Subgroups — #14307141

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11754615	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₄×#6668	C₂	1	1	yes	maximal, characteristic
4	#11746376	C₂	1	1	yes	maximal, characteristic
5	C₅×#4555	C₂	1	1	yes	maximal, characteristic
6	#11745976	C₂	1	1	yes	maximal, characteristic
7	#11745975	C₂	1	1	yes	maximal, characteristic
8	#10599523	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	#91815	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
12	C₅×#926	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	#91574	—	2	1	no	—
17	#91574	—	2	1	no	—
18	C₂×#6668	—	2	1	no	—
19	#91468	C₄	1	1	yes	characteristic, complemented
20	#91468	C₄	1	1	yes	characteristic, complemented
21	C₄×#1204	—	2	1	no	—
22	C₄×#1204	—	2	1	no	—
23	#91388	C₄	1	1	yes	characteristic, complemented
24	#91388	C₄	1	1	yes	characteristic, complemented
25	C₃×#3947	—	2	1	no	—
26	C₃×C₈×Dic₅	—	2	1	no	—
27	#90994	—	2	1	no	—
28	#69868	—	5	1	no	maximal, Hall
29	#65851	—	3	1	no	—
30	M₁₆×Dic₅	D₃	1	1	yes	characteristic
31	C₄×#683	—	3	1	no	—
32	C₅×#339	—	3	1	no	—
33	#64775	—	3	1	no	—
34	#64752	—	3	1	no	—
35	#64743	—	3	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×C₅×Dic₃	—	2	1	no	—
39	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
41	C₂×#1204	—	2	1	no	—
42	C₂×#1204	—	2	1	no	—
43	C₃×C₅×M₁₆	—	2	1	no	—
44	C₃×C₅×M₁₆	Q₈	1	2	yes	complemented
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	#6719	—	2	1	no	—
47	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
48	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
49	C₄×Dic₁₅	—	2	1	no	—
50	C₄×Dic₁₅	—	2	1	no	—
51	C₄×Dic₁₅	—	2	1	no	—
52	C₅×#217	—	2	1	no	—
53	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₄×C₅×Dic₃	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
62	C₃×#681	—	2	1	no	—
63	C₃×#681	Q₈	1	2	yes	complemented
64	C₂×C₃×#168	—	2	1	no	—
65	Dic₃⋊Dic₅	—	2	1	no	—
66	Dic₃⋊Dic₅	—	2	1	no	—
67	#6669	—	2	1	no	—
68	#6669	—	2	1	no	—
69	#6668	—	2	4	no	—
70	#6668	—	2	1	no	—
71	#6668	—	2	1	no	—
72	#5470	—	5	1	no	—
73	C₃×C₄×M₁₆	—	5	1	no	—
74	C₄×C₄⋊Dic₃	—	5	1	no	—
75	#4555	—	5	1	no	—
76	#4555	—	5	1	no	—
77	#4555	—	5	1	no	—
78	#4555	D₅	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
80	C₅×#117	—	3	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	#4072	—	3	1	no	—
83	C₂×#683	—	6	1	no	—
84	C₂×C₄×Dic₅	—	3	1	no	—
85	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
86	C₂×#681	C₂×D₃	1	1	yes	characteristic
87	#4036	—	3	1	no	—
88	#4036	—	3	1	no	—
89	#4034	—	3	1	no	—
90	#4034	—	3	1	no	—
91	#4024	—	6	1	no	—
92	#4024	—	6	1	no	—
93	C₄×Dic₁₀	—	6	1	no	—
94	C₄×Dic₁₀	—	6	1	no	—
95	#3963	—	6	1	no	—
96	#3947	—	2	1	no	—
97	C₈×Dic₅	—	2	1	no	—
98	#1986	—	15	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×Dic₁₅	—	2	2	no	—
107	C₂×Dic₁₅	—	2	1	no	—
108	C₂×Dic₁₅	—	2	1	no	—
109	C₂×Dic₁₅	—	4	1	no	—
110	C₂×Dic₁₅	—	4	1	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	4	1	no	—
118	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
122	#1204	—	4	2	no	—
123	#1204	—	4	2	no	—
124	C₃×C₅×C₈	—	2	2	no	—
125	C₃×#168	—	2	2	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×C₄²	—	5	1	no	—
129	#926	—	5	1	no	—
130	#926	C₂×D₅	1	1	yes	characteristic
131	C₂×C₄⋊Dic₃	—	10	1	no	—
132	#924	—	10	1	no	—
133	#924	—	10	1	no	—
134	C₂×C₄×Dic₃	—	5	1	no	—
135	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
136	#870	—	5	1	no	—
137	#870	—	5	1	no	—
138	#869	—	5	1	no	—
139	#869	—	5	1	no	—
140	C₄×Dic₆	—	10	1	no	—
141	C₄×Dic₆	—	10	1	no	—
142	C₃×#97	—	10	1	no	—
143	C₃×C₄×C₈	—	10	1	no	—
144	C₃⋊#95	—	10	1	no	—
145	C₂²×C₄×C₅	—	6	1	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×Dic₅	—	6	1	no	—
148	C₂²×Dic₅	D₁₂	1	1	yes	characteristic
149	C₂²×Dic₅	D₁₂	1	1	yes	characteristic
150	C₂×Dic₁₀	—	6	1	no	—
151	C₂×Dic₁₀	—	6	1	no	—
152	C₅×M₁₆	—	2	1	no	—
153	C₅×M₁₆	Dic₆	1	2	yes	complemented
154	C₂×C₅×C₈	—	2	1	no	—
155	C₅×C₄⋊C₄	—	3	1	no	—
156	C₅×C₄⋊C₄	—	3	1	no	—
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₄²×C₅	—	6	1	no	—
159	C₄²×C₅	—	6	1	no	—
160	C₄²×C₅	—	6	1	no	—
161	C₂²⋊Dic₅	—	6	1	no	—
162	C₄⋊Dic₅	—	3	1	no	—
163	C₄⋊Dic₅	—	3	1	no	—
164	C₄⋊Dic₅	—	6	1	no	—
165	C₄⋊Dic₅	—	6	1	no	—
166	#683	—	6	4	no	—
167	#683	—	6	1	no	—
168	#683	—	6	1	no	—
169	#683	—	6	1	no	—
170	#683	—	6	1	no	—
171	C₄×Dic₅	—	6	1	no	—
172	C₄×Dic₅	—	6	1	no	—
173	C₄×Dic₅	—	6	1	no	—
174	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
175	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
176	C₄×Dic₅	#67	1	1	yes	characteristic
177	C₄×Dic₅	#67	1	1	yes	characteristic
178	#681	—	2	1	no	—
179	#681	Dic₆	1	2	yes	complemented
180	C₂×#168	—	2	1	no	—
181	#533	—	15	1	no	—
182	C₄×M₁₆	—	5	1	no	—
183	C₄×C₄⋊C₄	—	15	1	no	—
184	#339	—	3	1	no	—
185	#339	—	15	1	no	—
186	#339	—	15	1	no	—
187	#339	—	15	1	no	—
188	C₂²×C₃×C₅	—	2	1	no	—
189	C₂²×C₃×C₅	—	2	1	no	—
190	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	#124	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
193	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
194	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
197	Dic₁₅	—	4	2	no	—
198	Dic₁₅	—	4	1	no	—
199	Dic₁₅	—	4	1	no	—
200	C₃×Dic₅	—	2	1	no	—
201	C₃×Dic₅	—	2	1	no	—
202	C₃×Dic₅	—	2	1	no	—
203	C₃×Dic₅	#104	1	2	yes	—
204	C₅×Dic₃	—	4	2	no	—
205	C₅×Dic₃	—	4	1	no	—
206	C₅×Dic₃	—	4	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	1	no	—
211	C₂²×Dic₃	—	10	1	no	—
212	C₂×Dic₆	—	10	1	no	—
213	C₂×Dic₆	—	10	1	no	—
214	C₃×M₁₆	—	2	1	no	—
215	C₃×M₁₆	—	5	2	no	—
216	C₃×M₁₆	—	10	1	no	—
217	C₃×M₁₆	Dic₁₀	1	2	yes	complemented
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	10	1	no	—
220	C₃×C₄²	—	5	1	no	—
221	C₃×C₄²	—	5	1	no	—
222	C₃×C₄²	—	5	1	no	—
223	C₃×C₄²	—	5	1	no	—
224	#217	—	2	1	no	—
225	#217	—	10	1	no	—
226	C₄⋊Dic₃	—	5	1	no	—
227	C₄⋊Dic₃	—	5	1	no	—
228	C₄⋊Dic₃	—	10	1	no	—
229	C₄⋊Dic₃	—	10	1	no	—
230	C₄⋊Dic₃	—	10	4	no	—
231	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
232	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
233	Dic₃⋊C₄	—	10	1	no	—
234	Dic₃⋊C₄	—	10	1	no	—
235	Dic₃⋊C₄	—	10	1	no	—
236	Dic₃⋊C₄	—	10	1	no	—
237	C₄×Dic₃	—	2	1	no	—
238	C₄×Dic₃	—	2	1	no	—
239	C₄×Dic₃	—	2	1	no	—
240	C₄×Dic₃	—	10	1	no	—
241	C₄×Dic₃	—	10	1	no	—
242	C₄×Dic₃	—	10	1	no	—
243	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	6	1	no	—
246	C₂×C₄×C₅	—	6	1	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	—	12	1	no	—
249	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
252	C₂×C₄×C₅	#235	1	1	yes	characteristic
253	C₂×C₄×C₅	#235	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
255	C₂×Dic₅	—	2	2	no	—
256	C₂×Dic₅	—	4	1	no	—
257	C₂×Dic₅	—	6	2	no	—
258	C₂×Dic₅	—	6	1	no	—
259	C₂×Dic₅	—	6	1	no	—
260	C₂×Dic₅	—	12	1	no	—
261	C₂×Dic₅	—	12	1	no	—
262	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
263	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
264	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
265	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
266	Dic₁₀	—	12	2	no	—
267	Dic₁₀	—	12	2	no	—
268	C₅×C₈	—	2	2	no	—
269	#168	—	2	2	no	—
270	C₂×M₁₆	—	5	1	no	—
271	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
272	C₄⋊Q₈	—	15	1	no	—
273	C₄⋊Q₈	—	15	1	no	—
274	#125	—	15	1	no	—
275	#125	—	15	1	no	—
276	C₂²⋊Q₈	—	30	1	no	—
277	C₂²⋊Q₈	—	30	1	no	—
278	C₄×Q₈	—	30	1	no	—
279	C₄×Q₈	—	30	1	no	—
280	#117	—	3	1	no	—
281	#117	—	15	1	no	—
282	C₂×C₄⋊C₄	—	30	1	no	—
283	C₂×C₄²	—	3	1	no	—
284	C₂×C₄²	—	5	1	no	—
285	C₂×C₄²	—	15	1	no	—
286	#97	—	10	1	no	—
287	C₄×C₈	—	10	1	no	—
288	#95	—	30	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	#391	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
293	C₂×C₃×C₅	#421	1	1	yes	characteristic
294	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	—	5	1	no	—
296	C₂×C₃×C₄	—	5	1	no	—
297	C₂×C₃×C₄	—	5	1	no	—
298	C₂×C₃×C₄	—	5	1	no	—
299	C₂×C₃×C₄	—	10	2	no	—
300	C₂×C₃×C₄	—	20	1	no	—
301	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
303	C₂×C₃×C₄	#709	1	1	yes	characteristic
304	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
305	C₂×C₃×C₄	#711	1	1	yes	characteristic
306	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	2	1	no	—
309	C₂×Dic₃	—	2	1	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	—	4	1	no	—
312	C₂×Dic₃	—	10	2	no	—
313	C₂×Dic₃	—	10	1	no	—
314	C₂×Dic₃	—	10	1	no	—
315	C₂×Dic₃	—	20	1	no	—
316	C₂×Dic₃	—	20	1	no	—
317	Dic₆	—	20	2	no	—
318	Dic₆	—	20	2	no	—
319	C₃×C₈	—	2	2	no	—
320	C₃×C₈	—	10	2	no	—
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	#869	1	1	yes	characteristic
324	C₂²×C₅	#875	1	1	yes	characteristic
325	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	C₄×C₅	—	12	2	no	—
327	C₄×C₅	—	12	1	no	—
328	C₄×C₅	—	12	1	no	—
329	C₄×C₅	C₄×Dic₆	1	1	yes	characteristic
330	C₄×C₅	C₄×Dic₆	1	1	yes	characteristic
331	C₄×C₅	#924	1	1	yes	characteristic
332	C₄×C₅	#924	1	1	yes	characteristic
333	Dic₅	—	2	1	no	—
334	Dic₅	—	2	1	no	—
335	Dic₅	—	2	1	no	—
336	Dic₅	—	12	2	no	—
337	Dic₅	—	12	1	no	—
338	Dic₅	—	12	1	no	—
339	Dic₅	#825	1	2	yes	—
340	C₂×Q₈	—	30	1	no	—
341	C₂×Q₈	—	30	1	no	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	—	5	1	no	—
344	C₂²×C₄	—	6	1	no	—
345	C₂²×C₄	—	30	1	no	—
346	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
347	M₁₆	—	2	1	no	—
348	M₁₆	—	5	2	no	—
349	M₁₆	—	10	1	no	—
350	M₁₆	#1204	1	2	yes	complemented
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	10	1	no	—
353	C₄⋊C₄	—	3	1	no	—
354	C₄⋊C₄	—	3	1	no	—
355	C₄⋊C₄	—	15	1	no	—
356	C₄⋊C₄	—	15	1	no	—
357	C₄⋊C₄	—	30	1	no	—
358	C₄⋊C₄	—	30	1	no	—
359	C₄⋊C₄	—	30	1	no	—
360	C₄⋊C₄	—	30	1	no	—
361	C₄⋊C₄	—	30	1	no	—
362	C₄⋊C₄	—	30	1	no	—
363	C₄⋊C₄	—	30	4	no	—
364	C₂²⋊C₄	—	6	1	no	—
365	C₂²⋊C₄	—	30	1	no	—
366	C₄²	—	5	1	no	—
367	C₄²	—	5	1	no	—
368	C₄²	—	5	1	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	6	1	no	—
371	C₄²	—	6	1	no	—
372	C₄²	—	6	1	no	—
373	C₄²	—	30	1	no	—
374	C₄²	—	30	1	no	—
375	C₄²	—	30	1	no	—
376	C₃×C₅	#1986	1	1	yes	characteristic, complemented, Hall
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₃	#4031	1	1	yes	characteristic
381	C₂²×C₃	#4034	1	1	yes	characteristic
382	C₃×C₄	—	5	2	no	—
383	C₃×C₄	—	10	1	no	—
384	C₃×C₄	—	10	1	no	—
385	C₃×C₄	—	10	1	no	—
386	C₃×C₄	C₄×Dic₁₀	1	1	yes	characteristic
387	C₃×C₄	#4024	1	1	yes	characteristic
388	C₃×C₄	#4033	1	1	yes	characteristic
389	C₃×C₄	#4042	1	1	yes	characteristic
390	Dic₃	—	4	2	no	—
391	Dic₃	—	4	1	no	—
392	Dic₃	—	4	1	no	—
393	Dic₃	—	20	2	no	—
394	Dic₃	—	20	1	no	—
395	Dic₃	—	20	1	no	—
396	C₂×C₅	—	2	1	no	—
397	C₂×C₅	—	2	1	no	—
398	C₂×C₅	#4929	1	1	yes	characteristic
399	C₂×C₅	C₂×#825	1	1	yes	characteristic
400	C₂×C₅	#5139	1	1	yes	characteristic
401	C₂³	D₅×D₁₂	1	1	yes	characteristic
402	Q₈	—	60	2	no	—
403	Q₈	—	60	2	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	6	1	no	—
410	C₂×C₄	—	6	1	no	—
411	C₂×C₄	—	10	2	no	—
412	C₂×C₄	—	12	1	no	—
413	C₂×C₄	—	12	1	no	—
414	C₂×C₄	—	20	1	no	—
415	C₂×C₄	—	30	2	no	—
416	C₂×C₄	—	30	1	no	—
417	C₂×C₄	—	30	1	no	—
418	C₂×C₄	—	60	1	no	—
419	C₂×C₄	—	60	1	no	—
420	C₂×C₄	D₅×Dic₆	1	1	yes	characteristic
421	C₂×C₄	#6771	1	1	yes	characteristic
422	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
423	C₂×C₄	#6782	1	1	yes	characteristic
424	C₂×C₄	C₂×#1204	1	1	yes	characteristic
425	C₂×C₄	D₅×#67	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	10	2	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	#64935	1	1	yes	characteristic
431	C₂×C₃	D₅×#104	1	1	yes	characteristic
432	C₂×C₃	#65110	1	1	yes	characteristic
433	C₅	#69868	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	#91350	1	1	yes	characteristic
437	C₂²	#91468	1	1	yes	characteristic
438	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
439	C₄	—	5	2	no	—
440	C₄	—	10	1	no	—
441	C₄	—	10	1	no	—
442	C₄	—	10	1	no	—
443	C₄	—	12	2	no	—
444	C₄	—	12	1	no	—
445	C₄	—	12	1	no	—
446	C₄	—	60	2	no	—
447	C₄	—	60	1	no	—
448	C₄	—	60	1	no	—
449	C₄	#91323	1	1	yes	characteristic
450	C₄	#91349	1	1	yes	characteristic
451	C₄	C₄×#1204	1	1	yes	characteristic
452	C₄	#91574	1	1	yes	characteristic
453	C₃	#10599523	1	1	yes	characteristic, complemented, Sylow
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	D₅×#825	1	1	yes	characteristic
457	C₂	#11748229	1	1	yes	characteristic
458	C₂	#11748933	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×#67
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1986
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
19. #91468	C₄	semidirect
20. #91468	C₄	semidirect
23. #91388	C₄	semidirect
24. #91388	C₄	semidirect
44. C₃×C₅×M₁₆	Q₈	semidirect
63. C₃×#681	Q₈	semidirect
153. C₅×M₁₆	Dic₆	semidirect
179. #681	Dic₆	semidirect
217. C₃×M₁₆	Dic₁₀	semidirect
350. M₁₆	#1204	semidirect
376. C₃×C₅	#1986	semidirect
433. C₅	#69868	semidirect
453. C₃	#10599523	semidirect

Maximal subgroups

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

subgroup	index
#11754615	2
C₃×M₁₆×Dic₅	2
C₄×#6668	2
#11746376	2
C₅×#4555	2
#11745976	2
#11745975	2
#10599523	3
#69868	5