Subgroups — #18072845

Order 4864.

584 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572267	C₂	1	1	yes	maximal, characteristic
2	D₁₉×#431	C₂	1	1	yes	maximal, characteristic
3	#14566031	C₂	1	1	yes	maximal, characteristic
4	#14561538	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561537	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561536	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	#11926600	—	2	1	no	—
10	#11926600	C₄	1	2	yes	complemented
11	#11926597	C₂²	1	1	yes	characteristic
12	#11926596	—	2	1	no	—
13	#11926596	C₄	1	2	yes	complemented
14	#11926596	C₄	1	2	yes	complemented
15	#11926595	—	2	1	no	—
16	#11926594	—	2	1	no	—
17	#11926568	C₂²	1	1	yes	characteristic
18	C₄⋊C₈×D₁₉	C₄	1	2	yes	complemented
19	#11926507	—	2	1	no	—
20	C₂²⋊C₈×D₁₉	—	2	1	no	—
21	M₁₆×Dic₁₉	—	2	1	no	—
22	C₄×C₈×D₁₉	—	2	1	no	—
23	#11926411	C₄	1	2	yes	—
24	#11926409	—	2	1	no	—
25	#11926406	C₄	1	2	yes	—
26	#11926401	—	2	1	no	—
27	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
28	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
29	#11926390	—	2	1	no	—
30	C₁₉×#431	C₂²	1	1	yes	characteristic
31	C₁₉×#423	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
46	C₂×#64520	—	2	1	no	—
47	C₂×C₈×D₁₉	—	2	2	no	—
48	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₉	D₄	1	1	yes	characteristic
53	C₄²×D₁₉	D₄	1	1	yes	characteristic
54	C₄²×D₁₉	Q₈	1	1	yes	characteristic
55	C₄²×D₁₉	Q₈	1	1	yes	characteristic
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
58	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₉×C₂²⋊C₈	—	2	1	no	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	C₁₉×#95	C₂×C₄	1	2	yes	—
62	C₁₉⋊#95	—	2	2	no	—
63	C₁₉⋊#95	—	2	2	no	—
64	C₁₉⋊#95	—	2	2	no	—
65	C₁₉⋊#95	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
67	(C₂×D₁₉)⋊C₈	—	2	2	no	—
68	(C₂×D₁₉)⋊C₈	—	2	2	no	—
69	(C₂×D₁₉)⋊C₈	—	2	2	no	—
70	#10597272	—	2	2	no	—
71	Dic₁₉⋊C₈	—	2	2	no	—
72	C₈×Dic₁₉	—	2	2	no	—
73	C₈×Dic₁₉	—	2	2	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
76	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₁₉	—	2	2	no	—
84	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	—	4	2	no	—
92	C₂×C₄×D₁₉	—	4	2	no	—
93	C₂×C₄×D₁₉	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₁₉	C₄²	1	1	yes	characteristic
95	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	4	2	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
116	(C₂×D₁₉)⋊C₄	—	4	4	no	—
117	C₄⋊Dic₁₉	—	4	2	no	—
118	C₄×Dic₁₉	—	4	1	no	—
119	C₄×Dic₁₉	—	4	1	no	—
120	C₄×Dic₁₉	C₄²	1	1	yes	characteristic
121	C₄×Dic₁₉	C₄²	1	1	yes	characteristic
122	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
132	#64520	—	4	1	no	—
133	#64520	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₈×D₁₉	—	4	4	no	—
137	#8096	—	19	1	no	maximal, Sylow
138	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×D₁₉	—	2	1	no	—
140	C₂²×D₁₉	—	2	1	no	—
141	C₂²×D₁₉	—	2	2	no	—
142	C₂²×D₁₉	—	4	1	no	—
143	C₂²×D₁₉	#95	1	1	yes	characteristic
144	C₂²×D₁₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	2	1	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	C₂×Dic₁₉	—	4	1	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	C₂×Dic₁₉	—	4	2	no	—
166	C₂×Dic₁₉	—	4	2	no	—
167	C₂×Dic₁₉	#95	1	1	yes	characteristic
168	C₂×Dic₁₉	#95	1	1	yes	characteristic
169	C₂×Dic₁₉	#95	1	1	yes	characteristic
170	C₂×Dic₁₉	#95	1	1	yes	characteristic
171	C₂×Dic₁₉	#95	1	1	yes	characteristic
172	C₂×Dic₁₉	#95	1	1	yes	characteristic
173	C₄×D₁₉	—	2	2	no	—
174	C₄×D₁₉	—	2	2	no	—
175	C₄×D₁₉	—	2	1	no	—
176	C₄×D₁₉	—	2	1	no	—
177	C₄×D₁₉	—	2	1	no	—
178	C₄×D₁₉	—	2	1	no	—
179	C₄×D₁₉	—	2	2	no	—
180	C₄×D₁₉	—	2	2	no	—
181	C₄×D₁₉	—	2	1	no	—
182	C₄×D₁₉	—	2	1	no	—
183	C₄×D₁₉	—	2	1	no	—
184	C₄×D₁₉	—	2	1	no	—
185	C₄×D₁₉	—	4	1	no	—
186	C₄×D₁₉	—	4	1	no	—
187	C₄×D₁₉	—	4	1	no	—
188	C₄×D₁₉	—	4	1	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₈×C₁₉	—	4	2	no	—
191	C₁₉⋊C₈	—	4	2	no	—
192	C₁₉⋊C₈	—	4	2	no	—
193	#2920	—	19	1	no	—
194	C₂×#431	—	19	1	no	—
195	#2283	—	19	1	no	—
196	#1303	—	19	1	no	—
197	#1303	—	19	1	no	—
198	#1303	—	19	1	no	—
199	#1303	D₁₉	1	1	yes	characteristic, complemented
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
203	C₂²×C₁₉	#416	1	1	yes	characteristic
204	C₂²×C₁₉	#416	1	1	yes	characteristic
205	C₂×D₁₉	—	2	1	no	—
206	C₂×D₁₉	—	2	1	no	—
207	C₂×D₁₉	—	2	1	no	—
208	C₂×D₁₉	—	2	1	no	—
209	C₂×D₁₉	—	2	1	no	—
210	C₂×D₁₉	—	4	2	no	—
211	C₂×D₁₉	—	4	2	no	—
212	C₂×D₁₉	#344	1	2	yes	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	8	2	no	—
217	C₄×C₁₉	#416	1	1	yes	characteristic
218	C₄×C₁₉	#416	1	1	yes	characteristic
219	C₄×C₁₉	#421	1	2	yes	—
220	C₄×C₁₉	#427	1	1	yes	characteristic
221	C₄×C₁₉	#427	1	1	yes	characteristic
222	Dic₁₉	—	2	1	no	—
223	Dic₁₉	—	2	1	no	—
224	Dic₁₉	—	2	1	no	—
225	Dic₁₉	—	2	1	no	—
226	Dic₁₉	—	2	1	no	—
227	Dic₁₉	—	2	1	no	—
228	Dic₁₉	—	8	2	no	—
229	C₂²×C₄²	—	19	1	no	—
230	#432	—	19	2	no	—
231	#432	—	38	1	no	—
232	#431	—	19	1	no	—
233	#431	—	19	2	no	—
234	#431	—	19	2	no	—
235	#431	—	38	1	no	—
236	#431	—	38	1	no	—
237	#431	—	38	1	no	—
238	#431	C₂×D₁₉	1	1	yes	characteristic
239	#423	—	19	1	no	—
240	#423	C₂×D₁₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	—	19	2	no	—
242	#407	—	38	1	no	—
243	C₂×C₂²⋊C₈	—	38	1	no	—
244	C₄×M₁₆	—	38	1	no	—
245	C₂×C₄×C₈	—	38	1	no	—
246	#383	—	19	2	no	—
247	#382	—	38	1	no	—
248	#381	—	19	2	no	—
249	#380	—	38	1	no	—
250	C₄×C₄⋊C₄	—	19	1	no	—
251	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	—	38	1	no	—
253	#376	—	38	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	#1733	1	1	yes	characteristic
257	C₂×C₁₉	#1735	1	1	yes	characteristic
258	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
259	D₁₉	—	2	2	no	—
260	D₁₉	—	4	1	no	—
261	C₂³×C₄	—	19	1	no	—
262	C₂³×C₄	—	19	1	no	—
263	C₂³×C₄	—	19	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	38	1	no	—
266	C₂²×C₈	—	38	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	38	1	no	—
269	C₂×C₂²⋊C₄	—	38	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	19	1	no	—
272	C₂×C₄²	—	19	1	no	—
273	C₂×C₄²	—	19	1	no	—
274	C₂×C₄²	—	19	1	no	—
275	C₂×C₄²	—	19	1	no	—
276	C₂×C₄²	—	19	1	no	—
277	C₂×C₄²	—	19	1	no	—
278	C₂×C₄²	—	19	1	no	—
279	C₂×C₄²	—	19	1	no	—
280	C₂×C₄²	—	19	1	no	—
281	C₂×C₄²	—	19	1	no	—
282	C₂×C₄²	—	38	1	no	—
283	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	19	2	no	—
286	C₄⋊C₈	—	19	2	no	—
287	C₄⋊C₈	—	38	2	no	—
288	C₄⋊C₈	—	38	1	no	—
289	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
290	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	38	2	no	—
293	C₂²⋊C₈	—	38	2	no	—
294	C₂²⋊C₈	—	38	2	no	—
295	C₂²⋊C₈	—	38	1	no	—
296	#97	—	38	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	38	2	no	—
299	C₄×C₈	—	38	2	no	—
300	C₄×C₈	—	38	1	no	—
301	#95	—	19	2	no	—
302	#95	—	38	2	no	—
303	#95	—	38	2	no	—
304	#95	—	38	2	no	—
305	#95	C₄×D₁₉	1	2	yes	—
306	C₁₉	#8096	1	1	yes	characteristic, complemented, Sylow
307	C₂⁴	—	19	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	19	1	no	—
310	C₂²×C₄	—	19	1	no	—
311	C₂²×C₄	—	19	1	no	—
312	C₂²×C₄	—	19	1	no	—
313	C₂²×C₄	—	19	1	no	—
314	C₂²×C₄	—	19	1	no	—
315	C₂²×C₄	—	19	1	no	—
316	C₂²×C₄	—	19	1	no	—
317	C₂²×C₄	—	19	1	no	—
318	C₂²×C₄	—	19	1	no	—
319	C₂²×C₄	—	19	1	no	—
320	C₂²×C₄	—	19	1	no	—
321	C₂²×C₄	—	19	1	no	—
322	C₂²×C₄	—	19	1	no	—
323	C₂²×C₄	—	19	1	no	—
324	C₂²×C₄	—	38	1	no	—
325	C₂²×C₄	—	38	1	no	—
326	C₂²×C₄	—	38	1	no	—
327	C₂²×C₄	—	38	1	no	—
328	C₂²×C₄	—	38	2	no	—
329	C₂²×C₄	—	76	2	no	—
330	C₂²×C₄	—	76	2	no	—
331	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
332	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
334	M₁₆	—	4	1	no	—
335	M₁₆	—	4	1	no	—
336	M₁₆	—	76	1	no	—
337	M₁₆	—	76	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	38	2	no	—
341	C₂×C₈	—	38	2	no	—
342	C₂×C₈	—	76	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	76	2	no	—
345	C₂²⋊C₄	—	76	4	no	—
346	C₄²	—	4	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	19	1	no	—
349	C₄²	—	19	1	no	—
350	C₄²	—	19	1	no	—
351	C₄²	—	19	1	no	—
352	C₄²	—	19	1	no	—
353	C₄²	—	19	1	no	—
354	C₄²	—	19	1	no	—
355	C₄²	—	19	1	no	—
356	C₄²	—	19	1	no	—
357	C₄²	—	19	1	no	—
358	C₄²	—	19	1	no	—
359	C₄²	—	19	1	no	—
360	C₄²	—	76	1	no	—
361	C₄²	—	76	1	no	—
362	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
363	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
364	C₄²	D₄×D₁₉	1	1	yes	characteristic
365	C₄²	Q₈×D₁₉	1	1	yes	characteristic
366	C₂³	—	19	1	no	—
367	C₂³	—	19	1	no	—
368	C₂³	—	38	2	no	—
369	C₂³	—	38	1	no	—
370	C₂³	—	38	1	no	—
371	C₂³	—	76	1	no	—
372	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	19	1	no	—
379	C₂×C₄	—	19	1	no	—
380	C₂×C₄	—	19	1	no	—
381	C₂×C₄	—	19	1	no	—
382	C₂×C₄	—	19	1	no	—
383	C₂×C₄	—	19	1	no	—
384	C₂×C₄	—	38	2	no	—
385	C₂×C₄	—	38	2	no	—
386	C₂×C₄	—	38	1	no	—
387	C₂×C₄	—	38	1	no	—
388	C₂×C₄	—	38	1	no	—
389	C₂×C₄	—	38	1	no	—
390	C₂×C₄	—	38	1	no	—
391	C₂×C₄	—	38	1	no	—
392	C₂×C₄	—	38	2	no	—
393	C₂×C₄	—	38	2	no	—
394	C₂×C₄	—	38	1	no	—
395	C₂×C₄	—	38	1	no	—
396	C₂×C₄	—	38	1	no	—
397	C₂×C₄	—	38	1	no	—
398	C₂×C₄	—	76	1	no	—
399	C₂×C₄	—	76	1	no	—
400	C₂×C₄	—	76	1	no	—
401	C₂×C₄	—	76	1	no	—
402	C₂×C₄	—	76	1	no	—
403	C₂×C₄	—	76	1	no	—
404	C₂×C₄	—	76	2	no	—
405	C₂×C₄	—	76	2	no	—
406	C₂×C₄	—	76	2	no	—
407	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
409	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
411	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
412	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
413	C₂×C₄	#10597358	1	1	yes	characteristic
414	C₂×C₄	#10597362	1	1	yes	characteristic
415	C₂×C₄	#10597362	1	1	yes	characteristic
416	C₂×C₄	#10597365	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	76	2	no	—
420	C₈	—	76	2	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	19	2	no	—
424	C₂²	—	38	1	no	—
425	C₂²	—	38	1	no	—
426	C₂²	—	38	1	no	—
427	C₂²	—	38	1	no	—
428	C₂²	—	38	1	no	—
429	C₂²	—	76	2	no	—
430	C₂²	—	76	2	no	—
431	C₂²	#95×D₁₉	1	1	yes	characteristic
432	C₂²	#11926537	1	1	yes	characteristic
433	C₂²	#11926539	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	38	1	no	—
439	C₄	—	38	1	no	—
440	C₄	—	38	1	no	—
441	C₄	—	38	1	no	—
442	C₄	—	38	1	no	—
443	C₄	—	38	1	no	—
444	C₄	—	152	2	no	—
445	C₄	#11926537	1	1	yes	characteristic
446	C₄	#11926539	1	1	yes	characteristic
447	C₄	#11926559	1	2	yes	—
448	C₄	#11926579	1	1	yes	characteristic
449	C₄	#11926581	1	1	yes	characteristic
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	38	2	no	—
453	C₂	—	76	1	no	—
454	C₂	#14563343	1	1	yes	characteristic
455	C₂	#14563350	1	1	yes	characteristic
456	C₂	D₁₉×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1303	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1303	D₁₉
hypocenter	C₁₉	#8096
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

Complements

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

N	H ≅ G/N	type
4. #14561538	C₂	semidirect
5. #14561537	C₂	semidirect
6. #14561536	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
10. #11926600	C₄	semidirect
13. #11926596	C₄	semidirect
14. #11926596	C₄	semidirect
18. C₄⋊C₈×D₁₉	C₄	semidirect
199. #1303	D₁₉	semidirect
306. C₁₉	#8096	semidirect

Maximal subgroups

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

subgroup	index
#14572267	2
D₁₉×#431	2
#14566031	2
#14561538	2
#14561537	2
#14561536	2
C₁₉×#1303	2
#8096	19