Subgroups — C₅×#70354 #14295636

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1759	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×Q₈×Dic₃	C₄	1	2	yes	complemented
13	C₅×D₄×Dic₃	—	2	2	no	—
14	C₅×D₄×Dic₃	C₄	1	2	yes	complemented
15	C₅×#926	—	2	1	no	—
16	C₅×#926	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	—	2	1	no	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₃×C₅×#104	C₄	1	4	yes	complemented
22	C₅×#837	C₄	1	4	yes	complemented
23	C₅×C₃⋊#95	—	2	2	no	—
24	C₅×#815	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	#70354	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₄×C₅×#41	—	3	1	no	—
28	C₂×C₅×#104	—	3	1	no	—
29	C₂×C₅×#104	D₃	1	1	yes	characteristic
30	C₄×C₅×M₁₆	—	3	1	no	—
31	C₅×#376	—	3	1	no	—
32	C₅×#339	—	3	1	no	—
33	C₅×#339	—	3	1	no	—
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	2	yes	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	2	2	no	—
46	C₂²×C₅×Dic₃	D₄	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
52	C₅×#217	—	2	1	no	—
53	C₅×#217	—	2	2	no	—
54	C₅×C₄⋊Dic₃	—	2	2	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	—	2	2	no	—
59	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
60	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₅×#208	—	2	1	no	—
64	C₅×#208	C₂×C₄	1	2	yes	complemented
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	Dic₃×#41	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic
68	C₂×#837	C₂×C₅	1	1	yes	characteristic
69	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
70	#4932	C₂×C₅	1	1	yes	characteristic, complemented
71	#4555	C₂×C₅	1	1	yes	characteristic, complemented
72	#4523	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×Q₈	—	3	2	no	—
77	C₄×C₅×D₄	—	3	2	no	—
78	C₄×C₅×D₄	—	6	2	no	—
79	C₅×#117	—	3	1	no	—
80	C₅×#117	—	6	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×C₄²×C₅	—	3	1	no	—
83	C₂×C₄²×C₅	—	6	1	no	—
84	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
85	C₅×#104	—	3	4	no	—
86	C₅×#104	Dic₃	1	4	yes	complemented
87	C₅×#97	—	6	1	no	—
88	C₄×C₅×C₈	—	6	1	no	—
89	C₅×#95	—	6	2	no	—
90	#1759	—	3	1	no	Sylow
91	C₂³×C₃×C₅	—	2	1	no	—
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₃×C₅×Q₈	C₄²	1	2	yes	—
95	C₃×C₅×D₄	—	2	2	no	—
96	C₃×C₅×D₄	—	2	2	no	—
97	C₃×C₅×D₄	—	2	1	no	—
98	C₃×C₅×D₄	C₄²	1	2	yes	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	2	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	4	2	no	—
113	C₂×C₅×Dic₃	—	4	4	no	—
114	C₂×C₅×Dic₃	—	4	2	no	—
115	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
116	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
117	C₃×C₅×C₈	—	2	2	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
122	Q₈×Dic₃	C₄×C₅	1	2	yes	complemented
123	D₄×Dic₃	—	2	2	no	—
124	D₄×Dic₃	C₄×C₅	1	2	yes	complemented
125	#926	—	2	1	no	—
126	#926	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₄×Dic₃	—	2	1	no	—
128	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
130	C₂×#208	C₂²×C₅	1	1	yes	characteristic
131	C₃×#104	C₄×C₅	1	4	yes	complemented
132	#837	C₄×C₅	1	4	yes	complemented
133	C₃⋊#95	—	2	2	no	—
134	#815	—	2	1	no	—
135	C₈×Dic₃	—	2	1	no	—
136	C₅×#41	—	2	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₅×#41	C₄×D₃	1	2	yes	—
139	C₅×#41	C₂×Dic₃	1	2	yes	—
140	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	3	2	no	—
146	C₂²×C₄×C₅	—	6	2	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	—	3	2	no	—
151	C₅×M₁₆	—	6	1	no	—
152	C₅×M₁₆	C₂×Dic₃	1	2	yes	complemented
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	6	1	no	—
155	C₅×C₄⋊C₄	—	3	2	no	—
156	C₅×C₄⋊C₄	—	6	2	no	—
157	C₅×C₂²⋊C₄	—	6	2	no	—
158	C₅×C₂²⋊C₄	—	6	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	3	2	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	3	2	no	—
164	C₄²×C₅	—	6	2	no	—
165	C₄²×C₅	—	6	1	no	—
166	C₄²×C₅	—	6	1	no	—
167	C₄²×C₅	C₂×Dic₃	1	2	yes	complemented
168	C₄×#41	—	3	1	no	—
169	C₂×#104	—	3	1	no	—
170	C₂×#104	C₅×D₃	1	1	yes	characteristic
171	C₄×M₁₆	—	3	1	no	—
172	#376	—	3	1	no	—
173	#339	—	3	1	no	—
174	#339	—	3	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
181	C₃×C₄×C₅	—	2	2	no	—
182	C₃×C₄×C₅	—	4	2	no	—
183	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
184	C₃×C₄×C₅	#117	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
187	C₅×Dic₃	—	2	2	no	—
188	C₅×Dic₃	—	2	2	no	—
189	C₅×Dic₃	—	4	2	no	—
190	C₅×Dic₃	—	4	2	no	—
191	C₃×#41	—	2	1	no	—
192	C₃×#41	—	2	1	no	—
193	C₃×#41	C₂×C₄×C₅	1	2	yes	—
194	C₃×#41	C₂×C₄×C₅	1	2	yes	—
195	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂²×Dic₃	—	2	1	no	—
202	C₂²×Dic₃	—	2	2	no	—
203	C₂²×Dic₃	C₅×D₄	1	2	yes	—
204	C₃×M₁₆	—	2	1	no	—
205	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	complemented
206	C₂×C₃×C₈	—	2	1	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	C₂×C₄×C₅	1	2	yes	complemented
209	#217	—	2	1	no	—
210	#217	—	2	2	no	—
211	C₄⋊Dic₃	—	2	2	no	—
212	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
213	C₄×Dic₃	—	2	1	no	—
214	C₄×Dic₃	—	2	1	no	—
215	C₄×Dic₃	—	2	2	no	—
216	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
217	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	complemented
218	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
219	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
220	#208	—	2	1	no	—
221	#208	C₂×C₄×C₅	1	2	yes	complemented
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂³×C₅	—	2	1	no	—
224	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	C₄×Dic₃	1	2	yes	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	2	1	no	—
230	C₅×D₄	C₄×Dic₃	1	2	yes	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	3	2	no	—
236	C₂×C₄×C₅	—	3	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	6	2	no	—
239	C₂×C₄×C₅	—	6	2	no	—
240	C₂×C₄×C₅	—	12	2	no	—
241	C₂×C₄×C₅	—	12	4	no	—
242	C₂×C₄×C₅	—	12	2	no	—
243	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	#237	1	1	yes	characteristic
247	C₂×C₄×C₅	#237	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	6	2	no	—
251	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
252	C₂×M₁₆	—	3	1	no	—
253	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
254	C₄×Q₈	—	3	2	no	—
255	C₄×D₄	—	3	2	no	—
256	C₄×D₄	—	6	2	no	—
257	#117	—	3	1	no	—
258	#117	—	6	1	no	—
259	C₂×C₄²	—	3	1	no	—
260	C₂×C₄²	—	3	1	no	—
261	C₂×C₄²	—	6	1	no	—
262	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
263	#104	—	3	4	no	—
264	#104	C₅×Dic₃	1	4	yes	complemented
265	#97	—	6	1	no	—
266	C₄×C₈	—	6	1	no	—
267	#95	—	6	2	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	—	4	2	no	—
271	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₃×C₅	#421	1	2	yes	—
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
275	C₃×Q₈	—	2	1	no	—
276	C₃×Q₈	C₄²×C₅	1	2	yes	—
277	C₃×D₄	—	2	2	no	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	2	1	no	—
280	C₃×D₄	C₄²×C₅	1	2	yes	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	4	2	no	—
286	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×C₄×C₅	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	C₅×#41	1	1	yes	characteristic
291	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
292	C₂×Dic₃	—	2	2	no	—
293	C₂×Dic₃	—	2	2	no	—
294	C₂×Dic₃	—	4	2	no	—
295	C₂×Dic₃	—	4	4	no	—
296	C₂×Dic₃	—	4	2	no	—
297	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
298	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
299	C₃×C₈	—	2	2	no	—
300	C₃⋊C₈	—	2	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
306	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	—	6	2	no	—
310	C₄×C₅	—	6	2	no	—
311	C₄×C₅	—	12	2	no	—
312	C₄×C₅	—	12	2	no	—
313	C₄×C₅	#877	1	1	yes	characteristic
314	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
315	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
316	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
317	#41	—	2	1	no	—
318	#41	—	2	1	no	—
319	#41	C₄×C₅×D₃	1	2	yes	—
320	#41	C₂×C₅×Dic₃	1	2	yes	—
321	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	3	2	no	—
327	C₂²×C₄	—	6	2	no	—
328	C₂²×C₄	—	6	1	no	—
329	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
330	M₁₆	—	2	1	no	—
331	M₁₆	—	3	2	no	—
332	M₁₆	—	6	1	no	—
333	M₁₆	C₂×C₅×Dic₃	1	2	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	6	1	no	—
336	C₄⋊C₄	—	3	2	no	—
337	C₄⋊C₄	—	6	2	no	—
338	C₂²⋊C₄	—	6	2	no	—
339	C₂²⋊C₄	—	6	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	3	2	no	—
342	C₄²	—	3	1	no	—
343	C₄²	—	3	1	no	—
344	C₄²	—	3	2	no	—
345	C₄²	—	6	2	no	—
346	C₄²	—	6	1	no	—
347	C₄²	—	6	1	no	—
348	C₄²	C₂×C₅×Dic₃	1	2	yes	complemented
349	C₃×C₅	#1759	1	1	yes	characteristic, complemented, Hall
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
359	C₃×C₄	C₅×#117	1	1	yes	characteristic
360	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
361	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
362	Dic₃	—	2	2	no	—
363	Dic₃	—	2	2	no	—
364	Dic₃	—	4	2	no	—
365	Dic₃	—	4	2	no	—
366	C₂×C₅	—	2	1	no	—
367	C₂×C₅	—	2	1	no	—
368	C₂×C₅	—	4	2	no	—
369	C₂×C₅	#4821	1	2	yes	—
370	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
371	C₂³	—	2	1	no	—
372	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	C₄×C₅×Dic₃	1	2	yes	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	1	no	—
378	D₄	C₄×C₅×Dic₃	1	2	yes	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	6	2	no	—
387	C₂×C₄	—	6	2	no	—
388	C₂×C₄	—	12	2	no	—
389	C₂×C₄	—	12	4	no	—
390	C₂×C₄	—	12	2	no	—
391	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
393	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
394	C₂×C₄	C₅×#237	1	1	yes	characteristic
395	C₂×C₄	C₅×#237	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	6	2	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	4	2	no	—
402	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₃	C₅×#421	1	2	yes	—
404	C₅	#70354	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
409	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
410	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	6	2	no	—
414	C₄	—	6	2	no	—
415	C₄	—	12	2	no	—
416	C₄	—	12	2	no	—
417	C₄	C₅×#877	1	1	yes	characteristic
418	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
419	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
420	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
421	C₃	C₅×#1759	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	C₅×#4821	1	2	yes	—
426	C₂	C₅×Dic₃×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₅×#1759
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
4. C₅×Dic₃×M₁₆	C₂	semidirect
5. C₅×#4932	C₂	semidirect
6. C₅×#4555	C₂	semidirect
7. C₅×#4523	C₂	semidirect
12. C₅×Q₈×Dic₃	C₄	semidirect
14. C₅×D₄×Dic₃	C₄	semidirect
21. C₃×C₅×#104	C₄	semidirect
22. C₅×#837	C₄	semidirect
26. #70354	C₅	direct (N × H)
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
51. C₃×C₄²×C₅	C₂×C₄	semidirect
60. C₄×C₅×Dic₃	C₂×C₄	semidirect
64. C₅×#208	C₂×C₄	semidirect
69. Dic₃×M₁₆	C₂×C₅	semidirect
70. #4932	C₂×C₅	semidirect
71. #4555	C₂×C₅	semidirect
72. #4523	C₂×C₅	semidirect
86. C₅×#104	Dic₃	semidirect
122. Q₈×Dic₃	C₄×C₅	semidirect
124. D₄×Dic₃	C₄×C₅	semidirect
131. C₃×#104	C₄×C₅	semidirect
132. #837	C₄×C₅	semidirect
152. C₅×M₁₆	C₂×Dic₃	semidirect
167. C₄²×C₅	C₂×Dic₃	semidirect
205. C₃×M₁₆	C₂×C₄×C₅	semidirect
208. C₃×C₄²	C₂×C₄×C₅	semidirect
217. C₄×Dic₃	C₂×C₄×C₅	semidirect
221. #208	C₂×C₄×C₅	semidirect
264. #104	C₅×Dic₃	semidirect
333. M₁₆	C₂×C₅×Dic₃	semidirect
348. C₄²	C₂×C₅×Dic₃	semidirect
349. C₃×C₅	#1759	semidirect
404. C₅	#70354	direct (N × H)
421. C₃	C₅×#1759	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₃×#41	2
C₂×C₃×C₅×#104	2
C₂×C₅×#837	2
C₅×Dic₃×M₁₆	2
C₅×#4932	2
C₅×#4555	2
C₅×#4523	2
C₅×#1759	3
#70354	5

Subgroups — C5×#70354 #14295636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70354 #14295636