Subgroups — C₅×#83914 #14427789

Order 1920.

1040 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	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5828	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	2	yes	maximal, complemented
5	C₅×#5188	C₂	1	2	yes	maximal, complemented
6	C₅×#5171	C₂	1	4	yes	maximal, complemented
7	C₅×#5157	C₂	1	2	yes	maximal, complemented
8	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3050	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×#946	C₂²	1	4	yes	—
18	C₅×#938	C₂²	1	4	yes	—
19	C₅×#937	—	2	2	no	—
20	C₅×#935	—	2	2	no	—
21	C₄×C₅×#67	—	2	4	no	—
22	C₅×#926	C₂²	1	2	yes	—
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	—	2	4	no	—
25	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
26	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
27	C₅×#835	C₂²	1	4	yes	complemented
28	C₅×#832	C₂²	1	4	yes	complemented
29	C₅×#818	C₂²	1	2	yes	complemented
30	C₅×#817	C₂²	1	2	yes	complemented
31	#83914	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
33	C₂³×C₅×C₈	—	3	1	no	—
34	C₅×#525	—	3	2	no	—
35	C₅×#467	—	3	2	no	—
36	C₅×#466	—	3	2	no	—
37	C₅×#465	—	3	4	no	—
38	C₅×#427	—	3	1	no	—
39	C₅×#416	—	3	2	no	—
40	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×#67	—	2	4	no	—
49	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	—	2	2	no	—
51	C₂×C₄×C₅×D₃	—	2	2	no	—
52	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
53	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
54	C₃×C₅×Q₁₆	—	2	2	no	—
55	C₃×C₅×SD₁₆	—	2	4	no	—
56	C₃×C₅×D₈	—	2	2	no	—
57	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×#217	—	2	2	no	—
61	C₅×#217	—	2	4	no	—
62	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
63	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
64	C₅×Dic₃⋊C₄	—	2	4	no	—
65	C₄×C₅×Dic₃	—	2	2	no	—
66	C₂×C₅×C₃⋊C₈	—	2	2	no	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₅×D₃×C₈	—	2	4	no	—
69	C₅×D₃×C₈	—	2	4	no	—
70	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
71	#5828	C₂×C₅	1	2	yes	complemented
72	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
73	#5233	C₂×C₅	1	2	yes	complemented
74	#5188	C₂×C₅	1	2	yes	complemented
75	#5171	C₂×C₅	1	4	yes	complemented
76	#5157	C₂×C₅	1	2	yes	complemented
77	#5106	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×C₅×#41	C₂×D₃	1	2	yes	—
79	C₂³×C₄×C₅	—	3	1	no	—
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
82	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
83	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
84	C₂²×C₅×C₈	—	3	1	no	—
85	C₂²×C₅×C₈	—	3	2	no	—
86	C₂²×C₅×C₈	—	3	2	no	—
87	C₂²×C₅×C₈	—	6	4	no	—
88	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	C₅×#123	—	6	2	no	—
90	C₅×C₂²⋊Q₈	—	3	4	no	—
91	C₅×#121	—	3	4	no	—
92	C₅×#120	—	6	2	no	—
93	C₄×C₅×D₄	—	6	4	no	—
94	C₅×#117	—	3	2	no	—
95	C₅×#107	—	3	2	no	—
96	C₅×#106	—	3	2	no	—
97	C₅×#103	—	3	4	no	—
98	C₅×#102	—	3	4	no	—
99	#3050	—	3	1	no	Sylow
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	—	2	2	no	—
103	C₂²×C₅×D₃	—	2	4	no	—
104	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	2	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	4	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	4	no	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₅×#67	—	4	8	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
120	C₄×C₅×D₃	—	2	4	no	—
121	C₄×C₅×D₃	—	2	2	no	—
122	C₄×C₅×D₃	—	2	2	no	—
123	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
124	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
125	C₅×C₃⋊C₈	—	2	2	no	—
126	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
127	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
128	C₃×#135	—	2	4	no	—
129	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
131	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
133	#946	C₂²×C₅	1	4	yes	—
134	#938	C₂²×C₅	1	4	yes	—
135	#937	—	2	2	no	—
136	#935	—	2	2	no	—
137	C₄×#67	—	2	4	no	—
138	#926	C₂²×C₅	1	2	yes	—
139	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂×D₃×C₈	—	2	4	no	—
141	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
142	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
143	#835	C₂²×C₅	1	4	yes	complemented
144	#832	C₂²×C₅	1	4	yes	complemented
145	#818	C₂²×C₅	1	2	yes	complemented
146	#817	C₂²×C₅	1	2	yes	complemented
147	C₂⁴×C₅	—	3	1	no	—
148	C₅×#41	—	2	4	no	—
149	C₅×#41	—	2	4	no	—
150	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	—	6	4	no	—
153	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	3	1	no	—
156	C₂²×C₄×C₅	—	3	2	no	—
157	C₂²×C₄×C₅	—	3	2	no	—
158	C₂²×C₄×C₅	—	6	2	no	—
159	C₂²×C₄×C₅	—	6	2	no	—
160	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₅×Q₁₆	—	2	2	no	—
162	C₅×SD₁₆	—	2	4	no	—
163	C₅×D₈	—	2	2	no	—
164	C₂×C₅×C₈	—	3	2	no	—
165	C₂×C₅×C₈	—	6	2	no	—
166	C₂×C₅×C₈	—	6	4	no	—
167	C₂×C₅×C₈	—	6	4	no	—
168	C₂×C₅×C₈	#67	1	4	yes	complemented
169	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
171	C₅×C₄⋊C₄	—	3	4	no	—
172	C₅×C₄⋊C₄	—	6	4	no	—
173	C₅×C₂²⋊C₄	—	6	4	no	—
174	C₅×C₂²⋊C₄	—	6	4	no	—
175	C₅×C₂²⋊C₄	—	6	2	no	—
176	C₄²×C₅	—	6	2	no	—
177	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
178	C₂³×C₈	—	3	1	no	—
179	#525	—	3	2	no	—
180	#467	—	3	2	no	—
181	#466	—	3	2	no	—
182	#465	—	3	4	no	—
183	#427	—	3	1	no	—
184	#416	—	3	2	no	—
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	4	2	no	—
187	C₂²×C₃×C₅	—	4	4	no	—
188	C₂²×C₃×C₅	#121	1	2	yes	—
189	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₅×D₃	—	2	8	no	—
191	C₂×C₅×D₃	—	2	2	no	—
192	C₂×C₅×D₃	—	2	2	no	—
193	C₂×C₅×D₃	#135	1	4	yes	complemented
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	#121	1	2	yes	—
196	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₅×Dic₃	—	2	2	no	—
199	C₅×Dic₃	—	4	4	no	—
200	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
201	C₃×#41	—	2	4	no	—
202	C₃×#41	—	2	4	no	—
203	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂×#67	—	2	4	no	—
209	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
210	C₂×C₄×D₃	—	2	2	no	—
211	C₂×C₄×D₃	—	2	2	no	—
212	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
213	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
214	C₃×Q₁₆	—	2	2	no	—
215	C₃×SD₁₆	—	2	4	no	—
216	C₃×D₈	—	2	2	no	—
217	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
218	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
219	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
220	#217	—	2	2	no	—
221	#217	—	2	4	no	—
222	(C₂×D₃)⋊C₄	—	2	4	no	—
223	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
224	Dic₃⋊C₄	—	2	4	no	—
225	C₄×Dic₃	—	2	2	no	—
226	C₂×C₃⋊C₈	—	2	2	no	—
227	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
228	D₃×C₈	—	2	4	no	—
229	D₃×C₈	—	2	4	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	—	3	2	no	—
232	C₂³×C₅	—	6	4	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
235	C₅×Q₈	—	2	2	no	—
236	C₅×Q₈	—	2	2	no	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	4	4	no	—
240	C₅×D₄	—	12	8	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	3	2	no	—
243	C₂×C₄×C₅	—	4	4	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	6	4	no	—
246	C₂×C₄×C₅	—	6	2	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	4	no	—
249	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	#237	1	2	yes	—
251	C₂×C₄×C₅	C₂×#67	1	2	yes	—
252	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
253	C₅×C₈	—	6	2	no	—
254	C₅×C₈	C₂×#67	1	2	yes	—
255	C₅×C₈	C₂×#67	1	2	yes	—
256	C₂×#41	C₂×C₅×D₃	1	2	yes	—
257	C₂³×C₄	—	3	1	no	—
258	#135	—	2	4	no	—
259	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
260	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
261	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
262	C₂²×C₈	—	3	1	no	—
263	C₂²×C₈	—	3	2	no	—
264	C₂²×C₈	—	3	2	no	—
265	C₂²×C₈	—	6	4	no	—
266	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
267	#123	—	6	2	no	—
268	C₂²⋊Q₈	—	3	4	no	—
269	#121	—	3	4	no	—
270	#120	—	6	2	no	—
271	C₄×D₄	—	6	4	no	—
272	#117	—	3	2	no	—
273	#107	—	3	2	no	—
274	#106	—	3	2	no	—
275	#103	—	3	4	no	—
276	#102	—	3	4	no	—
277	C₂×C₃×C₅	—	2	2	no	—
278	C₂×C₃×C₅	—	8	2	no	—
279	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂×#135	1	2	yes	—
281	C₅×D₃	—	2	4	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×D₃	—	2	2	no	—
285	C₂²×D₃	—	2	4	no	—
286	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
287	C₃×Q₈	—	2	2	no	—
288	C₃×Q₈	—	2	2	no	—
289	C₃×D₄	—	2	2	no	—
290	C₃×D₄	—	2	2	no	—
291	C₃×D₄	—	4	4	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	4	4	no	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₅×#41	1	2	yes	—
297	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
298	#67	—	4	8	no	—
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	2	4	no	—
301	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
302	C₄×D₃	—	2	4	no	—
303	C₄×D₃	—	2	2	no	—
304	C₄×D₃	—	2	2	no	—
305	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
306	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
307	C₃⋊C₈	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	3	4	no	—
310	C₂²×C₅	—	4	4	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	6	8	no	—
313	C₂²×C₅	—	6	2	no	—
314	C₂²×C₅	—	6	2	no	—
315	C₂²×C₅	#938	1	2	yes	—
316	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	6	2	no	—
319	C₄×C₅	—	12	4	no	—
320	C₄×C₅	#938	1	2	yes	—
321	C₄×C₅	C₂×#237	1	1	yes	characteristic
322	C₄×C₅	C₂²×#67	1	1	yes	characteristic
323	C₂⁴	—	3	1	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	6	4	no	—
329	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	2	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₂²×C₄	—	6	2	no	—
335	C₂²×C₄	—	6	2	no	—
336	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
337	Q₁₆	—	2	2	no	—
338	SD₁₆	—	2	4	no	—
339	D₈	—	2	2	no	—
340	C₂×C₈	—	3	2	no	—
341	C₂×C₈	—	6	2	no	—
342	C₂×C₈	—	6	4	no	—
343	C₂×C₈	—	6	4	no	—
344	C₂×C₈	C₅×#67	1	4	yes	complemented
345	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
347	C₄⋊C₄	—	3	4	no	—
348	C₄⋊C₄	—	6	4	no	—
349	C₂²⋊C₄	—	6	4	no	—
350	C₂²⋊C₄	—	6	4	no	—
351	C₂²⋊C₄	—	6	2	no	—
352	C₄²	—	6	2	no	—
353	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	4	no	—
357	C₂²×C₃	C₅×#121	1	2	yes	—
358	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₂×D₃	—	2	8	no	—
360	C₂×D₃	—	2	2	no	—
361	C₂×D₃	—	2	2	no	—
362	C₂×D₃	C₅×#135	1	4	yes	complemented
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	C₅×#121	1	2	yes	—
365	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
367	Dic₃	—	2	2	no	—
368	Dic₃	—	4	4	no	—
369	C₂×C₅	—	2	2	no	—
370	C₂×C₅	—	6	4	no	—
371	C₂×C₅	—	8	2	no	—
372	C₂×C₅	D₃×#135	1	2	yes	—
373	C₂×C₅	C₂×#938	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	3	2	no	—
376	C₂³	—	6	4	no	—
377	C₂³	—	6	2	no	—
378	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	12	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	3	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	6	4	no	—
390	C₂×C₄	—	6	2	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	—	6	4	no	—
393	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
394	C₂×C₄	C₅×#237	1	2	yes	—
395	C₂×C₄	C₂×C₅×#67	1	2	yes	—
396	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
397	C₈	—	6	2	no	—
398	C₈	C₂×C₅×#67	1	2	yes	—
399	C₈	C₂×C₅×#67	1	2	yes	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	8	2	no	—
402	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
403	C₂×C₃	C₂×C₅×#135	1	2	yes	—
404	D₃	—	2	4	no	—
405	C₅	#83914	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	2	2	no	—
407	C₂²	—	3	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	6	8	no	—
411	C₂²	—	6	2	no	—
412	C₂²	—	6	2	no	—
413	C₂²	C₅×#938	1	2	yes	—
414	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
415	C₄	—	4	2	no	—
416	C₄	—	6	2	no	—
417	C₄	—	12	4	no	—
418	C₄	C₅×#938	1	2	yes	—
419	C₄	C₂×C₅×#237	1	1	yes	characteristic
420	C₄	C₂²×C₅×#67	1	1	yes	characteristic
421	C₃	C₅×#3050	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	6	4	no	—
424	C₂	—	8	2	no	—
425	C₂	C₅×D₃×#135	1	2	yes	—
426	C₂	C₂×C₅×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₅×#3050
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₅×#5828	C₂	semidirect
3. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₅×#5233	C₂	semidirect
5. C₅×#5188	C₂	semidirect
6. C₅×#5171	C₂	semidirect
7. C₅×#5157	C₂	semidirect
8. C₅×#5106	C₂	semidirect
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
27. C₅×#835	C₂²	semidirect
28. C₅×#832	C₂²	semidirect
29. C₅×#818	C₂²	semidirect
30. C₅×#817	C₂²	semidirect
31. #83914	C₅	direct (N × H)
32. C₂×C₅×#135	D₃	semidirect
57. C₂×C₃×C₅×C₈	D₄	semidirect
70. C₂×C₃×#135	C₂×C₅	semidirect
71. #5828	C₂×C₅	semidirect
72. C₂²×D₃×C₈	C₂×C₅	semidirect
73. #5233	C₂×C₅	semidirect
74. #5188	C₂×C₅	semidirect
75. #5171	C₂×C₅	semidirect
76. #5157	C₂×C₅	semidirect
77. #5106	C₂×C₅	semidirect
81. C₂×C₅×Q₁₆	C₂×D₃	semidirect
82. C₂×C₅×SD₁₆	C₂×D₃	semidirect
83. C₂×C₅×D₈	C₂×D₃	semidirect
129. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
130. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
131. C₂×C₃×D₈	C₂²×C₅	semidirect
143. #835	C₂²×C₅	semidirect
144. #832	C₂²×C₅	semidirect
145. #818	C₂²×C₅	semidirect
146. #817	C₂²×C₅	semidirect
168. C₂×C₅×C₈	#67	semidirect
177. C₂×#135	C₅×D₃	semidirect
193. C₂×C₅×D₃	#135	semidirect
217. C₂×C₃×C₈	C₅×D₄	semidirect
259. C₂×Q₁₆	C₂×C₅×D₃	semidirect
260. C₂×SD₁₆	C₂×C₅×D₃	semidirect
261. C₂×D₈	C₂×C₅×D₃	semidirect
344. C₂×C₈	C₅×#67	semidirect
353. C₃×C₅	#3050	semidirect
362. C₂×D₃	C₅×#135	semidirect
405. C₅	#83914	direct (N × H)
421. C₃	C₅×#3050	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₅×#5828	2
C₂²×C₅×D₃×C₈	2
C₅×#5233	2
C₅×#5188	2
C₅×#5171	2
C₅×#5157	2
C₅×#5106	2
C₅×#3050	3
#83914	5

Subgroups — C5×#83914 #14427789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83914 #14427789