Subgroups — #18077101

Order 4864.

620 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64516	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926609	C₂	1	1	yes	maximal, characteristic
3	#14564570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64516	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₁₉	—	2	1	no	—
10	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
12	C₄×#64516	—	2	2	no	—
13	C₄×#64516	—	2	2	no	—
14	#11926609	—	2	2	no	—
15	#11926609	—	2	2	no	—
16	C₂×#10597274	C₄	1	1	yes	characteristic
17	C₂×#10597273	C₄	1	1	yes	characteristic
18	C₂×#10597278	C₄	1	1	yes	characteristic
19	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
20	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	#11926298	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	#11926274	—	2	2	no	—
25	#11926271	—	2	2	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×Dic₁₉⋊C₄	—	2	1	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂²×C₁₉⋊C₈	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
44	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
45	C₂×#64516	—	2	2	no	—
46	C₂×#64516	—	2	2	no	—
47	C₂×#64516	C₈	1	4	yes	complemented
48	C₂×C₈×D₁₉	—	2	4	no	—
49	C₂×C₈×D₁₉	—	4	2	no	—
50	C₂×C₈×D₁₉	—	4	2	no	—
51	C₄×D₇₆	—	2	1	no	—
52	C₄×D₇₆	—	2	1	no	—
53	C₄×D₇₆	D₄	1	2	yes	—
54	C₄×D₇₆	D₄	1	2	yes	—
55	C₄×Dic₃₈	—	2	1	no	—
56	C₄×Dic₃₈	—	2	1	no	—
57	C₄×Dic₃₈	—	2	1	no	—
58	C₄×Dic₃₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₄×C₈×C₁₉	—	2	1	no	—
65	#10597278	—	2	2	no	—
66	(C₂×D₁₉)⋊C₈	—	2	4	no	—
67	#10597274	—	2	2	no	—
68	#10597273	—	2	2	no	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₂³×D₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
77	C₂²×Dic₁₉	—	2	1	no	—
78	C₂²×Dic₁₉	—	2	1	no	—
79	C₂²×Dic₁₉	—	2	1	no	—
80	C₂×D₇₆	—	2	1	no	—
81	C₂×D₇₆	—	2	1	no	—
82	C₂×D₇₆	—	2	1	no	—
83	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
84	C₂×D₇₆	C₂×C₈	1	2	yes	—
85	C₂×D₇₆	M₁₆	1	2	yes	—
86	C₂×C₄×D₁₉	—	2	2	no	—
87	C₂×C₄×D₁₉	—	2	2	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×C₄×D₁₉	—	4	1	no	—
91	C₂×C₄×D₁₉	—	4	1	no	—
92	C₂×Dic₃₈	—	2	1	no	—
93	C₂×Dic₃₈	—	2	1	no	—
94	C₂×Dic₃₈	—	2	1	no	—
95	C₂×Dic₃₈	—	2	1	no	—
96	C₂×Dic₃₈	—	2	1	no	—
97	C₂×Dic₃₈	C₂×C₈	1	2	yes	complemented
98	C₂×C₈×C₁₉	—	2	1	no	—
99	C₂×C₈×C₁₉	—	2	1	no	—
100	C₂×C₈×C₁₉	—	2	1	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	complemented
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	(C₂×D₁₉)⋊C₄	—	2	2	no	—
115	(C₂×D₁₉)⋊C₄	—	2	2	no	—
116	C₄⋊Dic₁₉	—	2	1	no	—
117	C₄⋊Dic₁₉	—	2	1	no	—
118	C₄⋊Dic₁₉	—	2	1	no	—
119	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
120	Dic₁₉⋊C₄	—	4	1	no	—
121	Dic₁₉⋊C₄	—	4	1	no	—
122	C₄×Dic₁₉	—	4	1	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	2	1	no	—
125	C₂×C₁₉⋊C₈	—	2	1	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	C₂×C₁₉⋊C₈	—	2	1	no	—
128	C₂×C₁₉⋊C₈	—	2	1	no	—
129	C₂×C₁₉⋊C₈	—	2	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	complemented
133	#64516	—	2	8	no	—
134	C₈×D₁₉	—	4	8	no	—
135	#8945	—	19	1	no	maximal, Sylow
136	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
137	C₂²×D₁₉	—	2	2	no	—
138	C₂²×D₁₉	—	2	2	no	—
139	C₂²×D₁₉	—	2	2	no	—
140	C₂²×D₁₉	—	4	1	no	—
141	C₂²×D₁₉	—	4	1	no	—
142	C₂²×D₁₉	—	4	1	no	—
143	C₂²×D₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
158	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
160	C₂×Dic₁₉	—	2	2	no	—
161	C₂×Dic₁₉	—	2	2	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	C₂×Dic₁₉	—	4	1	no	—
164	C₂×Dic₁₉	—	4	1	no	—
165	C₂×Dic₁₉	—	4	1	no	—
166	C₂×Dic₁₉	—	4	1	no	—
167	C₂×Dic₁₉	—	4	1	no	—
168	C₂×Dic₁₉	—	4	1	no	—
169	D₇₆	—	2	2	no	—
170	D₇₆	—	2	2	no	—
171	D₇₆	—	2	2	no	—
172	D₇₆	C₂²⋊C₈	1	4	yes	—
173	C₄×D₁₉	—	4	2	no	—
174	C₄×D₁₉	—	4	2	no	—
175	C₄×D₁₉	—	4	2	no	—
176	C₄×D₁₉	—	4	2	no	—
177	Dic₃₈	—	2	2	no	—
178	Dic₃₈	—	2	2	no	—
179	Dic₃₈	—	4	1	no	—
180	Dic₃₈	—	4	1	no	—
181	C₈×C₁₉	—	2	2	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	—	8	1	no	—
185	C₁₉⋊C₈	—	2	2	no	—
186	C₁₉⋊C₈	—	4	2	no	—
187	C₁₉⋊C₈	—	4	1	no	—
188	C₂×C₄×SD₁₆	—	19	1	no	—
189	C₂×C₈×D₄	—	19	1	no	—
190	#1984	—	19	1	no	—
191	C₂×Q₈⋊C₈	—	19	1	no	—
192	C₂×D₄⋊C₈	—	19	1	no	—
193	#1277	D₁₉	1	1	yes	characteristic, complemented
194	#1273	—	19	1	no	—
195	C₂²×C₁₉	#386	1	1	yes	characteristic
196	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
197	C₂²×C₁₉	#435	1	1	yes	characteristic
198	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
199	C₂²×C₁₉	#440	1	1	yes	characteristic
200	C₂²×C₁₉	#443	1	1	yes	characteristic
201	C₂²×C₁₉	#444	1	1	yes	characteristic
202	C₂×D₁₉	—	2	4	no	—
203	C₂×D₁₉	—	4	2	no	—
204	C₂×D₁₉	—	4	2	no	—
205	C₂×D₁₉	—	4	2	no	—
206	C₂×D₁₉	—	4	2	no	—
207	C₂×D₁₉	—	4	2	no	—
208	C₂×D₁₉	—	4	2	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
212	C₄×C₁₉	#408	1	1	yes	characteristic
213	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
214	C₄×C₁₉	#435	1	1	yes	characteristic
215	C₄×C₁₉	#450	1	1	yes	characteristic
216	C₄×C₁₉	#452	1	1	yes	characteristic
217	C₄×C₁₉	#461	1	1	yes	characteristic
218	C₄×C₁₉	#463	1	1	yes	characteristic
219	Dic₁₉	—	4	2	no	—
220	Dic₁₉	—	4	2	no	—
221	Dic₁₉	—	8	1	no	—
222	C₂²×SD₁₆	—	19	1	no	—
223	C₂³×C₈	—	38	1	no	—
224	C₂×C₄×Q₈	—	19	1	no	—
225	C₂×C₄×D₄	—	19	1	no	—
226	C₄×SD₁₆	—	38	2	no	—
227	C₄×SD₁₆	—	38	2	no	—
228	C₈×D₄	—	38	2	no	—
229	C₈×D₄	—	38	2	no	—
230	C₂×#106	—	19	1	no	—
231	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
233	C₂×#103	—	19	1	no	—
234	C₂×#102	—	19	1	no	—
235	C₂×C₂²⋊C₈	—	38	1	no	—
236	C₂×C₄×C₈	—	19	1	no	—
237	C₂×C₄×C₈	—	19	1	no	—
238	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
239	#336	—	38	1	no	—
240	#336	—	38	1	no	—
241	Q₈⋊C₈	—	38	2	no	—
242	D₄⋊C₈	—	38	2	no	—
243	C₂×C₁₉	C₈×SD₁₆	1	1	yes	characteristic
244	C₂×C₁₉	SD₁₆⋊C₈	1	1	yes	characteristic
245	C₂×C₁₉	#1582	1	1	yes	characteristic
246	C₂×C₁₉	#1585	1	1	yes	characteristic
247	C₂×C₁₉	#1869	1	1	yes	characteristic
248	C₂×C₁₉	#1876	1	1	yes	characteristic
249	C₂×C₁₉	#1877	1	1	yes	characteristic
250	D₁₉	—	4	4	no	—
251	C₂²×Q₈	—	19	1	no	—
252	C₂²×D₄	—	19	1	no	—
253	C₂³×C₄	—	38	1	no	—
254	C₂×SD₁₆	—	19	4	no	—
255	C₂×SD₁₆	—	38	2	no	—
256	C₂×SD₁₆	—	38	2	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	19	1	no	—
260	C₂²×C₈	—	19	1	no	—
261	C₂²×C₈	—	38	4	no	—
262	C₂²×C₈	—	38	1	no	—
263	C₂²×C₈	—	76	2	no	—
264	C₂²×C₈	—	76	2	no	—
265	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
266	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
267	C₄×Q₈	—	38	1	no	—
268	C₄×Q₈	—	38	1	no	—
269	C₄×Q₈	—	38	1	no	—
270	C₄×Q₈	—	38	1	no	—
271	C₄×D₄	—	19	2	no	—
272	C₄×D₄	—	19	2	no	—
273	C₄×D₄	—	38	1	no	—
274	C₄×D₄	—	38	1	no	—
275	C₂×C₄⋊C₄	—	19	1	no	—
276	C₂×C₄⋊C₄	—	19	1	no	—
277	C₂×C₄⋊C₄	—	38	1	no	—
278	C₂×C₂²⋊C₄	—	38	1	no	—
279	C₂×C₄²	—	38	1	no	—
280	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
281	#106	—	38	2	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	D₇₆	1	2	yes	—
286	#103	—	38	2	no	—
287	#102	—	38	2	no	—
288	C₂²⋊C₈	—	38	4	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	38	1	no	—
292	C₄×C₈	—	38	1	no	—
293	C₄×C₈	—	38	1	no	—
294	C₄×C₈	—	38	1	no	—
295	C₁₉	#8945	1	1	yes	characteristic, complemented, Sylow
296	C₂⁴	—	38	1	no	—
297	C₂×Q₈	—	19	2	no	—
298	C₂×Q₈	—	38	1	no	—
299	C₂×Q₈	—	38	1	no	—
300	C₂×Q₈	—	38	1	no	—
301	C₂×Q₈	—	38	1	no	—
302	C₂×Q₈	—	38	1	no	—
303	C₂×D₄	—	19	2	no	—
304	C₂×D₄	—	19	2	no	—
305	C₂×D₄	—	19	2	no	—
306	C₂×D₄	—	38	1	no	—
307	C₂×D₄	—	38	1	no	—
308	C₂×D₄	—	38	1	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	—	38	2	no	—
312	C₂²×C₄	—	38	2	no	—
313	C₂²×C₄	—	38	1	no	—
314	C₂²×C₄	—	76	1	no	—
315	C₂²×C₄	—	76	1	no	—
316	C₂²×C₄	—	76	1	no	—
317	C₂²×C₄	—	76	1	no	—
318	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
320	C₂²×C₄	#64545	1	1	yes	characteristic
321	SD₁₆	—	38	8	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	19	2	no	—
334	C₂×C₈	—	38	1	no	—
335	C₂×C₈	—	38	1	no	—
336	C₂×C₈	—	38	2	no	—
337	C₂×C₈	—	38	1	no	—
338	C₂×C₈	—	38	1	no	—
339	C₂×C₈	—	38	1	no	—
340	C₂×C₈	—	76	8	no	—
341	C₂×C₈	—	76	1	no	—
342	C₂×C₈	—	76	1	no	—
343	C₂×C₈	C₈×D₁₉	1	2	yes	complemented
344	C₄⋊C₄	—	19	2	no	—
345	C₄⋊C₄	—	38	1	no	—
346	C₄⋊C₄	—	38	1	no	—
347	C₄⋊C₄	—	38	1	no	—
348	C₄⋊C₄	—	76	1	no	—
349	C₄⋊C₄	—	76	1	no	—
350	C₂²⋊C₄	—	38	2	no	—
351	C₂²⋊C₄	—	38	2	no	—
352	C₄²	—	76	1	no	—
353	C₄²	—	76	1	no	—
354	C₄²	C₂×D₇₆	1	1	yes	characteristic
355	C₄²	#64541	1	1	yes	characteristic
356	C₄²	D₄×D₁₉	1	1	yes	characteristic
357	C₄²	D₄×D₁₉	1	1	yes	characteristic
358	C₂³	—	38	2	no	—
359	C₂³	—	38	2	no	—
360	C₂³	—	38	2	no	—
361	C₂³	—	76	1	no	—
362	C₂³	—	76	1	no	—
363	C₂³	—	76	1	no	—
364	C₂³	—	76	1	no	—
365	C₂³	#10597339	1	1	yes	characteristic
366	Q₈	—	38	2	no	—
367	Q₈	—	38	2	no	—
368	Q₈	—	76	1	no	—
369	Q₈	—	76	1	no	—
370	D₄	—	19	4	no	—
371	D₄	—	38	2	no	—
372	D₄	—	38	2	no	—
373	D₄	—	38	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	38	2	no	—
377	C₂×C₄	—	38	2	no	—
378	C₂×C₄	—	76	1	no	—
379	C₂×C₄	—	76	1	no	—
380	C₂×C₄	—	76	1	no	—
381	C₂×C₄	—	76	1	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	—	76	2	no	—
384	C₂×C₄	—	76	2	no	—
385	C₂×C₄	—	76	2	no	—
386	C₂×C₄	—	76	1	no	—
387	C₂×C₄	—	76	1	no	—
388	C₂×C₄	—	76	1	no	—
389	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
390	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
391	C₂×C₄	#10597328	1	1	yes	characteristic
392	C₂×C₄	#10597330	1	1	yes	characteristic
393	C₂×C₄	#10597340	1	1	yes	characteristic
394	C₂×C₄	#10597341	1	1	yes	characteristic
395	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
396	C₂×C₄	#10597347	1	1	yes	characteristic
397	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
398	C₂×C₄	#10597353	1	1	yes	characteristic
399	C₂×C₄	#10597357	1	1	yes	characteristic
400	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
401	C₂×C₄	#10597362	1	1	yes	characteristic
402	C₂×C₄	#10597364	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	1	no	—
406	C₈	—	8	1	no	—
407	C₈	—	38	2	no	—
408	C₈	—	76	2	no	—
409	C₈	—	76	1	no	—
410	C₂²	—	38	4	no	—
411	C₂²	—	76	2	no	—
412	C₂²	—	76	2	no	—
413	C₂²	—	76	2	no	—
414	C₂²	—	76	2	no	—
415	C₂²	—	76	2	no	—
416	C₂²	—	76	2	no	—
417	C₂²	#11926422	1	1	yes	characteristic
418	C₂²	#11926609	1	1	yes	characteristic
419	C₂²	#11926614	1	1	yes	characteristic
420	C₂²	#11926631	1	1	yes	characteristic
421	C₂²	#11926643	1	1	yes	characteristic
422	C₂²	#11926660	1	1	yes	characteristic
423	C₂²	#11926665	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	76	2	no	—
427	C₄	—	76	2	no	—
428	C₄	—	152	1	no	—
429	C₄	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
430	C₄	#11926509	1	1	yes	characteristic
431	C₄	C₈×D₇₆	1	1	yes	characteristic
432	C₄	#11926617	1	1	yes	characteristic
433	C₄	#11926696	1	1	yes	characteristic
434	C₄	#11926709	1	1	yes	characteristic
435	C₄	#11926748	1	1	yes	characteristic
436	C₄	#11926758	1	1	yes	characteristic
437	C₂	—	76	4	no	—
438	C₂	#14562434	1	1	yes	characteristic
439	C₂	#14562446	1	1	yes	characteristic
440	C₂	#14562470	1	1	yes	characteristic
441	C₂	#14562491	1	1	yes	characteristic
442	C₂	#14563926	1	1	yes	characteristic
443	C₂	#14563963	1	1	yes	characteristic
444	C₂	#14563970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#8945
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
3. #14564570	C₂	semidirect
4. C₂×#11926274	C₂	semidirect
6. C₁₉⋊#1273	C₂	semidirect
7. C₁₉×#1277	C₂	semidirect
47. C₂×#64516	C₈	semidirect
97. C₂×Dic₃₈	C₂×C₈	semidirect
109. C₂×C₈×C₁₉	C₂×C₈	semidirect
132. C₂×C₁₉⋊C₈	SD₁₆	semidirect
193. #1277	D₁₉	semidirect
295. C₁₉	#8945	semidirect
343. C₂×C₈	C₈×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64516	2
C₂×#11926609	2
#14564570	2
C₂×#11926274	2
C₂×#11926271	2
C₁₉⋊#1273	2
C₁₉×#1277	2
#8945	19