Subgroups — #14418837

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	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747007	C₂	1	2	yes	maximal
5	#11747007	C₂	1	1	yes	maximal, characteristic
6	#11747003	C₂	1	2	yes	maximal
7	C₄×#6649	C₂	1	1	yes	maximal, characteristic
8	#11746848	C₂	1	2	yes	maximal, complemented
9	#11746847	C₂	1	2	yes	maximal, complemented
10	#11746846	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611693	—	3	1	no	maximal, Hall
13	C₂×C₃×Q₈×D₅	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic
16	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
17	C₃×D₅×C₄⋊C₄	C₄	1	2	yes	—
18	C₃×#4033	C₄	1	2	yes	—
19	C₃×#4033	C₄	1	1	yes	characteristic
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₂²	1	2	yes	—
22	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
24	C₂×#6649	C₂²	1	1	yes	characteristic
25	C₂×#6649	C₂²	1	2	yes	—
26	C₂×#6649	C₂²	1	1	yes	characteristic
27	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
28	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
29	#91087	C₂²	1	2	yes	—
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
32	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
33	C₅×#803	C₂²	1	2	yes	—
34	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
35	#90982	C₂²	1	2	yes	—
36	#90982	C₂²	1	2	yes	—
37	#90982	C₂²	1	2	yes	—
38	#90952	C₂²	1	1	yes	characteristic
39	#90952	C₂²	1	1	yes	characteristic
40	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
41	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
42	Q₈×#208	—	5	1	no	maximal, Hall
43	C₄×Q₈×D₅	D₃	1	1	yes	characteristic
44	C₅×#446	—	3	1	no	—
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	C₃×Q₈×D₅	—	2	4	no	—
56	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
62	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	C₂³	1	2	yes	—
68	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
74	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×#683	C₂×C₄	1	2	yes	—
77	C₃×#683	C₂×C₄	1	2	yes	—
78	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂³	1	2	yes	—
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	#6649	—	2	2	no	—
85	#6649	—	2	4	no	—
86	#6649	Q₈	1	4	yes	complemented
87	C₂×C₃×C₄×Q₈	—	5	1	no	—
88	#5024	—	5	1	no	—
89	#5024	—	5	2	no	—
90	#5024	—	5	2	no	—
91	#5024	D₅	1	1	yes	characteristic, complemented
92	Q₈×C₃⋊C₈	—	5	1	no	—
93	Q₈×C₃⋊C₈	—	5	1	no	—
94	#4924	—	5	1	no	—
95	#4924	—	5	2	no	—
96	C₄×#208	—	5	2	no	—
97	C₄×#208	—	5	1	no	—
98	C₂×Q₈×D₅	Dic₃	1	1	yes	characteristic
99	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
100	Q₈×Dic₅	Dic₃	1	1	yes	characteristic
101	C₂×#676	—	3	1	no	—
102	C₂×#676	—	3	1	no	—
103	C₂×#676	—	3	2	no	—
104	D₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
105	D₅×C₄⋊C₄	Dic₃	1	2	yes	—
106	#4033	Dic₃	1	2	yes	—
107	#4033	Dic₃	1	1	yes	characteristic
108	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
109	C₄²×D₅	C₂×D₃	1	2	yes	—
110	C₄×Dic₁₀	C₂×D₃	1	2	yes	—
111	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
112	C₅×C₄⋊C₈	—	3	2	no	—
113	C₅×C₄⋊C₈	—	3	1	no	—
114	C₅×#97	—	3	2	no	—
115	C₄×C₅×C₈	—	3	1	no	—
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×C₃×D₅	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×C₃×Dic₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
140	C₃×C₄×D₅	—	2	2	no	—
141	C₃×C₄×D₅	—	2	4	no	—
142	C₃×C₄×D₅	—	4	1	no	—
143	C₃×C₄×D₅	—	4	2	no	—
144	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
145	C₃×C₄×D₅	#41	1	2	yes	—
146	C₃×Dic₁₀	—	2	4	no	—
147	C₃×Dic₁₀	M₁₆	1	4	yes	complemented
148	C₃⋊#168	—	2	2	no	—
149	C₃⋊#168	—	2	1	no	—
150	C₃⋊#168	C₂×Q₈	1	2	yes	complemented
151	C₅×C₃⋊C₈	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	complemented
154	C₂²×C₃×Q₈	—	5	1	no	—
155	C₃×C₄×Q₈	—	5	1	no	—
156	C₃×C₄×Q₈	—	5	1	no	—
157	C₃×C₄×Q₈	—	5	2	no	—
158	C₃×C₄×Q₈	—	5	1	no	—
159	C₃×C₄×Q₈	—	5	2	no	—
160	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	—	5	2	no	—
162	C₂×C₃×C₄⋊C₄	—	5	1	no	—
163	C₂×C₃×C₄²	—	5	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×#208	—	5	1	no	—
166	C₂×#208	—	5	2	no	—
167	C₂×#208	—	5	1	no	—
168	C₄⋊(C₃⋊C₈)	—	5	1	no	—
169	C₄⋊(C₃⋊C₈)	—	5	2	no	—
170	C₄⋊(C₃⋊C₈)	—	5	2	no	—
171	C₄⋊(C₃⋊C₈)	—	5	2	no	—
172	C₄⋊(C₃⋊C₈)	—	5	2	no	—
173	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
174	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	—
175	#803	—	5	2	no	—
176	#803	—	5	1	no	—
177	#803	—	5	1	no	—
178	#803	C₂×D₅	1	2	yes	—
179	C₄×C₃⋊C₈	—	5	1	no	—
180	C₄×C₃⋊C₈	—	5	2	no	—
181	C₄×C₃⋊C₈	—	5	2	no	—
182	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
183	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
184	Q₈×D₅	—	2	4	no	—
185	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
186	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
187	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
189	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
190	C₂×Dic₁₀	C₂×Dic₃	1	2	yes	—
191	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
192	C₂×C₅×C₈	—	3	1	no	—
193	C₂×C₅×C₈	—	3	2	no	—
194	C₂×C₅×C₈	—	3	1	no	—
195	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
196	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
197	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₄²×C₅	C₂²×D₃	1	2	yes	—
199	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
200	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
201	#683	C₂×Dic₃	1	2	yes	—
202	#683	C₂×Dic₃	1	2	yes	—
203	#683	C₂×Dic₃	1	2	yes	—
204	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
205	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
206	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
207	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
208	C₄×Dic₅	C₂²×D₃	1	2	yes	—
209	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
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	—	5	1	no	—
217	#446	—	3	1	no	—
218	#446	—	15	2	no	—
219	#446	—	15	2	no	—
220	#446	—	15	1	no	—
221	C₈×Q₈	—	15	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	#423	—	15	1	no	—
224	#423	—	15	2	no	—
225	C₄×M₁₆	—	15	1	no	—
226	C₄×M₁₆	—	15	2	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	1	no	—
229	C₂×C₃×D₅	—	2	1	no	—
230	C₂×C₃×D₅	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	C₃×Dic₅	—	2	1	no	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	2	1	no	—
240	C₃×Dic₅	C₄×Q₈	1	2	yes	—
241	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	C₂×C₃×Q₈	—	5	2	no	—
244	C₂×C₃×Q₈	—	10	4	no	—
245	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	—	5	1	no	—
247	C₂²×C₃×C₄	—	5	2	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	2	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
251	C₃×C₄⋊C₄	—	5	2	no	—
252	C₃×C₄⋊C₄	—	5	2	no	—
253	C₃×C₄⋊C₄	—	5	2	no	—
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
257	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
258	C₃×C₄²	—	5	2	no	—
259	C₃×C₄²	—	5	2	no	—
260	C₃×C₄²	—	5	1	no	—
261	C₃×C₄²	—	5	1	no	—
262	C₃×C₄²	—	5	2	no	—
263	C₃×C₄²	—	5	1	no	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	C₃×C₄²	C₂²×D₅	1	2	yes	—
266	#208	—	5	4	no	—
267	#208	—	10	4	no	—
268	#208	—	10	2	no	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	2	no	—
272	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
273	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
275	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
276	C₅×Q₈	—	2	2	no	—
277	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
279	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
280	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
282	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
283	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
284	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
285	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
286	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
287	C₄×D₅	—	2	2	no	—
288	C₄×D₅	—	2	4	no	—
289	C₄×D₅	—	4	1	no	—
290	C₄×D₅	—	4	2	no	—
291	C₄×D₅	D₃×Q₈	1	2	yes	—
292	C₄×D₅	#239	1	2	yes	—
293	Dic₁₀	—	2	4	no	—
294	Dic₁₀	#208	1	4	yes	complemented
295	C₅×C₈	—	3	2	no	—
296	C₅×C₈	—	6	2	no	—
297	C₅×C₈	—	6	1	no	—
298	#168	—	3	2	no	—
299	#168	—	6	1	no	—
300	#168	—	6	2	no	—
301	C₂²×Q₈	—	5	1	no	—
302	C₂×M₁₆	—	15	1	no	—
303	C₂×M₁₆	—	15	1	no	—
304	C₂×M₁₆	—	15	2	no	—
305	C₄×Q₈	—	5	1	no	—
306	C₄×Q₈	—	5	1	no	—
307	C₄×Q₈	—	5	2	no	—
308	C₄×Q₈	—	5	1	no	—
309	C₄×Q₈	—	5	2	no	—
310	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	5	2	no	—
312	C₂×C₄⋊C₄	—	5	1	no	—
313	C₂×C₄²	—	5	2	no	—
314	C₂×C₄²	—	5	1	no	—
315	C₄⋊C₈	—	3	1	no	—
316	C₄⋊C₈	—	3	2	no	—
317	C₄⋊C₈	—	15	2	no	—
318	C₄⋊C₈	—	15	2	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	1	no	—
321	C₄⋊C₈	—	15	2	no	—
322	#97	—	3	2	no	—
323	#97	—	15	1	no	—
324	#97	—	15	1	no	—
325	#97	—	15	2	no	—
326	C₄×C₈	—	3	1	no	—
327	C₄×C₈	—	15	2	no	—
328	C₄×C₈	—	15	2	no	—
329	C₄×C₈	—	15	1	no	—
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	C₃×D₅	—	2	2	no	—
334	C₂³×C₃	—	5	1	no	—
335	C₃×Q₈	—	2	2	no	—
336	C₃×Q₈	—	5	4	no	—
337	C₃×Q₈	—	10	4	no	—
338	C₂×C₃×C₄	—	5	1	no	—
339	C₂×C₃×C₄	—	5	2	no	—
340	C₂×C₃×C₄	—	5	2	no	—
341	C₂×C₃×C₄	—	5	2	no	—
342	C₂×C₃×C₄	—	5	2	no	—
343	C₂×C₃×C₄	—	5	1	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	10	4	no	—
346	C₂×C₃×C₄	—	10	2	no	—
347	C₂×C₃×C₄	—	20	1	no	—
348	C₂×C₃×C₄	—	20	2	no	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
351	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
352	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
354	C₃⋊C₈	—	2	2	no	—
355	C₃⋊C₈	—	2	1	no	—
356	C₃⋊C₈	—	5	2	no	—
357	C₃⋊C₈	—	10	2	no	—
358	C₃⋊C₈	—	10	1	no	—
359	C₃⋊C₈	Q₈×D₅	1	2	yes	complemented
360	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
361	C₂×D₅	—	2	1	no	—
362	C₂×D₅	—	2	1	no	—
363	C₂×D₅	Q₈×Dic₃	1	2	yes	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	C₂×#208	1	2	yes	—
368	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
369	C₄×C₅	C₂×#239	1	1	yes	characteristic
370	Dic₅	—	2	1	no	—
371	Dic₅	—	2	2	no	—
372	Dic₅	—	2	1	no	—
373	Dic₅	C₂×#208	1	4	yes	—
374	Dic₅	Q₈×Dic₃	1	2	yes	—
375	C₂×Q₈	—	5	1	no	—
376	C₂×Q₈	—	5	2	no	—
377	C₂×Q₈	—	10	4	no	—
378	C₂×Q₈	D₅×Dic₃	1	1	yes	characteristic
379	C₂²×C₄	—	5	1	no	—
380	C₂²×C₄	—	5	2	no	—
381	C₂²×C₄	—	5	1	no	—
382	C₂²×C₄	—	5	2	no	—
383	C₂²×C₄	—	5	1	no	—
384	M₁₆	—	15	4	no	—
385	M₁₆	—	30	2	no	—
386	M₁₆	—	30	4	no	—
387	C₂×C₈	—	3	1	no	—
388	C₂×C₈	—	3	1	no	—
389	C₂×C₈	—	3	2	no	—
390	C₂×C₈	—	15	1	no	—
391	C₂×C₈	—	15	2	no	—
392	C₂×C₈	—	15	1	no	—
393	C₄⋊C₄	—	5	2	no	—
394	C₄⋊C₄	—	5	2	no	—
395	C₄⋊C₄	—	5	2	no	—
396	C₄⋊C₄	—	5	2	no	—
397	C₄⋊C₄	—	5	1	no	—
398	C₄⋊C₄	D₅×Dic₃	1	2	yes	—
399	C₄⋊C₄	D₅×Dic₃	1	1	yes	characteristic
400	C₄²	—	5	2	no	—
401	C₄²	—	5	2	no	—
402	C₄²	—	5	1	no	—
403	C₄²	—	5	1	no	—
404	C₄²	—	5	2	no	—
405	C₄²	—	5	1	no	—
406	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
407	C₄²	C₂×D₃×D₅	1	2	yes	—
408	C₃×C₅	Q₈×M₁₆	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	—	5	2	no	—
410	C₂²×C₃	—	10	1	no	—
411	C₂²×C₃	—	10	1	no	—
412	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	5	4	no	—
417	C₃×C₄	—	5	2	no	—
418	C₃×C₄	—	10	1	no	—
419	C₃×C₄	—	10	2	no	—
420	C₃×C₄	—	10	1	no	—
421	C₃×C₄	D₅×M₁₆	1	2	yes	—
422	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
423	C₃×C₄	D₅×#41	1	1	yes	characteristic
424	C₂×C₅	C₂²×#208	1	1	yes	characteristic
425	C₂×C₅	C₂×Q₈×Dic₃	1	1	yes	characteristic
426	C₂×C₅	#5819	1	1	yes	characteristic
427	D₅	—	2	2	no	—
428	C₂³	—	5	1	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	5	4	no	—
431	Q₈	—	10	4	no	—
432	C₂×C₄	—	5	1	no	—
433	C₂×C₄	—	5	2	no	—
434	C₂×C₄	—	5	2	no	—
435	C₂×C₄	—	5	2	no	—
436	C₂×C₄	—	5	2	no	—
437	C₂×C₄	—	5	1	no	—
438	C₂×C₄	—	5	1	no	—
439	C₂×C₄	—	10	4	no	—
440	C₂×C₄	—	10	2	no	—
441	C₂×C₄	—	20	1	no	—
442	C₂×C₄	—	20	2	no	—
443	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
444	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
445	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
446	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
448	C₈	—	3	2	no	—
449	C₈	—	6	1	no	—
450	C₈	—	6	2	no	—
451	C₈	—	15	2	no	—
452	C₈	—	30	2	no	—
453	C₈	—	30	1	no	—
454	C₂×C₃	—	10	2	no	—
455	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
456	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
457	C₂×C₃	#66084	1	1	yes	characteristic
458	C₅	Q₈×#208	1	1	yes	characteristic, complemented, Sylow
459	C₂²	—	5	2	no	—
460	C₂²	—	10	1	no	—
461	C₂²	—	10	1	no	—
462	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	5	4	no	—
467	C₄	—	5	2	no	—
468	C₄	—	10	2	no	—
469	C₄	—	10	1	no	—
470	C₄	—	10	1	no	—
471	C₄	D₅×#208	1	2	yes	—
472	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
473	C₄	D₅×#239	1	1	yes	characteristic
474	C₃	#10611693	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	10	2	no	—
476	C₂	C₂×D₅×#208	1	1	yes	characteristic
477	C₂	Q₈×D₅×Dic₃	1	1	yes	characteristic
478	C₂	#11755296	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×Q₈	C₂²
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	Q₈×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #11751125	C₂	semidirect
3. C₅×#5024	C₂	semidirect
8. #11746848	C₂	semidirect
9. #11746847	C₂	semidirect
10. #11746846	C₂	semidirect
11. C₃⋊C₈×Dic₁₀	C₂	semidirect
86. #6649	Q₈	semidirect
91. #5024	D₅	semidirect
147. C₃×Dic₁₀	M₁₆	semidirect
150. C₃⋊#168	C₂×Q₈	semidirect
153. C₅×C₃⋊C₈	C₂×Q₈	semidirect
294. Dic₁₀	#208	semidirect
359. C₃⋊C₈	Q₈×D₅	semidirect
408. C₃×C₅	Q₈×M₁₆	semidirect
458. C₅	Q₈×#208	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
C₃×C₄×Q₈×D₅	2
#11751125	2
C₅×#5024	2
#11747007	2
#11747003	2
C₄×#6649	2
#11746848	2
#11746847	2
#11746846	2
C₃⋊C₈×Dic₁₀	2
#10611693	3
Q₈×#208	5