Subgroups — C₅×#68345 #14284180

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5668	C₂	1	1	yes	maximal, characteristic
2	C₅×#4705	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4540	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4464	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1530	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	C₄	1	1	yes	characteristic
10	C₂×C₅×#237	C₄	1	1	yes	characteristic
11	C₃×C₅×#124	C₂²	1	1	yes	characteristic
12	C₅×#944	C₄	1	1	yes	characteristic
13	C₅×#940	C₄	1	1	yes	characteristic
14	C₂×C₅×D₃×C₈	—	2	1	no	—
15	C₅×#884	—	2	1	no	—
16	C₅×#884	—	2	1	no	—
17	C₅×#67⋊C₄	—	2	1	no	—
18	C₅×#67⋊C₄	—	2	1	no	—
19	C₅×#875	C₂²	1	1	yes	characteristic
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₃×C₅×#97	C₂²	1	1	yes	characteristic
22	C₃×C₅×#97	C₂²	1	1	yes	characteristic
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×#815	—	2	1	no	—
25	C₅×Dic₃⋊C₈	—	2	1	no	—
26	C₅×#803	C₂²	1	1	yes	characteristic
27	C₅×#803	C₂²	1	1	yes	characteristic
28	#68345	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#532	—	3	1	no	—
30	C₅×#432	—	3	1	no	—
31	C₂×C₅×#97	—	3	1	no	—
32	C₅×#329	—	3	1	no	—
33	C₅×#329	—	3	1	no	—
34	C₅×#329	—	3	1	no	—
35	C₅×#329	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₅×#67	—	2	1	no	—
39	C₂×C₅×#67	—	2	1	no	—
40	C₂×C₅×#67	—	2	1	no	—
41	C₂²×C₅×Dic₃	—	2	1	no	—
42	C₅×#239	—	4	2	no	—
43	C₅×#237	—	4	2	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	—	2	1	no	—
47	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
49	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
50	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
58	C₅×Dic₃⋊C₄	—	2	1	no	—
59	C₅×Dic₃⋊C₄	—	2	1	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₅×D₃×C₈	—	2	4	no	—
66	#5668	C₂×C₅	1	1	yes	characteristic
67	#4705	C₂×C₅	1	1	yes	characteristic, complemented
68	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#329	C₂×C₅	1	1	yes	characteristic, complemented
70	#4540	C₂×C₅	1	1	yes	characteristic, complemented
71	#4464	C₂×C₅	1	1	yes	characteristic, complemented
72	#4464	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	—	3	1	no	—
74	C₂×C₅×#41	—	3	1	no	—
75	C₂²×C₅×C₈	—	6	1	no	—
76	C₅×C₄⋊Q₈	—	3	1	no	—
77	C₅×#127	—	3	1	no	—
78	C₅×#124	—	3	1	no	—
79	C₅×#124	C₂×D₃	1	1	yes	characteristic
80	C₅×#121	—	6	1	no	—
81	C₅×#121	—	6	1	no	—
82	C₄×C₅×D₄	—	6	1	no	—
83	C₄×C₅×D₄	—	6	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₅×C₄⋊C₈	—	6	1	no	—
86	C₅×C₂²⋊C₈	—	6	1	no	—
87	C₅×#97	—	3	1	no	—
88	C₅×#97	—	3	1	no	—
89	C₅×#97	—	6	1	no	—
90	C₅×#97	C₂×D₃	1	1	yes	characteristic
91	C₅×#97	C₂×D₃	1	1	yes	characteristic
92	#1530	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	1	no	—
94	C₂²×C₅×D₃	—	2	1	no	—
95	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	4	1	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	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	C₅×#67	—	4	2	no	—
103	C₅×#67	—	4	2	no	—
104	C₅×#67	—	4	2	no	—
105	C₂×C₅×Dic₃	—	2	1	no	—
106	C₂×C₅×Dic₃	—	4	2	no	—
107	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₅×D₁₂	—	4	1	no	—
111	C₅×D₁₂	—	4	2	no	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₄×C₅×D₃	—	4	1	no	—
115	C₄×C₅×D₃	—	4	2	no	—
116	C₅×Dic₆	—	4	1	no	—
117	C₃×C₅×C₈	—	2	2	no	—
118	C₃×C₅×C₈	—	4	1	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₅×C₃⋊C₈	—	4	1	no	—
121	C₂×#239	C₄×C₅	1	1	yes	characteristic
122	C₂×#237	C₄×C₅	1	1	yes	characteristic
123	C₃×#124	C₂²×C₅	1	1	yes	characteristic
124	#944	C₄×C₅	1	1	yes	characteristic
125	#940	C₄×C₅	1	1	yes	characteristic
126	C₂×D₃×C₈	—	2	1	no	—
127	#884	—	2	1	no	—
128	#884	—	2	1	no	—
129	#67⋊C₄	—	2	1	no	—
130	#67⋊C₄	—	2	1	no	—
131	#875	C₂²×C₅	1	1	yes	characteristic
132	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
133	C₃×#97	C₂²×C₅	1	1	yes	characteristic
134	C₃×#97	C₂²×C₅	1	1	yes	characteristic
135	(C₂×D₃)⋊C₈	—	2	1	no	—
136	#815	—	2	1	no	—
137	Dic₃⋊C₈	—	2	1	no	—
138	#803	C₂²×C₅	1	1	yes	characteristic
139	#803	C₂²×C₅	1	1	yes	characteristic
140	C₅×#41	—	12	2	no	—
141	C₅×#41	—	12	2	no	—
142	C₂×C₅×Q₈	—	3	1	no	—
143	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
144	C₂×C₅×D₄	—	3	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	—	3	1	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	3	1	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	—	6	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	6	4	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₂×C₅×C₈	—	6	1	no	—
160	C₅×C₄⋊C₄	—	6	1	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	6	1	no	—
165	C₅×C₂²⋊C₄	—	6	1	no	—
166	C₄²×C₅	—	3	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	1	no	—
169	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
170	#532	—	3	1	no	—
171	#432	—	3	1	no	—
172	C₂×#97	—	3	1	no	—
173	#329	—	3	1	no	—
174	#329	—	3	1	no	—
175	#329	—	3	1	no	—
176	#329	C₅×D₃	1	1	yes	characteristic, complemented
177	C₂²×C₃×C₅	—	4	1	no	—
178	C₂²×C₃×C₅	—	4	1	no	—
179	C₂²×C₃×C₅	—	4	1	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	1	no	—
182	C₂×C₅×D₃	—	2	1	no	—
183	C₂×C₅×D₃	—	4	1	no	—
184	C₂×C₅×D₃	—	4	1	no	—
185	C₂×C₅×D₃	—	4	1	no	—
186	C₂×C₅×D₃	#100	1	2	yes	—
187	C₃×C₄×C₅	—	2	1	no	—
188	C₃×C₄×C₅	—	2	1	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	4	1	no	—
191	C₅×Dic₃	—	2	1	no	—
192	C₅×Dic₃	—	2	1	no	—
193	C₅×Dic₃	—	4	1	no	—
194	C₅×Dic₃	#104	1	2	yes	—
195	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×#67	—	2	1	no	—
198	C₂×#67	—	2	1	no	—
199	C₂×#67	—	2	1	no	—
200	C₂²×Dic₃	—	2	1	no	—
201	#239	—	4	2	no	—
202	#237	—	4	2	no	—
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	—	2	1	no	—
206	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
208	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
209	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	—	2	1	no	—
216	(C₂×D₃)⋊C₄	—	2	1	no	—
217	Dic₃⋊C₄	—	2	1	no	—
218	Dic₃⋊C₄	—	2	1	no	—
219	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
220	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
221	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂×C₃⋊C₈	—	2	1	no	—
224	D₃×C₈	—	2	4	no	—
225	C₂³×C₅	—	2	1	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂³×C₅	—	6	1	no	—
228	C₅×Q₈	—	4	1	no	—
229	C₅×Q₈	—	12	1	no	—
230	C₅×D₄	—	4	1	no	—
231	C₅×D₄	—	12	1	no	—
232	C₅×D₄	—	12	2	no	—
233	C₅×D₄	—	12	2	no	—
234	C₅×D₄	—	12	2	no	—
235	C₅×D₄	—	12	2	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	3	1	no	—
238	C₂×C₄×C₅	—	3	1	no	—
239	C₂×C₄×C₅	—	3	1	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	12	1	no	—
244	C₂×C₄×C₅	—	12	2	no	—
245	C₂×C₄×C₅	—	12	2	no	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	4	1	no	—
251	C₅×C₈	—	6	2	no	—
252	C₅×C₈	—	12	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂×#41	—	3	1	no	—
255	C₂²×C₈	—	6	1	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	#127	—	3	1	no	—
258	#124	—	3	1	no	—
259	#124	C₂×C₅×D₃	1	1	yes	characteristic
260	#121	—	6	1	no	—
261	#121	—	6	1	no	—
262	C₄×D₄	—	6	1	no	—
263	C₄×D₄	—	6	1	no	—
264	C₂×C₄²	—	3	1	no	—
265	C₄⋊C₈	—	6	1	no	—
266	C₂²⋊C₈	—	6	1	no	—
267	#97	—	3	1	no	—
268	#97	—	3	1	no	—
269	#97	—	6	1	no	—
270	#97	C₂×C₅×D₃	1	1	yes	characteristic
271	#97	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂×C₃×C₅	—	8	1	no	—
273	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
275	C₂×C₃×C₅	#421	1	1	yes	characteristic
276	C₅×D₃	—	2	2	no	—
277	C₅×D₃	—	8	1	no	—
278	C₂³×C₃	—	2	1	no	—
279	C₂²×D₃	—	2	1	no	—
280	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
281	C₃×Q₈	—	4	1	no	—
282	C₃×D₄	—	4	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	#67	—	4	2	no	—
288	#67	—	4	2	no	—
289	#67	—	4	2	no	—
290	C₂×Dic₃	—	2	1	no	—
291	C₂×Dic₃	—	4	2	no	—
292	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	D₁₂	—	4	1	no	—
296	D₁₂	—	4	2	no	—
297	C₄×D₃	—	2	2	no	—
298	C₄×D₃	—	2	2	no	—
299	C₄×D₃	—	4	1	no	—
300	C₄×D₃	—	4	2	no	—
301	Dic₆	—	4	1	no	—
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	4	1	no	—
304	C₃⋊C₈	—	2	2	no	—
305	C₃⋊C₈	—	4	1	no	—
306	C₂²×C₅	—	3	2	no	—
307	C₂²×C₅	—	4	1	no	—
308	C₂²×C₅	—	4	1	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	—	6	1	no	—
311	C₂²×C₅	—	6	1	no	—
312	C₂²×C₅	—	12	1	no	—
313	C₂²×C₅	—	12	1	no	—
314	C₂²×C₅	—	12	1	no	—
315	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	3	2	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	—	6	1	no	—
322	C₄×C₅	—	6	1	no	—
323	C₄×C₅	—	12	1	no	—
324	#41	—	12	2	no	—
325	#41	—	12	2	no	—
326	C₂×Q₈	—	3	1	no	—
327	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
328	C₂×D₄	—	3	1	no	—
329	C₂×D₄	—	6	1	no	—
330	C₂×D₄	—	6	1	no	—
331	C₂×D₄	—	6	1	no	—
332	C₂×D₄	—	6	1	no	—
333	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	6	4	no	—
342	C₂×C₈	—	6	1	no	—
343	C₂×C₈	—	6	1	no	—
344	C₄⋊C₄	—	6	1	no	—
345	C₄⋊C₄	—	6	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	6	1	no	—
349	C₂²⋊C₄	—	6	1	no	—
350	C₄²	—	3	1	no	—
351	C₄²	—	3	1	no	—
352	C₄²	—	3	1	no	—
353	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₃×C₅	#1530	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	4	1	no	—
356	C₂²×C₃	—	4	1	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	1	no	—
361	C₂×D₃	—	4	1	no	—
362	C₂×D₃	—	4	1	no	—
363	C₂×D₃	—	4	1	no	—
364	C₂×D₃	C₅×#100	1	2	yes	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	4	1	no	—
369	Dic₃	—	2	1	no	—
370	Dic₃	—	2	1	no	—
371	Dic₃	—	4	1	no	—
372	Dic₃	C₅×#104	1	2	yes	—
373	C₂×C₅	—	6	2	no	—
374	C₂×C₅	—	8	1	no	—
375	C₂×C₅	—	24	1	no	—
376	C₂×C₅	D₃×#100	1	1	yes	characteristic
377	C₂×C₅	D₃×#104	1	1	yes	characteristic
378	C₂×C₅	#4821	1	1	yes	characteristic
379	C₂³	—	2	1	no	—
380	C₂³	—	3	1	no	—
381	C₂³	—	6	1	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	12	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	12	1	no	—
386	D₄	—	12	2	no	—
387	D₄	—	12	2	no	—
388	D₄	—	12	2	no	—
389	D₄	—	12	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	3	1	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	6	2	no	—
395	C₂×C₄	—	6	2	no	—
396	C₂×C₄	—	6	1	no	—
397	C₂×C₄	—	12	1	no	—
398	C₂×C₄	—	12	2	no	—
399	C₂×C₄	—	12	2	no	—
400	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
401	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
402	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	6	2	no	—
406	C₈	—	12	1	no	—
407	C₂×C₃	—	8	1	no	—
408	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
409	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
410	C₂×C₃	C₅×#421	1	1	yes	characteristic
411	D₃	—	2	2	no	—
412	D₃	—	8	1	no	—
413	C₅	#68345	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	3	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	6	1	no	—
419	C₂²	—	6	1	no	—
420	C₂²	—	12	1	no	—
421	C₂²	—	12	1	no	—
422	C₂²	—	12	1	no	—
423	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	3	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	6	1	no	—
430	C₄	—	6	1	no	—
431	C₄	—	12	1	no	—
432	C₃	C₅×#1530	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	6	2	no	—
434	C₂	—	8	1	no	—
435	C₂	—	24	1	no	—
436	C₂	C₅×D₃×#100	1	1	yes	characteristic
437	C₂	C₅×D₃×#104	1	1	yes	characteristic
438	C₂	C₅×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#329	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5668	C₂
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#329	D₃
hypocenter	C₃	C₅×#1530
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#329

Complements

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

N	H ≅ G/N	type
2. C₅×#4705	C₂	semidirect
3. C₅×D₃×#97	C₂	semidirect
4. C₃×C₅×#329	C₂	semidirect
5. C₅×#4540	C₂	semidirect
6. C₅×#4464	C₂	semidirect
7. C₅×#4464	C₂	semidirect
28. #68345	C₅	direct (N × H)
35. C₅×#329	D₃	semidirect
67. #4705	C₂×C₅	semidirect
68. D₃×#97	C₂×C₅	semidirect
69. C₃×#329	C₂×C₅	semidirect
70. #4540	C₂×C₅	semidirect
71. #4464	C₂×C₅	semidirect
72. #4464	C₂×C₅	semidirect
176. #329	C₅×D₃	semidirect
354. C₃×C₅	#1530	semidirect
413. C₅	#68345	direct (N × H)
432. C₃	C₅×#1530	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5668	2
C₅×#4705	2
C₅×D₃×#97	2
C₃×C₅×#329	2
C₅×#4540	2
C₅×#4464	2
C₅×#1530	3
#68345	5

Subgroups — C5×#68345 #14284180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68345 #14284180