Subgroups — #18077384

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573643	C₂	1	1	yes	maximal, characteristic
2	#14564579	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10597289	C₂	1	1	yes	maximal, characteristic
4	#14562089	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561536	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561473	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926874	—	2	1	no	—
10	#11926834	C₄	1	1	yes	characteristic, complemented
11	#11926834	C₄	1	1	yes	characteristic, complemented
12	#11926749	C₄	1	1	yes	characteristic, complemented
13	#11926749	C₄	1	1	yes	characteristic, complemented
14	#11926695	—	2	1	no	—
15	C₄×#64526	—	2	1	no	—
16	C₄×#64526	—	2	1	no	—
17	#11926597	C₂²	1	1	yes	characteristic
18	C₂×#10597289	—	2	1	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	#11926306	—	2	1	no	—
22	#11926305	—	2	1	no	—
23	#11926305	—	2	1	no	—
24	#11926274	—	2	2	no	—
25	C₂²×M₁₆×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#436	—	2	1	no	—
28	C₁₉×#435	—	2	2	no	—
29	C₈×D₄×C₁₉	—	2	1	no	—
30	C₁₉×#423	C₂²	1	1	yes	characteristic
31	C₁₉×#407	—	2	1	no	—
32	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	4	2	no	—
38	C₂×M₁₆×C₁₉	—	4	2	no	—
39	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×#64526	—	2	1	no	—
52	C₂×#64526	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	#10597370	—	2	1	no	—
56	#10597370	—	2	1	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	#10597316	—	2	1	no	—
60	#10597315	C₂×C₄	1	1	yes	characteristic
61	#10597315	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₃₈	—	2	1	no	—
63	C₄×Dic₃₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
66	C₁₉×C₂²⋊C₈	—	2	2	no	—
67	C₁₉×C₂²⋊C₈	—	2	2	no	—
68	C₁₉×#97	—	2	1	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	#10597289	—	2	4	no	—
71	#10597289	—	2	1	no	—
72	#10597289	—	2	1	no	—
73	C₁₉⋊#95	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
75	#10597267	—	2	1	no	—
76	#10597267	—	2	1	no	—
77	#10597265	—	2	1	no	—
78	#10597265	—	2	1	no	—
79	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	C₂⁴×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×Dic₁₉	—	4	1	no	—
103	C₂×Dic₃₈	—	2	1	no	—
104	C₂×Dic₃₈	—	2	1	no	—
105	M₁₆×C₁₉	—	2	1	no	—
106	M₁₆×C₁₉	—	2	1	no	—
107	M₁₆×C₁₉	—	2	1	no	—
108	M₁₆×C₁₉	—	4	4	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	M₁₆×C₁₉	—	4	1	no	—
111	M₁₆×C₁₉	SD₁₆	1	2	yes	complemented
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	4	4	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	#41	1	1	yes	characteristic
127	C₂²⋊Dic₁₉	—	4	1	no	—
128	#64526	—	4	2	no	—
129	#64526	—	4	2	no	—
130	C₄⋊Dic₁₉	—	2	2	no	—
131	C₄⋊Dic₁₉	—	2	1	no	—
132	C₄⋊Dic₁₉	—	2	1	no	—
133	C₄⋊Dic₁₉	—	2	1	no	—
134	C₄⋊Dic₁₉	—	2	1	no	—
135	C₄⋊Dic₁₉	—	4	1	no	—
136	Dic₁₉⋊C₄	—	4	1	no	—
137	Dic₁₉⋊C₄	—	4	1	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	C₄×Dic₁₉	—	4	1	no	—
140	C₄×Dic₁₉	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	2	1	no	—
143	C₂×C₁₉⋊C₈	—	2	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	#8989	—	19	1	no	maximal, Sylow
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	8	1	no	—
153	C₂³×C₁₉	#121	1	1	yes	characteristic
154	D₄×C₁₉	—	2	1	no	—
155	D₄×C₁₉	—	2	1	no	—
156	D₄×C₁₉	—	2	1	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	#104	1	2	yes	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
182	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
184	C₂×Dic₁₉	—	4	2	no	—
185	C₂×Dic₁₉	—	4	1	no	—
186	C₂×Dic₁₉	—	4	1	no	—
187	C₂×Dic₁₉	—	8	1	no	—
188	C₂×Dic₁₉	—	8	1	no	—
189	Dic₃₈	—	4	2	no	—
190	Dic₃₈	—	4	1	no	—
191	Dic₃₈	—	4	1	no	—
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₁₉⋊C₈	—	4	2	no	—
196	C₁₉⋊C₈	—	4	1	no	—
197	C₁₉⋊C₈	—	4	1	no	—
198	#3101	—	19	1	no	—
199	D₄×M₁₆	D₁₉	1	1	yes	characteristic
200	#1986	—	19	1	no	—
201	C₄×#102	—	19	1	no	—
202	#1493	—	19	1	no	—
203	#1303	—	19	1	no	—
204	#1278	—	19	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	8	2	no	—
214	C₂²×C₁₉	—	8	2	no	—
215	C₂²×C₁₉	#386	1	1	yes	characteristic
216	C₂²×C₁₉	#461	1	1	yes	characteristic
217	C₂²×C₁₉	#463	1	1	yes	characteristic
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	4	1	no	—
223	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
224	C₄×C₁₉	#421	1	1	yes	characteristic
225	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
226	C₄×C₁₉	#440	1	1	yes	characteristic
227	C₄×C₁₉	#450	1	1	yes	characteristic
228	C₄×C₁₉	#452	1	1	yes	characteristic
229	Dic₁₉	—	8	2	no	—
230	Dic₁₉	—	8	1	no	—
231	Dic₁₉	—	8	1	no	—
232	C₂²×M₁₆	—	2	1	no	—
233	#533	—	19	1	no	—
234	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
235	#483	—	38	1	no	—
236	#476	—	19	1	no	—
237	#476	—	19	1	no	—
238	#461	—	19	1	no	—
239	#461	—	19	1	no	—
240	#450	—	38	1	no	—
241	C₄×SD₁₆	—	38	1	no	—
242	C₄×SD₁₆	—	38	1	no	—
243	#436	—	2	1	no	—
244	#435	—	2	2	no	—
245	C₈×D₄	—	2	1	no	—
246	#431	—	19	1	no	—
247	#423	C₂×D₁₉	1	1	yes	characteristic
248	C₂×#102	—	38	1	no	—
249	#407	—	2	1	no	—
250	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
251	C₂×C₄×C₈	—	19	1	no	—
252	C₄×C₄⋊C₄	—	19	1	no	—
253	#340	—	38	1	no	—
254	#339	—	38	1	no	—
255	#339	—	38	1	no	—
256	Q₈⋊C₈	—	38	2	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	—	4	2	no	—
260	C₂×C₁₉	—	8	1	no	—
261	C₂×C₁₉	#1871	1	1	yes	characteristic
262	C₂×C₁₉	#1877	1	1	yes	characteristic
263	C₂×C₁₉	#1881	1	1	yes	characteristic
264	C₂²×D₄	D₇₆	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂×SD₁₆	—	38	1	no	—
267	C₂×SD₁₆	—	38	1	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	4	2	no	—
271	C₂×M₁₆	—	4	2	no	—
272	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	38	1	no	—
276	C₄⋊Q₈	—	19	1	no	—
277	C₄⋊Q₈	—	19	1	no	—
278	#125	—	38	1	no	—
279	C₂²⋊Q₈	—	38	1	no	—
280	C₂²⋊Q₈	—	38	1	no	—
281	C₄×Q₈	—	38	1	no	—
282	C₄×Q₈	—	38	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	C₄×D₁₉	1	1	yes	characteristic
286	C₄×D₄	C₄×D₁₉	1	1	yes	characteristic
287	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
288	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
289	#117	—	38	1	no	—
290	C₂×C₄⋊C₄	—	38	1	no	—
291	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₄²	—	38	1	no	—
294	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
295	#106	—	38	1	no	—
296	#106	—	38	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	19	1	no	—
299	C₄⋊C₈	—	19	1	no	—
300	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
301	#103	—	38	1	no	—
302	#103	—	38	1	no	—
303	#102	—	38	4	no	—
304	#102	—	38	1	no	—
305	#102	—	38	1	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	38	1	no	—
309	#97	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	38	1	no	—
312	C₄×C₈	—	38	1	no	—
313	C₄×C₈	—	38	1	no	—
314	#95	—	38	1	no	—
315	C₁₉	#8989	1	1	yes	characteristic, complemented, Sylow
316	C₂⁴	—	2	1	no	—
317	C₂×Q₈	—	38	1	no	—
318	C₂×Q₈	—	38	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
323	C₂×D₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	76	1	no	—
334	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
335	C₂²×C₄	#64541	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
337	SD₁₆	—	76	2	no	—
338	SD₁₆	—	76	2	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	—	2	1	no	—
342	M₁₆	—	4	4	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	#64526	1	2	yes	complemented
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	4	no	—
350	C₂×C₈	—	38	2	no	—
351	C₂×C₈	—	38	1	no	—
352	C₂×C₈	—	38	1	no	—
353	C₂×C₈	—	76	1	no	—
354	C₂×C₈	—	76	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	38	2	no	—
357	C₄⋊C₄	—	38	1	no	—
358	C₄⋊C₄	—	38	1	no	—
359	C₄⋊C₄	—	38	1	no	—
360	C₄⋊C₄	—	38	1	no	—
361	C₄⋊C₄	—	76	1	no	—
362	C₄⋊C₄	—	76	1	no	—
363	C₄⋊C₄	—	76	1	no	—
364	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
365	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	76	1	no	—
371	C₄²	—	76	1	no	—
372	C₄²	—	76	1	no	—
373	C₄²	—	76	1	no	—
374	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
375	C₄²	#64541	1	1	yes	characteristic
376	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
377	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	8	1	no	—
384	C₂³	#10597376	1	1	yes	characteristic
385	Q₈	—	76	2	no	—
386	Q₈	—	76	1	no	—
387	Q₈	—	76	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	1	no	—
391	D₄	—	4	2	no	—
392	D₄	#10597282	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	76	1	no	—
410	C₂×C₄	—	76	1	no	—
411	C₂×C₄	—	152	1	no	—
412	C₂×C₄	—	152	1	no	—
413	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
415	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
416	C₂×C₄	#10597375	1	1	yes	characteristic
417	C₂×C₄	#10597376	1	1	yes	characteristic
418	C₂×C₄	#10597378	1	1	yes	characteristic
419	C₂×C₄	C₂×#64526	1	1	yes	characteristic
420	C₂×C₄	#10597396	1	1	yes	characteristic
421	C₂×C₄	#10597397	1	1	yes	characteristic
422	C₂×C₄	#10597399	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	76	2	no	—
427	C₈	—	76	1	no	—
428	C₈	—	76	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	#11926423	1	1	yes	characteristic
440	C₂²	#11926749	1	1	yes	characteristic
441	C₂²	#11926759	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	152	2	no	—
448	C₄	—	152	1	no	—
449	C₄	—	152	1	no	—
450	C₄	C₂×#10597282	1	1	yes	characteristic
451	C₄	#11926560	1	1	yes	characteristic
452	C₄	C₄×#64526	1	1	yes	characteristic
453	C₄	#11926644	1	1	yes	characteristic
454	C₄	#11926695	1	1	yes	characteristic
455	C₄	#11926706	1	1	yes	characteristic
456	C₂	—	2	1	no	—
457	C₂	—	2	1	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	1	no	—
460	C₂	#14563937	1	1	yes	characteristic
461	C₂	#14563969	1	1	yes	characteristic
462	C₂	#14563997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	D₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	D₄×M₁₆	D₁₉
hypocenter	C₁₉	#8989
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #14564579	C₂	semidirect
4. #14562089	C₂	semidirect
5. #14561536	C₂	semidirect
6. #14561473	C₂	semidirect
10. #11926834	C₄	semidirect
11. #11926834	C₄	semidirect
12. #11926749	C₄	semidirect
13. #11926749	C₄	semidirect
111. M₁₆×C₁₉	SD₁₆	semidirect
315. C₁₉	#8989	semidirect
345. M₁₆	#64526	semidirect

Maximal subgroups

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

subgroup	index
#14573643	2
#14564579	2
C₄×#10597289	2
#14562089	2
#14561536	2
#14561473	2
D₄×M₁₆×C₁₉	2
#8989	19