Subgroups — D₅×#5078 #14439813

Order 1920.

848 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	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	D₅×#869	C₂	1	1	yes	maximal, characteristic
3	#11751179	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5078	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅×#807	C₂	1	4	yes	maximal
6	#11747139	C₂	1	4	yes	maximal, complemented
7	C₄×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
8	#11746962	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746960	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×#500	—	3	1	no	maximal, Hall
11	C₂×C₃×Q₈×D₅	—	2	1	no	—
12	C₂×D₅×Dic₆	—	2	1	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	#91758	C₂²	1	1	yes	characteristic
15	C₅×#869	C₂²	1	1	yes	characteristic
16	C₃×#4090	—	2	1	no	—
17	C₃×D₅×C₄⋊C₄	—	2	1	no	—
18	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×#4034	—	2	1	no	—
20	C₃×#4034	C₂²	1	2	yes	—
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4015	C₂²	1	1	yes	characteristic
23	#91468	—	2	1	no	—
24	#91468	C₂²	1	2	yes	—
25	D₅×C₄⋊Dic₃	—	2	1	no	—
26	D₅×C₄⋊Dic₃	C₂²	1	2	yes	—
27	#91376	—	2	1	no	—
28	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
29	#91091	C₂²	1	4	yes	—
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₅×#807	C₂²	1	4	yes	—
32	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	#90990	C₂²	1	4	yes	—
34	#90989	C₂²	1	4	yes	—
35	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
36	C₂×#5078	—	5	1	no	maximal, Hall
37	D₅×C₄⋊Q₈	—	3	1	no	—
38	D₅×C₄⋊Q₈	D₃	1	1	yes	characteristic
39	C₅×#500	—	3	1	no	—
40	#65367	—	3	1	no	—
41	#65367	—	3	1	no	—
42	D₅×#107	—	3	4	no	—
43	#65163	—	3	4	no	—
44	C₄×C₈×D₅	—	3	1	no	—
45	#64971	—	3	1	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×Dic₃₀	—	2	1	no	—
48	C₂×C₅×Dic₆	—	2	1	no	—
49	C₃×Q₈×D₅	—	4	4	no	—
50	C₂×C₃×C₄×D₅	—	2	2	no	—
51	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
52	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
54	C₂×C₃×Dic₁₀	—	2	1	no	—
55	C₂×C₃×Dic₁₀	—	2	2	no	—
56	C₂×#1204	—	2	2	no	—
57	C₂×D₅×Dic₃	—	2	2	no	—
58	D₅×Dic₆	—	4	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₄⋊Dic₁₅	—	2	1	no	—
63	C₄⋊Dic₁₅	C₂³	1	2	yes	—
64	C₂×C₃⋊#168	C₂³	1	2	yes	—
65	C₅×C₄⋊Dic₃	—	2	1	no	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₃×C₄⋊Dic₅	—	2	1	no	—
69	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
70	C₃×#683	—	2	2	no	—
71	C₃×#683	—	2	2	no	—
72	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
73	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
75	#6668	—	2	2	no	—
76	#6668	—	2	2	no	—
77	D₅×C₃⋊C₈	Q₈	1	8	yes	complemented
78	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
79	C₂×#869	—	5	1	no	—
80	#5078	—	5	1	no	—
81	#5078	—	5	1	no	—
82	#5078	—	5	4	no	—
83	#5078	—	5	1	no	—
84	#5078	D₅	1	1	yes	characteristic, direct product factor
85	C₂×#807	—	5	4	no	—
86	C₂×C₄×C₃⋊C₈	—	5	1	no	—
87	C₂×Q₈×D₅	—	2	1	no	—
88	C₂×Q₈×D₅	—	6	1	no	—
89	C₅×C₄⋊Q₈	—	3	1	no	—
90	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
91	#4090	—	2	1	no	—
92	#4090	—	6	1	no	—
93	C₂×C₈×D₅	—	3	2	no	—
94	D₅×C₄⋊C₄	—	2	1	no	—
95	D₅×C₄⋊C₄	—	3	2	no	—
96	D₅×C₄⋊C₄	—	6	1	no	—
97	D₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
98	#4034	—	2	1	no	—
99	#4034	—	3	2	no	—
100	#4034	—	6	1	no	—
101	#4034	C₂×D₃	1	2	yes	—
102	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
103	#4015	—	3	1	no	—
104	#4015	C₂×D₃	1	1	yes	characteristic
105	C₅×#107	—	3	4	no	—
106	C₄×C₅×C₈	—	3	1	no	—
107	#3950	—	3	4	no	—
108	C₈×Dic₅	—	3	2	no	—
109	#3939	—	3	4	no	—
110	#3939	—	3	4	no	—
111	C₄×#168	—	3	1	no	—
112	C₂×#500	—	15	1	no	Sylow
113	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×Dic₁₅	—	2	2	no	—
120	Dic₃₀	—	4	2	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₅×Dic₆	—	4	2	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
127	C₃×C₄×D₅	—	4	4	no	—
128	C₃×C₄×D₅	D₈	1	4	yes	—
129	C₃×C₄×D₅	Q₁₆	1	4	yes	—
130	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
131	C₃×Dic₁₀	—	4	2	no	—
132	C₃×Dic₁₀	—	4	4	no	—
133	#1204	—	4	4	no	—
134	D₅×Dic₃	—	4	4	no	—
135	C₃⋊#168	C₂×Q₈	1	4	yes	complemented
136	C₅×C₃⋊C₈	C₂×Q₈	1	4	yes	complemented
137	C₂²×C₃×Q₈	—	10	1	no	—
138	C₂²×Dic₆	—	10	1	no	—
139	C₃×C₄⋊Q₈	—	5	2	no	—
140	C₃×C₄⋊Q₈	—	5	1	no	—
141	C₃×C₄⋊Q₈	—	10	1	no	—
142	C₃×C₄⋊Q₈	—	10	1	no	—
143	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	—	5	2	no	—
145	C₂×C₃×C₄⋊C₄	—	10	1	no	—
146	C₂×C₃×C₄²	—	5	1	no	—
147	C₂×C₄⋊Dic₃	—	5	2	no	—
148	C₂×C₄⋊Dic₃	—	10	1	no	—
149	C₂²×C₃⋊C₈	—	5	2	no	—
150	#869	—	5	1	no	—
151	#869	—	5	2	no	—
152	#869	—	10	1	no	—
153	#869	—	10	1	no	—
154	#869	C₂×D₅	1	1	yes	characteristic
155	#807	—	5	4	no	—
156	#807	—	5	4	no	—
157	#807	—	5	4	no	—
158	#807	C₂×D₅	1	4	yes	—
159	C₄×C₃⋊C₈	—	5	1	no	—
160	C₄×C₃⋊C₈	—	5	2	no	—
161	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	6	1	no	—
164	Q₈×D₅	—	4	4	no	—
165	Q₈×D₅	—	12	4	no	—
166	C₂×C₄×D₅	—	2	2	no	—
167	C₂×C₄×D₅	—	6	2	no	—
168	C₂×C₄×D₅	#67	1	1	yes	characteristic
169	C₂×C₄×D₅	#67	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
171	C₂×Dic₁₀	—	2	1	no	—
172	C₂×Dic₁₀	—	2	2	no	—
173	C₂×Dic₁₀	—	6	1	no	—
174	C₂×Dic₁₀	—	6	2	no	—
175	C₂×C₅×C₈	—	3	2	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	3	2	no	—
178	C₅×C₄⋊C₄	—	6	1	no	—
179	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
180	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₄⋊Dic₅	—	2	1	no	—
182	C₄⋊Dic₅	—	3	2	no	—
183	C₄⋊Dic₅	—	6	1	no	—
184	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
185	#683	—	2	2	no	—
186	#683	—	2	2	no	—
187	#683	—	6	2	no	—
188	#683	—	6	2	no	—
189	C₄×Dic₅	#67	1	1	yes	characteristic
190	C₄×Dic₅	#67	1	1	yes	characteristic
191	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
192	C₂×#168	—	3	2	no	—
193	C₈×D₅	—	3	8	no	—
194	C₂×C₄⋊Q₈	—	5	1	no	—
195	C₂×C₄⋊Q₈	—	15	1	no	—
196	#500	—	3	1	no	—
197	#500	—	15	1	no	—
198	#500	—	15	4	no	—
199	#500	—	15	1	no	—
200	#500	—	15	1	no	—
201	C₂×#107	—	15	4	no	—
202	C₂×C₄×C₈	—	15	1	no	—
203	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₃×D₅	C₄⋊Q₈	1	2	yes	—
205	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
206	C₂×C₃×D₅	C₂×Q₁₆	1	2	yes	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
209	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
210	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
211	Dic₁₅	—	4	2	no	—
212	C₃×Dic₅	—	4	2	no	—
213	C₃×Dic₅	C₄⋊Q₈	1	2	yes	—
214	C₃×Dic₅	C₂×D₈	1	2	yes	—
215	C₃×Dic₅	C₂×Q₁₆	1	2	yes	—
216	C₅×Dic₃	—	4	2	no	—
217	C₂×C₃×Q₈	—	2	1	no	—
218	C₂×C₃×Q₈	—	10	2	no	—
219	C₂×C₃×Q₈	—	10	1	no	—
220	C₂×C₃×Q₈	—	20	4	no	—
221	C₂²×C₃×C₄	—	5	1	no	—
222	C₂²×C₃×C₄	—	5	1	no	—
223	C₂²×C₃×C₄	—	5	1	no	—
224	C₂²×C₃×C₄	—	10	2	no	—
225	C₂²×Dic₃	—	10	2	no	—
226	C₂×Dic₆	—	2	1	no	—
227	C₂×Dic₆	—	10	2	no	—
228	C₂×Dic₆	—	10	1	no	—
229	C₂×Dic₆	—	20	4	no	—
230	C₃×C₄⋊C₄	—	2	1	no	—
231	C₃×C₄⋊C₄	—	5	2	no	—
232	C₃×C₄⋊C₄	—	10	2	no	—
233	C₃×C₄⋊C₄	—	10	2	no	—
234	C₃×C₄⋊C₄	—	10	1	no	—
235	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
236	C₃×C₄²	—	5	1	no	—
237	C₃×C₄²	—	5	1	no	—
238	C₃×C₄²	—	5	1	no	—
239	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
240	C₄⋊Dic₃	—	2	1	no	—
241	C₄⋊Dic₃	—	5	2	no	—
242	C₄⋊Dic₃	—	10	2	no	—
243	C₄⋊Dic₃	—	10	2	no	—
244	C₄⋊Dic₃	—	10	1	no	—
245	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
246	C₂×C₃⋊C₈	—	5	2	no	—
247	C₂×C₃⋊C₈	—	5	8	no	—
248	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
249	C₂²×D₅	C₂×#67	1	1	yes	characteristic
250	C₅×Q₈	—	4	2	no	—
251	C₅×Q₈	—	12	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
257	C₂×Dic₅	—	2	2	no	—
258	C₂×Dic₅	—	6	2	no	—
259	C₂×Dic₅	C₂×#67	1	1	yes	characteristic
260	C₂×Dic₅	C₂×#67	1	1	yes	characteristic
261	C₂×Dic₅	C₂×#67	1	1	yes	characteristic
262	C₄×D₅	—	4	4	no	—
263	C₄×D₅	—	12	4	no	—
264	C₄×D₅	#213	1	4	yes	—
265	C₄×D₅	#216	1	4	yes	—
266	C₄×D₅	D₃×Q₈	1	4	yes	—
267	Dic₁₀	—	4	2	no	—
268	Dic₁₀	—	4	4	no	—
269	Dic₁₀	—	12	2	no	—
270	Dic₁₀	—	12	4	no	—
271	C₅×C₈	—	3	4	no	—
272	#168	—	3	4	no	—
273	C₂²×Q₈	—	10	1	no	—
274	C₂²×Q₈	—	30	1	no	—
275	C₂²×C₈	—	15	2	no	—
276	C₄⋊Q₈	—	3	1	no	—
277	C₄⋊Q₈	—	5	2	no	—
278	C₄⋊Q₈	—	5	1	no	—
279	C₄⋊Q₈	—	10	1	no	—
280	C₄⋊Q₈	—	10	1	no	—
281	C₄⋊Q₈	—	15	2	no	—
282	C₄⋊Q₈	—	15	1	no	—
283	C₄⋊Q₈	—	30	1	no	—
284	C₄⋊Q₈	—	30	1	no	—
285	C₄⋊Q₈	D₃×D₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	—	5	2	no	—
287	C₂×C₄⋊C₄	—	10	1	no	—
288	C₂×C₄⋊C₄	—	15	2	no	—
289	C₂×C₄⋊C₄	—	30	1	no	—
290	C₂×C₄²	—	5	1	no	—
291	#107	—	3	4	no	—
292	#107	—	15	4	no	—
293	#107	—	15	4	no	—
294	#107	—	15	4	no	—
295	C₄×C₈	—	3	1	no	—
296	C₄×C₈	—	15	2	no	—
297	C₄×C₈	—	15	1	no	—
298	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
301	C₃×D₅	#500	1	4	yes	complemented
302	C₂³×C₃	—	5	1	no	—
303	C₃×Q₈	—	4	2	no	—
304	C₃×Q₈	—	20	4	no	—
305	C₃×Q₈	—	20	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	5	1	no	—
308	C₂×C₃×C₄	—	5	1	no	—
309	C₂×C₃×C₄	—	5	1	no	—
310	C₂×C₃×C₄	—	5	4	no	—
311	C₂×C₃×C₄	—	5	4	no	—
312	C₂×C₃×C₄	—	5	4	no	—
313	C₂×C₃×C₄	—	10	2	no	—
314	C₂×C₃×C₄	—	20	4	no	—
315	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
316	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
318	C₂×Dic₃	—	2	2	no	—
319	C₂×Dic₃	—	10	2	no	—
320	C₂×Dic₃	—	20	4	no	—
321	Dic₆	—	4	2	no	—
322	Dic₆	—	20	4	no	—
323	Dic₆	—	20	2	no	—
324	C₃⋊C₈	—	5	4	no	—
325	C₃⋊C₈	Q₈×D₅	1	4	yes	complemented
326	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
327	C₂×D₅	C₂×#213	1	2	yes	—
328	C₂×D₅	C₂×#216	1	2	yes	—
329	C₂×D₅	#944	1	2	yes	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	12	2	no	—
332	C₄×C₅	C₂×#213	1	2	yes	—
333	C₄×C₅	C₂×#216	1	2	yes	—
334	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
335	Dic₅	—	4	2	no	—
336	Dic₅	—	12	2	no	—
337	Dic₅	C₂×#213	1	2	yes	—
338	Dic₅	C₂×#216	1	2	yes	—
339	Dic₅	#944	1	2	yes	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	6	1	no	—
342	C₂×Q₈	—	10	2	no	—
343	C₂×Q₈	—	10	1	no	—
344	C₂×Q₈	—	20	4	no	—
345	C₂×Q₈	—	30	2	no	—
346	C₂×Q₈	—	30	1	no	—
347	C₂×Q₈	—	60	4	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	5	1	no	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	—	10	2	no	—
352	C₂²×C₄	—	30	2	no	—
353	C₂×C₈	—	3	2	no	—
354	C₂×C₈	—	15	8	no	—
355	C₂×C₈	—	15	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	10	2	no	—
361	C₄⋊C₄	—	10	2	no	—
362	C₄⋊C₄	—	10	1	no	—
363	C₄⋊C₄	—	15	2	no	—
364	C₄⋊C₄	—	30	2	no	—
365	C₄⋊C₄	—	30	2	no	—
366	C₄⋊C₄	—	30	1	no	—
367	C₄⋊C₄	C₂×D₃×D₅	1	2	yes	—
368	C₄²	—	5	1	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	5	1	no	—
371	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
372	C₃×C₅	C₂×#500	1	1	yes	characteristic, complemented, Hall
373	C₂²×C₃	—	5	2	no	—
374	C₂²×C₃	—	5	2	no	—
375	C₂²×C₃	—	5	2	no	—
376	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
377	C₃×C₄	—	4	2	no	—
378	C₃×C₄	—	5	2	no	—
379	C₃×C₄	—	5	2	no	—
380	C₃×C₄	—	5	2	no	—
381	C₃×C₄	—	20	2	no	—
382	C₃×C₄	D₅×D₈	1	2	yes	—
383	C₃×C₄	D₅×Q₁₆	1	2	yes	—
384	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
385	Dic₃	—	4	2	no	—
386	Dic₃	—	20	2	no	—
387	C₂×C₅	C₂²×#213	1	1	yes	characteristic
388	C₂×C₅	C₂²×#216	1	1	yes	characteristic
389	C₂×C₅	C₂×#944	1	1	yes	characteristic
390	D₅	#5078	1	4	yes	direct product factor
391	C₂³	—	5	1	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	12	2	no	—
394	Q₈	—	20	4	no	—
395	Q₈	—	20	2	no	—
396	Q₈	—	60	4	no	—
397	Q₈	—	60	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	5	4	no	—
403	C₂×C₄	—	5	4	no	—
404	C₂×C₄	—	5	4	no	—
405	C₂×C₄	—	6	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	20	4	no	—
408	C₂×C₄	—	30	2	no	—
409	C₂×C₄	—	60	4	no	—
410	C₂×C₄	D₅×#67	1	1	yes	characteristic
411	C₂×C₄	D₅×#67	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
413	C₈	—	3	4	no	—
414	C₈	—	15	4	no	—
415	C₂×C₃	—	5	4	no	—
416	C₂×C₃	D₅×C₄⋊Q₈	1	1	yes	characteristic
417	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
418	C₂×C₃	C₂×D₅×Q₁₆	1	1	yes	characteristic
419	C₅	C₂×#5078	1	1	yes	characteristic, complemented, Sylow
420	C₂²	—	5	2	no	—
421	C₂²	—	5	2	no	—
422	C₂²	—	5	2	no	—
423	C₂²	C₂×D₅×#67	1	1	yes	characteristic
424	C₄	—	4	2	no	—
425	C₄	—	5	2	no	—
426	C₄	—	5	2	no	—
427	C₄	—	5	2	no	—
428	C₄	—	12	2	no	—
429	C₄	—	20	2	no	—
430	C₄	—	60	2	no	—
431	C₄	D₅×#213	1	2	yes	—
432	C₄	D₅×#216	1	2	yes	—
433	C₄	D₃×Q₈×D₅	1	2	yes	—
434	C₃	D₅×#500	1	1	yes	characteristic, complemented, Sylow
435	C₂	—	5	4	no	—
436	C₂	C₂×D₅×#213	1	1	yes	characteristic
437	C₂	C₂×D₅×#216	1	1	yes	characteristic
438	C₂	D₅×#944	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅×#67
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×C₄⋊Q₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
hypercenter	C₄⋊Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#500
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #11751179	C₂	semidirect
4. C₅×#5078	C₂	semidirect
6. #11747139	C₂	semidirect
8. #11746962	C₂	semidirect
9. #11746960	C₂	semidirect
77. D₅×C₃⋊C₈	Q₈	semidirect
84. #5078	D₅	direct (N × H)
135. C₃⋊#168	C₂×Q₈	semidirect
136. C₅×C₃⋊C₈	C₂×Q₈	semidirect
301. C₃×D₅	#500	semidirect
325. C₃⋊C₈	Q₈×D₅	semidirect
372. C₃×C₅	C₂×#500	semidirect
390. D₅	#5078	direct (N × H)
419. C₅	C₂×#5078	semidirect
434. C₃	D₅×#500	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₅×C₄⋊Q₈	2
D₅×#869	2
#11751179	2
C₅×#5078	2
D₅×#807	2
#11747139	2
C₄×D₅×C₃⋊C₈	2
#11746962	2
#11746960	2
D₅×#500	3
C₂×#5078	5

Subgroups — D5×#5078 #14439813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#5078 #14439813