Subgroups — #14418813

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
4	#11750938	C₂	1	1	yes	maximal, characteristic
5	#11750938	C₂	1	2	yes	maximal
6	#11750931	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750929	C₂	1	2	yes	maximal, complemented
8	#11750808	C₂	1	2	yes	maximal
9	#11750802	C₂	1	2	yes	maximal, complemented
10	C₄×#6705	C₂	1	1	yes	maximal, characteristic
11	C₈×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611693	—	3	1	no	maximal, Hall
13	C₂×Q₈×D₁₅	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	Q₈×Dic₁₅	C₄	1	1	yes	characteristic
16	C₂×#6705	C₂²	1	1	yes	characteristic
17	C₂×#6705	C₂²	1	2	yes	—
18	C₂×#6705	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×D₁₅	C₄	1	1	yes	characteristic
20	C₄⋊C₄×D₁₅	C₄	1	2	yes	—
21	#91776	C₄	1	2	yes	—
22	#91776	C₄	1	1	yes	characteristic
23	C₄²×D₁₅	C₂²	1	1	yes	characteristic
24	C₄²×D₁₅	C₂²	1	2	yes	—
25	C₄×Dic₃₀	C₂²	1	2	yes	—
26	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×#97	C₂²	1	2	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	#91099	C₂²	1	1	yes	characteristic
32	#91099	C₂²	1	1	yes	characteristic
33	#91098	C₂²	1	2	yes	—
34	#91098	C₂²	1	2	yes	—
35	#91098	C₂²	1	2	yes	—
36	C₈×Dic₁₅	C₂²	1	2	yes	—
37	C₈×Dic₁₅	C₂²	1	2	yes	—
38	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
39	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
40	#91087	C₂²	1	2	yes	—
41	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
42	#79962	—	5	1	no	maximal, Hall
43	C₄×Q₈×D₅	—	3	1	no	—
44	C₅×#446	D₃	1	1	yes	characteristic, complemented
45	#65313	—	3	1	no	—
46	#65126	—	3	1	no	—
47	#65126	—	3	2	no	—
48	#65119	—	3	1	no	—
49	#65117	—	3	2	no	—
50	#64996	—	3	2	no	—
51	#64990	—	3	2	no	—
52	C₄×#676	—	3	1	no	—
53	C₈×Dic₁₀	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	Q₈×D₁₅	—	2	4	no	—
56	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
60	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
61	C₂×Dic₃₀	C₂×C₄	1	2	yes	—
62	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	2	yes	—
70	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
71	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
72	#6712	C₂×C₄	1	2	yes	—
73	#6712	C₂×C₄	1	2	yes	—
74	#6712	C₂×C₄	1	2	yes	—
75	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
77	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
78	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₅	C₂³	1	2	yes	—
80	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
81	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊#168	C₂³	1	2	yes	—
83	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
84	#6705	—	2	2	no	—
85	#6705	—	2	4	no	—
86	#6705	Q₈	1	4	yes	complemented
87	C₄×D₃×Q₈	—	5	1	no	—
88	C₃×#446	D₅	1	1	yes	characteristic, complemented
89	#5024	—	5	1	no	—
90	#4837	—	5	1	no	—
91	#4837	—	5	2	no	—
92	#4830	—	5	1	no	—
93	#4828	—	5	2	no	—
94	#4707	—	5	2	no	—
95	#4701	—	5	2	no	—
96	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
97	C₈×Dic₆	—	5	1	no	—
98	C₂×Q₈×D₅	—	3	1	no	—
99	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
100	Q₈×Dic₅	—	3	1	no	—
101	C₂×#676	—	3	1	no	—
102	C₂×#676	—	3	1	no	—
103	C₂×#676	—	3	2	no	—
104	D₅×C₄⋊C₄	—	3	2	no	—
105	D₅×C₄⋊C₄	—	3	1	no	—
106	#4033	—	3	1	no	—
107	#4033	—	3	2	no	—
108	C₄²×D₅	—	3	1	no	—
109	C₄²×D₅	—	3	2	no	—
110	C₄×Dic₁₀	—	3	2	no	—
111	C₄×Dic₁₀	—	3	1	no	—
112	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
113	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
114	C₅×#97	C₂×D₃	1	2	yes	—
115	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
116	#3947	—	3	1	no	—
117	#3947	—	3	1	no	—
118	#3946	—	3	2	no	—
119	#3946	—	3	2	no	—
120	#3946	—	3	2	no	—
121	C₈×Dic₅	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₄⋊#168	—	3	1	no	—
124	C₄⋊#168	—	3	2	no	—
125	#3935	—	3	2	no	—
126	C₄×#168	—	3	1	no	—
127	Q₈×M₁₆	—	15	1	no	Sylow
128	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
136	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
140	C₄×D₁₅	—	2	2	no	—
141	C₄×D₁₅	—	2	4	no	—
142	C₄×D₁₅	—	4	1	no	—
143	C₄×D₁₅	—	4	2	no	—
144	C₄×D₁₅	C₂×Q₈	1	2	yes	—
145	C₄×D₁₅	#41	1	2	yes	—
146	Dic₃₀	—	2	4	no	—
147	Dic₃₀	M₁₆	1	4	yes	complemented
148	C₃×C₅×C₈	—	2	2	no	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	C₂×Q₈	1	2	yes	complemented
151	C₃⋊#168	—	2	1	no	—
152	C₃⋊#168	—	2	2	no	—
153	C₃⋊#168	C₂×Q₈	1	2	yes	complemented
154	C₂×D₃×Q₈	—	5	1	no	—
155	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
156	Q₈×Dic₃	—	5	1	no	—
157	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
158	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
159	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
160	D₃×C₄⋊C₄	—	5	2	no	—
161	D₃×C₄⋊C₄	—	5	1	no	—
162	#887	—	5	1	no	—
163	#887	—	5	2	no	—
164	C₄²×D₃	—	5	1	no	—
165	C₄²×D₃	—	5	2	no	—
166	C₄×Dic₆	—	5	1	no	—
167	C₄×Dic₆	—	5	2	no	—
168	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
169	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
170	C₃×#97	C₂×D₅	1	2	yes	—
171	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
172	#815	—	5	1	no	—
173	#815	—	5	1	no	—
174	Dic₃⋊C₈	—	5	2	no	—
175	Dic₃⋊C₈	—	5	2	no	—
176	Dic₃⋊C₈	—	5	2	no	—
177	C₈×Dic₃	—	5	2	no	—
178	C₈×Dic₃	—	5	2	no	—
179	C₄⋊(C₃⋊C₈)	—	5	1	no	—
180	C₄⋊(C₃⋊C₈)	—	5	2	no	—
181	#803	—	5	2	no	—
182	C₄×C₃⋊C₈	—	5	1	no	—
183	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
184	Q₈×D₅	—	6	4	no	—
185	C₂×C₄×D₅	—	3	1	no	—
186	C₂×C₄×D₅	—	3	2	no	—
187	C₂×C₄×D₅	—	3	1	no	—
188	C₂×C₄×D₅	—	3	1	no	—
189	C₂×C₄×D₅	—	3	2	no	—
190	C₂×Dic₁₀	—	3	1	no	—
191	C₂×Dic₁₀	—	3	2	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
196	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
197	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₄²×C₅	C₂²×D₃	1	2	yes	—
199	C₄⋊Dic₅	—	3	2	no	—
200	C₄⋊Dic₅	—	3	1	no	—
201	#683	—	3	2	no	—
202	#683	—	3	2	no	—
203	#683	—	3	2	no	—
204	C₄×Dic₅	—	3	2	no	—
205	C₄×Dic₅	—	3	1	no	—
206	C₄×Dic₅	—	3	2	no	—
207	C₄×Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	3	2	no	—
209	C₄×Dic₅	—	3	1	no	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	—	3	1	no	—
212	C₂×#168	—	3	2	no	—
213	#676	—	3	4	no	—
214	#676	—	6	2	no	—
215	#676	—	6	4	no	—
216	C₂×C₄×Q₈	—	15	1	no	—
217	#446	—	15	1	no	—
218	#446	—	15	2	no	—
219	#446	—	15	2	no	—
220	#446	D₁₅	1	1	yes	characteristic, complemented
221	C₈×Q₈	—	15	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	#423	—	15	2	no	—
224	#423	—	15	1	no	—
225	C₄×M₁₆	—	15	2	no	—
226	C₄×M₁₆	—	15	1	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×D₁₅	—	2	1	no	—
229	C₂×D₁₅	—	2	1	no	—
230	C₂×D₁₅	C₄×Q₈	1	2	yes	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	2	1	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
235	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	Dic₁₅	—	2	1	no	—
238	Dic₁₅	—	2	2	no	—
239	Dic₁₅	—	2	1	no	—
240	Dic₁₅	C₄×Q₈	1	2	yes	—
241	Dic₁₅	C₂×M₁₆	1	4	yes	—
242	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
243	D₃×Q₈	—	10	4	no	—
244	C₂×C₄×D₃	—	5	1	no	—
245	C₂×C₄×D₃	—	5	2	no	—
246	C₂×C₄×D₃	—	5	1	no	—
247	C₂×C₄×D₃	—	5	1	no	—
248	C₂×C₄×D₃	—	5	2	no	—
249	C₂×Dic₆	—	5	1	no	—
250	C₂×Dic₆	—	5	2	no	—
251	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
255	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
256	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
257	C₃×C₄²	C₂²×D₅	1	2	yes	—
258	C₄⋊Dic₃	—	5	2	no	—
259	C₄⋊Dic₃	—	5	1	no	—
260	Dic₃⋊C₄	—	5	2	no	—
261	Dic₃⋊C₄	—	5	2	no	—
262	Dic₃⋊C₄	—	5	2	no	—
263	C₄×Dic₃	—	5	2	no	—
264	C₄×Dic₃	—	5	1	no	—
265	C₄×Dic₃	—	5	2	no	—
266	C₄×Dic₃	—	5	1	no	—
267	C₄×Dic₃	—	5	2	no	—
268	C₄×Dic₃	—	5	1	no	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	2	no	—
272	ΓL(1,𝔽₂₅)	—	5	4	no	—
273	ΓL(1,𝔽₂₅)	—	10	2	no	—
274	ΓL(1,𝔽₂₅)	—	10	4	no	—
275	C₂²×D₅	—	3	1	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
279	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
280	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
282	C₂×Dic₅	—	3	1	no	—
283	C₂×Dic₅	—	3	2	no	—
284	C₂×Dic₅	—	3	2	no	—
285	C₂×Dic₅	—	3	1	no	—
286	C₂×Dic₅	—	3	1	no	—
287	C₄×D₅	—	3	2	no	—
288	C₄×D₅	—	3	2	no	—
289	C₄×D₅	—	6	4	no	—
290	C₄×D₅	—	6	2	no	—
291	C₄×D₅	—	12	1	no	—
292	C₄×D₅	—	12	2	no	—
293	Dic₁₀	—	3	4	no	—
294	Dic₁₀	—	6	4	no	—
295	C₅×C₈	—	2	2	no	—
296	C₅×C₈	—	2	1	no	—
297	C₅×C₈	D₃×Q₈	1	2	yes	complemented
298	#168	—	3	2	no	—
299	#168	—	6	1	no	—
300	#168	—	6	2	no	—
301	C₂²×Q₈	—	15	1	no	—
302	C₂×M₁₆	—	15	1	no	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂×M₁₆	—	15	1	no	—
305	C₄×Q₈	—	15	1	no	—
306	C₄×Q₈	—	15	1	no	—
307	C₄×Q₈	—	15	2	no	—
308	C₄×Q₈	—	15	1	no	—
309	C₄×Q₈	—	15	2	no	—
310	C₄×Q₈	C₂×D₁₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	15	2	no	—
312	C₂×C₄⋊C₄	—	15	1	no	—
313	C₂×C₄²	—	15	2	no	—
314	C₂×C₄²	—	15	1	no	—
315	C₄⋊C₈	—	15	2	no	—
316	C₄⋊C₈	—	15	2	no	—
317	C₄⋊C₈	—	15	2	no	—
318	C₄⋊C₈	—	15	1	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
321	C₄⋊C₈	C₂×D₁₅	1	2	yes	—
322	#97	—	15	1	no	—
323	#97	—	15	1	no	—
324	#97	—	15	2	no	—
325	#97	C₂×D₁₅	1	2	yes	—
326	C₄×C₈	—	15	2	no	—
327	C₄×C₈	—	15	2	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
332	C₂×C₃×C₅	#568	1	1	yes	characteristic
333	D₁₅	—	2	2	no	—
334	C₂²×D₃	—	5	1	no	—
335	C₃×Q₈	—	2	2	no	—
336	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
339	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
341	C₂×Dic₃	—	5	1	no	—
342	C₂×Dic₃	—	5	2	no	—
343	C₂×Dic₃	—	5	2	no	—
344	C₂×Dic₃	—	5	1	no	—
345	C₂×Dic₃	—	5	1	no	—
346	C₄×D₃	—	5	2	no	—
347	C₄×D₃	—	5	2	no	—
348	C₄×D₃	—	10	4	no	—
349	C₄×D₃	—	10	2	no	—
350	C₄×D₃	—	20	1	no	—
351	C₄×D₃	—	20	2	no	—
352	Dic₆	—	5	4	no	—
353	Dic₆	—	10	4	no	—
354	C₃×C₈	—	2	2	no	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	Q₈×D₅	1	2	yes	complemented
357	C₃⋊C₈	—	5	2	no	—
358	C₃⋊C₈	—	10	1	no	—
359	C₃⋊C₈	—	10	2	no	—
360	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
361	C₂×D₅	—	3	2	no	—
362	C₂×D₅	—	6	1	no	—
363	C₂×D₅	—	6	1	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	D₃×M₁₆	1	2	yes	—
368	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
369	C₄×C₅	D₃×#41	1	1	yes	characteristic
370	Dic₅	—	3	4	no	—
371	Dic₅	—	3	2	no	—
372	Dic₅	—	6	1	no	—
373	Dic₅	—	6	2	no	—
374	Dic₅	—	6	1	no	—
375	C₂×Q₈	—	15	1	no	—
376	C₂×Q₈	—	15	2	no	—
377	C₂×Q₈	—	30	4	no	—
378	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
379	C₂²×C₄	—	15	1	no	—
380	C₂²×C₄	—	15	2	no	—
381	C₂²×C₄	—	15	1	no	—
382	C₂²×C₄	—	15	2	no	—
383	C₂²×C₄	—	15	1	no	—
384	M₁₆	—	15	4	no	—
385	M₁₆	—	30	4	no	—
386	M₁₆	—	30	2	no	—
387	C₂×C₈	—	15	1	no	—
388	C₂×C₈	—	15	2	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	C₂²×D₁₅	1	2	yes	—
391	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
392	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
393	C₄⋊C₄	—	15	2	no	—
394	C₄⋊C₄	—	15	2	no	—
395	C₄⋊C₄	—	15	2	no	—
396	C₄⋊C₄	—	15	2	no	—
397	C₄⋊C₄	—	15	1	no	—
398	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
399	C₄⋊C₄	C₄×D₁₅	1	1	yes	characteristic
400	C₄²	—	15	2	no	—
401	C₄²	—	15	2	no	—
402	C₄²	—	15	1	no	—
403	C₄²	—	15	1	no	—
404	C₄²	—	15	2	no	—
405	C₄²	—	15	1	no	—
406	C₄²	C₂²×D₁₅	1	1	yes	characteristic
407	C₄²	C₂²×D₁₅	1	2	yes	—
408	C₃×C₅	Q₈×M₁₆	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
410	C₂×D₃	—	5	2	no	—
411	C₂×D₃	—	10	1	no	—
412	C₂×D₃	—	10	1	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	D₅×M₁₆	1	2	yes	—
417	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
418	C₃×C₄	D₅×#41	1	1	yes	characteristic
419	Dic₃	—	5	4	no	—
420	Dic₃	—	5	2	no	—
421	Dic₃	—	10	1	no	—
422	Dic₃	—	10	2	no	—
423	Dic₃	—	10	1	no	—
424	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
425	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
426	C₂×C₅	#5750	1	1	yes	characteristic
427	D₅	—	6	2	no	—
428	C₂³	—	15	1	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	15	4	no	—
431	Q₈	—	30	4	no	—
432	C₂×C₄	—	15	1	no	—
433	C₂×C₄	—	15	2	no	—
434	C₂×C₄	—	15	2	no	—
435	C₂×C₄	—	15	2	no	—
436	C₂×C₄	—	15	2	no	—
437	C₂×C₄	—	15	1	no	—
438	C₂×C₄	—	15	1	no	—
439	C₂×C₄	—	30	4	no	—
440	C₂×C₄	—	30	2	no	—
441	C₂×C₄	—	60	1	no	—
442	C₂×C₄	—	60	2	no	—
443	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
445	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
446	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	1	no	—
450	C₈	—	15	2	no	—
451	C₈	—	30	2	no	—
452	C₈	—	30	1	no	—
453	C₈	Q₈×D₁₅	1	2	yes	complemented
454	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
455	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
456	C₂×C₃	#66084	1	1	yes	characteristic
457	D₃	—	10	2	no	—
458	C₅	#79962	1	1	yes	characteristic, complemented, Sylow
459	C₂²	—	15	2	no	—
460	C₂²	—	30	1	no	—
461	C₂²	—	30	1	no	—
462	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
463	C₄	—	2	2	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	2	no	—
466	C₄	—	15	2	no	—
467	C₄	—	15	4	no	—
468	C₄	—	30	1	no	—
469	C₄	—	30	2	no	—
470	C₄	—	30	1	no	—
471	C₄	M₁₆×D₁₅	1	2	yes	—
472	C₄	C₂×Q₈×D₁₅	1	1	yes	characteristic
473	C₄	#41×D₁₅	1	1	yes	characteristic
474	C₃	#10611693	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	30	2	no	—
476	C₂	C₄×Q₈×D₁₅	1	1	yes	characteristic
477	C₂	C₂×M₁₆×D₁₅	1	1	yes	characteristic
478	C₂	#11756509	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#446	C₂
prime radical	C₂²×D₁₅	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#446	D₁₅
hypocenter	C₃×C₅	Q₈×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#446	C₂	semidirect
3. #11751125	C₂	semidirect
6. #11750931	C₂	semidirect
7. #11750929	C₂	semidirect
9. #11750802	C₂	semidirect
11. C₈×Dic₃₀	C₂	semidirect
44. C₅×#446	D₃	semidirect
86. #6705	Q₈	semidirect
88. C₃×#446	D₅	semidirect
147. Dic₃₀	M₁₆	semidirect
150. C₃×C₅×C₈	C₂×Q₈	semidirect
153. C₃⋊#168	C₂×Q₈	semidirect
220. #446	D₁₅	semidirect
297. C₅×C₈	D₃×Q₈	semidirect
356. C₃×C₈	Q₈×D₅	semidirect
408. C₃×C₅	Q₈×M₁₆	semidirect
453. C₈	Q₈×D₁₅	semidirect
458. C₅	#79962	semidirect
474. C₃	#10611693	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×D₁₅	2
C₃×C₅×#446	2
#11751125	2
#11750938	2
#11750931	2
#11750929	2
#11750808	2
#11750802	2
C₄×#6705	2
C₈×Dic₃₀	2
#10611693	3
#79962	5