Subgroups — D₅×#5106 #14413309

Order 1920.

1024 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	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	D₅×#926	C₂	1	2	yes	maximal
3	#11751207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748458	C₂	1	2	yes	maximal, complemented
6	#11747672	C₂	1	2	yes	maximal, complemented
7	#11747671	C₂	1	2	yes	maximal, complemented
8	D₅×#818	C₂	1	2	yes	maximal, complemented
9	D₅×#817	C₂	1	2	yes	maximal, complemented
10	D₅×#427	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	#91815	C₂²	1	2	yes	—
14	C₅×#926	C₂²	1	2	yes	—
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₈×D₅	C₄	1	8	yes	complemented
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	D₅×#217	—	2	2	no	—
22	#91528	—	2	2	no	—
23	D₅×C₄⋊Dic₃	C₂²	1	4	yes	—
24	C₄×D₅×Dic₃	—	2	2	no	—
25	#91358	C₂²	1	4	yes	—
26	#91357	—	2	2	no	—
27	#91102	C₂²	1	2	yes	complemented
28	#91101	C₂²	1	2	yes	complemented
29	C₅×#818	C₂²	1	2	yes	complemented
30	C₅×#817	C₂²	1	2	yes	complemented
31	#90988	C₂²	1	4	yes	complemented
32	#90985	C₂²	1	4	yes	complemented
33	C₂×#5106	—	5	1	no	maximal, Hall
34	C₂²×C₈×D₅	D₃	1	1	yes	characteristic
35	D₅×#117	—	3	2	no	—
36	C₅×#427	—	3	1	no	—
37	#65395	—	3	1	no	—
38	#65287	—	3	2	no	—
39	#65169	—	3	2	no	—
40	D₅×#107	—	3	2	no	—
41	#65149	—	3	2	no	—
42	D₅×#106	—	3	2	no	—
43	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
47	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₂×D₅×Dic₃	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	#6719	—	2	2	no	—
57	C₄⋊Dic₁₅	C₂³	1	4	yes	—
58	C₄×Dic₁₅	—	2	2	no	—
59	C₅×#217	—	2	2	no	—
60	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
61	C₄×C₅×Dic₃	—	2	2	no	—
62	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×#168	C₂³	1	1	yes	characteristic
64	C₂×C₃×#168	C₂³	1	1	yes	characteristic
65	C₃×C₈×D₅	C₂×C₄	1	4	yes	—
66	C₃×C₈×D₅	C₂×C₄	1	4	yes	—
67	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
68	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
69	#6668	—	2	4	no	—
70	#6665	—	2	4	no	—
71	Dic₃×Dic₅	—	2	4	no	—
72	C₂³×C₃×C₈	—	5	1	no	—
73	C₂×#926	—	5	2	no	—
74	#5106	—	5	1	no	—
75	#5106	—	5	2	no	—
76	#5106	—	5	2	no	—
77	#5106	—	5	2	no	—
78	#5106	D₅	1	1	yes	characteristic, direct product factor
79	C₂×#818	—	5	2	no	—
80	C₂×#817	—	5	2	no	—
81	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	C₅×#117	—	3	2	no	—
84	#4072	—	3	2	no	—
85	C₂²×#168	C₂×D₃	1	1	yes	characteristic
86	C₂×C₈×D₅	Dic₃	1	8	yes	complemented
87	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
88	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
89	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
90	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
91	#4038	—	3	4	no	—
92	D₅×C₄⋊C₄	—	3	4	no	—
93	D₅×C₂²⋊C₄	—	6	2	no	—
94	#4023	—	6	2	no	—
95	#4018	—	6	2	no	—
96	C₄²×D₅	—	6	2	no	—
97	C₅×#107	—	3	2	no	—
98	C₅×#106	—	3	2	no	—
99	#3950	—	3	2	no	—
100	#3949	—	3	2	no	—
101	#3940	—	3	4	no	—
102	#3939	—	3	4	no	—
103	C₂×#427	—	15	1	no	Sylow
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	—	2	4	no	—
106	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
107	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×Dic₁₅	—	2	4	no	—
114	C₂×C₅×Dic₃	—	2	4	no	—
115	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
116	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
118	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
119	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
120	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
121	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
122	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
123	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
124	D₅×Dic₃	—	4	8	no	—
125	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
127	C₃×#168	C₂²×C₄	1	2	yes	—
128	C₃×#168	C₂²×C₄	1	2	yes	—
129	C₂³×C₃×C₄	—	5	1	no	—
130	C₂²×C₃×C₈	—	5	1	no	—
131	C₂²×C₃×C₈	—	5	8	no	—
132	C₂²×C₃×C₈	—	5	1	no	—
133	C₂²×C₃×C₈	—	5	1	no	—
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₂²×C₃×C₈	—	5	1	no	—
136	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
137	C₂×#217	—	10	2	no	—
138	#926	—	5	2	no	—
139	#926	—	5	4	no	—
140	#926	—	10	2	no	—
141	#926	—	10	2	no	—
142	#926	C₂×D₅	1	2	yes	—
143	C₂×C₄⋊Dic₃	—	5	4	no	—
144	C₂×C₄×Dic₃	—	10	2	no	—
145	#818	—	5	2	no	—
146	#818	—	5	4	no	—
147	#818	C₂×D₅	1	2	yes	complemented
148	#817	—	5	2	no	—
149	#817	—	5	4	no	—
150	#817	C₂×D₅	1	2	yes	complemented
151	C₂³×D₅	D₁₂	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₂²×Dic₅	D₁₂	1	1	yes	characteristic
154	C₂×C₄×D₅	—	6	4	no	—
155	C₂×C₄×D₅	Dic₆	1	4	yes	—
156	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
157	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂×Dic₃	1	4	yes	—
159	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
162	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	3	4	no	—
165	C₅×C₂²⋊C₄	—	6	2	no	—
166	C₄²×C₅	—	6	2	no	—
167	C₂²⋊Dic₅	—	6	2	no	—
168	#685	—	6	4	no	—
169	C₄⋊Dic₅	—	3	4	no	—
170	#683	—	6	4	no	—
171	C₄×Dic₅	—	6	2	no	—
172	C₄×Dic₅	—	6	4	no	—
173	C₂×#168	C₂×Dic₃	1	4	yes	complemented
174	C₂×#168	C₂²×D₃	1	1	yes	characteristic
175	C₂×#168	C₂²×D₃	1	1	yes	characteristic
176	C₈×D₅	C₂×Dic₃	1	4	yes	—
177	C₈×D₅	C₂×Dic₃	1	4	yes	—
178	C₈×D₅	C₂×Dic₃	1	4	yes	complemented
179	C₈×D₅	C₂×Dic₃	1	4	yes	complemented
180	C₂³×C₈	—	5	1	no	—
181	C₂×#117	—	15	2	no	—
182	#427	—	3	1	no	—
183	#427	—	15	2	no	—
184	#427	—	15	2	no	—
185	#427	—	15	2	no	—
186	#427	—	15	1	no	—
187	C₂×#107	—	15	2	no	—
188	C₂×#106	—	15	2	no	—
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
191	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₃×D₅	—	2	2	no	—
193	C₂×C₃×D₅	—	2	8	no	—
194	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
196	C₂×C₃×D₅	#135	1	4	yes	—
197	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
198	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
200	Dic₁₅	—	4	4	no	—
201	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
202	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
203	C₅×Dic₃	—	4	4	no	—
204	C₂⁴×C₃	—	5	1	no	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	4	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	—	5	4	no	—
210	C₂²×C₃×C₄	—	5	1	no	—
211	C₂²×C₃×C₄	—	5	1	no	—
212	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
213	C₂²×Dic₃	—	10	4	no	—
214	C₂×C₃×C₈	—	5	4	no	—
215	C₂×C₃×C₈	—	5	1	no	—
216	C₂×C₃×C₈	—	5	1	no	—
217	C₂×C₃×C₈	—	5	4	no	—
218	C₂×C₃×C₈	—	5	4	no	—
219	C₂×C₃×C₈	—	5	4	no	—
220	C₂×C₃×C₈	—	5	4	no	—
221	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
222	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
223	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
224	#217	—	2	2	no	—
225	#217	—	10	4	no	—
226	#217	—	10	2	no	—
227	C₄⋊Dic₃	—	5	4	no	—
228	C₄⋊Dic₃	—	10	4	no	—
229	C₄⋊Dic₃	C₂²×D₅	1	4	yes	—
230	C₄×Dic₃	—	2	2	no	—
231	C₄×Dic₃	—	10	4	no	—
232	C₄×Dic₃	—	10	2	no	—
233	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
234	C₂²×D₅	—	2	4	no	—
235	C₂²×D₅	C₄⋊Dic₃	1	4	yes	—
236	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
237	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
238	C₂×C₄×C₅	—	6	4	no	—
239	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
240	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
242	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
243	C₂×Dic₅	—	6	4	no	—
244	C₂×Dic₅	C₄⋊Dic₃	1	4	yes	—
245	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
246	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
247	C₄×D₅	—	12	8	no	—
248	C₄×D₅	C₄⋊Dic₃	1	4	yes	—
249	C₄×D₅	C₄⋊Dic₃	1	4	yes	—
250	C₄×D₅	C₂×Dic₆	1	2	yes	—
251	C₄×D₅	C₂×Dic₆	1	2	yes	—
252	C₄×D₅	C₂²×Dic₃	1	2	yes	—
253	C₄×D₅	C₂²×Dic₃	1	2	yes	—
254	C₅×C₈	C₂²×Dic₃	1	2	yes	—
255	C₅×C₈	C₂²×Dic₃	1	2	yes	—
256	#168	C₂²×Dic₃	1	2	yes	—
257	#168	C₂²×Dic₃	1	2	yes	—
258	C₂³×C₄	—	5	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	5	8	no	—
261	C₂²×C₈	—	5	1	no	—
262	C₂²×C₈	—	5	1	no	—
263	C₂²×C₈	—	5	1	no	—
264	C₂²×C₈	—	5	1	no	—
265	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
266	#117	—	3	2	no	—
267	#117	—	15	4	no	—
268	#117	—	15	2	no	—
269	#117	—	30	2	no	—
270	#117	—	30	2	no	—
271	C₂×C₄⋊C₄	—	15	4	no	—
272	C₂×C₂²⋊C₄	—	30	2	no	—
273	C₂×C₄²	—	30	2	no	—
274	#107	—	3	2	no	—
275	#107	—	15	4	no	—
276	#107	—	15	2	no	—
277	#106	—	3	2	no	—
278	#106	—	15	4	no	—
279	#106	—	15	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₃×C₅	C₂×#135	1	2	yes	—
283	C₃×D₅	—	2	2	no	—
284	C₃×D₅	#427	1	4	yes	complemented
285	C₂³×C₃	—	5	1	no	—
286	C₂³×C₃	—	5	1	no	—
287	C₂³×C₃	—	5	4	no	—
288	C₂³×C₃	—	10	4	no	—
289	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	—	5	1	no	—
291	C₂×C₃×C₄	—	5	1	no	—
292	C₂×C₃×C₄	—	5	4	no	—
293	C₂×C₃×C₄	—	5	2	no	—
294	C₂×C₃×C₄	—	5	2	no	—
295	C₂×C₃×C₄	—	5	2	no	—
296	C₂×C₃×C₄	—	5	2	no	—
297	C₂×C₃×C₄	—	5	4	no	—
298	C₂×C₃×C₄	—	5	4	no	—
299	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
300	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
301	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
302	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
303	C₂×Dic₃	—	2	4	no	—
304	C₂×Dic₃	—	10	4	no	—
305	C₂×Dic₃	—	20	8	no	—
306	C₃×C₈	—	5	2	no	—
307	C₃×C₈	—	5	2	no	—
308	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
309	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	C₂×C₄⋊Dic₃	1	2	yes	—
312	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
313	C₂×D₅	—	2	2	no	—
314	C₂×D₅	—	2	8	no	—
315	C₂×D₅	#904	1	4	yes	—
316	C₂×D₅	C₂×C₄⋊Dic₃	1	2	yes	—
317	C₂×D₅	C₂×C₄⋊Dic₃	1	2	yes	—
318	C₄×C₅	—	12	4	no	—
319	C₄×C₅	C₂×C₄⋊Dic₃	1	2	yes	—
320	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
321	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
322	Dic₅	—	12	4	no	—
323	Dic₅	C₂×C₄⋊Dic₃	1	2	yes	—
324	Dic₅	C₂×C₄⋊Dic₃	1	2	yes	—
325	C₂⁴	—	5	1	no	—
326	C₂²×C₄	—	5	1	no	—
327	C₂²×C₄	—	5	4	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	4	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	30	4	no	—
334	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
335	C₂×C₈	—	5	4	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	5	1	no	—
338	C₂×C₈	—	5	4	no	—
339	C₂×C₈	—	5	4	no	—
340	C₂×C₈	—	5	4	no	—
341	C₂×C₈	—	5	4	no	—
342	C₂×C₈	D₅×Dic₃	1	4	yes	complemented
343	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
344	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
345	C₄⋊C₄	—	3	4	no	—
346	C₄⋊C₄	—	15	4	no	—
347	C₄⋊C₄	—	30	4	no	—
348	C₂²⋊C₄	—	6	2	no	—
349	C₂²⋊C₄	—	30	4	no	—
350	C₂²⋊C₄	—	30	2	no	—
351	C₄²	—	6	2	no	—
352	C₄²	—	30	4	no	—
353	C₄²	—	30	2	no	—
354	C₃×C₅	C₂×#427	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	5	2	no	—
357	C₂²×C₃	—	5	4	no	—
358	C₂²×C₃	—	5	2	no	—
359	C₂²×C₃	—	10	8	no	—
360	C₂²×C₃	—	10	2	no	—
361	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
362	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
363	C₃×C₄	—	5	2	no	—
364	C₃×C₄	—	5	2	no	—
365	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
366	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
367	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
368	Dic₃	—	4	4	no	—
369	Dic₃	—	20	4	no	—
370	C₂×C₅	—	2	2	no	—
371	C₂×C₅	C₂×#904	1	2	yes	—
372	C₂×C₅	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
373	D₅	—	2	2	no	—
374	D₅	#5106	1	4	yes	direct product factor
375	C₂³	—	5	1	no	—
376	C₂³	—	5	4	no	—
377	C₂³	—	5	1	no	—
378	C₂³	—	10	4	no	—
379	C₂³	D₅×D₁₂	1	1	yes	characteristic
380	C₂×C₄	—	5	4	no	—
381	C₂×C₄	—	5	1	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	5	4	no	—
384	C₂×C₄	—	5	4	no	—
385	C₂×C₄	—	5	2	no	—
386	C₂×C₄	—	5	2	no	—
387	C₂×C₄	—	5	2	no	—
388	C₂×C₄	—	5	2	no	—
389	C₂×C₄	—	6	4	no	—
390	C₂×C₄	—	30	4	no	—
391	C₂×C₄	—	60	8	no	—
392	C₂×C₄	D₅×Dic₆	1	2	yes	—
393	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
394	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
395	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
396	C₈	—	5	2	no	—
397	C₈	—	5	2	no	—
398	C₈	C₂×D₅×Dic₃	1	2	yes	—
399	C₈	C₂×D₅×Dic₃	1	2	yes	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	5	4	no	—
402	C₂×C₃	—	10	2	no	—
403	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
404	C₂×C₃	D₅×#135	1	2	yes	—
405	C₅	C₂×#5106	1	1	yes	characteristic, complemented, Sylow
406	C₂²	—	2	2	no	—
407	C₂²	—	5	2	no	—
408	C₂²	—	5	4	no	—
409	C₂²	—	5	2	no	—
410	C₂²	—	10	8	no	—
411	C₂²	—	10	2	no	—
412	C₂²	D₅×C₄⋊Dic₃	1	2	yes	—
413	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
414	C₄	—	5	2	no	—
415	C₄	—	5	2	no	—
416	C₄	—	12	4	no	—
417	C₄	—	60	4	no	—
418	C₄	D₅×C₄⋊Dic₃	1	2	yes	—
419	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
420	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
421	C₃	D₅×#427	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	5	4	no	—
424	C₂	—	10	2	no	—
425	C₂	D₅×#904	1	2	yes	—
426	C₂	C₂×D₅×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₁₂
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#427
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #11751207	C₂	semidirect
4. C₅×#5106	C₂	semidirect
5. #11748458	C₂	semidirect
6. #11747672	C₂	semidirect
7. #11747671	C₂	semidirect
8. D₅×#818	C₂	semidirect
9. D₅×#817	C₂	semidirect
16. C₂×C₃×C₈×D₅	C₄	semidirect
27. #91102	C₂²	semidirect
28. #91101	C₂²	semidirect
29. C₅×#818	C₂²	semidirect
30. C₅×#817	C₂²	semidirect
31. #90988	C₂²	semidirect
32. #90985	C₂²	semidirect
53. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₂×C₃×#168	C₂×C₄	semidirect
67. C₃×C₈×D₅	C₂×C₄	semidirect
68. C₃×C₈×D₅	C₂×C₄	semidirect
78. #5106	D₅	direct (N × H)
86. C₂×C₈×D₅	Dic₃	semidirect
147. #818	C₂×D₅	semidirect
150. #817	C₂×D₅	semidirect
161. C₂×C₅×C₈	C₂×Dic₃	semidirect
173. C₂×#168	C₂×Dic₃	semidirect
178. C₈×D₅	C₂×Dic₃	semidirect
179. C₈×D₅	C₂×Dic₃	semidirect
221. C₂×C₃×C₈	C₄×D₅	semidirect
284. C₃×D₅	#427	semidirect
342. C₂×C₈	D₅×Dic₃	semidirect
354. C₃×C₅	C₂×#427	semidirect
374. D₅	#5106	direct (N × H)
405. C₅	C₂×#5106	semidirect
421. C₃	D₅×#427	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈×D₅	2
D₅×#926	2
#11751207	2
C₅×#5106	2
#11748458	2
#11747672	2
#11747671	2
D₅×#818	2
D₅×#817	2
D₅×#427	3
C₂×#5106	5

Subgroups — D5×#5106 #14413309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#5106 #14413309