Subgroups — #18077407

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#64520	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564555	C₂	1	1	yes	maximal, characteristic
3	C₄×#10597292	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562086	C₂	1	1	yes	maximal, characteristic
5	#14561537	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561471	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3103	C₂	1	1	yes	maximal, characteristic
8	#11926675	—	2	2	no	—
9	#11926675	—	2	1	no	—
10	Q₈×C₁₉⋊C₈	—	2	1	no	—
11	#11926568	—	2	1	no	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×#10597294	—	2	1	no	—
14	C₂×#10597294	—	2	1	no	—
15	C₂×#10597292	—	2	1	no	—
16	C₄×#64520	—	2	1	no	—
17	C₄×#64520	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926306	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#481	—	2	1	no	—
25	C₁₉×#475	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#475	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#460	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#460	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#448	—	2	1	no	—
30	C₄×SD₁₆×C₁₉	—	2	1	no	—
31	C₄×SD₁₆×C₁₉	—	2	1	no	—
32	C₁₉×#431	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×SD₁₆×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#124	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
48	C₄×D₄×C₁₉	—	2	1	no	—
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	D₄	1	1	yes	characteristic
58	C₂×#64520	D₄	1	1	yes	characteristic
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₁₉×#106	—	2	1	no	—
61	C₁₉×#106	—	2	1	no	—
62	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#103	—	2	1	no	—
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	#10597294	—	4	2	no	—
71	#10597294	—	4	2	no	—
72	#10597292	—	2	4	no	—
73	C₁₉⋊#95	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
78	#10597260	—	2	2	no	—
79	#10597260	—	2	1	no	—
80	C₄×C₁₉⋊C₈	—	2	2	no	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	#41×C₁₉	—	4	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	4	1	no	—
92	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×Dic₁₉	—	4	1	no	—
105	SD₁₆×C₁₉	—	4	2	no	—
106	SD₁₆×C₁₉	—	4	2	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	2	1	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	#41	1	1	yes	characteristic
128	C₄⋊Dic₁₉	—	2	2	no	—
129	C₄⋊Dic₁₉	—	4	1	no	—
130	C₄×Dic₁₉	—	4	1	no	—
131	C₄×Dic₁₉	—	4	1	no	—
132	#64520	—	2	1	no	—
133	#64520	—	2	1	no	—
134	#64520	—	2	1	no	—
135	#64520	—	4	1	no	—
136	#64520	—	4	1	no	—
137	#64520	SD₁₆	1	2	yes	complemented
138	C₂×C₁₉⋊C₈	—	2	1	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	2	1	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	#8992	—	19	1	no	maximal, Sylow
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	#121	1	1	yes	characteristic
147	Q₈×C₁₉	—	2	1	no	—
148	Q₈×C₁₉	—	2	1	no	—
149	Q₈×C₁₉	—	2	1	no	—
150	Q₈×C₁₉	—	4	2	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	#104	1	2	yes	complemented
154	D₄×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
183	C₂×Dic₁₉	—	4	2	no	—
184	C₂×Dic₁₉	—	8	1	no	—
185	C₂×Dic₁₉	—	8	1	no	—
186	C₈×C₁₉	—	4	1	no	—
187	C₈×C₁₉	—	4	1	no	—
188	C₁₉⋊C₈	—	2	2	no	—
189	C₁₉⋊C₈	—	4	2	no	—
190	C₁₉⋊C₈	—	4	1	no	—
191	C₁₉⋊C₈	—	4	2	no	—
192	#3103	D₁₉	1	1	yes	characteristic
193	Q₈×M₁₆	—	19	1	no	—
194	#1980	—	19	1	no	—
195	C₄×#103	—	19	1	no	—
196	#1492	—	19	1	no	—
197	#1303	—	19	1	no	—
198	#1278	—	19	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	#386	1	1	yes	characteristic
205	C₂²×C₁₉	#460	1	1	yes	characteristic
206	C₂²×C₁₉	#464	1	1	yes	characteristic
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	4	1	no	—
213	C₄×C₁₉	—	4	1	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
216	C₄×C₁₉	#421	1	1	yes	characteristic
217	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
218	C₄×C₁₉	#440	1	1	yes	characteristic
219	C₄×C₁₉	#448	1	1	yes	characteristic
220	C₄×C₁₉	#449	1	1	yes	characteristic
221	Dic₁₉	—	8	2	no	—
222	#532	C₂×D₁₉	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
224	#481	—	2	1	no	—
225	#475	Dic₁₉	1	1	yes	characteristic, complemented
226	#475	Dic₁₉	1	1	yes	characteristic, complemented
227	#460	Dic₁₉	1	1	yes	characteristic, complemented
228	#460	Dic₁₉	1	1	yes	characteristic, complemented
229	#448	—	2	1	no	—
230	#446	—	38	2	no	—
231	#446	—	38	1	no	—
232	C₈×Q₈	—	38	1	no	—
233	C₄×SD₁₆	—	2	1	no	—
234	C₄×SD₁₆	—	2	1	no	—
235	#431	C₂×D₁₉	1	1	yes	characteristic
236	#423	—	19	1	no	—
237	#423	—	38	1	no	—
238	C₂×#104	—	38	1	no	—
239	C₂×#104	—	38	1	no	—
240	C₂×#103	—	38	1	no	—
241	C₄×M₁₆	—	19	1	no	—
242	C₄×M₁₆	—	38	1	no	—
243	C₂×C₄×C₈	—	19	1	no	—
244	C₄×C₄⋊C₄	—	19	1	no	—
245	#340	—	38	1	no	—
246	D₄⋊C₈	—	38	2	no	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	16	1	no	—
250	C₂×C₁₉	#1871	1	1	yes	characteristic
251	C₂×C₁₉	#1880	1	1	yes	characteristic
252	C₂×C₁₉	#1881	1	1	yes	characteristic
253	C₂×#41	—	2	1	no	—
254	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×SD₁₆	—	2	1	no	—
257	C₂×M₁₆	—	19	1	no	—
258	C₂×M₁₆	—	19	1	no	—
259	C₂×M₁₆	—	38	1	no	—
260	C₂²×C₈	—	38	1	no	—
261	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
262	#127	C₂×Dic₁₉	1	1	yes	characteristic
263	#124	—	2	1	no	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
269	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
270	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
271	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	38	1	no	—
276	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	38	1	no	—
279	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
280	#106	—	2	1	no	—
281	#106	—	2	1	no	—
282	C₄⋊C₈	—	19	2	no	—
283	C₄⋊C₈	—	38	2	no	—
284	C₄⋊C₈	—	38	2	no	—
285	C₄⋊C₈	—	38	1	no	—
286	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
287	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
288	#104	—	76	2	no	—
289	#104	—	76	2	no	—
290	#103	—	2	1	no	—
291	#103	—	2	1	no	—
292	#103	—	38	4	no	—
293	#102	—	2	1	no	—
294	#102	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	#97	—	38	2	no	—
297	#97	—	38	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	38	2	no	—
300	C₄×C₈	—	38	1	no	—
301	C₄×C₈	—	38	1	no	—
302	C₄×C₈	—	38	1	no	—
303	#95	—	38	1	no	—
304	C₁₉	#8992	1	1	yes	characteristic, complemented, Sylow
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	4	1	no	—
308	#41	—	4	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
314	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	#64543	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
326	SD₁₆	—	4	2	no	—
327	SD₁₆	—	4	2	no	—
328	M₁₆	—	19	2	no	—
329	M₁₆	—	38	1	no	—
330	M₁₆	—	38	1	no	—
331	M₁₆	—	38	1	no	—
332	M₁₆	—	76	1	no	—
333	M₁₆	—	76	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	38	1	no	—
337	C₂×C₈	—	38	2	no	—
338	C₂×C₈	—	38	2	no	—
339	C₂×C₈	—	38	1	no	—
340	C₂×C₈	—	76	1	no	—
341	C₂×C₈	—	76	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	38	2	no	—
350	C₄⋊C₄	—	76	1	no	—
351	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	76	1	no	—
360	C₄²	—	76	1	no	—
361	C₄²	D₄×D₁₉	1	1	yes	characteristic
362	C₄²	#64543	1	1	yes	characteristic
363	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
365	C₂³	—	4	1	no	—
366	C₂³	#10597385	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	1	no	—
373	Q₈	#10597294	1	2	yes	complemented
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	76	2	no	—
394	C₂×C₄	—	152	1	no	—
395	C₂×C₄	—	152	1	no	—
396	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
397	C₂×C₄	#10597360	1	1	yes	characteristic
398	C₂×C₄	#10597361	1	1	yes	characteristic
399	C₂×C₄	#10597362	1	1	yes	characteristic
400	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
401	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
402	C₂×C₄	#10597381	1	1	yes	characteristic
403	C₂×C₄	#10597383	1	1	yes	characteristic
404	C₂×C₄	#10597385	1	1	yes	characteristic
405	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	—	38	2	no	—
409	C₈	—	76	2	no	—
410	C₈	—	76	1	no	—
411	C₈	—	76	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	#11926424	1	1	yes	characteristic
418	C₂²	#11926742	1	1	yes	characteristic
419	C₂²	#11926764	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	152	2	no	—
429	C₄	C₂×#10597294	1	1	yes	characteristic
430	C₄	#11926561	1	1	yes	characteristic
431	C₄	SD₁₆×Dic₁₉	1	1	yes	characteristic
432	C₄	#11926645	1	1	yes	characteristic
433	C₄	#11926681	1	1	yes	characteristic
434	C₄	#11926688	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	16	1	no	—
438	C₂	#14563938	1	1	yes	characteristic
439	C₂	#14563992	1	1	yes	characteristic
440	C₂	#14563999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3103	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3103	D₁₉
hypocenter	C₁₉	#8992
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3103

Complements

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

N	H ≅ G/N	type
1. Q₈×#64520	C₂	semidirect
3. C₄×#10597292	C₂	semidirect
5. #14561537	C₂	semidirect
6. #14561471	C₂	semidirect
25. C₁₉×#475	C₄	semidirect
26. C₁₉×#475	C₄	semidirect
27. C₁₉×#460	C₄	semidirect
28. C₁₉×#460	C₄	semidirect
137. #64520	SD₁₆	semidirect
153. Q₈×C₁₉	#104	semidirect
225. #475	Dic₁₉	semidirect
226. #475	Dic₁₉	semidirect
227. #460	Dic₁₉	semidirect
228. #460	Dic₁₉	semidirect
304. C₁₉	#8992	semidirect
373. Q₈	#10597294	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#64520	2
#14564555	2
C₄×#10597292	2
#14562086	2
#14561537	2
#14561471	2
C₁₉×#3103	2
#8992	19