	2	4	no	—
445	C₂²×C₅	—	3	4	no	—
446	C₂²×C₅	—	3	2	no	—
447	C₂²×C₅	—	6	4	no	—
448	C₂²×C₅	—	6	4	no	—
449	C₂²×C₅	—	6	4	no	—
450	C₂²×C₅	—	12	16	no	—
451	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
452	C₄×C₅	—	2	4	no	—
453	C₄×C₅	—	2	4	no	—
454	C₄×C₅	—	2	1	no	—
455	C₄×C₅	—	3	4	no	—
456	C₄×C₅	—	6	4	no	—
457	C₄×C₅	—	6	4	no	—
458	C₄×C₅	—	6	1	no	—
459	C₄×C₅	D₃×#41	1	4	yes	—
460	C₂⁴	—	3	4	no	—
461	C₂×Q₈	—	3	4	no	—
462	C₂×Q₈	—	3	2	no	—
463	C₂×Q₈	—	12	4	no	—
464	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
465	C₂×D₄	—	3	4	no	—
466	C₂×D₄	—	3	8	no	—
467	C₂×D₄	—	3	2	no	—
468	C₂×D₄	—	3	4	no	—
469	C₂×D₄	—	6	8	no	—
470	C₂×D₄	—	12	8	no	—
471	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
472	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
473	C₂²×C₄	—	3	2	no	—
474	C₂²×C₄	—	3	4	no	—
475	C₂²×C₄	—	3	4	no	—
476	C₂²×C₄	—	3	1	no	—
477	C₂²×C₄	—	3	4	no	—
478	C₂²×C₄	—	3	4	no	—
479	C₂²×C₄	—	3	4	no	—
480	C₂²×C₄	—	6	16	no	—
481	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
482	C₄⋊C₄	—	3	4	no	—
483	C₄⋊C₄	—	3	2	no	—
484	C₄⋊C₄	—	3	8	no	—
485	C₄⋊C₄	—	3	4	no	—
486	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
487	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
488	C₂²⋊C₄	—	3	8	no	—
489	C₂²⋊C₄	—	3	4	no	—
490	C₂²⋊C₄	—	3	8	no	—
491	C₂²⋊C₄	—	3	8	no	—
492	C₂²⋊C₄	—	3	4	no	—
493	C₂²⋊C₄	—	3	4	no	—
494	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
495	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
496	C₄²	—	3	4	no	—
497	C₄²	—	3	8	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	2	no	—
500	C₄²	C₂²×C₅×D₃	1	4	yes	—
501	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
502	C₃×C₅	C₂×#555	1	1	yes	characteristic, complemented, Hall
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	4	no	—
505	C₂²×C₃	—	2	4	no	—
506	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
507	C₂×D₃	—	2	4	no	—
508	C₂×D₃	—	2	4	no	—
509	C₂×D₃	—	2	4	no	—
510	C₂×D₃	—	4	16	no	—
511	C₂×D₃	C₂×C₅×#41	1	4	yes	—
512	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
513	C₃×C₄	—	2	4	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	2	4	no	—
516	C₃×C₄	C₂×C₅×#41	1	4	yes	—
517	Dic₃	—	2	4	no	—
518	Dic₃	—	2	1	no	—
519	Dic₃	—	2	4	no	—
520	Dic₃	C₂×C₅×#41	1	4	yes	—
521	C₂×C₅	—	3	4	no	—
522	C₂×C₅	—	4	4	no	—
523	C₂×C₅	—	12	4	no	—
524	C₂×C₅	C₂×D₃×#41	1	2	yes	—
525	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂³	—	3	1	no	—
527	C₂³	—	3	4	no	—
528	C₂³	—	6	8	no	—
529	C₂³	—	6	8	no	—
530	C₂³	—	6	8	no	—
531	C₂³	C₂³×C₅×D₃	1	4	yes	—
532	Q₈	—	4	2	no	—
533	Q₈	—	12	4	no	—
534	Q₈	—	12	2	no	—
535	D₄	—	2	4	no	—
536	D₄	—	4	4	no	—
537	D₄	—	6	8	no	—
538	D₄	—	6	4	no	—
539	D₄	—	12	4	no	—
540	D₄	—	12	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	3	2	no	—
543	C₂×C₄	—	3	8	no	—
544	C₂×C₄	—	3	4	no	—
545	C₂×C₄	—	3	1	no	—
546	C₂×C₄	—	3	4	no	—
547	C₂×C₄	—	6	8	no	—
548	C₂×C₄	—	6	8	no	—
549	C₂×C₄	—	6	8	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	6	8	no	—
552	C₂×C₄	—	6	8	no	—
553	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
554	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
556	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
557	C₂×C₃	—	4	4	no	—
558	C₂×C₃	C₂²×C₅×#41	1	2	yes	—
559	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
560	D₃	—	4	4	no	—
561	D₃	C₅×#555	1	4	yes	direct product factor
562	C₅	D₃×#555	1	1	yes	characteristic, direct product factor, Sylow
563	C₂²	—	2	4	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	3	4	no	—
567	C₂²	—	3	2	no	—
568	C₂²	—	6	4	no	—
569	C₂²	—	6	4	no	—
570	C₂²	—	6	4	no	—
571	C₂²	—	12	16	no	—
572	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
573	C₄	—	2	4	no	—
574	C₄	—	2	4	no	—
575	C₄	—	2	1	no	—
576	C₄	—	3	4	no	—
577	C₄	—	6	4	no	—
578	C₄	—	6	4	no	—
579	C₄	—	6	1	no	—
580	C₄	C₅×D₃×#41	1	4	yes	—
581	C₃	C₂×C₅×#555	1	1	yes	characteristic, complemented, Sylow
582	C₂	—	3	4	no	—
583	C₂	—	4	4	no	—
584	C₂	—	12	4	no	—
585	C₂	C₂×C₅×D₃×#41	1	2	yes	—
586	C₂	C₅×D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#555	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#555	D₃
hypocenter	C₃	C₂×C₅×#555
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#555

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#555	C₂	semidirect
2. C₅×#5734	C₂	semidirect
3. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₅×D₃×#124	C₂	semidirect
5. C₅×#5670	C₂	semidirect
6. C₅×#5616	C₂	semidirect
7. C₅×D₃×#121	C₂	semidirect
8. C₅×#5563	C₂	semidirect
9. C₄×C₅×D₃×D₄	C₂	semidirect
10. C₅×#5532	C₂	semidirect
11. C₅×D₃×#117	C₂	semidirect
17. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₃×C₅×#124	C₂²	semidirect
19. C₃×C₅×#121	C₂²	semidirect
20. C₃×C₄×C₅×D₄	C₂²	semidirect
21. C₃×C₅×#117	C₂²	semidirect
22. C₅×#947	C₂²	semidirect
23. C₅×#944	C₂²	semidirect
24. C₅×#939	C₂²	semidirect
25. C₅×#938	C₂²	semidirect
26. C₅×#936	C₂²	semidirect
27. C₅×D₄×Dic₃	C₂²	semidirect
28. C₅×#930	C₂²	semidirect
29. C₄×C₅×#67	C₂²	semidirect
30. C₅×#926	C₂²	semidirect
31. C₅×#895	C₂²	semidirect
32. C₅×#893	C₂²	semidirect
33. C₅×#892	C₂²	semidirect
34. C₅×#892	C₂²	semidirect
37. C₅×#888	C₂²	semidirect
38. C₅×#885	C₂²	semidirect
39. C₅×#885	C₂²	semidirect
40. C₅×#884	C₂²	semidirect
41. C₅×#67⋊C₄	C₂²	semidirect
44. C₅×#877	C₂²	semidirect
45. C₅×#875	C₂²	semidirect
46. C₄×C₅×D₁₂	C₂²	semidirect
47. C₅×#872	C₂²	semidirect
50. C₅×#869	C₂²	semidirect
51. D₃×#555	C₅	direct (N × H)
57. C₅×#555	D₃	direct (N × H)
105. C₃×#555	C₂×C₅	semidirect
106. #5734	C₂×C₅	semidirect
107. D₃×C₄⋊Q₈	C₂×C₅	semidirect
108. D₃×#124	C₂×C₅	semidirect
109. #5670	C₂×C₅	semidirect
110. #5616	C₂×C₅	semidirect
111. D₃×#121	C₂×C₅	semidirect
112. #5563	C₂×C₅	semidirect
113. C₄×D₃×D₄	C₂×C₅	semidirect
114. #5532	C₂×C₅	semidirect
115. D₃×#117	C₂×C₅	semidirect
123. C₅×C₄⋊Q₈	C₂×D₃	semidirect
129. C₅×#124	C₂×D₃	semidirect
135. C₅×#121	C₂×D₃	semidirect
141. C₄×C₅×D₄	C₂×D₃	semidirect
147. C₅×#117	C₂×D₃	semidirect
190. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
191. C₃×#124	C₂²×C₅	semidirect
192. C₃×#121	C₂²×C₅	semidirect
193. C₃×C₄×D₄	C₂²×C₅	semidirect
194. C₃×#117	C₂²×C₅	semidirect
195. #947	C₂²×C₅	semidirect
196. #944	C₂²×C₅	semidirect
197. #939	C₂²×C₅	semidirect
198. #938	C₂²×C₅	semidirect
199. #936	C₂²×C₅	semidirect
200. D₄×Dic₃	C₂²×C₅	semidirect
201. #930	C₂²×C₅	semidirect
202. C₄×#67	C₂²×C₅	semidirect
203. #926	C₂²×C₅	semidirect
204. #895	C₂²×C₅	semidirect
205. #893	C₂²×C₅	semidirect
206. #892	C₂²×C₅	semidirect
207. #892	C₂²×C₅	semidirect
210. #888	C₂²×C₅	semidirect
211. #885	C₂²×C₅	semidirect
212. #885	C₂²×C₅	semidirect
213. #884	C₂²×C₅	semidirect
214. #67⋊C₄	C₂²×C₅	semidirect
217. #877	C₂²×C₅	semidirect
218. #875	C₂²×C₅	semidirect
219. C₄×D₁₂	C₂²×C₅	semidirect
220. #872	C₂²×C₅	semidirect
223. #869	C₂²×C₅	semidirect
271. #555	C₅×D₃	direct (N × H)
375. C₄⋊Q₈	C₂×C₅×D₃	semidirect
381. #124	C₂×C₅×D₃	semidirect
387. #121	C₂×C₅×D₃	semidirect
393. C₄×D₄	C₂×C₅×D₃	semidirect
399. #117	C₂×C₅×D₃	semidirect
410. C₅×D₃	#555	direct (N × H)
502. C₃×C₅	C₂×#555	semidirect
561. D₃	C₅×#555	direct (N × H)
562. C₅	D₃×#555	direct (N × H)
581. C₃	C₂×C₅×#555	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#555	2
C₅×#5734	2
C₅×D₃×C₄⋊Q₈	2
C₅×D₃×#124	2
C₅×#5670	2
C₅×#5616	2
C₅×D₃×#121	2
C₅×#5563	2
C₄×C₅×D₃×D₄	2
C₅×#5532	2
C₅×D₃×#117	2
C₂×C₅×#555	3
D₃×#555	5

Subgroups — C5×D3×#555 #14483910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#555 #14483910