Subgroups — C₅×#68730 #14307120

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5517	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic
5	C₅×#4555	C₂	1	1	yes	maximal, characteristic
6	C₅×#4532	C₂	1	1	yes	maximal, characteristic
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic
8	C₅×#1986	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×#926	C₂²	1	1	yes	characteristic
13	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₅×#890	C₄	1	1	yes	characteristic, complemented
18	C₅×#890	C₄	1	1	yes	characteristic, complemented
19	C₅×#888	C₄	1	1	yes	characteristic, complemented
20	C₅×#888	C₄	1	1	yes	characteristic, complemented
21	C₅×#878	—	2	1	no	—
22	C₅×#878	—	2	1	no	—
23	C₄×C₅×Dic₆	—	2	1	no	—
24	C₄×C₅×Dic₆	—	2	1	no	—
25	C₅×C₃⋊#95	—	2	1	no	—
26	C₅×#815	—	2	1	no	—
27	C₅×C₈×Dic₃	—	2	1	no	—
28	#68730	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#533	—	3	1	no	—
30	C₄×C₅×M₁₆	—	3	1	no	—
31	C₄×C₅×C₄⋊C₄	—	3	1	no	—
32	C₅×#339	—	3	1	no	—
33	C₅×#339	—	3	1	no	—
34	C₅×#339	—	3	1	no	—
35	C₅×#339	D₃	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₅×Dic₃	—	2	1	no	—
39	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
41	C₂×C₅×Dic₆	—	2	1	no	—
42	C₂×C₅×Dic₆	—	2	1	no	—
43	C₃×C₅×M₁₆	—	2	1	no	—
44	C₃×C₅×M₁₆	Q₈	1	2	yes	complemented
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₅×#217	—	2	1	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₅×Dic₃⋊C₄	—	2	4	no	—
58	C₅×Dic₃⋊C₄	—	2	1	no	—
59	C₅×Dic₃⋊C₄	—	2	1	no	—
60	C₅×Dic₃⋊C₄	—	2	1	no	—
61	C₅×Dic₃⋊C₄	—	2	1	no	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₄×C₅×Dic₃	—	2	1	no	—
64	C₄×C₅×Dic₃	—	2	1	no	—
65	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
67	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
68	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
69	C₅×#208	—	2	1	no	—
70	C₅×#208	Q₈	1	2	yes	complemented
71	C₂×C₅×C₃⋊C₈	—	2	1	no	—
72	#5517	C₂×C₅	1	1	yes	characteristic
73	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic
74	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic
75	C₃×#339	C₂×C₅	1	1	yes	characteristic
76	#4555	C₂×C₅	1	1	yes	characteristic
77	#4532	C₂×C₅	1	1	yes	characteristic
78	#4523	C₂×C₅	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₅×C₄⋊Q₈	—	3	1	no	—
82	C₅×C₄⋊Q₈	—	3	1	no	—
83	C₅×#125	—	3	1	no	—
84	C₅×#125	—	3	1	no	—
85	C₅×C₂²⋊Q₈	—	6	1	no	—
86	C₅×C₂²⋊Q₈	—	6	1	no	—
87	C₄×C₅×Q₈	—	6	1	no	—
88	C₄×C₅×Q₈	—	6	1	no	—
89	C₅×#117	—	3	1	no	—
90	C₅×#117	C₂×D₃	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	—	6	1	no	—
92	C₂×C₄²×C₅	—	3	1	no	—
93	C₂×C₄²×C₅	—	3	1	no	—
94	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
95	C₅×#97	—	6	1	no	—
96	C₄×C₅×C₈	—	6	1	no	—
97	C₅×#95	—	6	1	no	—
98	#1986	—	3	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	—	2	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₅×Dic₆	—	4	2	no	—
123	C₅×Dic₆	—	4	2	no	—
124	C₃×C₅×C₈	—	2	2	no	—
125	C₅×C₃⋊C₈	—	2	2	no	—
126	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
127	C₃×#117	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
129	#926	C₂²×C₅	1	1	yes	characteristic
130	C₂×Dic₃⋊C₄	—	2	1	no	—
131	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂×#208	C₂²×C₅	1	1	yes	characteristic
134	#890	C₄×C₅	1	1	yes	characteristic, complemented
135	#890	C₄×C₅	1	1	yes	characteristic, complemented
136	#888	C₄×C₅	1	1	yes	characteristic, complemented
137	#888	C₄×C₅	1	1	yes	characteristic, complemented
138	#878	—	2	1	no	—
139	#878	—	2	1	no	—
140	C₄×Dic₆	—	2	1	no	—
141	C₄×Dic₆	—	2	1	no	—
142	C₃⋊#95	—	2	1	no	—
143	#815	—	2	1	no	—
144	C₈×Dic₃	—	2	1	no	—
145	C₂×C₅×Q₈	—	6	1	no	—
146	C₂×C₅×Q₈	—	6	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	3	1	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	—	3	2	no	—
154	C₅×M₁₆	—	6	1	no	—
155	C₅×M₁₆	Dic₆	1	2	yes	complemented
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	6	1	no	—
158	C₅×C₄⋊C₄	—	3	1	no	—
159	C₅×C₄⋊C₄	—	3	1	no	—
160	C₅×C₄⋊C₄	—	6	1	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₅×C₄⋊C₄	—	6	1	no	—
164	C₅×C₄⋊C₄	—	6	1	no	—
165	C₅×C₄⋊C₄	—	6	1	no	—
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	6	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	3	1	no	—
175	C₄²×C₅	—	3	1	no	—
176	C₄²×C₅	—	3	1	no	—
177	C₄²×C₅	—	3	1	no	—
178	C₄²×C₅	—	6	1	no	—
179	C₄²×C₅	—	6	1	no	—
180	C₄²×C₅	—	6	1	no	—
181	#533	—	3	1	no	—
182	C₄×M₁₆	—	3	1	no	—
183	C₄×C₄⋊C₄	—	3	1	no	—
184	#339	—	3	1	no	—
185	#339	—	3	1	no	—
186	#339	—	3	1	no	—
187	#339	C₅×D₃	1	1	yes	characteristic
188	C₂²×C₃×C₅	—	2	1	no	—
189	C₂²×C₃×C₅	—	2	1	no	—
190	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	#124	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	—	4	1	no	—
195	C₃×C₄×C₅	—	4	1	no	—
196	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
197	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
198	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
200	C₅×Dic₃	—	2	1	no	—
201	C₅×Dic₃	—	2	1	no	—
202	C₅×Dic₃	—	2	1	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₅×Dic₃	—	4	1	no	—
205	C₅×Dic₃	—	4	1	no	—
206	C₅×Dic₃	#104	1	2	yes	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×Dic₃	—	2	1	no	—
210	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
211	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
212	C₂×Dic₆	—	2	1	no	—
213	C₂×Dic₆	—	2	1	no	—
214	C₃×M₁₆	—	2	1	no	—
215	C₃×M₁₆	C₅×Q₈	1	2	yes	complemented
216	C₂×C₃×C₈	—	2	1	no	—
217	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
218	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₃×C₄²	—	2	1	no	—
222	C₃×C₄²	—	2	1	no	—
223	#217	—	2	1	no	—
224	C₄⋊Dic₃	—	2	1	no	—
225	C₄⋊Dic₃	—	2	1	no	—
226	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
228	Dic₃⋊C₄	—	2	4	no	—
229	Dic₃⋊C₄	—	2	1	no	—
230	Dic₃⋊C₄	—	2	1	no	—
231	Dic₃⋊C₄	—	2	1	no	—
232	Dic₃⋊C₄	—	2	1	no	—
233	C₄×Dic₃	—	2	1	no	—
234	C₄×Dic₃	—	2	1	no	—
235	C₄×Dic₃	—	2	1	no	—
236	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
237	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
238	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
239	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
240	#208	—	2	1	no	—
241	#208	C₅×Q₈	1	2	yes	complemented
242	C₂×C₃⋊C₈	—	2	1	no	—
243	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
244	C₅×Q₈	—	12	2	no	—
245	C₅×Q₈	—	12	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	3	1	no	—
250	C₂×C₄×C₅	—	3	1	no	—
251	C₂×C₄×C₅	—	3	1	no	—
252	C₂×C₄×C₅	—	3	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	—	6	1	no	—
258	C₂×C₄×C₅	—	6	1	no	—
259	C₂×C₄×C₅	—	12	1	no	—
260	C₂×C₄×C₅	—	12	1	no	—
261	C₂×C₄×C₅	—	12	1	no	—
262	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂×C₄×C₅	#235	1	1	yes	characteristic
265	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	#237	1	1	yes	characteristic
267	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	6	2	no	—
270	C₂×M₁₆	—	3	1	no	—
271	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
272	C₄⋊Q₈	—	3	1	no	—
273	C₄⋊Q₈	—	3	1	no	—
274	#125	—	3	1	no	—
275	#125	—	3	1	no	—
276	C₂²⋊Q₈	—	6	1	no	—
277	C₂²⋊Q₈	—	6	1	no	—
278	C₄×Q₈	—	6	1	no	—
279	C₄×Q₈	—	6	1	no	—
280	#117	—	3	1	no	—
281	#117	C₂×C₅×D₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	—	6	1	no	—
283	C₂×C₄²	—	3	1	no	—
284	C₂×C₄²	—	3	1	no	—
285	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
286	#97	—	6	1	no	—
287	C₄×C₈	—	6	1	no	—
288	#95	—	6	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	#391	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
293	C₂×C₃×C₅	#421	1	1	yes	characteristic
294	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	4	1	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
304	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
306	C₂×Dic₃	—	2	2	no	—
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	2	1	no	—
309	C₂×Dic₃	—	2	1	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	—	4	1	no	—
312	C₂×Dic₃	—	4	1	no	—
313	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
317	Dic₆	—	4	2	no	—
318	Dic₆	—	4	2	no	—
319	C₃×C₈	—	2	2	no	—
320	C₃⋊C₈	—	2	2	no	—
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₅	#885	1	1	yes	characteristic
325	C₂²×C₅	#888	1	1	yes	characteristic
326	C₄×C₅	—	3	2	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	—	4	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	6	1	no	—
331	C₄×C₅	—	6	1	no	—
332	C₄×C₅	—	6	1	no	—
333	C₄×C₅	—	12	2	no	—
334	C₄×C₅	—	12	1	no	—
335	C₄×C₅	—	12	1	no	—
336	C₄×C₅	C₄×Dic₆	1	1	yes	characteristic
337	C₄×C₅	#878	1	1	yes	characteristic
338	C₄×C₅	#887	1	1	yes	characteristic
339	C₄×C₅	#896	1	1	yes	characteristic
340	C₂×Q₈	—	6	1	no	—
341	C₂×Q₈	—	6	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
347	M₁₆	—	2	1	no	—
348	M₁₆	—	3	2	no	—
349	M₁₆	—	6	1	no	—
350	M₁₆	C₅×Dic₆	1	2	yes	complemented
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	6	1	no	—
353	C₄⋊C₄	—	3	1	no	—
354	C₄⋊C₄	—	3	1	no	—
355	C₄⋊C₄	—	6	1	no	—
356	C₄⋊C₄	—	6	1	no	—
357	C₄⋊C₄	—	6	1	no	—
358	C₄⋊C₄	—	6	1	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	6	1	no	—
361	C₄⋊C₄	—	6	4	no	—
362	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
363	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	6	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	3	1	no	—
370	C₄²	—	3	1	no	—
371	C₄²	—	3	1	no	—
372	C₄²	—	3	1	no	—
373	C₄²	—	6	1	no	—
374	C₄²	—	6	1	no	—
375	C₄²	—	6	1	no	—
376	C₃×C₅	#1986	1	1	yes	characteristic, complemented, Hall
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₃	C₅×#124	1	1	yes	characteristic
381	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	—	4	1	no	—
384	C₃×C₄	—	4	1	no	—
385	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
386	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
387	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
388	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
389	Dic₃	—	2	1	no	—
390	Dic₃	—	2	1	no	—
391	Dic₃	—	2	1	no	—
392	Dic₃	—	4	2	no	—
393	Dic₃	—	4	1	no	—
394	Dic₃	—	4	1	no	—
395	Dic₃	C₅×#104	1	2	yes	—
396	C₂×C₅	—	2	1	no	—
397	C₂×C₅	—	2	1	no	—
398	C₂×C₅	#4646	1	1	yes	characteristic
399	C₂×C₅	D₃×#104	1	1	yes	characteristic
400	C₂×C₅	#4821	1	1	yes	characteristic
401	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
402	Q₈	—	12	2	no	—
403	Q₈	—	12	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	3	1	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	3	1	no	—
410	C₂×C₄	—	3	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	—	6	2	no	—
415	C₂×C₄	—	6	1	no	—
416	C₂×C₄	—	6	1	no	—
417	C₂×C₄	—	12	1	no	—
418	C₂×C₄	—	12	1	no	—
419	C₂×C₄	—	12	1	no	—
420	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
421	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
422	C₂×C₄	C₅×#235	1	1	yes	characteristic
423	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
424	C₂×C₄	C₅×#237	1	1	yes	characteristic
425	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	6	2	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	C₅×#391	1	1	yes	characteristic
431	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
432	C₂×C₃	C₅×#421	1	1	yes	characteristic
433	C₅	#68730	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
437	C₂²	C₅×#885	1	1	yes	characteristic
438	C₂²	C₅×#888	1	1	yes	characteristic
439	C₄	—	3	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	6	1	no	—
444	C₄	—	6	1	no	—
445	C₄	—	6	1	no	—
446	C₄	—	12	2	no	—
447	C₄	—	12	1	no	—
448	C₄	—	12	1	no	—
449	C₄	C₄×C₅×Dic₆	1	1	yes	characteristic
450	C₄	C₅×#878	1	1	yes	characteristic
451	C₄	C₅×#887	1	1	yes	characteristic
452	C₄	C₅×#896	1	1	yes	characteristic
453	C₃	C₅×#1986	1	1	yes	characteristic, complemented, Sylow
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	C₅×#4646	1	1	yes	characteristic
457	C₂	C₅×D₃×#104	1	1	yes	characteristic
458	C₂	C₅×#4821	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×#339	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#339	D₃
hypocenter	C₃	C₅×#1986
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#339

Complements

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

N	H ≅ G/N	type
17. C₅×#890	C₄	semidirect
18. C₅×#890	C₄	semidirect
19. C₅×#888	C₄	semidirect
20. C₅×#888	C₄	semidirect
28. #68730	C₅	direct (N × H)
44. C₃×C₅×M₁₆	Q₈	semidirect
70. C₅×#208	Q₈	semidirect
134. #890	C₄×C₅	semidirect
135. #890	C₄×C₅	semidirect
136. #888	C₄×C₅	semidirect
137. #888	C₄×C₅	semidirect
155. C₅×M₁₆	Dic₆	semidirect
215. C₃×M₁₆	C₅×Q₈	semidirect
241. #208	C₅×Q₈	semidirect
350. M₁₆	C₅×Dic₆	semidirect
376. C₃×C₅	#1986	semidirect
433. C₅	#68730	direct (N × H)
453. C₃	C₅×#1986	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5517	2
C₅×Dic₃×M₁₆	2
C₄×C₅×Dic₃⋊C₄	2
C₃×C₅×#339	2
C₅×#4555	2
C₅×#4532	2
C₅×#4523	2
C₅×#1986	3
#68730	5

Subgroups — C5×#68730 #14307120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68730 #14307120