Subgroups — #18072781

Order 4864.

544 conjugacy classes of subgroups.

The subgroup lattice has 440 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	C₂×#11926600	C₂	1	1	yes	maximal, characteristic
3	D₁₉×#431	C₂	1	1	yes	maximal, characteristic
4	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561531	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561530	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	#11926600	—	2	1	no	—
10	#11926600	—	2	1	no	—
11	#11926600	—	2	1	no	—
12	#11926600	C₄	1	2	yes	—
13	#11926600	C₄	1	2	yes	—
14	#11926600	C₄	1	2	yes	—
15	#11926597	C₂²	1	1	yes	characteristic
16	#11926596	—	2	1	no	—
17	#11926596	—	2	1	no	—
18	#11926596	C₄	1	2	yes	—
19	#11926595	—	2	1	no	—
20	#11926594	C₄	1	2	yes	—
21	#11926568	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×D₁₉	—	2	1	no	—
24	#11926507	—	2	1	no	—
25	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
26	C₂²⋊C₈×D₁₉	C₄	1	2	yes	—
27	M₁₆×Dic₁₉	—	2	1	no	—
28	C₂×#10597272	—	2	1	no	—
29	C₄×C₈×D₁₉	—	2	1	no	—
30	C₁₉×#431	C₂²	1	1	yes	characteristic
31	C₁₉×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊C₈	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	Q₈	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
42	C₂×#64520	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₈×D₁₉	—	2	2	no	—
45	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₉	D₄	1	1	yes	characteristic
50	C₄²×D₁₉	D₄	1	1	yes	characteristic
51	C₄²×D₁₉	D₄	1	1	yes	characteristic
52	C₄²×D₁₉	D₄	1	1	yes	characteristic
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
58	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₉	—	2	1	no	—
60	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
61	(C₂×D₁₉)⋊C₈	—	2	2	no	—
62	(C₂×D₁₉)⋊C₈	—	2	2	no	—
63	(C₂×D₁₉)⋊C₈	—	2	2	no	—
64	(C₂×D₁₉)⋊C₈	—	2	2	no	—
65	(C₂×D₁₉)⋊C₈	—	2	2	no	—
66	#10597272	—	2	2	no	—
67	#10597272	—	2	2	no	—
68	#10597272	—	2	2	no	—
69	Dic₁₉⋊C₈	—	2	2	no	—
70	C₈×Dic₁₉	—	2	2	no	—
71	C₈×Dic₁₉	—	2	2	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	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	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
82	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	4	2	no	—
90	C₂×C₄×D₁₉	—	4	2	no	—
91	C₂×C₄×D₁₉	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₁₉	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₉	C₂²⋊C₄	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	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄×Dic₁₉	C₄²	1	1	yes	characteristic
115	C₄×Dic₁₉	C₄²	1	1	yes	characteristic
116	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
126	#64520	—	4	1	no	—
127	#64520	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	2	2	no	—
130	C₂×C₁₉⋊C₈	—	2	2	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₈×D₁₉	—	4	4	no	—
134	#8080	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂²×D₁₉	—	2	1	no	—
137	C₂²×D₁₉	—	2	1	no	—
138	C₂²×D₁₉	—	2	2	no	—
139	C₂²×D₁₉	—	4	1	no	—
140	C₂²×D₁₉	#95	1	1	yes	characteristic
141	C₂²×D₁₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	—	2	1	no	—
156	C₂×Dic₁₉	—	4	1	no	—
157	C₂×Dic₁₉	—	4	1	no	—
158	C₂×Dic₁₉	#95	1	1	yes	characteristic
159	C₂×Dic₁₉	#95	1	1	yes	characteristic
160	C₂×Dic₁₉	#95	1	1	yes	characteristic
161	C₂×Dic₁₉	#95	1	1	yes	characteristic
162	C₂×Dic₁₉	#95	1	1	yes	characteristic
163	C₂×Dic₁₉	#95	1	1	yes	characteristic
164	C₄×D₁₉	—	2	2	no	—
165	C₄×D₁₉	—	2	2	no	—
166	C₄×D₁₉	—	2	1	no	—
167	C₄×D₁₉	—	2	1	no	—
168	C₄×D₁₉	—	2	1	no	—
169	C₄×D₁₉	—	2	1	no	—
170	C₄×D₁₉	—	2	1	no	—
171	C₄×D₁₉	—	2	1	no	—
172	C₄×D₁₉	—	2	1	no	—
173	C₄×D₁₉	—	2	1	no	—
174	C₄×D₁₉	—	2	2	no	—
175	C₄×D₁₉	—	2	2	no	—
176	C₄×D₁₉	—	4	1	no	—
177	C₄×D₁₉	—	4	1	no	—
178	C₄×D₁₉	—	4	1	no	—
179	C₄×D₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	2	no	—
182	C₈×C₁₉	—	4	2	no	—
183	C₁₉⋊C₈	—	4	2	no	—
184	C₁₉⋊C₈	—	4	2	no	—
185	C₁₉⋊C₈	—	4	2	no	—
186	#2920	—	19	1	no	—
187	C₂×#432	—	19	1	no	—
188	C₂×#431	—	19	1	no	—
189	#1301	—	19	1	no	—
190	#1301	—	19	1	no	—
191	#1301	—	19	1	no	—
192	#1301	D₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
196	C₂²×C₁₉	#427	1	1	yes	characteristic
197	C₂²×C₁₉	#427	1	1	yes	characteristic
198	C₂×D₁₉	—	2	1	no	—
199	C₂×D₁₉	—	2	1	no	—
200	C₂×D₁₉	—	2	1	no	—
201	C₂×D₁₉	—	2	1	no	—
202	C₂×D₁₉	—	2	1	no	—
203	C₂×D₁₉	—	4	2	no	—
204	C₂×D₁₉	—	4	2	no	—
205	C₂×D₁₉	#344	1	2	yes	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	#416	1	1	yes	characteristic
210	C₄×C₁₉	#416	1	1	yes	characteristic
211	C₄×C₁₉	#416	1	1	yes	characteristic
212	C₄×C₁₉	#416	1	1	yes	characteristic
213	C₄×C₁₉	#430	1	2	yes	—
214	Dic₁₉	—	2	1	no	—
215	Dic₁₉	—	2	1	no	—
216	Dic₁₉	—	2	1	no	—
217	Dic₁₉	—	2	1	no	—
218	Dic₁₉	—	2	1	no	—
219	Dic₁₉	—	2	1	no	—
220	C₂²×C₄²	—	19	1	no	—
221	#432	—	19	2	no	—
222	#432	—	19	2	no	—
223	#432	—	19	2	no	—
224	#432	—	38	1	no	—
225	#432	—	38	1	no	—
226	#432	—	38	1	no	—
227	#431	—	19	1	no	—
228	#431	—	19	2	no	—
229	#431	—	19	2	no	—
230	#431	—	38	1	no	—
231	#431	—	38	1	no	—
232	#431	—	38	1	no	—
233	#431	C₂×D₁₉	1	1	yes	characteristic
234	#423	—	19	1	no	—
235	#423	C₂×D₁₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	19	1	no	—
237	C₂×C₄⋊C₈	—	38	1	no	—
238	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
239	#407	—	38	1	no	—
240	C₂×C₂²⋊C₈	—	19	2	no	—
241	C₂×C₂²⋊C₈	—	38	1	no	—
242	C₄×M₁₆	—	38	1	no	—
243	C₂×#97	—	38	1	no	—
244	C₂×C₄×C₈	—	38	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	#1735	1	1	yes	characteristic
248	C₂×C₁₉	#1738	1	1	yes	characteristic
249	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
250	D₁₉	—	2	2	no	—
251	D₁₉	—	4	1	no	—
252	C₂³×C₄	—	19	1	no	—
253	C₂³×C₄	—	19	1	no	—
254	C₂³×C₄	—	19	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	38	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	38	2	no	—
259	C₂²×C₈	—	38	1	no	—
260	C₂×C₄²	—	19	1	no	—
261	C₂×C₄²	—	19	1	no	—
262	C₂×C₄²	—	19	1	no	—
263	C₂×C₄²	—	19	1	no	—
264	C₂×C₄²	—	19	1	no	—
265	C₂×C₄²	—	19	1	no	—
266	C₂×C₄²	—	19	1	no	—
267	C₂×C₄²	—	19	1	no	—
268	C₂×C₄²	—	19	1	no	—
269	C₂×C₄²	—	19	1	no	—
270	C₂×C₄²	—	19	1	no	—
271	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	19	2	no	—
276	C₄⋊C₈	—	19	2	no	—
277	C₄⋊C₈	—	38	2	no	—
278	C₄⋊C₈	—	38	1	no	—
279	C₄⋊C₈	—	38	1	no	—
280	C₄⋊C₈	—	38	1	no	—
281	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
282	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
283	C₂²⋊C₈	—	19	2	no	—
284	C₂²⋊C₈	—	38	2	no	—
285	C₂²⋊C₈	—	38	2	no	—
286	C₂²⋊C₈	—	38	2	no	—
287	C₂²⋊C₈	—	38	2	no	—
288	C₂²⋊C₈	—	38	2	no	—
289	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
290	#97	—	38	2	no	—
291	#97	—	38	2	no	—
292	#97	—	38	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	38	2	no	—
295	C₄×C₈	—	38	2	no	—
296	C₄×C₈	—	38	1	no	—
297	C₁₉	#8080	1	1	yes	characteristic, complemented, Sylow
298	C₂⁴	—	19	1	no	—
299	C₂²×C₄	—	19	1	no	—
300	C₂²×C₄	—	19	1	no	—
301	C₂²×C₄	—	19	1	no	—
302	C₂²×C₄	—	19	1	no	—
303	C₂²×C₄	—	19	1	no	—
304	C₂²×C₄	—	19	1	no	—
305	C₂²×C₄	—	19	1	no	—
306	C₂²×C₄	—	19	1	no	—
307	C₂²×C₄	—	19	1	no	—
308	C₂²×C₄	—	19	1	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	—	38	1	no	—
315	C₂²×C₄	—	38	1	no	—
316	C₂²×C₄	—	38	1	no	—
317	C₂²×C₄	—	38	1	no	—
318	C₂²×C₄	—	76	2	no	—
319	C₂²×C₄	—	76	2	no	—
320	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	76	1	no	—
326	M₁₆	—	76	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	38	2	no	—
333	C₂×C₈	—	38	2	no	—
334	C₂×C₈	—	38	2	no	—
335	C₂×C₈	—	76	4	no	—
336	C₂×C₈	—	76	1	no	—
337	C₂×C₈	—	76	1	no	—
338	C₄²	—	19	1	no	—
339	C₄²	—	19	1	no	—
340	C₄²	—	19	1	no	—
341	C₄²	—	19	1	no	—
342	C₄²	—	19	1	no	—
343	C₄²	—	19	1	no	—
344	C₄²	—	19	1	no	—
345	C₄²	—	19	1	no	—
346	C₄²	—	19	1	no	—
347	C₄²	—	19	1	no	—
348	C₄²	—	19	1	no	—
349	C₄²	—	19	1	no	—
350	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
351	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
352	C₄²	D₄×D₁₉	1	1	yes	characteristic
353	C₄²	D₄×D₁₉	1	1	yes	characteristic
354	C₂³	—	19	1	no	—
355	C₂³	—	19	1	no	—
356	C₂³	—	38	2	no	—
357	C₂³	—	38	1	no	—
358	C₂³	—	38	1	no	—
359	C₂³	—	76	1	no	—
360	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	19	1	no	—
364	C₂×C₄	—	19	1	no	—
365	C₂×C₄	—	19	1	no	—
366	C₂×C₄	—	19	1	no	—
367	C₂×C₄	—	19	1	no	—
368	C₂×C₄	—	19	1	no	—
369	C₂×C₄	—	38	2	no	—
370	C₂×C₄	—	38	2	no	—
371	C₂×C₄	—	38	1	no	—
372	C₂×C₄	—	38	1	no	—
373	C₂×C₄	—	38	1	no	—
374	C₂×C₄	—	38	1	no	—
375	C₂×C₄	—	38	1	no	—
376	C₂×C₄	—	38	1	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	1	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	38	2	no	—
382	C₂×C₄	—	38	2	no	—
383	C₂×C₄	—	76	1	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	—	76	1	no	—
386	C₂×C₄	—	76	1	no	—
387	C₂×C₄	—	76	1	no	—
388	C₂×C₄	—	76	1	no	—
389	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
393	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
395	C₂×C₄	#10597358	1	1	yes	characteristic
396	C₂×C₄	#10597362	1	1	yes	characteristic
397	C₂×C₄	#10597362	1	1	yes	characteristic
398	C₂×C₄	#10597365	1	1	yes	characteristic
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	76	2	no	—
403	C₈	—	76	2	no	—
404	C₈	—	76	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	19	2	no	—
408	C₂²	—	38	1	no	—
409	C₂²	—	38	1	no	—
410	C₂²	—	38	1	no	—
411	C₂²	—	38	1	no	—
412	C₂²	—	38	1	no	—
413	C₂²	—	76	2	no	—
414	C₂²	—	76	2	no	—
415	C₂²	#95×D₁₉	1	1	yes	characteristic
416	C₂²	#11926579	1	1	yes	characteristic
417	C₂²	#11926581	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	38	1	no	—
422	C₄	—	38	1	no	—
423	C₄	—	38	1	no	—
424	C₄	—	38	1	no	—
425	C₄	—	38	1	no	—
426	C₄	—	38	1	no	—
427	C₄	#11926537	1	1	yes	characteristic
428	C₄	#11926537	1	1	yes	characteristic
429	C₄	#11926539	1	1	yes	characteristic
430	C₄	#11926539	1	1	yes	characteristic
431	C₄	#11926591	1	2	yes	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	38	2	no	—
435	C₂	—	76	1	no	—
436	C₂	#14563350	1	1	yes	characteristic
437	C₂	#14563360	1	1	yes	characteristic
438	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×#1301	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1301	D₁₉
hypocenter	C₁₉	#8080
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

Complements

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

N	H ≅ G/N	type
4. #14561532	C₂	semidirect
5. #14561531	C₂	semidirect
6. #14561530	C₂	semidirect
7. C₁₉×#1301	C₂	semidirect
192. #1301	D₁₉	semidirect
297. C₁₉	#8080	semidirect

Maximal subgroups

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

subgroup	index
#14572267	2
C₂×#11926600	2
D₁₉×#431	2
#14561532	2
#14561531	2
#14561530	2
C₁₉×#1301	2
#8080	19