Subgroups — #14418841

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×D₁₅⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#6705	C₂	1	1	yes	maximal, characteristic
3	C₅×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64968	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747822	C₂	1	2	yes	maximal, complemented
6	#11747599	C₂	1	2	yes	maximal
7	#11747594	C₂	1	2	yes	maximal
8	#11747569	C₂	1	2	yes	maximal, complemented
9	#11747015	C₂	1	1	yes	maximal, characteristic
10	#11746862	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746857	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈×#676	—	3	1	no	maximal, Hall
13	C₂×D₁₅⋊Q₈	C₄	1	1	yes	characteristic
14	C₂×#6705	C₂²	1	1	yes	characteristic
15	C₂×#6705	C₂²	1	1	yes	characteristic
16	C₄²×D₁₅	C₂²	1	1	yes	characteristic
17	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
18	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
19	C₄×#1204	C₂²	1	2	yes	—
20	#91437	C₄	1	1	yes	characteristic
21	#91404	C₄	1	2	yes	—
22	C₄×#1200	C₂²	1	2	yes	—
23	#91344	C₄	1	1	yes	characteristic
24	#91331	C₄	1	1	yes	characteristic
25	#91325	C₄	1	2	yes	—
26	C₂×#6651	C₂²	1	2	yes	—
27	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	#91099	C₂²	1	1	yes	characteristic
29	#91099	C₂²	1	1	yes	characteristic
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
32	C₅×C₈×Dic₃	C₂²	1	2	yes	—
33	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₃×#3947	C₂²	1	2	yes	—
35	C₃×#3946	C₂²	1	2	yes	—
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
37	Dic₃⋊#168	C₂²	1	2	yes	—
38	#90983	C₂²	1	2	yes	—
39	#90982	C₂²	1	2	yes	—
40	#90952	C₂²	1	2	yes	—
41	Dic₃×#168	C₂²	1	2	yes	—
42	#79962	—	5	1	no	maximal, Hall
43	C₄×Q₈×D₅	—	3	1	no	—
44	C₅×C₈×Q₈	—	3	1	no	—
45	Q₈×#168	—	3	1	no	—
46	#65126	—	3	2	no	—
47	#65126	—	3	1	no	—
48	#65120	—	3	1	no	—
49	#65120	—	3	2	no	—
50	C₄×#676	—	3	1	no	—
51	C₄×#676	—	3	2	no	—
52	#64968	—	3	2	no	—
53	#64968	D₃	1	1	yes	characteristic, complemented
54	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
59	C₂×#1204	C₂×C₄	1	2	yes	—
60	C₂×#1200	C₂×C₄	1	2	yes	—
61	C₂×#1200	C₂×C₄	1	2	yes	—
62	D₁₅⋊Q₈	—	2	4	no	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
67	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	#6705	—	2	2	no	—
72	#6705	Q₈	1	4	yes	complemented
73	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₄×C₅×Dic₃	C₂³	1	2	yes	—
76	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
77	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×#683	C₂×C₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂³	1	2	yes	—
80	C₂×C₃×#168	C₂³	1	2	yes	—
81	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
82	#6669	C₂×C₄	1	2	yes	—
83	#6668	C₂×C₄	1	2	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
85	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
86	#6651	—	2	4	no	—
87	C₄×D₃×Q₈	—	5	1	no	—
88	C₃×#446	—	5	1	no	—
89	#5024	—	5	1	no	—
90	#4837	—	5	2	no	—
91	#4837	—	5	1	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	D₅	1	1	yes	characteristic, complemented
98	C₂×Q₈×D₅	—	3	1	no	—
99	C₄×C₅×Q₈	—	3	1	no	—
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	1	no	—
105	D₅×C₄⋊C₄	—	3	2	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	C₂×D₃	1	1	yes	characteristic
112	C₅×C₄⋊C₈	—	3	2	no	—
113	C₅×C₄⋊C₈	—	3	1	no	—
114	C₄×C₅×C₈	—	3	2	no	—
115	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
116	#3947	—	3	1	no	—
117	#3947	—	3	1	no	—
118	#3947	—	3	2	no	—
119	#3947	C₂×D₃	1	2	yes	—
120	#3946	—	3	2	no	—
121	#3946	—	3	2	no	—
122	#3946	C₂×D₃	1	2	yes	—
123	C₄⋊#168	—	3	2	no	—
124	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
125	C₄×#168	—	3	1	no	—
126	C₄×#168	—	3	2	no	—
127	Q₈×M₁₆	—	15	1	no	Sylow
128	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
135	C₄×D₁₅	—	2	2	no	—
136	C₄×D₁₅	—	4	1	no	—
137	C₄×D₁₅	C₂×Q₈	1	2	yes	—
138	C₄×D₁₅	#41	1	2	yes	—
139	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
140	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
141	C₅×Dic₆	M₁₆	1	4	yes	complemented
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₃×Dic₁₀	—	2	2	no	—
145	#1204	—	2	4	no	—
146	#1200	—	2	4	no	—
147	#1200	—	4	2	no	—
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	C₂×Q₈	1	2	yes	complemented
150	C₃⋊#168	—	2	1	no	—
151	C₃⋊#168	C₂×Q₈	1	2	yes	complemented
152	C₃×#168	—	2	2	no	—
153	C₅×C₃⋊C₈	—	2	2	no	—
154	C₂×D₃×Q₈	—	5	1	no	—
155	C₃×C₄×Q₈	—	5	1	no	—
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	1	no	—
161	D₃×C₄⋊C₄	—	5	2	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	2	no	—
167	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
168	C₃×C₄⋊C₈	—	5	2	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×#97	—	5	2	no	—
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	C₂×D₅	1	2	yes	—
177	C₈×Dic₃	—	5	2	no	—
178	C₈×Dic₃	C₂×D₅	1	2	yes	—
179	C₄⋊(C₃⋊C₈)	—	5	2	no	—
180	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
181	#803	—	5	2	no	—
182	C₄×C₃⋊C₈	—	5	1	no	—
183	C₂×C₅×Q₈	—	3	1	no	—
184	Q₈×D₅	—	6	4	no	—
185	C₂×C₄×D₅	—	3	1	no	—
186	C₂×C₄×D₅	—	3	1	no	—
187	C₂×C₄×D₅	—	3	2	no	—
188	C₂×C₄×D₅	—	3	1	no	—
189	C₂×C₄×D₅	—	3	2	no	—
190	C₂×Dic₁₀	—	3	2	no	—
191	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
192	C₂×C₅×C₈	—	3	2	no	—
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₅×C₄⋊C₄	—	3	2	no	—
196	C₅×C₄⋊C₄	—	3	1	no	—
197	C₄²×C₅	—	3	2	no	—
198	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₄⋊Dic₅	—	3	2	no	—
200	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
201	#683	—	3	2	no	—
202	#683	—	3	2	no	—
203	#683	C₄×D₃	1	2	yes	—
204	C₄×Dic₅	—	3	1	no	—
205	C₄×Dic₅	—	3	1	no	—
206	C₄×Dic₅	—	3	1	no	—
207	C₄×Dic₅	—	3	2	no	—
208	C₄×Dic₅	—	3	2	no	—
209	C₄×Dic₅	C₂²×D₃	1	2	yes	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	—	3	1	no	—
212	C₂×#168	C₂²×D₃	1	2	yes	—
213	#676	—	3	4	no	—
214	#676	—	6	4	no	—
215	#676	—	6	2	no	—
216	C₂×C₄×Q₈	—	15	1	no	—
217	#446	—	5	1	no	—
218	#446	—	15	2	no	—
219	#446	—	15	2	no	—
220	#446	—	15	1	no	—
221	C₈×Q₈	—	3	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	1	no	—
232	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
233	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
234	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	Dic₁₅	—	2	1	no	—
236	Dic₁₅	—	2	1	no	—
237	Dic₁₅	C₄×Q₈	1	2	yes	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	2	2	no	—
240	C₅×Dic₃	—	2	2	no	—
241	C₅×Dic₃	C₂×M₁₆	1	4	yes	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	D₃×Q₈	—	10	4	no	—
244	C₂×C₄×D₃	—	5	1	no	—
245	C₂×C₄×D₃	—	5	1	no	—
246	C₂×C₄×D₃	—	5	2	no	—
247	C₂×C₄×D₃	—	5	1	no	—
248	C₂×C₄×D₃	—	5	2	no	—
249	C₂×Dic₆	—	5	2	no	—
250	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
251	C₂×C₃×C₈	—	5	2	no	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₄²	—	5	2	no	—
257	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
258	C₄⋊Dic₃	—	5	2	no	—
259	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
260	Dic₃⋊C₄	—	5	2	no	—
261	Dic₃⋊C₄	—	5	2	no	—
262	Dic₃⋊C₄	C₄×D₅	1	2	yes	—
263	C₄×Dic₃	—	5	1	no	—
264	C₄×Dic₃	—	5	1	no	—
265	C₄×Dic₃	—	5	1	no	—
266	C₄×Dic₃	—	5	2	no	—
267	C₄×Dic₃	—	5	2	no	—
268	C₄×Dic₃	C₂²×D₅	1	2	yes	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
272	ΓL(1,𝔽₂₅)	—	5	4	no	—
273	ΓL(1,𝔽₂₅)	—	10	4	no	—
274	ΓL(1,𝔽₂₅)	—	10	2	no	—
275	C₂²×D₅	—	3	1	no	—
276	C₅×Q₈	—	3	4	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	2	no	—
279	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
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	1	no	—
284	C₂×Dic₅	—	3	1	no	—
285	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
286	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
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	2	no	—
292	C₄×D₅	—	12	1	no	—
293	Dic₁₀	—	2	2	no	—
294	Dic₁₀	—	6	4	no	—
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	6	2	no	—
297	C₅×C₈	D₃×Q₈	1	2	yes	complemented
298	#168	—	2	2	no	—
299	#168	—	3	2	no	—
300	#168	—	6	1	no	—
301	C₂²×Q₈	—	15	1	no	—
302	C₂×M₁₆	—	15	2	no	—
303	C₂×M₁₆	—	15	1	no	—
304	C₂×M₁₆	—	15	1	no	—
305	C₄×Q₈	—	3	1	no	—
306	C₄×Q₈	—	5	1	no	—
307	C₄×Q₈	—	15	2	no	—
308	C₄×Q₈	—	15	2	no	—
309	C₄×Q₈	—	15	1	no	—
310	C₄×Q₈	—	15	1	no	—
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	—	3	2	no	—
316	C₄⋊C₈	—	3	1	no	—
317	C₄⋊C₈	—	5	2	no	—
318	C₄⋊C₈	—	5	1	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	2	no	—
321	C₄⋊C₈	—	15	2	no	—
322	#97	—	5	2	no	—
323	#97	—	15	2	no	—
324	#97	—	15	1	no	—
325	#97	—	15	1	no	—
326	C₄×C₈	—	3	2	no	—
327	C₄×C₈	—	15	2	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	D₃×D₅	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	—	10	2	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
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	1	no	—
343	C₂×Dic₃	—	5	1	no	—
344	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
345	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
346	C₄×D₃	—	5	2	no	—
347	C₄×D₃	—	5	2	no	—
348	C₄×D₃	—	10	2	no	—
349	C₄×D₃	—	10	4	no	—
350	C₄×D₃	—	20	2	no	—
351	C₄×D₃	—	20	1	no	—
352	Dic₆	—	10	4	no	—
353	Dic₆	#676	1	4	yes	complemented
354	C₃×C₈	—	2	1	no	—
355	C₃×C₈	—	10	2	no	—
356	C₃×C₈	Q₈×D₅	1	2	yes	complemented
357	C₃⋊C₈	—	2	2	no	—
358	C₃⋊C₈	—	5	2	no	—
359	C₃⋊C₈	—	10	1	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	1	no	—
365	C₄×C₅	—	3	4	no	—
366	C₄×C₅	—	6	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	—	2	2	no	—
371	Dic₅	—	2	2	no	—
372	Dic₅	—	3	2	no	—
373	Dic₅	—	6	1	no	—
374	Dic₅	—	6	1	no	—
375	C₂×Q₈	—	3	1	no	—
376	C₂×Q₈	—	5	1	no	—
377	C₂×Q₈	—	15	2	no	—
378	C₂×Q₈	—	30	4	no	—
379	C₂²×C₄	—	15	2	no	—
380	C₂²×C₄	—	15	2	no	—
381	C₂²×C₄	—	15	1	no	—
382	C₂²×C₄	—	15	1	no	—
383	C₂²×C₄	—	15	1	no	—
384	M₁₆	—	15	4	no	—
385	M₁₆	—	30	2	no	—
386	M₁₆	—	30	4	no	—
387	C₂×C₈	—	3	2	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	—	15	1	no	—
391	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
392	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
393	C₄⋊C₄	—	3	2	no	—
394	C₄⋊C₄	—	3	1	no	—
395	C₄⋊C₄	—	5	2	no	—
396	C₄⋊C₄	—	5	1	no	—
397	C₄⋊C₄	—	15	2	no	—
398	C₄⋊C₄	—	15	2	no	—
399	C₄⋊C₄	—	15	2	no	—
400	C₄²	—	3	2	no	—
401	C₄²	—	5	2	no	—
402	C₄²	—	15	2	no	—
403	C₄²	—	15	2	no	—
404	C₄²	—	15	1	no	—
405	C₄²	—	15	1	no	—
406	C₄²	—	15	1	no	—
407	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
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	1	no	—
414	C₃×C₄	—	10	2	no	—
415	C₃×C₄	—	10	2	no	—
416	C₃×C₄	C₂×#676	1	2	yes	—
417	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
418	C₃×C₄	D₅×#41	1	1	yes	characteristic
419	Dic₃	—	2	2	no	—
420	Dic₃	—	5	2	no	—
421	Dic₃	—	10	1	no	—
422	Dic₃	—	10	1	no	—
423	Dic₃	C₂×#676	1	4	yes	—
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	—	3	4	no	—
430	Q₈	—	10	2	no	—
431	Q₈	—	30	4	no	—
432	C₂×C₄	—	3	2	no	—
433	C₂×C₄	—	3	2	no	—
434	C₂×C₄	—	5	2	no	—
435	C₂×C₄	—	5	2	no	—
436	C₂×C₄	—	15	1	no	—
437	C₂×C₄	—	15	2	no	—
438	C₂×C₄	—	15	2	no	—
439	C₂×C₄	—	15	1	no	—
440	C₂×C₄	—	15	1	no	—
441	C₂×C₄	—	30	4	no	—
442	C₂×C₄	—	30	2	no	—
443	C₂×C₄	—	60	1	no	—
444	C₂×C₄	—	60	2	no	—
445	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
446	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	6	2	no	—
450	C₈	—	10	2	no	—
451	C₈	—	15	2	no	—
452	C₈	—	30	1	no	—
453	C₈	D₁₅⋊Q₈	1	2	yes	complemented
454	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
455	C₂×C₃	C₂²×#676	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	C₂×C₄×D₃×D₅	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	3	4	no	—
465	C₄	—	6	2	no	—
466	C₄	—	10	2	no	—
467	C₄	—	10	2	no	—
468	C₄	—	15	2	no	—
469	C₄	—	30	1	no	—
470	C₄	—	30	1	no	—
471	C₄	D₃×#676	1	2	yes	—
472	C₄	C₂×D₁₅⋊Q₈	1	1	yes	characteristic
473	C₄	#92016	1	1	yes	characteristic
474	C₃	Q₈×#676	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	30	2	no	—
476	C₂	C₄×D₁₅⋊Q₈	1	1	yes	characteristic
477	C₂	C₂×D₃×#676	1	1	yes	characteristic
478	C₂	#11753953	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	C₂²×D₁₅	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	Q₈×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₅×C₈×Dic₆	C₂	semidirect
4. C₃×#64968	C₂	semidirect
5. #11747822	C₂	semidirect
8. #11747569	C₂	semidirect
10. #11746862	C₂	semidirect
11. #11746857	C₂	semidirect
53. #64968	D₃	semidirect
72. #6705	Q₈	semidirect
97. C₈×Dic₆	D₅	semidirect
141. C₅×Dic₆	M₁₆	semidirect
149. C₃×C₅×C₈	C₂×Q₈	semidirect
151. C₃⋊#168	C₂×Q₈	semidirect
297. C₅×C₈	D₃×Q₈	semidirect
353. Dic₆	#676	semidirect
356. C₃×C₈	Q₈×D₅	semidirect
408. C₃×C₅	Q₈×M₁₆	semidirect
453. C₈	D₁₅⋊Q₈	semidirect
458. C₅	#79962	semidirect
474. C₃	Q₈×#676	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₅⋊Q₈	2
C₄×#6705	2
C₅×C₈×Dic₆	2
C₃×#64968	2
#11747822	2
#11747599	2
#11747594	2
#11747569	2
#11747015	2
#11746862	2
#11746857	2
Q₈×#676	3
#79962	5