Subgroups — #14299533

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3954	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#90992	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748346	C₂	1	1	yes	maximal, characteristic
5	C₂×(C₂×D₃)⋊#168	C₂	1	1	yes	maximal, characteristic
6	#11746379	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745984	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602794	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×#6710	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	1	yes	characteristic
14	C₅×D₃×M₁₆	—	2	2	no	—
15	C₅×D₃×M₁₆	—	2	2	no	—
16	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
17	C₂×C₅×D₃×C₈	—	2	1	no	—
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×#3954	—	2	2	no	—
21	#90992	—	2	2	no	—
22	(C₂×D₃)⋊#168	—	2	1	no	—
23	(C₂×D₃)⋊#168	—	2	1	no	—
24	(C₂×D₃)⋊#168	C₄	1	2	yes	—
25	(C₂×D₃)⋊#168	C₄	1	2	yes	—
26	#70713	—	5	1	no	maximal, Hall
27	C₂²×C₅×M₁₆	—	3	1	no	—
28	#65496	—	3	1	no	—
29	C₂×C₂²⋊#168	—	3	1	no	—
30	C₂×#3954	—	3	1	no	—
31	C₂×#3954	D₃	1	1	yes	characteristic, complemented
32	#64778	—	3	1	no	—
33	#64778	—	3	1	no	—
34	C₂³×C₅×D₃	Q₈	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	Q₈	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
45	C₃×C₅×M₁₆	—	2	1	no	—
46	C₃×C₅×M₁₆	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	#6710	—	2	1	no	—
49	#6710	—	2	1	no	—
50	C₂×C₃⋊#168	—	2	1	no	—
51	C₂×C₃⋊#168	—	2	1	no	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
54	C₅×#208	—	2	1	no	—
55	C₅×#208	D₄	1	2	yes	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
58	C₅×D₃×C₈	—	2	4	no	—
59	C₃×#681	—	2	1	no	—
60	C₃×#681	—	2	1	no	—
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	C₂×C₃×#168	—	2	1	no	—
64	C₂×C₃×#168	C₂×C₄	1	2	yes	—
65	C₂×D₃×M₁₆	D₅	1	1	yes	characteristic
66	C₂×C₃×#108	—	5	1	no	—
67	#5126	—	5	1	no	—
68	C₂×#822	—	5	1	no	—
69	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
70	#4558	—	5	1	no	—
71	#4552	—	5	1	no	—
72	C₂³×C₄×C₅	—	3	1	no	—
73	C₂×C₅×M₁₆	—	3	1	no	—
74	C₂×C₅×M₁₆	—	6	1	no	—
75	C₂×C₅×M₁₆	—	6	2	no	—
76	C₂×C₅×M₁₆	—	6	2	no	—
77	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	—	6	1	no	—
79	C₂×#681	—	3	1	no	—
80	C₂×#681	C₂×D₃	1	1	yes	characteristic
81	C₂²×#168	—	3	1	no	—
82	C₂²×#168	C₂×D₃	1	1	yes	characteristic
83	C₂²⋊#168	—	3	2	no	—
84	C₂²⋊#168	—	3	2	no	—
85	C₂²⋊#168	—	6	1	no	—
86	C₂²⋊#168	—	6	1	no	—
87	#3954	—	2	2	no	—
88	#3954	—	6	2	no	—
89	#1855	—	15	1	no	Sylow
90	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₅×D₃	—	2	1	no	—
92	C₂²×C₅×D₃	—	2	1	no	—
93	C₂²×C₅×D₃	—	2	2	no	—
94	C₂²×C₅×D₃	—	4	1	no	—
95	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	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	1	no	—
104	C₂×C₅×Dic₃	—	2	1	no	—
105	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×C₅×D₃	—	2	1	no	—
108	C₄×C₅×D₃	—	2	1	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	2	1	no	—
111	C₄×C₅×D₃	—	2	1	no	—
112	C₄×C₅×D₃	—	2	1	no	—
113	C₄×C₅×D₃	—	2	1	no	—
114	C₄×C₅×D₃	—	2	1	no	—
115	C₃×C₅×C₈	—	2	2	no	—
116	C₃⋊#168	—	2	2	no	—
117	C₃⋊#168	—	4	1	no	—
118	C₃×#168	—	2	2	no	—
119	C₃×#168	—	4	1	no	—
120	C₅×C₃⋊C₈	—	2	2	no	—
121	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
122	C₂×C₃×M₁₆	—	5	1	no	—
123	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
124	C₂²×C₃×C₈	—	5	1	no	—
125	C₂×#208	—	5	1	no	—
126	C₂×#208	C₂×D₅	1	1	yes	characteristic
127	C₂²×C₃⋊C₈	—	5	1	no	—
128	D₃×M₁₆	—	2	2	no	—
129	D₃×M₁₆	—	2	2	no	—
130	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
131	C₂×D₃×C₈	—	2	1	no	—
132	C₃×#108	—	10	2	no	—
133	#822	—	10	2	no	—
134	(C₂×D₃)⋊C₈	—	5	2	no	—
135	(C₂×D₃)⋊C₈	—	5	2	no	—
136	(C₂×D₃)⋊C₈	—	10	1	no	—
137	(C₂×D₃)⋊C₈	—	10	1	no	—
138	C₂⁴×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₅×M₁₆	—	2	1	no	—
150	C₅×M₁₆	—	3	2	no	—
151	C₅×M₁₆	—	6	4	no	—
152	C₅×M₁₆	—	6	1	no	—
153	C₅×M₁₆	#67	1	2	yes	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	6	4	no	—
156	C₂×C₅×C₈	—	6	1	no	—
157	#681	—	2	1	no	—
158	#681	—	2	1	no	—
159	#681	—	6	1	no	—
160	#681	—	6	1	no	—
161	C₂×#168	—	2	1	no	—
162	C₂×#168	—	2	1	no	—
163	C₂×#168	—	2	1	no	—
164	C₂×#168	—	3	2	no	—
165	C₂×#168	—	6	1	no	—
166	C₂×#168	—	6	1	no	—
167	C₂×#168	—	6	1	no	—
168	C₂×#168	C₄×D₃	1	2	yes	—
169	C₂²×M₁₆	—	3	1	no	—
170	C₂×#108	—	5	1	no	—
171	C₂×#108	—	15	1	no	—
172	#407	—	15	1	no	—
173	C₂×C₂²⋊C₈	—	15	1	no	—
174	#341	—	15	1	no	—
175	#341	—	15	1	no	—
176	C₂²×C₃×C₅	—	2	1	no	—
177	C₂²×C₃×C₅	—	2	1	no	—
178	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	1	no	—
182	C₂×C₅×D₃	—	2	1	no	—
183	C₂×C₅×D₃	—	2	1	no	—
184	C₂×C₅×D₃	—	2	1	no	—
185	C₂×C₅×D₃	—	2	1	no	—
186	C₂×C₅×D₃	—	4	2	no	—
187	C₂×C₅×D₃	—	4	2	no	—
188	C₂×C₅×D₃	#108	1	2	yes	complemented
189	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	#120	1	1	yes	characteristic
192	C₃×C₄×C₅	#123	1	1	yes	characteristic
193	C₅×Dic₃	—	2	1	no	—
194	C₅×Dic₃	—	2	1	no	—
195	C₂³×D₃	Dic₁₀	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
197	C₂²×Dic₃	Dic₁₀	1	1	yes	characteristic
198	C₂×C₄×D₃	—	2	1	no	—
199	C₂×C₄×D₃	—	2	1	no	—
200	C₂×C₄×D₃	—	2	1	no	—
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
203	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
204	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	—	10	1	no	—
208	C₃×M₁₆	—	10	1	no	—
209	C₃×M₁₆	C₂²⋊D₅	1	2	yes	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	5	2	no	—
212	C₂×C₃×C₈	—	10	1	no	—
213	C₂×C₃×C₈	—	10	1	no	—
214	C₂×C₃×C₈	—	10	1	no	—
215	#208	—	2	1	no	—
216	#208	—	10	1	no	—
217	#208	—	10	1	no	—
218	#208	C₂²⋊D₅	1	2	yes	—
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂×C₃⋊C₈	—	5	2	no	—
221	C₂×C₃⋊C₈	—	10	1	no	—
222	C₂×C₃⋊C₈	—	10	1	no	—
223	C₂×C₃⋊C₈	—	10	1	no	—
224	ΓL(1,𝔽₂₅)	—	2	4	no	—
225	D₃×C₈	—	2	4	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂³×C₅	—	3	1	no	—
228	C₂³×C₅	—	6	2	no	—
229	C₂³×C₅	—	6	1	no	—
230	C₂³×C₅	—	6	1	no	—
231	C₂³×C₅	—	12	1	no	—
232	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₅	—	3	1	no	—
234	C₂×C₄×C₅	—	3	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	1	no	—
239	C₂×C₄×C₅	—	6	1	no	—
240	C₂×C₄×C₅	—	6	1	no	—
241	C₂×C₄×C₅	—	6	1	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×C₅	#235	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	#239	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	6	2	no	—
253	#168	—	2	2	no	—
254	#168	—	4	1	no	—
255	#168	—	6	2	no	—
256	#168	—	12	1	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₂×M₁₆	—	3	1	no	—
259	C₂×M₁₆	—	5	1	no	—
260	C₂×M₁₆	—	6	1	no	—
261	C₂×M₁₆	—	6	2	no	—
262	C₂×M₁₆	—	6	2	no	—
263	C₂×M₁₆	—	15	1	no	—
264	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
265	C₂²×C₈	—	5	1	no	—
266	C₂²×C₈	—	6	1	no	—
267	C₂²×C₈	—	15	1	no	—
268	#108	—	10	2	no	—
269	#108	—	30	2	no	—
270	C₂²⋊C₈	—	15	2	no	—
271	C₂²⋊C₈	—	15	2	no	—
272	C₂²⋊C₈	—	30	1	no	—
273	C₂²⋊C₈	—	30	1	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	2	1	no	—
276	C₂×C₃×C₅	#385	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
278	C₂×C₃×C₅	#430	1	1	yes	characteristic
279	C₅×D₃	—	2	2	no	—
280	C₅×D₃	—	4	1	no	—
281	C₂³×C₃	C₂×Dic₁₀	1	1	yes	characteristic
282	C₂²×D₃	—	2	1	no	—
283	C₂²×D₃	—	2	1	no	—
284	C₂²×D₃	—	2	2	no	—
285	C₂²×D₃	—	4	1	no	—
286	C₂²×D₃	#683	1	1	yes	characteristic
287	C₂²×D₃	#683	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	#709	1	1	yes	characteristic
290	C₂×C₃×C₄	#709	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
294	C₂×Dic₃	—	2	1	no	—
295	C₂×Dic₃	—	2	1	no	—
296	C₂×Dic₃	#683	1	1	yes	characteristic
297	C₂×Dic₃	#683	1	1	yes	characteristic
298	C₄×D₃	—	2	1	no	—
299	C₄×D₃	—	2	1	no	—
300	C₄×D₃	—	2	1	no	—
301	C₄×D₃	—	2	1	no	—
302	C₄×D₃	—	2	1	no	—
303	C₄×D₃	—	2	1	no	—
304	C₄×D₃	—	2	1	no	—
305	C₄×D₃	—	2	1	no	—
306	C₃×C₈	—	2	2	no	—
307	C₃×C₈	—	10	2	no	—
308	C₃×C₈	—	20	1	no	—
309	C₃⋊C₈	—	2	2	no	—
310	C₃⋊C₈	—	10	2	no	—
311	C₃⋊C₈	—	20	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	3	2	no	—
315	C₂²×C₅	—	6	1	no	—
316	C₂²×C₅	—	6	1	no	—
317	C₂²×C₅	—	6	1	no	—
318	C₂²×C₅	—	6	1	no	—
319	C₂²×C₅	—	6	1	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
323	C₂²×C₅	#896	1	1	yes	characteristic
324	C₂²×C₅	#946	1	1	yes	characteristic
325	C₄×C₅	—	6	1	no	—
326	C₄×C₅	—	6	1	no	—
327	C₄×C₅	#893	1	1	yes	characteristic
328	C₄×C₅	#894	1	1	yes	characteristic
329	C₄×C₅	C₄×#67	1	1	yes	characteristic
330	C₄×C₅	#937	1	1	yes	characteristic
331	C₂⁴	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	6	1	no	—
338	C₂²×C₄	—	6	1	no	—
339	C₂²×C₄	—	6	1	no	—
340	C₂²×C₄	—	6	1	no	—
341	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
342	M₁₆	—	2	1	no	—
343	M₁₆	—	3	2	no	—
344	M₁₆	—	6	4	no	—
345	M₁₆	—	6	1	no	—
346	M₁₆	—	10	1	no	—
347	M₁₆	—	10	1	no	—
348	M₁₆	—	30	1	no	—
349	M₁₆	—	30	1	no	—
350	M₁₆	#1201	1	2	yes	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	6	4	no	—
354	C₂×C₈	—	6	1	no	—
355	C₂×C₈	—	10	1	no	—
356	C₂×C₈	—	10	1	no	—
357	C₂×C₈	—	10	1	no	—
358	C₂×C₈	—	15	2	no	—
359	C₂×C₈	—	30	1	no	—
360	C₂×C₈	—	30	1	no	—
361	C₂×C₈	—	30	1	no	—
362	C₃×C₅	#1855	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	C₂×#683	1	1	yes	characteristic
366	C₂²×C₃	#4070	1	1	yes	characteristic
367	C₂²×C₃	#4070	1	1	yes	characteristic
368	C₂×D₃	—	2	1	no	—
369	C₂×D₃	—	2	1	no	—
370	C₂×D₃	—	2	1	no	—
371	C₂×D₃	—	2	1	no	—
372	C₂×D₃	—	2	1	no	—
373	C₂×D₃	—	4	2	no	—
374	C₂×D₃	—	4	2	no	—
375	C₂×D₃	#3954	1	2	yes	complemented
376	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
377	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
378	C₃×C₄	#4075	1	1	yes	characteristic
379	C₃×C₄	#4099	1	1	yes	characteristic
380	Dic₃	—	2	1	no	—
381	Dic₃	—	2	1	no	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	6	2	no	—
385	C₂×C₅	—	12	1	no	—
386	C₂×C₅	D₃×#108	1	1	yes	characteristic
387	C₂×C₅	#4893	1	1	yes	characteristic
388	C₂×C₅	#4989	1	1	yes	characteristic
389	C₂³	—	3	1	no	—
390	C₂³	—	3	1	no	—
391	C₂³	—	6	2	no	—
392	C₂³	—	6	1	no	—
393	C₂³	—	6	1	no	—
394	C₂³	—	12	1	no	—
395	C₂³	D₃×Dic₁₀	1	1	yes	characteristic
396	C₂×C₄	—	3	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	6	1	no	—
399	C₂×C₄	—	6	1	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	—	6	1	no	—
402	C₂×C₄	—	6	1	no	—
403	C₂×C₄	—	6	1	no	—
404	C₂×C₄	—	6	1	no	—
405	C₂×C₄	—	6	1	no	—
406	C₂×C₄	—	6	1	no	—
407	C₂×C₄	—	6	1	no	—
408	C₂×C₄	#6769	1	1	yes	characteristic
409	C₂×C₄	#6771	1	1	yes	characteristic
410	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
411	C₂×C₄	C₂×#1201	1	1	yes	characteristic
412	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
413	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	6	2	no	—
416	C₈	—	10	2	no	—
417	C₈	—	20	1	no	—
418	C₈	—	30	2	no	—
419	C₈	—	60	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	C₂×#3954	1	1	yes	characteristic
423	C₂×C₃	#65413	1	1	yes	characteristic
424	C₂×C₃	#65499	1	1	yes	characteristic
425	D₃	—	2	2	no	—
426	D₃	—	4	1	no	—
427	C₅	#70713	1	1	yes	characteristic, complemented, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	3	2	no	—
431	C₂²	—	6	1	no	—
432	C₂²	—	6	1	no	—
433	C₂²	—	6	1	no	—
434	C₂²	—	6	1	no	—
435	C₂²	—	6	1	no	—
436	C₂²	—	12	2	no	—
437	C₂²	—	12	2	no	—
438	C₂²	#91352	1	1	yes	characteristic
439	C₂²	#91369	1	1	yes	characteristic
440	C₂²	D₃×#683	1	1	yes	characteristic
441	C₄	—	6	1	no	—
442	C₄	—	6	1	no	—
443	C₄	#91351	1	1	yes	characteristic
444	C₄	C₄×#1201	1	1	yes	characteristic
445	C₄	#91446	1	1	yes	characteristic
446	C₄	#91568	1	1	yes	characteristic
447	C₃	#10602794	1	1	yes	characteristic, complemented, Sylow
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	6	2	no	—
451	C₂	—	12	1	no	—
452	C₂	D₃×#3954	1	1	yes	characteristic
453	C₂	#11748172	1	1	yes	characteristic
454	C₂	#11748716	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₅×D₃	Q₈
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1855
LCS	G ▷ C₂×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
2. C₂×C₃×#3954	C₂	semidirect
3. C₂×#90992	C₂	semidirect
6. #11746379	C₂	semidirect
7. #11745984	C₂	semidirect
31. C₂×#3954	D₃	semidirect
188. C₂×C₅×D₃	#108	semidirect
362. C₃×C₅	#1855	semidirect
375. C₂×D₃	#3954	semidirect
427. C₅	#70713	semidirect
447. C₃	#10602794	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂×C₃×#3954	2
C₂×#90992	2
#11748346	2
C₂×(C₂×D₃)⋊#168	2
#11746379	2
#11745984	2
#10602794	3
#70713	5