Subgroups — #14411452

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91796	C₂	1	1	yes	maximal, characteristic
2	C₂×#91790	C₂	1	1	yes	maximal, characteristic
3	#11756281	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	M₁₆×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
7	#11751098	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750809	C₂	1	2	yes	maximal, complemented
9	#11750808	C₂	1	2	yes	maximal, complemented
10	#11750790	C₂	1	2	yes	maximal, complemented
11	C₄×C₈×D₁₅	C₂	1	2	yes	maximal, complemented
12	#10610280	—	3	1	no	maximal, Hall
13	C₂×#6817	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
18	C₂×#6710	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	#91796	C₄	1	8	yes	complemented
21	#91790	C₄	1	8	yes	complemented
22	C₂×#6705	C₂²	1	2	yes	—
23	C₂×#6705	C₂²	1	2	yes	—
24	C₂×C₈×D₁₅	C₂²	1	2	yes	—
25	C₂×C₈×D₁₅	C₂²	1	2	yes	—
26	#91782	C₄	1	2	yes	—
27	#91776	C₄	1	2	yes	—
28	#91770	C₄	1	4	yes	—
29	#91761	C₂²	1	2	yes	—
30	C₄²×D₁₅	C₂²	1	2	yes	—
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
33	#91099	C₂²	1	2	yes	—
34	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
35	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
37	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
38	C₈×Dic₁₅	C₂²	1	2	yes	—
39	#91087	C₂²	1	2	yes	—
40	C₄×C₃⋊#168	C₂²	1	2	yes	—
41	#78549	—	5	1	no	maximal, Hall
42	C₂×#4053	—	3	1	no	—
43	C₂×#4047	—	3	1	no	—
44	#65856	—	3	1	no	—
45	C₅×#405	D₃	1	1	yes	characteristic, complemented
46	M₁₆×Dic₅	—	3	1	no	—
47	C₂×C₈×Dic₅	—	3	1	no	—
48	#65286	—	3	1	no	—
49	#64997	—	3	2	no	—
50	#64996	—	3	2	no	—
51	#64978	—	3	2	no	—
52	C₄×C₈×D₅	—	3	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×#1220	C₂×C₄	1	2	yes	—
55	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
56	#6817	C₂×C₄	1	4	yes	—
57	#6817	C₂×C₄	1	4	yes	—
58	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
60	C₂×C₄×D₁₅	C₂³	1	2	yes	—
61	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	2	yes	—
70	#6714	C₂×C₄	1	4	yes	—
71	#6712	C₂×C₄	1	4	yes	—
72	C₄×Dic₁₅	C₂×C₄	1	4	yes	—
73	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
74	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
75	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
76	#6710	C₂×C₄	1	4	yes	complemented
77	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
78	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
79	C₂×C₃⋊#168	C₂³	1	2	yes	—
80	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
81	#6705	C₂×C₄	1	8	yes	complemented
82	#6705	C₂×C₄	1	8	yes	complemented
83	C₈×D₁₅	C₂×C₄	1	8	yes	complemented
84	C₈×D₁₅	C₂×C₄	1	8	yes	complemented
85	C₂×#907	—	5	1	no	—
86	C₂×#901	—	5	1	no	—
87	#5522	—	5	1	no	—
88	C₃×#405	D₅	1	1	yes	characteristic, complemented
89	Dic₃×M₁₆	—	5	1	no	—
90	C₂×C₈×Dic₃	—	5	1	no	—
91	#4997	—	5	1	no	—
92	#4708	—	5	2	no	—
93	#4707	—	5	2	no	—
94	#4689	—	5	2	no	—
95	C₄×D₃×C₈	—	5	2	no	—
96	C₂×#709	—	3	1	no	—
97	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
98	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
99	C₅×#117	C₂×D₃	1	1	yes	characteristic
100	C₂×C₄×Dic₅	—	3	1	no	—
101	C₂×#681	—	3	1	no	—
102	C₂²×#168	—	3	1	no	—
103	#4053	—	3	8	no	—
104	#4047	—	3	8	no	—
105	C₂×#676	—	3	2	no	—
106	C₂×#676	—	3	2	no	—
107	C₂×C₈×D₅	—	3	2	no	—
108	C₂×C₈×D₅	—	3	2	no	—
109	#4039	—	3	2	no	—
110	#4033	—	3	2	no	—
111	#4027	—	3	4	no	—
112	#4018	—	3	2	no	—
113	C₄²×D₅	—	3	2	no	—
114	C₅×#97	C₂×D₃	1	2	yes	—
115	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
116	#3947	—	3	2	no	—
117	C₈×Dic₅	—	3	1	no	—
118	C₈×Dic₅	—	3	1	no	—
119	C₈×Dic₅	—	3	1	no	—
120	C₈×Dic₅	—	3	1	no	—
121	C₈×Dic₅	—	3	2	no	—
122	#3935	—	3	2	no	—
123	C₄×#168	—	3	2	no	—
124	C₄×#131	—	15	1	no	Sylow
125	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	#1220	C₄²	1	8	yes	—
133	C₂×Dic₁₅	—	2	4	no	—
134	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
135	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
136	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
137	D₆₀	C₄²	1	4	yes	—
138	C₄×D₁₅	—	2	8	no	—
139	C₄×D₁₅	C₂²×C₄	1	4	yes	—
140	C₄×D₁₅	C₂²×C₄	1	4	yes	—
141	Dic₃₀	C₄²	1	4	yes	—
142	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
144	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
145	C₃⋊#168	C₂²×C₄	1	2	yes	—
146	C₃⋊#168	C₂²×C₄	1	4	yes	—
147	C₃⋊#168	C₂²×C₄	1	2	yes	—
148	C₂×#235	—	5	1	no	—
149	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
150	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
151	C₃×#117	C₂×D₅	1	1	yes	characteristic
152	C₂×C₄×Dic₃	—	5	1	no	—
153	C₂×#208	—	5	1	no	—
154	C₂²×C₃⋊C₈	—	5	1	no	—
155	#907	—	5	8	no	—
156	#901	—	5	8	no	—
157	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
158	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
159	C₂×D₃×C₈	—	5	2	no	—
160	C₂×D₃×C₈	—	5	2	no	—
161	#893	—	5	2	no	—
162	#887	—	5	2	no	—
163	#67⋊C₄	—	5	4	no	—
164	#872	—	5	2	no	—
165	C₄²×D₃	—	5	2	no	—
166	C₃×#97	C₂×D₅	1	2	yes	—
167	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
168	#815	—	5	2	no	—
169	C₈×Dic₃	—	5	1	no	—
170	C₈×Dic₃	—	5	2	no	—
171	C₈×Dic₃	—	5	1	no	—
172	C₈×Dic₃	—	5	1	no	—
173	C₈×Dic₃	—	5	1	no	—
174	#803	—	5	2	no	—
175	C₄×C₃⋊C₈	—	5	2	no	—
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₂²⋊D₅	—	3	2	no	—
178	C₂²×Dic₅	—	3	2	no	—
179	#709	—	3	4	no	—
180	#709	—	3	4	no	—
181	C₂×D₂₀	—	3	1	no	—
182	C₂×C₄×D₅	—	3	2	no	—
183	C₂×C₄×D₅	—	3	4	no	—
184	C₂×Dic₁₀	—	3	1	no	—
185	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
186	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
187	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
189	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
191	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
192	C₄²×C₅	C₂²×D₃	1	2	yes	—
193	#685	—	3	4	no	—
194	#683	—	3	4	no	—
195	C₄×Dic₅	—	3	4	no	—
196	C₄×Dic₅	—	3	2	no	—
197	C₄×Dic₅	—	3	1	no	—
198	C₄×Dic₅	—	3	1	no	—
199	#681	—	3	4	no	—
200	C₂×#168	—	3	4	no	—
201	C₂×#168	—	3	1	no	—
202	C₂×#168	—	3	2	no	—
203	C₂×#168	—	3	1	no	—
204	#676	—	3	8	no	—
205	#676	—	3	8	no	—
206	C₈×D₅	—	3	8	no	—
207	C₈×D₅	—	3	8	no	—
208	C₂×#131	—	15	1	no	—
209	C₂×#131	—	15	1	no	—
210	C₄×#41	—	15	1	no	—
211	#405	—	15	1	no	—
212	#405	—	15	2	no	—
213	#405	—	15	2	no	—
214	#405	D₁₅	1	1	yes	characteristic, complemented
215	C₄×M₁₆	—	15	1	no	—
216	C₄×M₁₆	—	15	2	no	—
217	C₂×C₄×C₈	—	15	1	no	—
218	C₂×C₄×C₈	—	15	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
221	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×D₁₅	—	2	4	no	—
223	C₂×D₁₅	C₂×C₄²	1	4	yes	—
224	C₃×C₄×C₅	—	2	4	no	—
225	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
226	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
228	Dic₁₅	—	2	2	no	—
229	Dic₁₅	C₂×C₄²	1	4	yes	—
230	Dic₁₅	#131	1	4	yes	complemented
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂×#67	—	5	2	no	—
233	C₂²×Dic₃	—	5	2	no	—
234	#235	—	5	4	no	—
235	#235	—	5	4	no	—
236	C₂×D₁₂	—	5	1	no	—
237	C₂×C₄×D₃	—	5	2	no	—
238	C₂×C₄×D₃	—	5	4	no	—
239	C₂×Dic₆	—	5	1	no	—
240	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
241	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
242	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
244	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
245	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
246	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
247	C₃×C₄²	C₂²×D₅	1	2	yes	—
248	(C₂×D₃)⋊C₄	—	5	4	no	—
249	Dic₃⋊C₄	—	5	4	no	—
250	C₄×Dic₃	—	5	4	no	—
251	C₄×Dic₃	—	5	2	no	—
252	C₄×Dic₃	—	5	1	no	—
253	C₄×Dic₃	—	5	1	no	—
254	#208	—	5	4	no	—
255	C₂×C₃⋊C₈	—	5	4	no	—
256	C₂×C₃⋊C₈	—	5	1	no	—
257	C₂×C₃⋊C₈	—	5	2	no	—
258	C₂×C₃⋊C₈	—	5	1	no	—
259	ΓL(1,𝔽₂₅)	—	5	8	no	—
260	ΓL(1,𝔽₂₅)	—	5	8	no	—
261	D₃×C₈	—	5	8	no	—
262	D₃×C₈	—	5	8	no	—
263	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂²×D₅	—	3	2	no	—
265	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
269	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₂²⋊D₅	—	3	8	no	—
271	C₂×Dic₅	—	3	2	no	—
272	C₂×Dic₅	—	3	2	no	—
273	C₂×Dic₅	—	3	2	no	—
274	C₂×Dic₅	—	6	4	no	—
275	D₂₀	—	3	4	no	—
276	C₄×D₅	—	3	4	no	—
277	C₄×D₅	—	3	4	no	—
278	C₄×D₅	—	6	8	no	—
279	Dic₁₀	—	3	4	no	—
280	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
281	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
282	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
283	#168	—	3	2	no	—
284	#168	—	3	4	no	—
285	#168	—	3	2	no	—
286	C₂×#41	—	15	1	no	—
287	#131	—	15	8	no	—
288	#131	—	15	8	no	—
289	C₂×M₁₆	—	15	1	no	—
290	C₂×M₁₆	—	15	2	no	—
291	C₂×M₁₆	—	15	2	no	—
292	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
293	C₂²×C₈	—	15	1	no	—
294	C₂²×C₈	—	15	2	no	—
295	C₂²×C₈	—	15	2	no	—
296	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
297	C₄×Q₈	—	15	2	no	—
298	C₄×D₄	—	15	2	no	—
299	C₄×D₄	—	15	4	no	—
300	#117	—	15	2	no	—
301	#117	C₂×D₁₅	1	1	yes	characteristic
302	C₂×C₄²	—	15	1	no	—
303	C₂×C₄²	—	15	2	no	—
304	#97	—	15	2	no	—
305	#97	—	15	2	no	—
306	#97	C₂×D₁₅	1	2	yes	—
307	C₄×C₈	—	15	1	no	—
308	C₄×C₈	—	15	2	no	—
309	C₄×C₈	—	15	1	no	—
310	C₄×C₈	—	15	1	no	—
311	C₄×C₈	—	15	1	no	—
312	C₄×C₈	—	15	2	no	—
313	C₄×C₈	C₂×D₁₅	1	2	yes	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂×#131	1	2	yes	—
317	D₁₅	—	2	4	no	—
318	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂²×D₃	—	5	2	no	—
320	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
321	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
325	#67	—	5	8	no	—
326	C₂×Dic₃	—	5	2	no	—
327	C₂×Dic₃	—	5	2	no	—
328	C₂×Dic₃	—	5	2	no	—
329	C₂×Dic₃	—	10	4	no	—
330	D₁₂	—	5	4	no	—
331	C₄×D₃	—	5	4	no	—
332	C₄×D₃	—	5	4	no	—
333	C₄×D₃	—	10	8	no	—
334	Dic₆	—	5	4	no	—
335	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
336	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
337	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
338	C₃⋊C₈	—	5	2	no	—
339	C₃⋊C₈	—	5	4	no	—
340	C₃⋊C₈	—	5	2	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	C₄²×D₃	1	2	yes	—
343	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
344	C₂×D₅	—	3	4	no	—
345	C₂×D₅	—	6	4	no	—
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	C₄²×D₃	1	2	yes	—
348	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
350	Dic₅	—	3	4	no	—
351	Dic₅	—	3	4	no	—
352	Dic₅	—	6	2	no	—
353	#41	—	15	4	no	—
354	#41	—	15	4	no	—
355	C₂×Q₈	—	15	1	no	—
356	C₂×D₄	—	15	2	no	—
357	C₂×D₄	—	15	1	no	—
358	C₂²×C₄	—	15	2	no	—
359	C₂²×C₄	—	15	2	no	—
360	C₂²×C₄	—	15	4	no	—
361	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
362	M₁₆	—	15	4	no	—
363	M₁₆	—	15	8	no	—
364	M₁₆	—	15	8	no	—
365	M₁₆	C₄×D₁₅	1	4	yes	complemented
366	C₂×C₈	—	15	4	no	—
367	C₂×C₈	—	15	1	no	—
368	C₂×C₈	—	15	1	no	—
369	C₂×C₈	—	15	2	no	—
370	C₂×C₈	—	15	8	no	—
371	C₂×C₈	—	15	8	no	—
372	C₂×C₈	C₄×D₁₅	1	4	yes	complemented
373	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
374	C₂×C₈	C₂²×D₁₅	1	2	yes	—
375	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
376	C₄⋊C₄	—	15	4	no	—
377	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
378	C₂²⋊C₄	—	15	4	no	—
379	C₂²⋊C₄	C₄×D₁₅	1	2	yes	—
380	C₄²	—	15	4	no	—
381	C₄²	—	15	2	no	—
382	C₄²	—	15	1	no	—
383	C₄²	—	15	1	no	—
384	C₄²	C₂²×D₁₅	1	2	yes	—
385	C₃×C₅	C₄×#131	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	C₄²×D₅	1	2	yes	—
388	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
389	C₂×D₃	—	5	4	no	—
390	C₂×D₃	—	10	4	no	—
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	C₄²×D₅	1	2	yes	—
393	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
394	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
395	Dic₃	—	5	4	no	—
396	Dic₃	—	5	4	no	—
397	Dic₃	—	10	2	no	—
398	C₂×C₅	—	2	2	no	—
399	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
400	C₂×C₅	D₃×#131	1	2	yes	—
401	D₅	—	6	4	no	—
402	C₂³	—	15	2	no	—
403	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
404	Q₈	—	15	4	no	—
405	D₄	—	15	8	no	—
406	D₄	—	15	4	no	—
407	C₂×C₄	—	15	2	no	—
408	C₂×C₄	—	15	2	no	—
409	C₂×C₄	—	15	4	no	—
410	C₂×C₄	—	15	4	no	—
411	C₂×C₄	—	15	2	no	—
412	C₂×C₄	—	30	8	no	—
413	C₂×C₄	—	30	4	no	—
414	C₂×C₄	C₂×C₄×D₁₅	1	4	yes	—
415	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
417	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
418	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
419	C₈	—	15	2	no	—
420	C₈	—	15	2	no	—
421	C₈	—	15	4	no	—
422	C₈	C₂×C₄×D₁₅	1	2	yes	—
423	C₈	C₂×C₄×D₁₅	1	4	yes	—
424	C₈	C₂×C₄×D₁₅	1	2	yes	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
427	C₂×C₃	D₅×#131	1	2	yes	—
428	D₃	—	10	4	no	—
429	C₅	#78549	1	1	yes	characteristic, complemented, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	15	4	no	—
432	C₂²	—	30	4	no	—
433	C₂²	C₄²×D₁₅	1	2	yes	—
434	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	15	4	no	—
437	C₄	—	15	4	no	—
438	C₄	—	30	2	no	—
439	C₄	C₄²×D₁₅	1	2	yes	—
440	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
441	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
442	C₃	#10610280	1	1	yes	characteristic, complemented, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	30	4	no	—
445	C₂	C₂×C₄²×D₁₅	1	1	yes	characteristic
446	C₂	D₁₅×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6817	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#405	D₁₅
hypocenter	C₃×C₅	C₄×#131
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#405	C₂	semidirect
5. M₁₆×Dic₁₅	C₂	semidirect
6. C₂×C₈×Dic₁₅	C₂	semidirect
7. #11751098	C₂	semidirect
8. #11750809	C₂	semidirect
9. #11750808	C₂	semidirect
10. #11750790	C₂	semidirect
11. C₄×C₈×D₁₅	C₂	semidirect
20. #91796	C₄	semidirect
21. #91790	C₄	semidirect
45. C₅×#405	D₃	semidirect
62. C₃×C₅×M₁₆	C₂×C₄	semidirect
63. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
76. #6710	C₂×C₄	semidirect
77. C₂×C₃⋊#168	C₂×C₄	semidirect
81. #6705	C₂×C₄	semidirect
82. #6705	C₂×C₄	semidirect
83. C₈×D₁₅	C₂×C₄	semidirect
84. C₈×D₁₅	C₂×C₄	semidirect
88. C₃×#405	D₅	semidirect
185. C₅×M₁₆	C₄×D₃	semidirect
186. C₂×C₅×C₈	C₄×D₃	semidirect
214. #405	D₁₅	semidirect
230. Dic₁₅	#131	semidirect
240. C₃×M₁₆	C₄×D₅	semidirect
241. C₂×C₃×C₈	C₄×D₅	semidirect
365. M₁₆	C₄×D₁₅	semidirect
372. C₂×C₈	C₄×D₁₅	semidirect
385. C₃×C₅	C₄×#131	semidirect
429. C₅	#78549	semidirect
442. C₃	#10610280	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91796	2
C₂×#91790	2
#11756281	2
C₃×C₅×#405	2
M₁₆×Dic₁₅	2
C₂×C₈×Dic₁₅	2
#11751098	2
#11750809	2
#11750808	2
#11750790	2
C₄×C₈×D₁₅	2
#10610280	3
#78549	5