Subgroups — C₄×C₅×#837 #14295571

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#837	C₂	1	2	yes	maximal
3	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4532	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#104	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₃×C₄×C₅×Q₈	C₄	1	2	yes	complemented
9	C₃×C₄×C₅×D₄	—	2	2	no	—
10	C₃×C₄×C₅×D₄	C₄	1	2	yes	complemented
11	C₃×C₅×#117	—	2	1	no	—
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	—	2	1	no	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	—	2	2	no	—
16	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#208	C₂²	1	2	yes	—
18	C₅×#837	C₄	1	8	yes	direct product factor
19	C₅×#803	—	2	1	no	—
20	C₄×C₅×C₃⋊C₈	—	2	1	no	—
21	C₄×#837	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₄×C₅×#41	D₃	1	1	yes	characteristic
23	C₂×C₅×#104	—	3	2	no	—
24	C₄×C₅×M₁₆	—	3	1	no	—
25	C₄³×C₅	—	3	1	no	—
26	C₅×#339	—	3	2	no	—
27	C₃×C₅×#41	—	2	2	no	—
28	C₃×C₅×#41	C₂×C₄	1	4	yes	—
29	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₅×D₄	—	2	1	no	—
31	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	—	2	2	no	—
37	C₃×C₅×C₄⋊C₄	—	2	2	no	—
38	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
39	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
40	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
41	C₃×C₄²×C₅	—	2	2	no	—
42	C₃×C₄²×C₅	—	2	1	no	—
43	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₄×C₅×Dic₃	—	2	8	no	—
47	C₄×C₅×Dic₃	—	2	2	no	—
48	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
49	C₅×#208	—	2	2	no	—
50	C₅×#208	C₂×C₄	1	4	yes	complemented
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
53	C₂×#837	C₂×C₅	1	2	yes	—
54	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
55	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
56	#4532	C₂×C₅	1	2	yes	complemented
57	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
58	C₂×C₅×M₁₆	—	3	2	no	—
59	C₄×C₅×Q₈	Dic₃	1	2	yes	complemented
60	C₄×C₅×D₄	—	2	2	no	—
61	C₄×C₅×D₄	Dic₃	1	2	yes	complemented
62	C₅×#117	—	2	1	no	—
63	C₅×#117	C₂×D₃	1	1	yes	characteristic
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	—	3	2	no	—
66	C₂×C₄²×C₅	—	6	2	no	—
67	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
68	C₅×#104	—	3	8	no	—
69	C₅×#97	—	6	1	no	—
70	C₄×C₅×C₈	—	6	1	no	—
71	C₄×#104	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
74	C₃×C₅×Q₈	—	2	1	no	—
75	C₃×C₅×Q₈	C₄²	1	2	yes	complemented
76	C₃×C₅×D₄	—	2	4	no	—
77	C₃×C₅×D₄	—	2	1	no	—
78	C₃×C₅×D₄	C₄²	1	2	yes	complemented
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	4	4	no	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₅×Dic₃	—	2	8	no	—
91	C₂×C₅×Dic₃	—	2	4	no	—
92	C₅×C₃⋊C₈	—	2	4	no	—
93	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
94	C₃×C₄×Q₈	C₄×C₅	1	2	yes	complemented
95	C₃×C₄×D₄	—	2	2	no	—
96	C₃×C₄×D₄	C₄×C₅	1	2	yes	complemented
97	C₃×#117	—	2	1	no	—
98	C₃×#117	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×C₄²	—	2	1	no	—
100	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₄×Dic₃	—	2	2	no	—
102	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
103	C₂×#208	C₂²×C₅	1	2	yes	—
104	#837	C₄×C₅	1	8	yes	direct product factor
105	#803	—	2	1	no	—
106	C₄×C₃⋊C₈	—	2	1	no	—
107	C₅×#41	—	2	2	no	—
108	C₅×#41	C₄×D₃	1	4	yes	—
109	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	6	2	no	—
115	C₂²×C₄×C₅	#67	1	2	yes	—
116	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₅×M₁₆	—	3	4	no	—
118	C₅×M₁₆	—	6	2	no	—
119	C₂×C₅×C₈	—	6	2	no	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
122	C₅×C₂²⋊C₄	—	2	1	no	—
123	C₅×C₂²⋊C₄	—	2	2	no	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	2	1	no	—
126	C₄²×C₅	—	3	4	no	—
127	C₄²×C₅	—	6	8	no	—
128	C₄²×C₅	—	6	2	no	—
129	C₄²×C₅	C₂×Dic₃	1	2	yes	—
130	C₄²×C₅	#67	1	1	yes	characteristic
131	C₄²×C₅	#67	1	1	yes	characteristic
132	C₄×#41	C₅×D₃	1	1	yes	characteristic
133	C₂×#104	—	3	2	no	—
134	C₄×M₁₆	—	3	1	no	—
135	C₄³	—	3	1	no	—
136	#339	—	3	2	no	—
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	—	2	2	no	—
139	C₂²×C₃×C₅	—	4	2	no	—
140	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
142	C₃×C₄×C₅	—	2	2	no	—
143	C₃×C₄×C₅	—	2	2	no	—
144	C₃×C₄×C₅	—	4	2	no	—
145	C₃×C₄×C₅	#104	1	4	yes	complemented
146	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
147	C₃×C₄×C₅	#117	1	1	yes	characteristic
148	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
149	C₅×Dic₃	—	2	8	no	—
150	C₃×#41	—	2	2	no	—
151	C₃×#41	C₂×C₄×C₅	1	4	yes	—
152	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
153	C₂×C₃×D₄	—	2	1	no	—
154	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
155	C₂²×C₃×C₄	—	2	1	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
158	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
159	C₂²×Dic₃	—	2	2	no	—
160	C₃×C₄⋊C₄	—	2	2	no	—
161	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
162	C₃×C₂²⋊C₄	—	2	1	no	—
163	C₃×C₂²⋊C₄	—	2	2	no	—
164	C₃×C₄²	—	2	2	no	—
165	C₃×C₄²	—	2	1	no	—
166	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
167	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
168	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
169	C₄×Dic₃	—	2	8	no	—
170	C₄×Dic₃	—	2	2	no	—
171	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
172	#208	—	2	2	no	—
173	#208	C₂×C₄×C₅	1	4	yes	complemented
174	C₂×C₃⋊C₈	—	2	2	no	—
175	C₂³×C₅	—	2	1	no	—
176	C₂³×C₅	C₂×#67	1	1	yes	characteristic
177	C₅×Q₈	—	2	1	no	—
178	C₅×Q₈	C₄×Dic₃	1	2	yes	complemented
179	C₅×D₄	—	2	4	no	—
180	C₅×D₄	—	2	1	no	—
181	C₅×D₄	C₄×Dic₃	1	2	yes	complemented
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	4	4	no	—
187	C₂×C₄×C₅	—	6	8	no	—
188	C₂×C₄×C₅	—	6	4	no	—
189	C₂×C₄×C₅	#217	1	2	yes	—
190	C₂×C₄×C₅	#217	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
192	C₂×C₄×C₅	#235	1	2	yes	—
193	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
195	C₅×C₈	—	6	4	no	—
196	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
197	C₂×M₁₆	—	3	2	no	—
198	C₄×Q₈	C₅×Dic₃	1	2	yes	complemented
199	C₄×D₄	—	2	2	no	—
200	C₄×D₄	C₅×Dic₃	1	2	yes	complemented
201	#117	—	2	1	no	—
202	#117	C₂×C₅×D₃	1	1	yes	characteristic
203	C₂×C₄²	—	2	1	no	—
204	C₂×C₄²	—	3	2	no	—
205	C₂×C₄²	—	6	2	no	—
206	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
207	#104	—	3	8	no	—
208	#97	—	6	1	no	—
209	C₄×C₈	—	6	1	no	—
210	C₂×C₃×C₅	—	2	2	no	—
211	C₂×C₃×C₅	—	4	2	no	—
212	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂×#104	1	2	yes	—
214	C₂³×C₃	—	2	1	no	—
215	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
216	C₃×Q₈	—	2	1	no	—
217	C₃×Q₈	C₄²×C₅	1	2	yes	complemented
218	C₃×D₄	—	2	4	no	—
219	C₃×D₄	—	2	1	no	—
220	C₃×D₄	C₄²×C₅	1	2	yes	complemented
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	4	4	no	—
226	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
227	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
228	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
229	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₅×#41	1	2	yes	—
232	C₂×Dic₃	—	2	8	no	—
233	C₂×Dic₃	—	2	4	no	—
234	C₃⋊C₈	—	2	4	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	4	2	no	—
238	C₂²×C₅	C₄×#67	1	2	yes	—
239	C₂²×C₅	C₂×#217	1	1	yes	characteristic
240	C₄×C₅	—	2	2	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	4	2	no	—
243	C₄×C₅	—	6	8	no	—
244	C₄×C₅	#837	1	4	yes	direct product factor
245	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
246	C₄×C₅	#926	1	1	yes	characteristic
247	C₄×C₅	C₄×#67	1	2	yes	—
248	#41	—	2	2	no	—
249	#41	C₄×C₅×D₃	1	4	yes	—
250	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
251	C₂×D₄	—	2	1	no	—
252	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	6	2	no	—
256	C₂²×C₄	C₅×#67	1	2	yes	—
257	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
258	M₁₆	—	3	4	no	—
259	M₁₆	—	6	2	no	—
260	C₂×C₈	—	6	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
263	C₂²⋊C₄	—	2	1	no	—
264	C₂²⋊C₄	—	2	2	no	—
265	C₄²	—	2	2	no	—
266	C₄²	—	2	1	no	—
267	C₄²	—	3	4	no	—
268	C₄²	—	6	8	no	—
269	C₄²	—	6	2	no	—
270	C₄²	C₂×C₅×Dic₃	1	2	yes	—
271	C₄²	C₅×#67	1	1	yes	characteristic
272	C₄²	C₅×#67	1	1	yes	characteristic
273	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	4	2	no	—
277	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
279	C₃×C₄	—	2	2	no	—
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	4	2	no	—
282	C₃×C₄	C₅×#104	1	4	yes	complemented
283	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
284	C₃×C₄	C₅×#117	1	1	yes	characteristic
285	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
286	Dic₃	—	2	8	no	—
287	C₂×C₅	—	2	2	no	—
288	C₂×C₅	—	4	2	no	—
289	C₂×C₅	C₄×#217	1	1	yes	characteristic
290	C₂×C₅	C₂×#837	1	2	yes	—
291	C₂³	—	2	1	no	—
292	C₂³	C₂×C₅×#67	1	1	yes	characteristic
293	Q₈	—	2	1	no	—
294	Q₈	C₄×C₅×Dic₃	1	2	yes	complemented
295	D₄	—	2	4	no	—
296	D₄	—	2	1	no	—
297	D₄	C₄×C₅×Dic₃	1	2	yes	complemented
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	6	8	no	—
304	C₂×C₄	—	6	4	no	—
305	C₂×C₄	C₅×#217	1	2	yes	—
306	C₂×C₄	C₅×#217	1	2	yes	—
307	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
308	C₂×C₄	C₅×#235	1	2	yes	—
309	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
310	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
311	C₈	—	6	4	no	—
312	C₂×C₃	—	2	2	no	—
313	C₂×C₃	—	4	2	no	—
314	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₃	C₂×C₅×#104	1	2	yes	—
316	C₅	C₄×#837	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	C₄×C₅×#67	1	2	yes	—
321	C₂²	C₂×C₅×#217	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	4	2	no	—
325	C₄	—	6	8	no	—
326	C₄	C₅×#837	1	4	yes	direct product factor
327	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
328	C₄	C₅×#926	1	1	yes	characteristic
329	C₄	C₄×C₅×#67	1	2	yes	—
330	C₃	C₄×C₅×#104	1	1	yes	characteristic, complemented, Sylow
331	C₂	—	2	2	no	—
332	C₂	—	4	2	no	—
333	C₂	C₄×C₅×#217	1	1	yes	characteristic
334	C₂	C₂×C₅×#837	1	2	yes	—

	subgroup	G/H
center	C₄²×C₅	#67
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₄×C₅×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
3. C₄²×C₅×Dic₃	C₂	semidirect
4. C₄×C₅×#208	C₂	semidirect
5. C₅×#4532	C₂	semidirect
8. C₃×C₄×C₅×Q₈	C₄	semidirect
10. C₃×C₄×C₅×D₄	C₄	semidirect
18. C₅×#837	C₄	direct (N × H)
21. C₄×#837	C₅	direct (N × H)
48. C₄×C₅×Dic₃	C₂×C₄	semidirect
50. C₅×#208	C₂×C₄	semidirect
54. C₄²×Dic₃	C₂×C₅	semidirect
55. C₄×#208	C₂×C₅	semidirect
56. #4532	C₂×C₅	semidirect
59. C₄×C₅×Q₈	Dic₃	semidirect
61. C₄×C₅×D₄	Dic₃	semidirect
75. C₃×C₅×Q₈	C₄²	semidirect
78. C₃×C₅×D₄	C₄²	semidirect
94. C₃×C₄×Q₈	C₄×C₅	semidirect
96. C₃×C₄×D₄	C₄×C₅	semidirect
104. #837	C₄×C₅	direct (N × H)
145. C₃×C₄×C₅	#104	semidirect
171. C₄×Dic₃	C₂×C₄×C₅	semidirect
173. #208	C₂×C₄×C₅	semidirect
178. C₅×Q₈	C₄×Dic₃	semidirect
181. C₅×D₄	C₄×Dic₃	semidirect
198. C₄×Q₈	C₅×Dic₃	semidirect
200. C₄×D₄	C₅×Dic₃	semidirect
217. C₃×Q₈	C₄²×C₅	semidirect
220. C₃×D₄	C₄²×C₅	semidirect
244. C₄×C₅	#837	direct (N × H)
273. C₃×C₅	C₄×#104	semidirect
282. C₃×C₄	C₅×#104	semidirect
294. Q₈	C₄×C₅×Dic₃	semidirect
297. D₄	C₄×C₅×Dic₃	semidirect
316. C₅	C₄×#837	direct (N × H)
326. C₄	C₅×#837	direct (N × H)
330. C₃	C₄×C₅×#104	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₂×C₅×#837	2
C₄²×C₅×Dic₃	2
C₄×C₅×#208	2
C₅×#4532	2
C₄×C₅×#104	3
C₄×#837	5

Subgroups — C4×C5×#837 #14295571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#837 #14295571