Subgroups — C₅×#68759 #14301435

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5521	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic
4	C₅×#5120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5004	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1885	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
15	C₅×#926	C₂²	1	1	yes	characteristic
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₅×#893	—	2	2	no	—
18	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
19	C₅×#875	—	2	2	no	—
20	C₅×#875	C₄	1	4	yes	complemented
21	C₄×C₅×D₁₂	—	2	2	no	—
22	C₅×#823	—	2	2	no	—
23	C₅×#816	—	2	2	no	—
24	C₅×#810	—	2	2	no	—
25	#68759	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#124	—	3	1	no	—
27	C₅×#518	—	3	1	no	—
28	C₅×#419	—	3	1	no	—
29	C₅×#419	—	3	1	no	—
30	C₂×C₅×#100	—	3	1	no	—
31	C₅×#339	—	3	1	no	—
32	C₅×#339	D₃	1	1	yes	characteristic, complemented
33	C₂³×C₅×D₃	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
42	C₂×C₅×D₁₂	D₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	—	2	4	no	—
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₅×Dic₆	—	2	1	no	—
46	C₂×C₅×Dic₆	—	2	1	no	—
47	C₂×C₅×Dic₆	—	2	1	no	—
48	C₂×C₅×Dic₆	—	2	1	no	—
49	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	complemented
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
58	C₅×#217	—	2	1	no	—
59	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
61	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	#5521	C₂×C₅	1	1	yes	characteristic
67	C₂×#875	C₂×C₅	1	1	yes	characteristic
68	C₂×#823	C₂×C₅	1	1	yes	characteristic
69	#5120	C₂×C₅	1	1	yes	characteristic, complemented
70	#5004	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
72	#4523	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×C₅×Q₈	—	3	1	no	—
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂×C₅×M₁₆	—	3	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₅×#124	—	3	4	no	—
78	C₅×#124	—	6	2	no	—
79	C₄×C₅×D₄	—	6	2	no	—
80	C₄×C₅×D₄	—	6	2	no	—
81	C₅×#117	—	3	1	no	—
82	C₅×#117	C₂×D₃	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
84	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	C₅×#103	—	6	2	no	—
87	C₅×#103	—	6	2	no	—
88	C₅×#100	—	6	2	no	—
89	#1885	—	3	1	no	Sylow
90	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₅×D₃	—	2	2	no	—
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	—	4	4	no	—
94	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	4	2	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	4	1	no	—
107	C₂×C₅×Dic₃	—	4	1	no	—
108	C₅×D₁₂	—	2	2	no	—
109	C₅×D₁₂	—	2	2	no	—
110	C₅×D₁₂	—	2	2	no	—
111	C₅×D₁₂	—	2	2	no	—
112	C₄×C₅×D₃	—	8	4	no	—
113	C₅×Dic₆	—	2	2	no	—
114	C₅×Dic₆	—	2	2	no	—
115	C₅×Dic₆	—	4	1	no	—
116	C₅×Dic₆	—	4	1	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
120	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
122	C₃×#117	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
124	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
125	#926	C₂²×C₅	1	1	yes	characteristic
126	C₂×#208	C₂²×C₅	1	1	yes	characteristic
127	#893	—	2	2	no	—
128	D₃×C₂²⋊C₄	—	2	2	no	—
129	#875	—	2	2	no	—
130	#875	C₄×C₅	1	4	yes	complemented
131	C₄×D₁₂	—	2	2	no	—
132	#823	—	2	2	no	—
133	#816	—	2	2	no	—
134	#810	—	2	2	no	—
135	C₂⁴×C₅	—	3	2	no	—
136	C₂×C₅×Q₈	—	3	2	no	—
137	C₂×C₅×Q₈	—	6	1	no	—
138	C₂×C₅×Q₈	—	6	1	no	—
139	C₂×C₅×Q₈	—	6	1	no	—
140	C₂×C₅×Q₈	—	6	1	no	—
141	C₂×C₅×Q₈	—	6	1	no	—
142	C₂×C₅×D₄	—	3	2	no	—
143	C₂×C₅×D₄	—	3	2	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	6	4	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₅×M₁₆	—	2	1	no	—
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	—	6	1	no	—
155	C₅×M₁₆	—	6	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	6	1	no	—
158	C₅×C₄⋊C₄	—	3	2	no	—
159	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₅×C₂²⋊C₄	—	6	8	no	—
162	C₅×C₂²⋊C₄	—	6	4	no	—
163	C₅×C₂²⋊C₄	—	6	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	6	1	no	—
167	C₄²×C₅	C₄×D₃	1	2	yes	complemented
168	C₂×#124	—	3	1	no	—
169	#518	—	3	1	no	—
170	#419	—	3	1	no	—
171	#419	—	3	1	no	—
172	C₂×#100	—	3	1	no	—
173	#339	—	3	1	no	—
174	#339	C₅×D₃	1	1	yes	characteristic, complemented
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃×C₅	#120	1	1	yes	characteristic
178	C₂²×C₃×C₅	#123	1	1	yes	characteristic
179	C₂×C₅×D₃	—	2	4	no	—
180	C₂×C₅×D₃	—	4	4	no	—
181	C₂×C₅×D₃	—	4	4	no	—
182	C₂×C₅×D₃	—	8	2	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	#121	1	1	yes	characteristic
188	C₃×C₄×C₅	#121	1	1	yes	characteristic
189	C₅×Dic₃	—	4	2	no	—
190	C₅×Dic₃	—	4	2	no	—
191	C₂³×D₃	C₅×D₄	1	2	yes	—
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
194	C₂²×Dic₃	—	2	1	no	—
195	C₂×D₁₂	—	2	1	no	—
196	C₂×D₁₂	—	2	1	no	—
197	C₂×D₁₂	—	2	1	no	—
198	C₂×D₁₂	—	2	1	no	—
199	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
200	C₂×D₁₂	C₅×D₄	1	2	yes	—
201	C₂×C₄×D₃	—	2	4	no	—
202	C₂×Dic₆	—	2	1	no	—
203	C₂×Dic₆	—	2	1	no	—
204	C₂×Dic₆	—	2	1	no	—
205	C₂×Dic₆	—	2	1	no	—
206	C₂×Dic₆	—	2	1	no	—
207	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	complemented
208	C₃×M₁₆	—	2	1	no	—
209	C₃×M₁₆	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₃×C₄²	C₂×C₄×C₅	1	2	yes	complemented
216	#217	—	2	1	no	—
217	(C₂×D₃)⋊C₄	—	2	4	no	—
218	(C₂×D₃)⋊C₄	—	2	8	no	—
219	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
220	C₄×Dic₃	—	2	1	no	—
221	#208	—	2	1	no	—
222	#208	—	2	1	no	—
223	C₂×C₃⋊C₈	—	2	1	no	—
224	C₂³×C₅	—	3	4	no	—
225	C₂³×C₅	—	6	2	no	—
226	C₂³×C₅	—	6	2	no	—
227	C₂³×C₅	—	12	4	no	—
228	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
229	C₅×Q₈	—	6	2	no	—
230	C₅×Q₈	—	6	2	no	—
231	C₅×Q₈	—	12	1	no	—
232	C₅×Q₈	—	12	1	no	—
233	C₅×D₄	—	6	2	no	—
234	C₅×D₄	—	6	2	no	—
235	C₅×D₄	—	6	2	no	—
236	C₅×D₄	—	6	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	12	1	no	—
243	C₂×C₄×C₅	—	12	1	no	—
244	C₂×C₄×C₅	—	24	4	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	#239	1	1	yes	characteristic
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	12	1	no	—
253	C₂²×Q₈	—	3	1	no	—
254	C₂²×D₄	—	3	1	no	—
255	C₂×M₁₆	—	3	1	no	—
256	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
257	#124	—	3	4	no	—
258	#124	—	6	2	no	—
259	C₄×D₄	—	6	2	no	—
260	C₄×D₄	—	6	2	no	—
261	#117	—	3	1	no	—
262	#117	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	6	2	no	—
264	C₂×C₂²⋊C₄	—	6	2	no	—
265	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
266	#103	—	6	2	no	—
267	#103	—	6	2	no	—
268	#100	—	6	2	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	—	2	1	no	—
271	C₂×C₃×C₅	#386	1	1	yes	characteristic
272	C₂×C₃×C₅	#455	1	2	yes	—
273	C₅×D₃	—	4	4	no	—
274	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂²×D₃	—	2	2	no	—
276	C₂²×D₃	—	2	2	no	—
277	C₂²×D₃	—	4	4	no	—
278	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
287	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
288	C₂×Dic₃	—	2	2	no	—
289	C₂×Dic₃	—	2	2	no	—
290	C₂×Dic₃	—	4	1	no	—
291	C₂×Dic₃	—	4	1	no	—
292	D₁₂	—	2	2	no	—
293	D₁₂	—	2	2	no	—
294	D₁₂	—	2	2	no	—
295	D₁₂	—	2	2	no	—
296	C₄×D₃	—	8	4	no	—
297	Dic₆	—	2	2	no	—
298	Dic₆	—	2	2	no	—
299	Dic₆	—	4	1	no	—
300	Dic₆	—	4	1	no	—
301	C₃×C₈	—	4	1	no	—
302	C₃⋊C₈	—	4	1	no	—
303	C₂²×C₅	—	2	2	no	—
304	C₂²×C₅	—	6	4	no	—
305	C₂²×C₅	—	12	4	no	—
306	C₂²×C₅	—	12	4	no	—
307	C₂²×C₅	—	24	2	no	—
308	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₅	#882	1	1	yes	characteristic
310	C₂²×C₅	#894	1	1	yes	characteristic
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	12	2	no	—
314	C₄×C₅	—	12	2	no	—
315	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
316	C₄×C₅	#884	1	1	yes	characteristic
317	C₄×C₅	#893	1	1	yes	characteristic
318	C₄×C₅	#895	1	1	yes	characteristic
319	C₂⁴	—	3	2	no	—
320	C₂×Q₈	—	3	2	no	—
321	C₂×Q₈	—	6	1	no	—
322	C₂×Q₈	—	6	1	no	—
323	C₂×Q₈	—	6	1	no	—
324	C₂×Q₈	—	6	1	no	—
325	C₂×Q₈	—	6	1	no	—
326	C₂×D₄	—	3	2	no	—
327	C₂×D₄	—	3	2	no	—
328	C₂×D₄	—	6	1	no	—
329	C₂×D₄	—	6	1	no	—
330	C₂×D₄	—	6	1	no	—
331	C₂×D₄	—	6	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	6	4	no	—
334	C₂²×C₄	—	6	1	no	—
335	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
336	M₁₆	—	2	1	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	6	1	no	—
339	M₁₆	—	6	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	6	1	no	—
342	C₄⋊C₄	—	3	2	no	—
343	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	6	8	no	—
346	C₂²⋊C₄	—	6	4	no	—
347	C₂²⋊C₄	—	6	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	6	1	no	—
351	C₄²	C₄×C₅×D₃	1	2	yes	complemented
352	C₃×C₅	#1885	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂²×C₃	C₅×#120	1	1	yes	characteristic
356	C₂²×C₃	C₅×#123	1	1	yes	characteristic
357	C₂×D₃	—	2	4	no	—
358	C₂×D₃	—	4	4	no	—
359	C₂×D₃	—	4	4	no	—
360	C₂×D₃	—	8	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
364	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
365	C₃×C₄	C₅×#121	1	1	yes	characteristic
366	C₃×C₄	C₅×#121	1	1	yes	characteristic
367	Dic₃	—	4	2	no	—
368	Dic₃	—	4	2	no	—
369	C₂×C₅	—	2	1	no	—
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	12	4	no	—
372	C₂×C₅	#4665	1	1	yes	characteristic
373	C₂×C₅	#4825	1	2	yes	—
374	C₂³	—	3	4	no	—
375	C₂³	—	6	2	no	—
376	C₂³	—	6	2	no	—
377	C₂³	—	12	4	no	—
378	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
379	Q₈	—	6	2	no	—
380	Q₈	—	6	2	no	—
381	Q₈	—	12	1	no	—
382	Q₈	—	12	1	no	—
383	D₄	—	6	2	no	—
384	D₄	—	6	2	no	—
385	D₄	—	6	2	no	—
386	D₄	—	6	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	6	2	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	—	12	1	no	—
393	C₂×C₄	—	12	1	no	—
394	C₂×C₄	—	24	4	no	—
395	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
396	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
397	C₂×C₄	C₅×#235	1	1	yes	characteristic
398	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
399	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
400	C₂×C₄	C₅×#239	1	1	yes	characteristic
401	C₈	—	4	1	no	—
402	C₈	—	12	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	C₅×#386	1	1	yes	characteristic
406	C₂×C₃	C₅×#455	1	2	yes	—
407	D₃	—	4	4	no	—
408	C₅	#68759	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	6	4	no	—
411	C₂²	—	12	4	no	—
412	C₂²	—	12	4	no	—
413	C₂²	—	24	2	no	—
414	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²	C₅×#882	1	1	yes	characteristic
416	C₂²	C₅×#894	1	1	yes	characteristic
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	12	2	no	—
420	C₄	—	12	2	no	—
421	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
422	C₄	C₅×#884	1	1	yes	characteristic
423	C₄	C₅×#893	1	1	yes	characteristic
424	C₄	C₅×#895	1	1	yes	characteristic
425	C₃	C₅×#1885	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	12	4	no	—
429	C₂	C₅×#4665	1	1	yes	characteristic
430	C₂	C₅×#4825	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	#882
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#339	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#339	D₃
hypocenter	C₃	C₅×#1885
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#339

Complements

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

N	H ≅ G/N	type
4. C₅×#5120	C₂	semidirect
5. C₅×#5004	C₂	semidirect
6. C₃×C₅×#339	C₂	semidirect
7. C₅×#4523	C₂	semidirect
20. C₅×#875	C₄	semidirect
25. #68759	C₅	direct (N × H)
32. C₅×#339	D₃	semidirect
49. C₂×C₅×Dic₆	C₂×C₄	semidirect
57. C₃×C₄²×C₅	C₂×C₄	semidirect
69. #5120	C₂×C₅	semidirect
70. #5004	C₂×C₅	semidirect
71. C₃×#339	C₂×C₅	semidirect
72. #4523	C₂×C₅	semidirect
130. #875	C₄×C₅	semidirect
167. C₄²×C₅	C₄×D₃	semidirect
174. #339	C₅×D₃	semidirect
207. C₂×Dic₆	C₂×C₄×C₅	semidirect
215. C₃×C₄²	C₂×C₄×C₅	semidirect
351. C₄²	C₄×C₅×D₃	semidirect
352. C₃×C₅	#1885	semidirect
408. C₅	#68759	direct (N × H)
425. C₃	C₅×#1885	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5521	2
C₂×C₅×#875	2
C₂×C₅×#823	2
C₅×#5120	2
C₅×#5004	2
C₃×C₅×#339	2
C₅×#4523	2
C₅×#1885	3
#68759	5

Subgroups — C5×#68759 #14301435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68759 #14301435