Subgroups — C₅×#68941 #14299516

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#5126	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#822	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1855	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₅×D₃×M₁₆	—	2	2	no	—
17	C₅×D₃×M₁₆	—	2	2	no	—
18	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
19	C₂×C₅×D₃×C₈	—	2	1	no	—
20	C₅×#822	—	2	2	no	—
21	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
22	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
23	C₅×(C₂×D₃)⋊C₈	C₄	1	2	yes	—
24	C₅×(C₂×D₃)⋊C₈	C₄	1	2	yes	—
25	C₅×#819	—	2	2	no	—
26	#68941	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂²×C₅×M₁₆	—	3	1	no	—
28	C₂×C₅×#108	—	3	1	no	—
29	C₂×C₅×#108	—	3	1	no	—
30	C₅×#407	—	3	1	no	—
31	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
32	C₅×#341	—	3	1	no	—
33	C₅×#341	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₅×D₃	Q₈	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	Q₈	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
45	C₃×C₅×M₁₆	—	2	1	no	—
46	C₃×C₅×M₁₆	—	2	1	no	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	D₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
54	C₅×#208	—	2	1	no	—
55	C₅×#208	—	2	1	no	—
56	C₅×#208	—	2	1	no	—
57	C₅×#208	D₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
63	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
64	C₅×D₃×C₈	—	2	4	no	—
65	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic
66	#5126	C₂×C₅	1	1	yes	characteristic
67	C₂×#822	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic
69	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#341	C₂×C₅	1	1	yes	characteristic, complemented
71	#4558	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂³×C₄×C₅	—	3	1	no	—
73	C₂×C₅×M₁₆	—	3	1	no	—
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	—	6	1	no	—
76	C₂×C₅×M₁₆	—	6	2	no	—
77	C₂×C₅×M₁₆	—	6	2	no	—
78	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₂²×C₅×C₈	—	6	1	no	—
82	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	C₅×#108	—	6	2	no	—
84	C₅×#108	—	6	2	no	—
85	C₅×C₂²⋊C₈	—	3	2	no	—
86	C₅×C₂²⋊C₈	—	3	2	no	—
87	C₅×C₂²⋊C₈	—	6	1	no	—
88	C₅×C₂²⋊C₈	—	6	1	no	—
89	#1855	—	3	1	no	Sylow
90	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₅×D₃	—	2	1	no	—
92	C₂²×C₅×D₃	—	2	1	no	—
93	C₂²×C₅×D₃	—	2	2	no	—
94	C₂²×C₅×D₃	—	4	1	no	—
95	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₂×C₅×Dic₃	—	2	1	no	—
105	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×C₅×D₃	—	2	1	no	—
108	C₄×C₅×D₃	—	2	1	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	2	1	no	—
111	C₄×C₅×D₃	—	2	1	no	—
112	C₄×C₅×D₃	—	2	1	no	—
113	C₄×C₅×D₃	—	2	1	no	—
114	C₄×C₅×D₃	—	2	1	no	—
115	C₃×C₅×C₈	—	2	2	no	—
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₅×C₃⋊C₈	—	4	1	no	—
121	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
124	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
125	C₂×#208	C₂²×C₅	1	1	yes	characteristic
126	C₂×#208	C₂²×C₅	1	1	yes	characteristic
127	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
128	D₃×M₁₆	—	2	2	no	—
129	D₃×M₁₆	—	2	2	no	—
130	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
131	C₂×D₃×C₈	—	2	1	no	—
132	#822	—	2	2	no	—
133	(C₂×D₃)⋊C₈	—	2	1	no	—
134	(C₂×D₃)⋊C₈	—	2	1	no	—
135	(C₂×D₃)⋊C₈	C₄×C₅	1	2	yes	—
136	(C₂×D₃)⋊C₈	C₄×C₅	1	2	yes	—
137	#819	—	2	2	no	—
138	C₂⁴×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₅×M₁₆	—	2	1	no	—
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	—	2	1	no	—
152	C₅×M₁₆	—	3	2	no	—
153	C₅×M₁₆	—	6	4	no	—
154	C₅×M₁₆	—	6	1	no	—
155	C₅×M₁₆	—	6	1	no	—
156	C₅×M₁₆	—	6	1	no	—
157	C₅×M₁₆	D₁₂	1	2	yes	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	3	2	no	—
163	C₂×C₅×C₈	—	6	4	no	—
164	C₂×C₅×C₈	—	6	1	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₂×C₅×C₈	—	6	1	no	—
167	C₂×C₅×C₈	—	6	1	no	—
168	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
169	C₂²×M₁₆	—	3	1	no	—
170	C₂×#108	—	3	1	no	—
171	C₂×#108	—	3	1	no	—
172	#407	—	3	1	no	—
173	C₂×C₂²⋊C₈	—	3	1	no	—
174	#341	—	3	1	no	—
175	#341	C₅×D₃	1	1	yes	characteristic, complemented
176	C₂²×C₃×C₅	—	2	1	no	—
177	C₂²×C₃×C₅	—	2	1	no	—
178	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	1	no	—
182	C₂×C₅×D₃	—	2	1	no	—
183	C₂×C₅×D₃	—	2	1	no	—
184	C₂×C₅×D₃	—	2	1	no	—
185	C₂×C₅×D₃	—	2	1	no	—
186	C₂×C₅×D₃	—	4	2	no	—
187	C₂×C₅×D₃	—	4	2	no	—
188	C₂×C₅×D₃	#108	1	2	yes	complemented
189	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	#120	1	1	yes	characteristic
192	C₃×C₄×C₅	#123	1	1	yes	characteristic
193	C₅×Dic₃	—	2	1	no	—
194	C₅×Dic₃	—	2	1	no	—
195	C₂³×D₃	C₅×Q₈	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂²×Dic₃	C₅×Q₈	1	1	yes	characteristic
198	C₂×C₄×D₃	—	2	1	no	—
199	C₂×C₄×D₃	—	2	1	no	—
200	C₂×C₄×D₃	—	2	1	no	—
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
205	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	—	2	1	no	—
208	C₃×M₁₆	—	2	1	no	—
209	C₃×M₁₆	C₅×D₄	1	2	yes	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
215	#208	—	2	1	no	—
216	#208	—	2	1	no	—
217	#208	—	2	1	no	—
218	#208	C₅×D₄	1	2	yes	—
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂×C₃⋊C₈	—	2	1	no	—
221	C₂×C₃⋊C₈	—	2	1	no	—
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
224	ΓL(1,𝔽₂₅)	—	2	4	no	—
225	D₃×C₈	—	2	4	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂³×C₅	—	3	1	no	—
228	C₂³×C₅	—	6	2	no	—
229	C₂³×C₅	—	6	1	no	—
230	C₂³×C₅	—	6	1	no	—
231	C₂³×C₅	—	12	1	no	—
232	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₅	—	3	1	no	—
234	C₂×C₄×C₅	—	3	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	1	no	—
239	C₂×C₄×C₅	—	6	1	no	—
240	C₂×C₄×C₅	—	6	1	no	—
241	C₂×C₄×C₅	—	6	1	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
247	C₂×C₄×C₅	#235	1	1	yes	characteristic
248	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	#237	1	1	yes	characteristic
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	4	1	no	—
254	C₅×C₈	—	6	2	no	—
255	C₅×C₈	—	6	2	no	—
256	C₅×C₈	—	12	1	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₂×M₁₆	—	3	1	no	—
259	C₂×M₁₆	—	3	1	no	—
260	C₂×M₁₆	—	6	1	no	—
261	C₂×M₁₆	—	6	2	no	—
262	C₂×M₁₆	—	6	2	no	—
263	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂²×C₈	—	3	1	no	—
266	C₂²×C₈	—	6	1	no	—
267	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
268	#108	—	6	2	no	—
269	#108	—	6	2	no	—
270	C₂²⋊C₈	—	3	2	no	—
271	C₂²⋊C₈	—	3	2	no	—
272	C₂²⋊C₈	—	6	1	no	—
273	C₂²⋊C₈	—	6	1	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	2	1	no	—
276	C₂×C₃×C₅	#385	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
278	C₂×C₃×C₅	#430	1	1	yes	characteristic
279	C₅×D₃	—	2	2	no	—
280	C₅×D₃	—	4	1	no	—
281	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
282	C₂²×D₃	—	2	1	no	—
283	C₂²×D₃	—	2	1	no	—
284	C₂²×D₃	—	2	2	no	—
285	C₂²×D₃	—	4	1	no	—
286	C₂²×D₃	C₅×C₄⋊C₄	1	1	yes	characteristic
287	C₂²×D₃	C₅×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
293	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
294	C₂×Dic₃	—	2	1	no	—
295	C₂×Dic₃	—	2	1	no	—
296	C₂×Dic₃	C₅×C₄⋊C₄	1	1	yes	characteristic
297	C₂×Dic₃	C₅×C₄⋊C₄	1	1	yes	characteristic
298	C₄×D₃	—	2	1	no	—
299	C₄×D₃	—	2	1	no	—
300	C₄×D₃	—	2	1	no	—
301	C₄×D₃	—	2	1	no	—
302	C₄×D₃	—	2	1	no	—
303	C₄×D₃	—	2	1	no	—
304	C₄×D₃	—	2	1	no	—
305	C₄×D₃	—	2	1	no	—
306	C₃×C₈	—	2	2	no	—
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	—	4	1	no	—
309	C₃⋊C₈	—	2	2	no	—
310	C₃⋊C₈	—	2	2	no	—
311	C₃⋊C₈	—	4	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	3	2	no	—
315	C₂²×C₅	—	6	1	no	—
316	C₂²×C₅	—	6	1	no	—
317	C₂²×C₅	—	6	1	no	—
318	C₂²×C₅	—	6	1	no	—
319	C₂²×C₅	—	6	1	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
323	C₂²×C₅	#896	1	1	yes	characteristic
324	C₂²×C₅	#897	1	1	yes	characteristic
325	C₄×C₅	—	6	1	no	—
326	C₄×C₅	—	6	1	no	—
327	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
328	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
329	C₄×C₅	#882	1	1	yes	characteristic
330	C₄×C₅	#883	1	1	yes	characteristic
331	C₂⁴	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	6	1	no	—
338	C₂²×C₄	—	6	1	no	—
339	C₂²×C₄	—	6	1	no	—
340	C₂²×C₄	—	6	1	no	—
341	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	3	2	no	—
346	M₁₆	—	6	4	no	—
347	M₁₆	—	6	1	no	—
348	M₁₆	—	6	1	no	—
349	M₁₆	—	6	1	no	—
350	M₁₆	C₅×D₁₂	1	2	yes	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	3	2	no	—
356	C₂×C₈	—	6	4	no	—
357	C₂×C₈	—	6	1	no	—
358	C₂×C₈	—	6	1	no	—
359	C₂×C₈	—	6	1	no	—
360	C₂×C₈	—	6	1	no	—
361	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
362	C₃×C₅	#1855	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
366	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
367	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂×D₃	—	2	1	no	—
369	C₂×D₃	—	2	1	no	—
370	C₂×D₃	—	2	1	no	—
371	C₂×D₃	—	2	1	no	—
372	C₂×D₃	—	2	1	no	—
373	C₂×D₃	—	4	2	no	—
374	C₂×D₃	—	4	2	no	—
375	C₂×D₃	C₅×#108	1	2	yes	complemented
376	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
377	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
378	C₃×C₄	C₅×#120	1	1	yes	characteristic
379	C₃×C₄	C₅×#123	1	1	yes	characteristic
380	Dic₃	—	2	1	no	—
381	Dic₃	—	2	1	no	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	6	2	no	—
385	C₂×C₅	—	12	1	no	—
386	C₂×C₅	#4668	1	1	yes	characteristic
387	C₂×C₅	D₃×#108	1	1	yes	characteristic
388	C₂×C₅	#4893	1	1	yes	characteristic
389	C₂³	—	3	1	no	—
390	C₂³	—	3	1	no	—
391	C₂³	—	6	2	no	—
392	C₂³	—	6	1	no	—
393	C₂³	—	6	1	no	—
394	C₂³	—	12	1	no	—
395	C₂³	C₅×D₃×Q₈	1	1	yes	characteristic
396	C₂×C₄	—	3	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	6	1	no	—
399	C₂×C₄	—	6	1	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	—	6	1	no	—
402	C₂×C₄	—	6	1	no	—
403	C₂×C₄	—	6	1	no	—
404	C₂×C₄	—	6	1	no	—
405	C₂×C₄	—	6	1	no	—
406	C₂×C₄	—	6	1	no	—
407	C₂×C₄	—	6	1	no	—
408	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
410	C₂×C₄	C₅×#235	1	1	yes	characteristic
411	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
412	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
413	C₂×C₄	C₅×#237	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	6	2	no	—
418	C₈	—	6	2	no	—
419	C₈	—	12	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	C₅×#385	1	1	yes	characteristic
423	C₂×C₃	C₂×C₅×#108	1	1	yes	characteristic
424	C₂×C₃	C₅×#430	1	1	yes	characteristic
425	D₃	—	2	2	no	—
426	D₃	—	4	1	no	—
427	C₅	#68941	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	3	2	no	—
431	C₂²	—	6	1	no	—
432	C₂²	—	6	1	no	—
433	C₂²	—	6	1	no	—
434	C₂²	—	6	1	no	—
435	C₂²	—	6	1	no	—
436	C₂²	—	12	2	no	—
437	C₂²	—	12	2	no	—
438	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
439	C₂²	C₅×#896	1	1	yes	characteristic
440	C₂²	C₅×#897	1	1	yes	characteristic
441	C₄	—	6	1	no	—
442	C₄	—	6	1	no	—
443	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
444	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
445	C₄	C₅×#882	1	1	yes	characteristic
446	C₄	C₅×#883	1	1	yes	characteristic
447	C₃	C₅×#1855	1	1	yes	characteristic, complemented, Sylow
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	6	2	no	—
451	C₂	—	12	1	no	—
452	C₂	C₅×#4668	1	1	yes	characteristic
453	C₂	C₅×D₃×#108	1	1	yes	characteristic
454	C₂	C₅×#4893	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#341	C₂
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₅×D₃	Q₈
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#341	D₃
hypocenter	C₃	C₅×#1855
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#341

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#822	C₂	semidirect
5. C₂×C₅×#819	C₂	semidirect
6. C₃×C₅×#341	C₂	semidirect
7. C₅×#4558	C₂	semidirect
26. #68941	C₅	direct (N × H)
33. C₅×#341	D₃	semidirect
67. C₂×#822	C₂×C₅	semidirect
69. C₂×#819	C₂×C₅	semidirect
70. C₃×#341	C₂×C₅	semidirect
71. #4558	C₂×C₅	semidirect
175. #341	C₅×D₃	semidirect
188. C₂×C₅×D₃	#108	semidirect
362. C₃×C₅	#1855	semidirect
375. C₂×D₃	C₅×#108	semidirect
427. C₅	#68941	direct (N × H)
447. C₃	C₅×#1855	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₅×#5126	2
C₂×C₅×#822	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#819	2
C₃×C₅×#341	2
C₅×#4558	2
C₅×#1855	3
#68941	5

Subgroups — C5×#68941 #14299516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68941 #14299516