Subgroups — #18077317

Order 4864.

660 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	C₂×#11926741	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564442	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926274	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64526	—	2	1	no	—
9	C₂×C₄×Dic₃₈	—	2	1	no	—
10	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
11	#11926741	—	2	2	no	—
12	#11926741	C₄	1	4	yes	complemented
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597289	—	2	1	no	—
15	C₂×#10597289	—	2	2	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926442	—	2	1	no	—
18	#11926441	—	2	2	no	—
19	#11926414	C₂²	1	1	yes	characteristic
20	#11926413	—	2	1	no	—
21	C₄⋊C₄×Dic₁₉	—	2	1	no	—
22	#11926274	—	2	2	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	—	2	1	no	—
26	C₂×C₁₉×#102	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×#127	—	2	1	no	—
34	C₁₉×#127	—	2	1	no	—
35	C₁₉×#127	—	2	1	no	—
36	C₁₉×#127	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×#64526	—	2	4	no	—
42	C₂×#64526	—	4	2	no	—
43	C₂×#64526	—	4	2	no	—
44	C₂×C₄⋊Dic₁₉	—	2	1	no	—
45	C₂×C₄⋊Dic₁₉	—	2	1	no	—
46	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
48	C₂×Dic₁₉⋊C₄	—	2	1	no	—
49	C₂×Dic₁₉⋊C₄	—	2	2	no	—
50	C₂×Dic₁₉⋊C₄	—	2	2	no	—
51	C₂×C₄×Dic₁₉	—	2	1	no	—
52	C₂×C₄×Dic₁₉	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₄×Dic₃₈	—	2	1	no	—
56	C₄×Dic₃₈	—	2	1	no	—
57	C₄×Dic₃₈	—	4	2	no	—
58	C₄×Dic₃₈	—	4	2	no	—
59	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
60	C₄×Dic₃₈	D₄	1	2	yes	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×#102	—	4	2	no	—
64	C₁₉×#102	—	4	2	no	—
65	C₁₉×#95	—	2	1	no	—
66	#10597289	—	2	4	no	—
67	#10597289	—	4	4	no	—
68	C₁₉⋊#95	—	2	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₂⁴×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₁₉	—	2	1	no	—
96	C₂²×Dic₁₉	—	2	1	no	—
97	C₂²×Dic₁₉	—	2	2	no	—
98	C₂×Dic₃₈	—	2	1	no	—
99	C₂×Dic₃₈	—	2	1	no	—
100	C₂×Dic₃₈	—	2	1	no	—
101	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
102	C₂×Dic₃₈	D₈	1	2	yes	—
103	C₂×Dic₃₈	SD₁₆	1	2	yes	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
111	C₄²×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	—	4	1	no	—
113	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₉	#41	1	1	yes	characteristic
116	C₄²×C₁₉	#41	1	1	yes	characteristic
117	#64526	—	4	8	no	—
118	C₄⋊Dic₁₉	—	2	1	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	1	no	—
122	C₄⋊Dic₁₉	—	4	1	no	—
123	C₄⋊Dic₁₉	—	4	2	no	—
124	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
125	Dic₁₉⋊C₄	—	2	2	no	—
126	Dic₁₉⋊C₄	—	2	2	no	—
127	Dic₁₉⋊C₄	—	4	4	no	—
128	Dic₁₉⋊C₄	—	8	2	no	—
129	C₄×Dic₁₉	—	2	2	no	—
130	C₄×Dic₁₉	—	2	2	no	—
131	C₄×Dic₁₉	—	4	4	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	#8979	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	8	1	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	#120	1	1	yes	characteristic
147	D₄×C₁₉	—	4	4	no	—
148	D₄×C₁₉	—	4	2	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	8	2	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	8	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
179	C₂×Dic₁₉	—	2	2	no	—
180	C₂×Dic₁₉	—	2	2	no	—
181	C₂×Dic₁₉	—	2	2	no	—
182	C₂×Dic₁₉	—	2	2	no	—
183	C₂×Dic₁₉	—	4	1	no	—
184	C₂×Dic₁₉	—	4	1	no	—
185	C₂×Dic₁₉	—	4	2	no	—
186	C₂×Dic₁₉	—	4	2	no	—
187	C₂×Dic₁₉	—	4	2	no	—
188	Dic₃₈	—	2	2	no	—
189	Dic₃₈	—	2	2	no	—
190	Dic₃₈	—	2	2	no	—
191	Dic₃₈	#102	1	4	yes	complemented
192	C₈×C₁₉	—	8	1	no	—
193	C₁₉⋊C₈	—	4	2	no	—
194	C₁₉⋊C₈	—	4	2	no	—
195	C₂×#460	—	19	1	no	—
196	Q₈×C₄⋊C₄	—	19	1	no	—
197	#1982	D₁₉	1	1	yes	characteristic
198	#1957	—	19	1	no	—
199	C₂×Q₈⋊C₈	—	19	1	no	—
200	#1296	—	19	1	no	—
201	#1279	—	19	1	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	—	16	1	no	—
206	C₂²×C₁₉	—	16	1	no	—
207	C₂²×C₁₉	—	16	1	no	—
208	C₂²×C₁₉	—	16	1	no	—
209	C₂²×C₁₉	#386	1	1	yes	characteristic
210	C₂²×C₁₉	#447	1	1	yes	characteristic
211	C₂²×C₁₉	#448	1	1	yes	characteristic
212	C₂²×C₁₉	#448	1	1	yes	characteristic
213	C₂²×C₁₉	#449	1	1	yes	characteristic
214	C₂²×C₁₉	#453	1	1	yes	characteristic
215	C₂²×C₁₉	#454	1	1	yes	characteristic
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
221	C₄×C₁₉	#417	1	1	yes	characteristic
222	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
223	C₄×C₁₉	#440	1	1	yes	characteristic
224	C₄×C₁₉	#460	1	1	yes	characteristic
225	C₄×C₁₉	#464	1	1	yes	characteristic
226	C₄×C₁₉	#480	1	1	yes	characteristic
227	C₄×C₁₉	#481	1	1	yes	characteristic
228	Dic₁₉	—	2	4	no	—
229	Dic₁₉	—	4	2	no	—
230	Dic₁₉	—	8	2	no	—
231	C₂²×SD₁₆	—	38	1	no	—
232	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
233	C₂×C₄×Q₈	—	19	1	no	—
234	C₂×C₄×Q₈	—	38	1	no	—
235	#460	—	19	4	no	—
236	#460	—	38	2	no	—
237	C₂×C₄⋊C₈	—	19	1	no	—
238	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
239	C₂×#102	—	2	1	no	—
240	C₂×#102	—	2	1	no	—
241	C₂×#102	—	38	1	no	—
242	C₂×#102	—	38	2	no	—
243	C₂×C₄×C₈	—	19	1	no	—
244	#389	—	38	2	no	—
245	#389	—	38	1	no	—
246	#384	—	19	1	no	—
247	#384	—	38	1	no	—
248	C₄×C₄⋊C₄	—	38	1	no	—
249	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
250	Q₈⋊C₈	—	38	2	no	—
251	C₂×C₁₉	—	16	2	no	—
252	C₂×C₁₉	#1621	1	1	yes	characteristic
253	C₂×C₁₉	#1623	1	1	yes	characteristic
254	C₂×C₁₉	#1626	1	1	yes	characteristic
255	C₂×C₁₉	#1627	1	1	yes	characteristic
256	C₂×C₁₉	#1874	1	1	yes	characteristic
257	C₂×C₁₉	#1880	1	1	yes	characteristic
258	C₂×C₁₉	#1883	1	1	yes	characteristic
259	C₂²×Q₈	—	19	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂×SD₁₆	—	38	4	no	—
264	C₂×SD₁₆	—	76	2	no	—
265	C₂×SD₁₆	—	76	2	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	38	1	no	—
268	C₂²×C₈	—	38	1	no	—
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	C₄×D₁₉	1	2	yes	—
273	C₄×Q₈	—	19	2	no	—
274	C₄×Q₈	—	19	2	no	—
275	C₄×Q₈	—	38	1	no	—
276	C₄×Q₈	—	38	1	no	—
277	C₄×Q₈	—	76	2	no	—
278	C₄×Q₈	—	76	2	no	—
279	C₂×C₄⋊C₄	—	19	1	no	—
280	C₂×C₄⋊C₄	—	19	2	no	—
281	C₂×C₄⋊C₄	—	38	1	no	—
282	C₂×C₄⋊C₄	—	38	2	no	—
283	C₂×C₄⋊C₄	—	38	1	no	—
284	C₂×C₄⋊C₄	—	38	1	no	—
285	C₂×C₄⋊C₄	—	38	2	no	—
286	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	38	1	no	—
290	C₂×C₄²	—	38	2	no	—
291	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	19	2	no	—
295	C₄⋊C₈	—	38	1	no	—
296	#102	—	4	2	no	—
297	#102	—	4	2	no	—
298	#102	—	38	4	no	—
299	#102	—	76	4	no	—
300	C₄×C₈	—	38	1	no	—
301	C₄×C₈	—	38	1	no	—
302	#95	—	2	1	no	—
303	#95	—	38	2	no	—
304	C₁₉	#8979	1	1	yes	characteristic, complemented, Sylow
305	C₂⁴	—	4	1	no	—
306	C₂×Q₈	—	19	2	no	—
307	C₂×Q₈	—	19	2	no	—
308	C₂×Q₈	—	19	2	no	—
309	C₂×Q₈	—	38	1	no	—
310	C₂×Q₈	—	38	1	no	—
311	C₂×Q₈	—	38	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	38	1	no	—
331	C₂²×C₄	—	38	1	no	—
332	C₂²×C₄	—	38	2	no	—
333	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
336	SD₁₆	—	76	8	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	38	2	no	—
341	C₂×C₈	—	38	2	no	—
342	C₂×C₈	—	76	1	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	—	76	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	19	2	no	—
350	C₄⋊C₄	—	38	2	no	—
351	C₄⋊C₄	—	38	1	no	—
352	C₄⋊C₄	—	38	2	no	—
353	C₄⋊C₄	—	76	2	no	—
354	C₄⋊C₄	—	76	4	no	—
355	C₄⋊C₄	—	76	1	no	—
356	C₄⋊C₄	—	76	1	no	—
357	C₄⋊C₄	—	76	1	no	—
358	C₄⋊C₄	—	76	1	no	—
359	C₄⋊C₄	—	152	2	no	—
360	C₄⋊C₄	#64526	1	2	yes	complemented
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	38	2	no	—
364	C₄²	—	38	2	no	—
365	C₄²	—	76	4	no	—
366	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
367	C₄²	#64541	1	1	yes	characteristic
368	C₄²	D₄×D₁₉	1	1	yes	characteristic
369	C₄²	#64543	1	1	yes	characteristic
370	C₂³	—	4	2	no	—
371	C₂³	—	8	1	no	—
372	C₂³	—	8	1	no	—
373	C₂³	—	8	1	no	—
374	C₂³	—	8	1	no	—
375	C₂³	—	8	1	no	—
376	C₂³	—	8	1	no	—
377	C₂³	#10597383	1	1	yes	characteristic
378	Q₈	—	19	4	no	—
379	Q₈	—	38	2	no	—
380	Q₈	—	38	2	no	—
381	Q₈	—	38	2	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	38	2	no	—
401	C₂×C₄	—	38	2	no	—
402	C₂×C₄	—	38	2	no	—
403	C₂×C₄	—	38	2	no	—
404	C₂×C₄	—	76	1	no	—
405	C₂×C₄	—	76	1	no	—
406	C₂×C₄	—	76	2	no	—
407	C₂×C₄	—	76	2	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
410	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	#10597329	1	1	yes	characteristic
412	C₂×C₄	#10597330	1	1	yes	characteristic
413	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
414	C₂×C₄	#10597357	1	1	yes	characteristic
415	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
416	C₂×C₄	#10597361	1	1	yes	characteristic
417	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
418	C₂×C₄	#10597378	1	1	yes	characteristic
419	C₂×C₄	C₂×#64526	1	1	yes	characteristic
420	C₂×C₄	#10597384	1	1	yes	characteristic
421	C₂×C₄	#10597396	1	1	yes	characteristic
422	C₂×C₄	#10597397	1	1	yes	characteristic
423	C₈	—	8	1	no	—
424	C₈	—	76	2	no	—
425	C₈	—	76	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	16	1	no	—
430	C₂²	—	16	1	no	—
431	C₂²	—	16	1	no	—
432	C₂²	—	16	1	no	—
433	C₂²	#11926420	1	1	yes	characteristic
434	C₂²	#11926676	1	1	yes	characteristic
435	C₂²	#11926681	1	1	yes	characteristic
436	C₂²	#11926682	1	1	yes	characteristic
437	C₂²	#11926687	1	1	yes	characteristic
438	C₂²	#11926710	1	1	yes	characteristic
439	C₂²	#11926715	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	38	4	no	—
445	C₄	—	76	2	no	—
446	C₄	—	152	2	no	—
447	C₄	#102×D₁₉	1	1	yes	characteristic
448	C₄	#11926542	1	1	yes	characteristic
449	C₄	C₄×#64526	1	1	yes	characteristic
450	C₄	#11926644	1	1	yes	characteristic
451	C₄	#11926741	1	1	yes	characteristic
452	C₄	#11926763	1	1	yes	characteristic
453	C₄	#11926856	1	1	yes	characteristic
454	C₄	#11926861	1	1	yes	characteristic
455	C₂	—	16	2	no	—
456	C₂	#14562699	1	1	yes	characteristic
457	C₂	#14562712	1	1	yes	characteristic
458	C₂	#14562729	1	1	yes	characteristic
459	C₂	#14562737	1	1	yes	characteristic
460	C₂	#14563949	1	1	yes	characteristic
461	C₂	#14563993	1	1	yes	characteristic
462	C₂	#14564008	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1982	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1982	D₁₉
hypocenter	C₁₉	#8979
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1982

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₄×Dic₃₈	C₂	semidirect
4. C₂×#11926274	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561476	C₂	semidirect
12. #11926741	C₄	semidirect
110. C₄⋊C₄×C₁₉	SD₁₆	semidirect
191. Dic₃₈	#102	semidirect
304. C₁₉	#8979	semidirect
360. C₄⋊C₄	#64526	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926741	2
C₄⋊C₄×Dic₃₈	2
#14564442	2
C₂×#11926274	2
#14561519	2
#14561476	2
C₁₉×#1982	2
#8979	19