Subgroups — D₅×#5197 #14417945

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#135	C₂	1	1	yes	maximal, characteristic
2	D₅×#948	C₂	1	2	yes	maximal, complemented
3	#11751298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5197	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749441	C₂	1	2	yes	maximal, complemented
6	#11749437	C₂	1	2	yes	maximal, complemented
7	D₅×#837	C₂	1	2	yes	maximal, complemented
8	#11748071	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748067	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#444	—	3	1	no	maximal, Hall
13	C₃×D₅×#41	C₂²	1	2	yes	—
14	C₃×C₅×#135	C₂²	1	1	yes	characteristic
15	#91837	C₂²	1	2	yes	complemented
16	C₅×#948	C₂²	1	2	yes	complemented
17	C₃×#4096	C₂²	1	2	yes	—
18	C₃×#4065	C₄	1	1	yes	characteristic, complemented
19	C₃×D₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
20	C₃×#4062	C₄	1	2	yes	complemented
21	C₃×D₅×SD₁₆	C₄	1	2	yes	complemented
22	C₃×#4058	C₄	1	1	yes	characteristic, complemented
23	C₃×D₅×D₈	C₄	1	1	yes	characteristic, complemented
24	C₃×#4050	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
27	#91284	—	2	2	no	—
28	#91284	C₂²	1	2	yes	complemented
29	#91283	—	2	2	no	—
30	#91283	C₂²	1	2	yes	complemented
31	D₅×#208	—	2	2	no	—
32	D₅×#208	C₂²	1	2	yes	—
33	C₂×D₅×C₃⋊C₈	—	2	2	no	—
34	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
35	#91121	C₂²	1	2	yes	complemented
36	#91103	C₂²	1	1	yes	characteristic, complemented
37	#91099	C₂²	1	1	yes	characteristic, complemented
38	C₅×#837	C₂²	1	2	yes	complemented
39	C₅×#819	C₂²	1	1	yes	characteristic, complemented
40	C₅×#815	C₂²	1	1	yes	characteristic, complemented
41	#90991	C₂²	1	2	yes	complemented
42	#90977	C₂²	1	2	yes	complemented
43	#90976	C₂²	1	2	yes	complemented
44	#90954	C₂²	1	1	yes	characteristic, complemented
45	#90953	C₂²	1	1	yes	characteristic, complemented
46	C₂×#5197	—	5	1	no	maximal, Hall
47	D₅×#135	D₃	1	1	yes	characteristic
48	D₅×#131	—	3	2	no	—
49	C₅×#444	—	3	1	no	—
50	#65486	—	3	1	no	—
51	#65434	—	3	2	no	—
52	#65183	—	3	1	no	—
53	D₅×#108	—	3	1	no	—
54	#65112	—	3	2	no	—
55	D₅×#104	—	3	2	no	—
56	#65006	—	3	1	no	—
57	D₅×#97	—	3	1	no	—
58	C₃×C₅×#41	C₂³	1	2	yes	—
59	C₃×#713	C₂×C₄	1	2	yes	—
60	C₃×Q₈×D₅	C₂×C₄	1	2	yes	—
61	C₃×#711	—	2	2	no	—
62	C₃×#711	C₂×C₄	1	2	yes	—
63	C₃×D₄×D₅	—	2	2	no	—
64	C₃×D₄×D₅	C₂×C₄	1	2	yes	—
65	C₃×#709	—	2	2	no	—
66	C₃×#709	C₂³	1	2	yes	—
67	C₂×C₃×C₄×D₅	—	2	2	no	—
68	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
69	C₂×D₅×Dic₃	—	2	1	no	—
70	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
71	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
72	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
75	#6710	—	2	2	no	—
76	#6710	C₂³	1	2	yes	—
77	C₂×C₃⋊#168	—	2	2	no	—
78	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₅×#208	—	2	2	no	—
81	C₅×#208	C₂³	1	2	yes	—
82	C₂×C₅×C₃⋊C₈	—	2	2	no	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₃×#689	C₂×C₄	1	2	yes	complemented
85	C₃×#688	C₂×C₄	1	2	yes	complemented
86	C₃×#687	C₂×C₄	1	2	yes	complemented
87	C₃×#686	C₂×C₄	1	2	yes	complemented
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
90	C₃×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
91	C₃×#677	C₂×C₄	1	2	yes	complemented
92	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
93	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
94	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
95	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
96	Dic₃×Dic₅	—	2	1	no	—
97	#6649	—	2	2	no	—
98	#6649	—	2	2	no	—
99	#6649	—	2	2	no	—
100	D₅×C₃⋊C₈	—	2	2	no	—
101	D₅×C₃⋊C₈	—	2	2	no	—
102	D₅×C₃⋊C₈	—	2	2	no	—
103	D₅×C₃⋊C₈	D₄	1	2	yes	—
104	D₅×C₃⋊C₈	D₄	1	2	yes	—
105	C₂×C₃×#135	—	5	1	no	—
106	C₂×#948	—	5	2	no	—
107	C₂×#837	—	5	2	no	—
108	#5197	—	5	1	no	—
109	#5197	—	5	2	no	—
110	#5197	—	5	2	no	—
111	#5197	—	5	1	no	—
112	#5197	—	5	1	no	—
113	#5197	D₅	1	1	yes	characteristic, direct product factor
114	C₂×#819	—	5	1	no	—
115	C₂×#815	—	5	1	no	—
116	D₅×#41	C₂×D₃	1	2	yes	—
117	C₅×#135	C₂×D₃	1	1	yes	characteristic
118	C₅×#131	—	3	2	no	—
119	#4096	C₂×D₃	1	2	yes	—
120	#4094	—	3	2	no	—
121	#4065	Dic₃	1	1	yes	characteristic, complemented
122	D₅×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
123	#4062	Dic₃	1	2	yes	complemented
124	D₅×SD₁₆	Dic₃	1	2	yes	complemented
125	#4058	Dic₃	1	1	yes	characteristic, complemented
126	D₅×D₈	Dic₃	1	1	yes	characteristic, complemented
127	#4053	—	3	2	no	—
128	#4053	—	6	2	no	—
129	D₅×M₁₆	—	3	2	no	—
130	D₅×M₁₆	—	6	2	no	—
131	#4050	C₂×D₃	1	1	yes	characteristic
132	#4047	—	3	2	no	—
133	#4047	—	6	2	no	—
134	C₂×C₈×D₅	—	3	1	no	—
135	C₂×C₈×D₅	—	6	2	no	—
136	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
137	C₄²×D₅	—	3	1	no	—
138	C₅×#108	—	3	1	no	—
139	C₅×#104	—	3	2	no	—
140	C₅×#97	—	3	1	no	—
141	#3969	—	3	2	no	—
142	#3957	—	3	2	no	—
143	#3954	—	3	2	no	—
144	#3951	—	3	1	no	—
145	#3947	—	3	1	no	—
146	#3947	—	3	1	no	—
147	#3937	—	3	2	no	—
148	#3935	—	3	1	no	—
149	C₂×#444	—	15	1	no	Sylow
150	C₂²×C₃×D₅	—	2	2	no	—
151	C₂²×C₃×D₅	#41	1	1	yes	characteristic
152	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
153	C₃×C₅×D₄	—	2	2	no	—
154	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
157	C₂×Dic₁₅	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	1	no	—
159	C₃×C₂²⋊D₅	—	2	2	no	—
160	C₃×C₂²⋊D₅	—	2	2	no	—
161	C₃×C₂²⋊D₅	—	2	2	no	—
162	C₂×C₃×Dic₅	—	2	2	no	—
163	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
164	C₃×D₂₀	—	2	2	no	—
165	C₃×D₂₀	C₂²×C₄	1	2	yes	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×C₄×D₅	—	2	2	no	—
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
172	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
173	C₃×Dic₁₀	—	2	2	no	—
174	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
175	D₅×Dic₃	—	4	2	no	—
176	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₃⋊#168	—	2	2	no	—
179	C₃⋊#168	C₂×D₄	1	2	yes	—
180	C₃×#168	C₂²×C₄	1	1	yes	characteristic
181	C₃×#168	C₂²×C₄	1	1	yes	characteristic
182	C₅×C₃⋊C₈	—	2	2	no	—
183	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
184	C₂×C₃×#41	—	5	2	no	—
185	C₃×#135	—	5	2	no	—
186	C₃×#135	—	5	1	no	—
187	C₃×#135	—	5	2	no	—
188	C₃×#135	—	5	1	no	—
189	C₃×#135	—	5	1	no	—
190	C₃×#135	C₂×D₅	1	1	yes	characteristic
191	C₂×C₃×Q₁₆	—	5	1	no	—
192	C₂×C₃×SD₁₆	—	5	2	no	—
193	C₂×C₃×D₈	—	5	1	no	—
194	C₂²×C₃×C₈	—	5	1	no	—
195	#948	—	5	2	no	—
196	#948	—	5	2	no	—
197	#948	—	5	2	no	—
198	#948	—	10	2	no	—
199	#948	—	10	2	no	—
200	#948	C₂×D₅	1	2	yes	complemented
201	C₂×C₄×Dic₃	—	5	1	no	—
202	C₂×#208	—	5	2	no	—
203	C₂×#208	—	10	2	no	—
204	C₂²×C₃⋊C₈	—	5	1	no	—
205	C₂²×C₃⋊C₈	—	10	2	no	—
206	#837	—	5	2	no	—
207	#837	—	5	2	no	—
208	#837	—	5	2	no	—
209	#837	C₂×D₅	1	2	yes	complemented
210	#819	—	5	1	no	—
211	#819	—	5	2	no	—
212	#819	C₂×D₅	1	1	yes	characteristic, complemented
213	#815	—	5	1	no	—
214	#815	—	5	1	no	—
215	#815	—	5	1	no	—
216	#815	C₂×D₅	1	1	yes	characteristic, complemented
217	C₅×#41	C₂²×D₃	1	2	yes	—
218	#713	C₂×Dic₃	1	2	yes	—
219	Q₈×D₅	C₂×Dic₃	1	2	yes	—
220	#711	—	2	2	no	—
221	#711	C₂×Dic₃	1	2	yes	—
222	D₄×D₅	—	2	2	no	—
223	D₄×D₅	C₂×Dic₃	1	2	yes	—
224	#709	—	2	2	no	—
225	#709	C₂²×D₃	1	2	yes	—
226	C₂×C₄×D₅	—	2	2	no	—
227	C₂×C₄×D₅	—	6	1	no	—
228	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
229	C₅×Q₁₆	C₂×Dic₃	1	1	yes	characteristic, complemented
230	C₅×SD₁₆	C₂×Dic₃	1	2	yes	complemented
231	C₅×D₈	C₂×Dic₃	1	1	yes	characteristic, complemented
232	C₅×M₁₆	—	3	2	no	—
233	C₅×M₁₆	—	6	2	no	—
234	C₂×C₅×C₈	—	3	1	no	—
235	C₂×C₅×C₈	—	6	2	no	—
236	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
237	C₄²×C₅	—	3	1	no	—
238	#689	C₂×Dic₃	1	2	yes	complemented
239	#688	C₂×Dic₃	1	2	yes	complemented
240	#687	C₂×Dic₃	1	2	yes	complemented
241	#686	C₂×Dic₃	1	2	yes	complemented
242	C₄×Dic₅	—	3	1	no	—
243	C₄×Dic₅	—	6	1	no	—
244	#681	—	3	2	no	—
245	#681	—	6	2	no	—
246	C₂×#168	—	3	1	no	—
247	C₂×#168	—	6	2	no	—
248	C₂×#168	C₂²×D₃	1	1	yes	characteristic
249	Dic₂₀	C₂×Dic₃	1	1	yes	characteristic, complemented
250	D₄₀	C₂×Dic₃	1	1	yes	characteristic, complemented
251	#677	C₂×Dic₃	1	2	yes	complemented
252	#676	—	6	2	no	—
253	#676	—	6	2	no	—
254	#676	—	6	2	no	—
255	C₈×D₅	—	3	2	no	—
256	C₈×D₅	—	3	2	no	—
257	C₈×D₅	—	6	2	no	—
258	C₈×D₅	—	6	2	no	—
259	C₈×D₅	—	6	2	no	—
260	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
261	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
262	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
263	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
264	C₂×#135	—	5	1	no	—
265	C₂×#131	—	15	2	no	—
266	#444	—	3	1	no	—
267	#444	—	15	1	no	—
268	#444	—	15	2	no	—
269	#444	—	15	1	no	—
270	#444	—	15	2	no	—
271	#444	—	15	1	no	—
272	C₂×#108	—	15	1	no	—
273	C₂×#104	—	15	2	no	—
274	C₂×#97	—	15	1	no	—
275	C₂²×C₃×C₅	—	2	2	no	—
276	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
277	C₂×C₃×D₅	—	2	2	no	—
278	C₂×C₃×D₅	—	2	2	no	—
279	C₂×C₃×D₅	—	4	4	no	—
280	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
281	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
282	C₃×C₄×C₅	—	2	2	no	—
283	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
284	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
285	Dic₁₅	—	4	1	no	—
286	C₃×Dic₅	—	2	2	no	—
287	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
288	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
289	C₅×Dic₃	—	4	1	no	—
290	C₃×#41	—	5	2	no	—
291	C₃×#41	—	5	2	no	—
292	C₃×#41	—	5	2	no	—
293	C₃×#41	—	10	2	no	—
294	C₃×#41	—	10	2	no	—
295	C₃×#41	C₂²×D₅	1	2	yes	—
296	C₂×C₃×Q₈	—	5	2	no	—
297	C₂×C₃×D₄	—	5	2	no	—
298	C₂×C₃×D₄	—	10	2	no	—
299	C₂²×C₃×C₄	—	5	1	no	—
300	C₂²×C₃×C₄	—	10	2	no	—
301	C₂²×Dic₃	—	10	1	no	—
302	C₃×Q₁₆	—	5	2	no	—
303	C₃×Q₁₆	—	5	1	no	—
304	C₃×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
305	C₃×SD₁₆	—	5	2	no	—
306	C₃×SD₁₆	—	5	2	no	—
307	C₃×SD₁₆	—	5	2	no	—
308	C₃×SD₁₆	C₄×D₅	1	2	yes	complemented
309	C₃×D₈	—	5	2	no	—
310	C₃×D₈	—	5	1	no	—
311	C₃×D₈	C₄×D₅	1	1	yes	characteristic, complemented
312	C₂×C₃×C₈	—	5	1	no	—
313	C₂×C₃×C₈	—	5	1	no	—
314	C₂×C₃×C₈	—	5	1	no	—
315	C₂×C₃×C₈	—	5	1	no	—
316	C₂×C₃×C₈	—	5	1	no	—
317	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
318	C₄×Dic₃	—	5	1	no	—
319	C₄×Dic₃	—	10	1	no	—
320	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
321	#208	—	2	2	no	—
322	#208	—	5	2	no	—
323	#208	—	10	2	no	—
324	#208	—	10	2	no	—
325	#208	—	10	2	no	—
326	#208	—	10	2	no	—
327	#208	C₂²×D₅	1	2	yes	—
328	C₂×C₃⋊C₈	—	2	2	no	—
329	C₂×C₃⋊C₈	—	5	1	no	—
330	C₂×C₃⋊C₈	—	5	2	no	—
331	C₂×C₃⋊C₈	—	5	2	no	—
332	C₂×C₃⋊C₈	—	10	2	no	—
333	C₂×C₃⋊C₈	—	10	2	no	—
334	C₂×C₃⋊C₈	—	10	2	no	—
335	C₂×C₃⋊C₈	—	10	2	no	—
336	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
337	C₂²×D₅	—	2	2	no	—
338	C₂²×D₅	#237	1	1	yes	characteristic
339	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
340	C₅×D₄	—	2	2	no	—
341	C₅×D₄	C₂²×Dic₃	1	2	yes	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
345	C₂²⋊D₅	—	2	2	no	—
346	C₂²⋊D₅	—	2	2	no	—
347	C₂²⋊D₅	—	2	2	no	—
348	C₂×Dic₅	—	2	2	no	—
349	C₂×Dic₅	—	6	1	no	—
350	C₂×Dic₅	#237	1	1	yes	characteristic
351	D₂₀	—	2	2	no	—
352	D₂₀	C₂²×Dic₃	1	2	yes	—
353	C₄×D₅	—	2	2	no	—
354	C₄×D₅	—	2	2	no	—
355	C₄×D₅	—	2	2	no	—
356	C₄×D₅	—	12	2	no	—
357	C₄×D₅	D₃×D₄	1	1	yes	characteristic
358	C₄×D₅	D₃×D₄	1	1	yes	characteristic
359	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
360	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
361	Dic₁₀	—	2	2	no	—
362	Dic₁₀	C₂²×Dic₃	1	2	yes	—
363	C₅×C₈	—	3	2	no	—
364	C₅×C₈	—	6	2	no	—
365	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
366	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
367	#168	—	3	2	no	—
368	#168	—	6	2	no	—
369	#168	C₂²×Dic₃	1	1	yes	characteristic
370	#168	C₂²×Dic₃	1	1	yes	characteristic
371	C₂×#41	—	5	2	no	—
372	#135	—	5	2	no	—
373	#135	—	5	1	no	—
374	#135	—	5	2	no	—
375	#135	—	5	1	no	—
376	#135	—	5	1	no	—
377	#135	D₃×D₅	1	1	yes	characteristic
378	C₂×Q₁₆	—	5	1	no	—
379	C₂×SD₁₆	—	5	2	no	—
380	C₂×D₈	—	5	1	no	—
381	#131	—	3	2	no	—
382	#131	—	15	2	no	—
383	#131	—	15	2	no	—
384	#131	—	15	2	no	—
385	#131	—	30	2	no	—
386	#131	—	30	2	no	—
387	C₂×M₁₆	—	15	2	no	—
388	C₂×M₁₆	—	30	2	no	—
389	C₂²×C₈	—	5	1	no	—
390	C₂²×C₈	—	15	1	no	—
391	C₂²×C₈	—	30	2	no	—
392	C₂×C₄²	—	15	1	no	—
393	#108	—	3	1	no	—
394	#108	—	15	2	no	—
395	#108	—	15	1	no	—
396	#104	—	3	2	no	—
397	#104	—	15	2	no	—
398	#104	—	15	2	no	—
399	#104	—	15	2	no	—
400	#97	—	3	1	no	—
401	#97	—	15	1	no	—
402	#97	—	15	1	no	—
403	#97	—	15	1	no	—
404	C₂×C₃×C₅	—	2	1	no	—
405	C₂×C₃×C₅	—	4	2	no	—
406	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
407	C₃×D₅	—	2	1	no	—
408	C₃×D₅	—	4	2	no	—
409	C₃×D₅	#444	1	2	yes	complemented
410	C₂³×C₃	—	5	1	no	—
411	C₂³×C₃	—	10	2	no	—
412	C₃×Q₈	—	5	2	no	—
413	C₃×Q₈	—	10	2	no	—
414	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
415	C₃×D₄	—	2	2	no	—
416	C₃×D₄	—	5	2	no	—
417	C₃×D₄	—	10	2	no	—
418	C₃×D₄	—	10	2	no	—
419	C₃×D₄	—	10	2	no	—
420	C₃×D₄	—	10	2	no	—
421	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	5	1	no	—
424	C₂×C₃×C₄	—	5	1	no	—
425	C₂×C₃×C₄	—	5	1	no	—
426	C₂×C₃×C₄	—	5	1	no	—
427	C₂×C₃×C₄	—	5	1	no	—
428	C₂×C₃×C₄	—	10	2	no	—
429	C₂×C₃×C₄	—	10	2	no	—
430	C₂×C₃×C₄	—	10	2	no	—
431	C₂×C₃×C₄	—	10	2	no	—
432	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
433	C₂×Dic₃	—	2	1	no	—
434	C₂×Dic₃	—	10	1	no	—
435	C₂×Dic₃	—	20	2	no	—
436	C₃×C₈	—	5	1	no	—
437	C₃×C₈	—	5	1	no	—
438	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
439	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
440	C₃⋊C₈	—	2	2	no	—
441	C₃⋊C₈	—	5	2	no	—
442	C₃⋊C₈	—	10	2	no	—
443	C₃⋊C₈	D₄×D₅	1	2	yes	—
444	C₂²×C₅	—	2	2	no	—
445	C₂²×C₅	C₂×#237	1	1	yes	characteristic
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	2	2	no	—
448	C₂×D₅	—	4	4	no	—
449	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
450	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	12	1	no	—
453	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
454	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
455	Dic₅	—	2	2	no	—
456	Dic₅	—	12	1	no	—
457	Dic₅	D₄×Dic₃	1	1	yes	characteristic
458	Dic₅	D₄×Dic₃	1	1	yes	characteristic
459	#41	—	5	2	no	—
460	#41	—	5	2	no	—
461	#41	—	5	2	no	—
462	#41	—	10	2	no	—
463	#41	—	10	2	no	—
464	#41	C₂×D₃×D₅	1	2	yes	—
465	C₂×Q₈	—	5	2	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	10	2	no	—
468	C₂²×C₄	—	5	1	no	—
469	C₂²×C₄	—	10	2	no	—
470	C₂²×C₄	—	30	1	no	—
471	Q₁₆	—	5	2	no	—
472	Q₁₆	—	5	1	no	—
473	Q₁₆	D₅×Dic₃	1	1	yes	characteristic, complemented
474	SD₁₆	—	5	2	no	—
475	SD₁₆	—	5	2	no	—
476	SD₁₆	—	5	2	no	—
477	SD₁₆	D₅×Dic₃	1	2	yes	complemented
478	D₈	—	5	2	no	—
479	D₈	—	5	1	no	—
480	D₈	D₅×Dic₃	1	1	yes	characteristic, complemented
481	M₁₆	—	3	2	no	—
482	M₁₆	—	6	2	no	—
483	M₁₆	—	15	2	no	—
484	M₁₆	—	30	2	no	—
485	M₁₆	—	30	2	no	—
486	M₁₆	—	30	2	no	—
487	M₁₆	—	30	2	no	—
488	C₂×C₈	—	3	1	no	—
489	C₂×C₈	—	5	1	no	—
490	C₂×C₈	—	5	1	no	—
491	C₂×C₈	—	5	1	no	—
492	C₂×C₈	—	5	1	no	—
493	C₂×C₈	—	5	1	no	—
494	C₂×C₈	—	6	2	no	—
495	C₂×C₈	—	15	2	no	—
496	C₂×C₈	—	15	2	no	—
497	C₂×C₈	—	15	1	no	—
498	C₂×C₈	—	30	2	no	—
499	C₂×C₈	—	30	2	no	—
500	C₂×C₈	—	30	2	no	—
501	C₂×C₈	—	30	2	no	—
502	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
503	C₄²	—	3	1	no	—
504	C₄²	—	15	1	no	—
505	C₄²	—	30	1	no	—
506	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	5	1	no	—
509	C₂²×C₃	—	5	1	no	—
510	C₂²×C₃	—	10	2	no	—
511	C₂²×C₃	—	10	2	no	—
512	C₂²×C₃	—	20	4	no	—
513	C₂²×C₃	D₅×#41	1	1	yes	characteristic
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	—	5	1	no	—
516	C₃×C₄	—	5	1	no	—
517	C₃×C₄	—	10	2	no	—
518	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
519	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
520	Dic₃	—	4	1	no	—
521	Dic₃	—	20	1	no	—
522	C₂×C₅	—	2	1	no	—
523	C₂×C₅	—	4	2	no	—
524	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
525	D₅	—	2	1	no	—
526	D₅	—	4	2	no	—
527	D₅	#5197	1	2	yes	direct product factor
528	C₂³	—	5	1	no	—
529	C₂³	—	10	2	no	—
530	Q₈	—	5	2	no	—
531	Q₈	—	10	2	no	—
532	Q₈	C₂×D₅×Dic₃	1	2	yes	—
533	D₄	—	2	2	no	—
534	D₄	—	5	2	no	—
535	D₄	—	10	2	no	—
536	D₄	—	10	2	no	—
537	D₄	—	10	2	no	—
538	D₄	—	10	2	no	—
539	D₄	C₂×D₅×Dic₃	1	2	yes	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	5	1	no	—
542	C₂×C₄	—	5	1	no	—
543	C₂×C₄	—	5	1	no	—
544	C₂×C₄	—	5	1	no	—
545	C₂×C₄	—	5	1	no	—
546	C₂×C₄	—	6	1	no	—
547	C₂×C₄	—	10	2	no	—
548	C₂×C₄	—	10	2	no	—
549	C₂×C₄	—	10	2	no	—
550	C₂×C₄	—	10	2	no	—
551	C₂×C₄	—	30	1	no	—
552	C₂×C₄	—	60	2	no	—
553	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
554	C₈	—	3	2	no	—
555	C₈	—	5	1	no	—
556	C₈	—	5	1	no	—
557	C₈	—	6	2	no	—
558	C₈	—	15	2	no	—
559	C₈	—	30	2	no	—
560	C₈	C₂×D₅×Dic₃	1	1	yes	characteristic
561	C₈	C₂×D₅×Dic₃	1	1	yes	characteristic
562	C₂×C₃	—	2	1	no	—
563	C₂×C₃	—	4	2	no	—
564	C₂×C₃	—	5	2	no	—
565	C₂×C₃	—	10	1	no	—
566	C₂×C₃	—	20	2	no	—
567	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
568	C₅	C₂×#5197	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	5	1	no	—
571	C₂²	—	5	1	no	—
572	C₂²	—	10	2	no	—
573	C₂²	—	10	2	no	—
574	C₂²	—	20	4	no	—
575	C₂²	D₅×#237	1	1	yes	characteristic
576	C₄	—	2	2	no	—
577	C₄	—	5	1	no	—
578	C₄	—	5	1	no	—
579	C₄	—	10	2	no	—
580	C₄	—	12	1	no	—
581	C₄	—	60	1	no	—
582	C₄	D₃×D₄×D₅	1	1	yes	characteristic
583	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
584	C₃	D₅×#444	1	1	yes	characteristic, complemented, Sylow
585	C₂	—	2	1	no	—
586	C₂	—	4	2	no	—
587	C₂	—	5	2	no	—
588	C₂	—	10	1	no	—
589	C₂	—	20	2	no	—
590	C₂	D₄×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×D₄×D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×#135	C₂²
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×D₅×#135	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#135	D₃×D₅
hypocenter	C₃×C₅	C₂×#444
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
2. D₅×#948	C₂	semidirect
3. #11751298	C₂	semidirect
4. C₅×#5197	C₂	semidirect
5. #11749441	C₂	semidirect
6. #11749437	C₂	semidirect
7. D₅×#837	C₂	semidirect
8. #11748071	C₂	semidirect
9. #11748067	C₂	semidirect
10. D₅×#819	C₂	semidirect
11. D₅×#815	C₂	semidirect
15. #91837	C₂²	semidirect
16. C₅×#948	C₂²	semidirect
18. C₃×#4065	C₄	semidirect
19. C₃×D₅×Q₁₆	C₄	semidirect
20. C₃×#4062	C₄	semidirect
21. C₃×D₅×SD₁₆	C₄	semidirect
22. C₃×#4058	C₄	semidirect
23. C₃×D₅×D₈	C₄	semidirect
28. #91284	C₂²	semidirect
30. #91283	C₂²	semidirect
35. #91121	C₂²	semidirect
36. #91103	C₂²	semidirect
37. #91099	C₂²	semidirect
38. C₅×#837	C₂²	semidirect
39. C₅×#819	C₂²	semidirect
40. C₅×#815	C₂²	semidirect
41. #90991	C₂²	semidirect
42. #90977	C₂²	semidirect
43. #90976	C₂²	semidirect
44. #90954	C₂²	semidirect
45. #90953	C₂²	semidirect
70. C₃×C₅×Q₁₆	C₂×C₄	semidirect
71. C₃×C₅×SD₁₆	C₂×C₄	semidirect
72. C₃×C₅×D₈	C₂×C₄	semidirect
84. C₃×#689	C₂×C₄	semidirect
85. C₃×#688	C₂×C₄	semidirect
86. C₃×#687	C₂×C₄	semidirect
87. C₃×#686	C₂×C₄	semidirect
89. C₃×Dic₂₀	C₂×C₄	semidirect
90. C₃×D₄₀	C₂×C₄	semidirect
91. C₃×#677	C₂×C₄	semidirect
113. #5197	D₅	direct (N × H)
121. #4065	Dic₃	semidirect
122. D₅×Q₁₆	Dic₃	semidirect
123. #4062	Dic₃	semidirect
124. D₅×SD₁₆	Dic₃	semidirect
125. #4058	Dic₃	semidirect
126. D₅×D₈	Dic₃	semidirect
200. #948	C₂×D₅	semidirect
209. #837	C₂×D₅	semidirect
212. #819	C₂×D₅	semidirect
216. #815	C₂×D₅	semidirect
229. C₅×Q₁₆	C₂×Dic₃	semidirect
230. C₅×SD₁₆	C₂×Dic₃	semidirect
231. C₅×D₈	C₂×Dic₃	semidirect
238. #689	C₂×Dic₃	semidirect
239. #688	C₂×Dic₃	semidirect
240. #687	C₂×Dic₃	semidirect
241. #686	C₂×Dic₃	semidirect
249. Dic₂₀	C₂×Dic₃	semidirect
250. D₄₀	C₂×Dic₃	semidirect
251. #677	C₂×Dic₃	semidirect
304. C₃×Q₁₆	C₄×D₅	semidirect
308. C₃×SD₁₆	C₄×D₅	semidirect
311. C₃×D₈	C₄×D₅	semidirect
409. C₃×D₅	#444	semidirect
473. Q₁₆	D₅×Dic₃	semidirect
477. SD₁₆	D₅×Dic₃	semidirect
480. D₈	D₅×Dic₃	semidirect
506. C₃×C₅	C₂×#444	semidirect
527. D₅	#5197	direct (N × H)
568. C₅	C₂×#5197	semidirect
584. C₃	D₅×#444	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₅×#135	2
D₅×#948	2
#11751298	2
C₅×#5197	2
#11749441	2
#11749437	2
D₅×#837	2
#11748071	2
#11748067	2
D₅×#819	2
D₅×#815	2
D₅×#444	3
C₂×#5197	5

Subgroups — D5×#5197 #14417945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#5197 #14417945