Subgroups — #14295318

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic
2	C₂×#91114	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#217	C₂	1	1	yes	maximal, characteristic
4	C₂×#90953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745967	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745967	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600241	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
12	C₂×C₅×#217	C₄	1	2	yes	—
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	—	2	2	no	—
16	C₂×C₃×#681	—	2	2	no	—
17	C₂×C₃×#681	C₄	1	4	yes	complemented
18	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	#91114	C₄	1	4	yes	complemented
21	C₅×C₃⋊#95	C₄	1	2	yes	—
22	#90953	—	2	2	no	—
23	Dic₃×#168	—	2	2	no	—
24	#71983	—	5	1	no	maximal, Hall
25	C₂²×#681	D₃	1	1	yes	characteristic
26	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
27	C₂×C₂²⋊#168	—	3	1	no	—
28	C₂×#3935	—	3	1	no	—
29	C₂×C₄×#168	—	3	1	no	—
30	#64744	—	3	1	no	—
31	#64744	—	3	1	no	—
32	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
42	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
43	C₂×C₃⋊#168	—	2	1	no	—
44	C₂×C₃⋊#168	—	2	1	no	—
45	C₂×C₃⋊#168	—	2	1	no	—
46	C₂×C₃⋊#168	—	2	1	no	—
47	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
48	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
49	C₅×#217	—	2	4	no	—
50	C₄×C₅×Dic₃	—	2	1	no	—
51	C₄×C₅×Dic₃	—	2	1	no	—
52	C₄×C₅×Dic₃	—	2	1	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₃×#681	—	2	8	no	—
55	C₂×C₃×#168	—	2	1	no	—
56	C₂×C₃×#168	—	2	1	no	—
57	C₂×C₃×#168	C₂×C₄	1	2	yes	—
58	C₂×C₃×#168	C₂×C₄	1	2	yes	—
59	C₂×C₃×#168	D₄	1	2	yes	—
60	C₂×C₃×#168	D₄	1	2	yes	—
61	C₂²×C₃×M₁₆	—	5	1	no	—
62	C₄×#217	D₅	1	1	yes	characteristic
63	C₂×#830	—	5	1	no	—
64	C₂×#815	—	5	1	no	—
65	C₂×C₈×Dic₃	—	5	1	no	—
66	#4550	—	5	1	no	—
67	#4550	—	5	1	no	—
68	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
70	C₂×C₄²×C₅	—	3	1	no	—
71	C₂×C₄²×C₅	—	3	1	no	—
72	C₂×#681	—	2	2	no	—
73	C₂×#681	—	2	2	no	—
74	C₂×#681	Dic₃	1	4	yes	complemented
75	C₂²×#168	—	3	1	no	—
76	C₂²×#168	—	3	1	no	—
77	C₂²×#168	C₂×D₃	1	1	yes	characteristic
78	C₂²×#168	C₂×D₃	1	1	yes	characteristic
79	C₅×#95	—	3	2	no	—
80	C₂²⋊#168	—	3	4	no	—
81	#3935	—	6	2	no	—
82	C₄×#168	—	6	2	no	—
83	#1753	—	15	1	no	Sylow
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	C₄²	1	2	yes	—
89	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	M₁₆	1	4	yes	complemented
109	C₃⋊#168	—	2	2	no	—
110	C₃⋊#168	—	2	2	no	—
111	C₃×#168	—	2	2	no	—
112	C₃×#168	C₂²⋊C₄	1	4	yes	complemented
113	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
114	C₂×C₃×M₁₆	—	5	4	no	—
115	C₂×C₃×M₁₆	—	10	2	no	—
116	C₂×C₃×M₁₆	—	10	2	no	—
117	C₂²×C₃×C₈	—	5	1	no	—
118	C₂²×C₃×C₈	—	5	1	no	—
119	C₂×#217	Dic₅	1	2	yes	—
120	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
121	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
122	C₂²×C₃⋊C₈	—	5	1	no	—
123	C₂²×C₃⋊C₈	—	5	1	no	—
124	C₃⋊#95	Dic₅	1	2	yes	—
125	#830	—	5	4	no	—
126	#815	—	10	2	no	—
127	C₈×Dic₃	—	10	2	no	—
128	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	3	2	no	—
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₅×C₂²⋊C₄	—	6	4	no	—
140	C₄²×C₅	—	6	1	no	—
141	C₄²×C₅	—	6	1	no	—
142	C₄²×C₅	—	6	1	no	—
143	C₄²×C₅	—	6	1	no	—
144	#681	—	2	8	no	—
145	C₂×#168	—	2	1	no	—
146	C₂×#168	—	2	1	no	—
147	C₂×#168	—	3	2	no	—
148	C₂×#168	—	3	2	no	—
149	C₂×#168	—	6	1	no	—
150	C₂×#168	—	6	1	no	—
151	C₂×#168	—	6	1	no	—
152	C₂×#168	—	6	1	no	—
153	C₂×#168	C₂×Dic₃	1	2	yes	—
154	C₂×#168	C₂×Dic₃	1	2	yes	—
155	C₂×#168	#67	1	2	yes	—
156	C₂×#168	#67	1	2	yes	—
157	C₂²×M₁₆	—	5	1	no	—
158	C₂×C₂²⋊C₈	—	15	1	no	—
159	C₂×#97	—	15	1	no	—
160	C₂×C₄×C₈	—	15	1	no	—
161	C₄×C₂²⋊C₄	—	3	1	no	—
162	#336	—	15	1	no	—
163	#336	—	15	1	no	—
164	C₂²×C₃×C₅	—	2	2	no	—
165	C₂²×C₃×C₅	—	2	2	no	—
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	—	4	2	no	—
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
173	C₂²×C₃×C₅	#131	1	2	yes	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃×C₄×C₅	#117	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₅×Dic₃	—	2	4	no	—
180	C₅×Dic₃	—	4	2	no	—
181	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
187	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
188	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
191	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
192	C₃×M₁₆	—	10	8	no	—
193	C₂×C₃×C₈	—	5	2	no	—
194	C₂×C₃×C₈	—	5	2	no	—
195	C₂×C₃×C₈	—	5	2	no	—
196	C₂×C₃×C₈	—	5	2	no	—
197	C₂×C₃×C₈	—	10	1	no	—
198	C₂×C₃×C₈	—	10	1	no	—
199	#217	—	2	4	no	—
200	C₄×Dic₃	—	2	1	no	—
201	C₄×Dic₃	—	2	1	no	—
202	C₄×Dic₃	—	2	1	no	—
203	C₄×Dic₃	—	2	1	no	—
204	C₂×C₃⋊C₈	—	5	2	no	—
205	C₂×C₃⋊C₈	—	5	2	no	—
206	C₂×C₃⋊C₈	—	10	1	no	—
207	C₂×C₃⋊C₈	—	10	1	no	—
208	C₂×C₃⋊C₈	—	10	1	no	—
209	C₂×C₃⋊C₈	—	10	1	no	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	2	1	no	—
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	C₄×Dic₃	1	2	yes	—
215	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	3	4	no	—
223	C₂×C₄×C₅	—	6	2	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	2	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	6	2	no	—
228	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	#235	1	1	yes	characteristic
231	C₂×C₄×C₅	#235	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
235	#168	—	2	2	no	—
236	#168	—	6	2	no	—
237	#168	—	6	2	no	—
238	#168	#217	1	4	yes	complemented
239	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
240	C₂×M₁₆	—	5	4	no	—
241	C₂×M₁₆	—	10	2	no	—
242	C₂×M₁₆	—	10	2	no	—
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	—	15	1	no	—
246	C₂²×C₈	—	15	1	no	—
247	C₂×C₂²⋊C₄	—	3	2	no	—
248	C₂×C₄²	—	3	1	no	—
249	C₂×C₄²	—	3	1	no	—
250	C₂²⋊C₈	—	15	4	no	—
251	#97	—	30	2	no	—
252	C₄×C₈	—	30	2	no	—
253	#95	—	3	2	no	—
254	C₂×C₃×C₅	—	4	2	no	—
255	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
257	C₂×C₃×C₅	#405	1	1	yes	characteristic
258	C₂×C₃×C₅	#435	1	2	yes	—
259	C₂×C₃×C₅	#436	1	2	yes	—
260	C₂³×C₃	—	2	2	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	1	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	C₄×Dic₅	1	2	yes	—
265	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
273	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
276	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
277	C₂×C₃×C₄	#711	1	1	yes	characteristic
278	C₂×C₃×C₄	#711	1	1	yes	characteristic
279	C₂×Dic₃	—	2	2	no	—
280	C₂×Dic₃	—	2	2	no	—
281	C₂×Dic₃	—	2	2	no	—
282	C₂×Dic₃	—	2	2	no	—
283	C₂×Dic₃	—	2	2	no	—
284	C₂×Dic₃	#681	1	4	yes	complemented
285	C₃×C₈	—	5	4	no	—
286	C₃×C₈	—	10	2	no	—
287	C₃⋊C₈	—	10	2	no	—
288	C₃⋊C₈	—	10	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	D₃×M₁₆	1	2	yes	—
295	C₂²×C₅	#907	1	2	yes	—
296	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
297	C₂²×C₅	C₄×#67	1	1	yes	characteristic
298	C₂²×C₅	C₄×#67	1	1	yes	characteristic
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	6	4	no	—
301	C₄×C₅	—	12	2	no	—
302	C₄×C₅	#926	1	1	yes	characteristic
303	C₄×C₅	C₄×#67	1	1	yes	characteristic
304	C₄×C₅	C₄×#67	1	1	yes	characteristic
305	C₄×C₅	C₂×#217	1	1	yes	characteristic
306	C₂⁴	D₃×Dic₅	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	3	2	no	—
312	C₂²×C₄	—	3	2	no	—
313	C₂²×C₄	D₅×Dic₃	1	2	yes	—
314	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
315	C₂²×C₄	#1200	1	2	yes	—
316	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
317	M₁₆	—	10	8	no	—
318	C₂×C₈	—	5	2	no	—
319	C₂×C₈	—	5	2	no	—
320	C₂×C₈	—	5	2	no	—
321	C₂×C₈	—	5	2	no	—
322	C₂×C₈	—	10	1	no	—
323	C₂×C₈	—	10	1	no	—
324	C₂×C₈	—	15	2	no	—
325	C₂×C₈	—	15	2	no	—
326	C₂×C₈	—	30	1	no	—
327	C₂×C₈	—	30	1	no	—
328	C₂×C₈	—	30	1	no	—
329	C₂×C₈	—	30	1	no	—
330	C₂²⋊C₄	—	6	4	no	—
331	C₄²	—	6	1	no	—
332	C₄²	—	6	1	no	—
333	C₄²	—	6	1	no	—
334	C₄²	—	6	1	no	—
335	C₃×C₅	#1753	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	C₂×#681	1	2	yes	—
342	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
343	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
344	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
345	C₂²×C₃	#4094	1	2	yes	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	#4023	1	1	yes	characteristic
348	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₃×C₄	#4027	1	1	yes	characteristic
350	C₃×C₄	#4027	1	1	yes	characteristic
351	Dic₃	—	2	4	no	—
352	Dic₃	—	4	2	no	—
353	C₂×C₅	—	4	2	no	—
354	C₂×C₅	Dic₃×M₁₆	1	1	yes	characteristic
355	C₂×C₅	#5122	1	1	yes	characteristic
356	C₂×C₅	#5127	1	2	yes	—
357	C₂×C₅	#5128	1	2	yes	—
358	C₂×C₅	C₄×#217	1	1	yes	characteristic
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	Dic₃×Dic₅	1	2	yes	—
364	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	3	4	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	6	2	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	Dic₃×Dic₅	1	2	yes	—
378	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
379	C₂×C₄	#6782	1	1	yes	characteristic
380	C₂×C₄	#6782	1	1	yes	characteristic
381	C₂×C₄	C₂×#1200	1	1	yes	characteristic
382	C₂×C₄	D₅×#67	1	1	yes	characteristic
383	C₂×C₄	D₅×#67	1	1	yes	characteristic
384	C₈	—	5	4	no	—
385	C₈	—	10	2	no	—
386	C₈	—	30	2	no	—
387	C₈	—	30	2	no	—
388	C₂×C₃	—	4	2	no	—
389	C₂×C₃	C₄×#681	1	1	yes	characteristic
390	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
391	C₂×C₃	#65286	1	1	yes	characteristic
392	C₂×C₃	#65300	1	2	yes	—
393	C₂×C₃	#65301	1	2	yes	—
394	C₅	#71983	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	D₃×#681	1	2	yes	—
401	C₂²	#91288	1	2	yes	—
402	C₂²	C₂×Dic₃×Dic₅	1	1	yes	characteristic
403	C₂²	Dic₅×#67	1	1	yes	characteristic
404	C₂²	Dic₅×#67	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	6	4	no	—
407	C₄	—	12	2	no	—
408	C₄	#91528	1	1	yes	characteristic
409	C₄	D₅×#217	1	1	yes	characteristic
410	C₄	#91552	1	1	yes	characteristic
411	C₄	#91552	1	1	yes	characteristic
412	C₃	#10600241	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	4	2	no	—
414	C₂	Dic₃×#681	1	1	yes	characteristic
415	C₂	#11748327	1	1	yes	characteristic
416	C₂	#11748484	1	2	yes	—
417	C₂	#11748501	1	2	yes	—
418	C₂	Dic₅×#217	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	#1753
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. C₂×#90953	C₂	semidirect
5. C₂×Dic₃×#168	C₂	semidirect
6. #11745967	C₂	semidirect
7. #11745967	C₂	semidirect
17. C₂×C₃×#681	C₄	semidirect
20. #91114	C₄	semidirect
74. C₂×#681	Dic₃	semidirect
108. C₂×C₅×Dic₃	M₁₆	semidirect
112. C₃×#168	C₂²⋊C₄	semidirect
238. #168	#217	semidirect
284. C₂×Dic₃	#681	semidirect
335. C₃×C₅	#1753	semidirect
394. C₅	#71983	semidirect
412. C₃	#10600241	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×#681	2
C₂×#91114	2
C₄×C₅×#217	2
C₂×#90953	2
C₂×Dic₃×#168	2
#11745967	2
#10600241	3
#71983	5