Subgroups — Dic₅×#825 #14295609

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	Dic₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#825	C₂	1	1	yes	maximal, characteristic
3	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90978	C₂	1	1	yes	maximal, characteristic
6	#11746376	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745976	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×#104	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	#91815	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	Dic₅×#67	—	2	2	no	—
17	C₂×Dic₃×Dic₅	—	2	2	no	—
18	Dic₅×D₁₂	C₄	1	2	yes	complemented
19	C₄×D₃×Dic₅	—	2	1	no	—
20	#91371	—	2	1	no	—
21	Dic₅×Dic₆	C₄	1	2	yes	complemented
22	C₅×#825	C₄	1	4	yes	complemented
23	C₃×#3947	—	2	1	no	—
24	C₃×C₈×Dic₅	—	2	1	no	—
25	#90978	C₄	1	4	yes	complemented
26	C₄×#825	—	5	1	no	maximal, Hall
27	#41×Dic₅	—	3	1	no	—
28	C₂×C₅×#104	—	3	1	no	—
29	C₂×#3969	—	3	1	no	—
30	M₁₆×Dic₅	D₃	1	1	yes	characteristic, complemented
31	C₄²×Dic₅	—	3	1	no	—
32	#64775	—	3	1	no	—
33	#64743	—	3	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₅	—	2	1	no	—
36	C₂×C₅×#67	—	2	1	no	—
37	C₂²×C₅×Dic₃	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	C₂×C₄	1	2	yes	—
41	C₅×#235	C₂×C₄	1	2	yes	—
42	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	D₄	1	2	yes	—
46	C₂×D₃×Dic₅	—	2	2	no	—
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	#6719	—	2	1	no	—
51	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₅	—	2	1	no	—
53	C₄×Dic₁₅	—	2	1	no	—
54	C₄×Dic₁₅	C₂×C₄	1	2	yes	complemented
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
57	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
58	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
59	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
60	C₃×#681	—	2	1	no	—
61	C₃×#681	C₂×C₄	1	2	yes	complemented
62	C₂×C₃×#168	—	2	1	no	—
63	Dic₃⋊Dic₅	—	2	2	no	—
64	(C₂×D₃)⋊Dic₅	—	2	2	no	—
65	Dic₃×Dic₅	—	2	8	no	—
66	Dic₃×Dic₅	—	2	2	no	—
67	C₄×#235	—	5	1	no	—
68	C₃×C₄×M₁₆	—	5	1	no	—
69	C₂×#825	—	5	1	no	—
70	C₂×#825	D₅	1	1	yes	characteristic
71	C₄²×Dic₃	—	5	1	no	—
72	#4555	—	5	1	no	—
73	#4555	—	5	1	no	—
74	C₂×C₅×#41	—	3	1	no	—
75	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	—	3	1	no	—
77	Q₈×Dic₅	—	3	2	no	—
78	D₄×Dic₅	—	3	2	no	—
79	D₄×Dic₅	—	6	2	no	—
80	#4072	—	3	1	no	—
81	#4072	—	6	1	no	—
82	C₂×C₄×Dic₅	—	3	1	no	—
83	C₂×C₄×Dic₅	—	6	2	no	—
84	C₂×C₄×Dic₅	—	6	1	no	—
85	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
86	C₂×#681	C₂×D₃	1	1	yes	characteristic
87	C₅×#104	—	3	4	no	—
88	#3969	—	3	4	no	—
89	#3947	—	2	1	no	—
90	C₈×Dic₅	—	2	1	no	—
91	C₄×#104	—	15	1	no	Sylow
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×Dic₁₅	—	2	4	no	—
101	C₂×Dic₁₅	—	2	2	no	—
102	C₂×Dic₁₅	—	2	2	no	—
103	C₅×#67	—	2	2	no	—
104	C₅×#67	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	4	no	—
106	C₂×C₅×Dic₃	—	2	1	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₅×D₁₂	—	2	1	no	—
109	C₅×D₁₂	C₄²	1	2	yes	complemented
110	C₄×C₅×D₃	—	2	2	no	—
111	C₄×C₅×D₃	—	2	2	no	—
112	C₅×Dic₆	—	2	1	no	—
113	C₅×Dic₆	C₄²	1	2	yes	complemented
114	C₂×C₃×Dic₅	—	2	4	no	—
115	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
117	D₃×Dic₅	—	4	4	no	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃×#168	—	2	2	no	—
120	C₂×#235	C₂×D₅	1	1	yes	characteristic
121	C₂×C₃×M₁₆	—	5	1	no	—
122	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
123	C₂×C₃×C₄²	—	5	1	no	—
124	C₄×#67	—	10	2	no	—
125	#926	—	5	1	no	—
126	C₂×C₄×Dic₃	—	5	1	no	—
127	C₂×C₄×Dic₃	—	10	2	no	—
128	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
129	C₄×D₁₂	—	5	2	no	—
130	#872	—	10	1	no	—
131	C₄²×D₃	—	10	1	no	—
132	C₄×Dic₆	—	5	2	no	—
133	C₃×#97	—	10	1	no	—
134	C₃×C₄×C₈	—	10	1	no	—
135	#825	—	5	4	no	—
136	#825	Dic₅	1	4	yes	direct product factor
137	C₅×#41	—	3	2	no	—
138	C₅×#41	—	3	2	no	—
139	C₅×#41	—	6	1	no	—
140	C₅×#41	—	6	1	no	—
141	C₂×C₅×Q₈	—	3	1	no	—
142	C₂×C₅×D₄	—	3	1	no	—
143	C₂×C₅×D₄	—	6	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×Dic₅	—	6	1	no	—
148	C₂²×Dic₅	—	6	2	no	—
149	C₂²×Dic₅	D₁₂	1	2	yes	—
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	C₄×D₃	1	2	yes	complemented
152	C₂×C₅×C₈	—	2	1	no	—
153	C₄²×C₅	—	3	2	no	—
154	C₄²×C₅	—	6	1	no	—
155	C₂²⋊Dic₅	—	6	1	no	—
156	C₂²⋊Dic₅	—	6	2	no	—
157	C₄⋊Dic₅	—	3	2	no	—
158	C₄⋊Dic₅	—	6	2	no	—
159	C₄×Dic₅	—	3	2	no	—
160	C₄×Dic₅	—	6	8	no	—
161	C₄×Dic₅	—	6	1	no	—
162	C₄×Dic₅	—	6	1	no	—
163	C₄×Dic₅	—	6	2	no	—
164	C₄×Dic₅	C₄×D₃	1	2	yes	—
165	C₄×Dic₅	#67	1	1	yes	characteristic
166	C₄×Dic₅	#67	1	1	yes	characteristic
167	#681	—	2	1	no	—
168	#681	C₄×D₃	1	2	yes	complemented
169	C₂×#168	—	2	1	no	—
170	C₄×#41	—	15	1	no	—
171	C₂×#104	—	3	1	no	—
172	C₂×#104	—	15	1	no	—
173	C₄×M₁₆	—	5	1	no	—
174	C₄³	—	15	1	no	—
175	#339	—	15	1	no	—
176	#339	—	15	1	no	—
177	C₂²×C₃×C₅	—	2	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	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	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	Dic₁₅	—	2	4	no	—
188	Dic₁₅	—	4	2	no	—
189	C₃×Dic₅	—	2	2	no	—
190	C₃×Dic₅	#104	1	4	yes	complemented
191	C₅×Dic₃	—	2	4	no	—
192	C₅×Dic₃	—	2	2	no	—
193	C₂²×C₃×C₄	—	5	2	no	—
194	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
195	C₂×#67	—	2	1	no	—
196	C₂²×Dic₃	—	2	1	no	—
197	C₂²×Dic₃	—	10	1	no	—
198	#235	—	2	1	no	—
199	#235	—	2	1	no	—
200	#235	C₄×D₅	1	2	yes	—
201	#235	C₂×Dic₅	1	2	yes	—
202	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×C₄×D₃	—	10	2	no	—
205	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	—	5	2	no	—
208	C₃×M₁₆	—	10	1	no	—
209	C₃×M₁₆	C₂×Dic₅	1	2	yes	complemented
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	10	1	no	—
212	C₃×C₄²	—	5	2	no	—
213	C₃×C₄²	—	5	1	no	—
214	C₃×C₄²	—	5	1	no	—
215	#217	—	10	1	no	—
216	(C₂×D₃)⋊C₄	—	10	2	no	—
217	C₄⋊Dic₃	—	5	2	no	—
218	Dic₃⋊C₄	—	10	2	no	—
219	C₄×Dic₃	—	2	1	no	—
220	C₄×Dic₃	—	5	2	no	—
221	C₄×Dic₃	—	10	2	no	—
222	C₄×Dic₃	—	10	8	no	—
223	C₄×Dic₃	—	10	1	no	—
224	C₄×Dic₃	—	10	1	no	—
225	C₄×Dic₃	C₂×Dic₅	1	2	yes	complemented
226	C₂³×C₅	—	6	1	no	—
227	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
228	C₅×Q₈	—	3	2	no	—
229	C₅×Q₈	—	6	1	no	—
230	C₅×D₄	—	3	2	no	—
231	C₅×D₄	—	6	2	no	—
232	C₅×D₄	—	6	2	no	—
233	C₅×D₄	—	6	1	no	—
234	C₂×C₄×C₅	—	6	4	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	2	no	—
238	C₂×C₄×C₅	—	6	2	no	—
239	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₄×C₅	#235	1	1	yes	characteristic
243	C₂×C₄×C₅	#235	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
245	C₂×Dic₅	—	2	4	no	—
246	C₂×Dic₅	—	6	4	no	—
247	C₂×Dic₅	—	6	2	no	—
248	C₂×Dic₅	—	6	2	no	—
249	C₂×Dic₅	—	12	4	no	—
250	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
251	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
252	C₅×C₈	—	2	2	no	—
253	#168	—	2	2	no	—
254	C₂×#41	—	3	1	no	—
255	C₂×M₁₆	—	5	1	no	—
256	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
257	C₄×Q₈	—	15	2	no	—
258	C₄×D₄	—	15	2	no	—
259	C₄×D₄	—	30	2	no	—
260	#117	—	15	1	no	—
261	#117	—	30	1	no	—
262	C₂×C₄²	—	3	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	15	1	no	—
265	C₂×C₄²	—	30	1	no	—
266	C₂×C₄²	—	30	2	no	—
267	#104	—	3	4	no	—
268	#104	—	15	4	no	—
269	#97	—	10	1	no	—
270	C₄×C₈	—	10	1	no	—
271	C₂×C₃×C₅	—	2	1	no	—
272	C₂×C₃×C₅	—	2	1	no	—
273	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#104	1	2	yes	—
275	C₅×D₃	—	4	2	no	—
276	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
277	C₂²×D₃	—	2	1	no	—
278	C₂×C₃×C₄	—	5	2	no	—
279	C₂×C₃×C₄	—	5	2	no	—
280	C₂×C₃×C₄	—	10	4	no	—
281	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	#711	1	1	yes	characteristic
285	C₂×C₃×C₄	#711	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
287	#67	—	2	2	no	—
288	#67	—	2	2	no	—
289	C₂×Dic₃	—	2	4	no	—
290	C₂×Dic₃	—	2	1	no	—
291	C₂×Dic₃	—	2	2	no	—
292	C₂×Dic₃	—	10	4	no	—
293	C₂×Dic₃	—	10	2	no	—
294	C₂×Dic₃	—	10	2	no	—
295	D₁₂	—	2	1	no	—
296	D₁₂	C₄×Dic₅	1	2	yes	complemented
297	C₄×D₃	—	2	2	no	—
298	C₄×D₃	—	2	2	no	—
299	C₄×D₃	—	20	4	no	—
300	Dic₆	—	2	1	no	—
301	Dic₆	C₄×Dic₅	1	2	yes	complemented
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	10	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	6	2	no	—
306	C₂²×C₅	—	12	2	no	—
307	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
308	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
309	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
310	C₄×C₅	—	6	4	no	—
311	C₄×C₅	—	6	2	no	—
312	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
313	C₄×C₅	#872	1	1	yes	characteristic
314	C₄×C₅	C₄×#67	1	1	yes	characteristic
315	C₄×C₅	C₄×#67	1	1	yes	characteristic
316	Dic₅	—	2	2	no	—
317	Dic₅	—	6	4	no	—
318	Dic₅	—	12	2	no	—
319	Dic₅	#825	1	4	yes	direct product factor
320	#41	—	3	2	no	—
321	#41	—	3	2	no	—
322	#41	—	6	1	no	—
323	#41	—	6	1	no	—
324	C₂×Q₈	—	3	1	no	—
325	C₂×D₄	—	3	1	no	—
326	C₂×D₄	—	6	1	no	—
327	C₂²×C₄	—	5	2	no	—
328	C₂²×C₄	—	6	1	no	—
329	C₂²×C₄	—	6	1	no	—
330	C₂²×C₄	—	30	2	no	—
331	C₂²×C₄	—	30	1	no	—
332	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
333	M₁₆	—	2	1	no	—
334	M₁₆	—	5	2	no	—
335	M₁₆	—	10	1	no	—
336	M₁₆	D₃×Dic₅	1	2	yes	complemented
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	10	1	no	—
339	C₄⋊C₄	—	15	2	no	—
340	C₄⋊C₄	—	30	2	no	—
341	C₂²⋊C₄	—	30	2	no	—
342	C₂²⋊C₄	—	30	1	no	—
343	C₄²	—	3	2	no	—
344	C₄²	—	5	2	no	—
345	C₄²	—	5	1	no	—
346	C₄²	—	5	1	no	—
347	C₄²	—	6	1	no	—
348	C₄²	—	15	2	no	—
349	C₄²	—	30	2	no	—
350	C₄²	—	30	8	no	—
351	C₄²	—	30	1	no	—
352	C₄²	—	30	1	no	—
353	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
356	C₂²×C₃	#4027	1	1	yes	characteristic
357	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
358	C₂×D₃	—	2	2	no	—
359	C₂×D₃	—	4	2	no	—
360	C₃×C₄	—	5	4	no	—
361	C₃×C₄	—	10	2	no	—
362	C₃×C₄	#4023	1	1	yes	characteristic
363	C₃×C₄	#4027	1	1	yes	characteristic
364	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
365	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
366	Dic₃	—	2	4	no	—
367	Dic₃	—	2	2	no	—
368	Dic₃	—	10	4	no	—
369	Dic₃	—	20	2	no	—
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	12	2	no	—
373	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
374	C₂×C₅	C₂×#825	1	2	yes	—
375	C₂³	—	6	1	no	—
376	C₂³	D₅×D₁₂	1	1	yes	characteristic
377	Q₈	—	3	2	no	—
378	Q₈	—	6	1	no	—
379	D₄	—	3	2	no	—
380	D₄	—	6	2	no	—
381	D₄	—	6	2	no	—
382	D₄	—	6	1	no	—
383	C₂×C₄	—	5	2	no	—
384	C₂×C₄	—	5	2	no	—
385	C₂×C₄	—	6	4	no	—
386	C₂×C₄	—	6	2	no	—
387	C₂×C₄	—	6	1	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	6	2	no	—
390	C₂×C₄	—	10	4	no	—
391	C₂×C₄	—	30	4	no	—
392	C₂×C₄	—	30	2	no	—
393	C₂×C₄	—	30	2	no	—
394	C₂×C₄	—	60	4	no	—
395	C₂×C₄	#6772	1	1	yes	characteristic
396	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
397	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
398	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
399	C₂×C₄	#6782	1	1	yes	characteristic
400	C₂×C₄	D₅×#67	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	10	2	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	D₅×#104	1	2	yes	—
406	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
407	D₃	—	4	2	no	—
408	C₅	C₄×#825	1	1	yes	characteristic, complemented, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	6	2	no	—
411	C₂²	—	12	2	no	—
412	C₂²	#91405	1	1	yes	characteristic
413	C₂²	Dic₅×D₁₂	1	1	yes	characteristic
414	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
415	C₄	—	5	4	no	—
416	C₄	—	6	4	no	—
417	C₄	—	6	2	no	—
418	C₄	—	10	2	no	—
419	C₄	—	30	4	no	—
420	C₄	—	60	2	no	—
421	C₄	C₄×D₃×Dic₅	1	1	yes	characteristic
422	C₄	#91398	1	1	yes	characteristic
423	C₄	#91440	1	1	yes	characteristic
424	C₄	Dic₅×#67	1	1	yes	characteristic
425	C₃	Dic₅×#104	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	12	2	no	—
429	C₂	D₅×#825	1	2	yes	—
430	C₂	Dic₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×#67
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	C₄×#104
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₃×M₁₆×Dic₅	C₂	semidirect
4. C₄×Dic₃×Dic₅	C₂	semidirect
6. #11746376	C₂	semidirect
7. #11745976	C₂	semidirect
18. Dic₅×D₁₂	C₄	semidirect
21. Dic₅×Dic₆	C₄	semidirect
22. C₅×#825	C₄	semidirect
25. #90978	C₄	semidirect
30. M₁₆×Dic₅	D₃	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
54. C₄×Dic₁₅	C₂×C₄	semidirect
56. C₄×C₅×Dic₃	C₂×C₄	semidirect
61. C₃×#681	C₂×C₄	semidirect
109. C₅×D₁₂	C₄²	semidirect
113. C₅×Dic₆	C₄²	semidirect
136. #825	Dic₅	direct (N × H)
151. C₅×M₁₆	C₄×D₃	semidirect
168. #681	C₄×D₃	semidirect
190. C₃×Dic₅	#104	semidirect
209. C₃×M₁₆	C₂×Dic₅	semidirect
225. C₄×Dic₃	C₂×Dic₅	semidirect
296. D₁₂	C₄×Dic₅	semidirect
301. Dic₆	C₄×Dic₅	semidirect
319. Dic₅	#825	direct (N × H)
336. M₁₆	D₃×Dic₅	semidirect
353. C₃×C₅	C₄×#104	semidirect
408. C₅	C₄×#825	semidirect
425. C₃	Dic₅×#104	semidirect

Maximal subgroups

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

subgroup	index
Dic₅×#235	2
C₂×C₅×#825	2
C₃×M₁₆×Dic₅	2
C₄×Dic₃×Dic₅	2
C₂×#90978	2
#11746376	2
#11745976	2
Dic₅×#104	3
C₄×#825	5

Subgroups — Dic5×#825 #14295609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×#825 #14295609