Subgroups — #18072237

Order 4864.

550 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572266	C₂	1	1	yes	maximal, characteristic
2	#14572263	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926596	C₂	1	1	yes	maximal, characteristic
4	#14561486	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561485	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	#11926600	—	2	1	no	—
10	#11926599	—	2	1	no	—
11	#11926599	—	2	1	no	—
12	#11926598	C₄	1	2	yes	—
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926596	—	2	1	no	—
15	#11926596	—	2	1	no	—
16	#11926596	—	2	1	no	—
17	#11926596	—	2	1	no	—
18	#11926595	—	2	1	no	—
19	#11926595	—	2	1	no	—
20	#11926595	—	2	1	no	—
21	#11926567	C₄	1	2	yes	—
22	#11926566	—	2	1	no	—
23	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
24	#11926507	C₄	1	2	yes	—
25	#11926506	C₄	1	2	yes	—
26	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
27	C₄×#64520	C₂²	1	1	yes	characteristic
28	C₄×#64515	—	2	1	no	—
29	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
30	C₁₉×#431	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×#64520	C₂×C₄	1	2	yes	—
43	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
44	C₂×#64515	—	2	2	no	—
45	C₄²×D₁₉	D₄	1	1	yes	characteristic
46	C₄²×D₁₉	D₄	1	1	yes	characteristic
47	C₄²×D₁₉	D₄	1	1	yes	characteristic
48	C₄²×D₁₉	D₄	1	1	yes	characteristic
49	C₄²×D₁₉	D₄	1	1	yes	characteristic
50	C₄²×D₁₉	D₄	1	1	yes	characteristic
51	C₄²×D₁₉	Q₈	1	1	yes	characteristic
52	C₄²×D₁₉	Q₈	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×C₂²⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₉×#97	—	2	1	no	—
58	C₄×C₈×C₁₉	—	2	1	no	—
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	Dic₁₉⋊C₈	—	2	2	no	—
68	Dic₁₉⋊C₈	—	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	#10597260	—	2	1	no	—
76	C₄×C₁₉⋊C₈	—	2	1	no	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₂³×D₁₉	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
83	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
84	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
85	C₂×C₄×D₁₉	—	2	2	no	—
86	C₂×C₄×D₁₉	—	2	2	no	—
87	C₂×C₄×D₁₉	—	4	2	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₉	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₉	C₄⋊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	M₁₆×C₁₉	—	2	2	no	—
103	M₁₆×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	4	2	no	—
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₁₉	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
124	#64520	—	2	2	no	—
125	#64520	—	2	2	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	C₂×C₁₉⋊C₈	—	2	2	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	2	no	—
130	#64515	—	4	4	no	—
131	#7936	—	19	1	no	maximal, Sylow
132	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
133	C₂²×D₁₉	—	2	1	no	—
134	C₂²×D₁₉	—	2	1	no	—
135	C₂²×D₁₉	—	4	1	no	—
136	C₂²×D₁₉	—	4	1	no	—
137	C₂²×D₁₉	#95	1	1	yes	characteristic
138	C₂²×D₁₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#131	1	2	yes	—
149	C₂×C₄×C₁₉	#131	1	2	yes	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	2	no	—
153	C₂×Dic₁₉	—	4	1	no	—
154	C₂×Dic₁₉	#95	1	1	yes	characteristic
155	C₂×Dic₁₉	#95	1	1	yes	characteristic
156	C₂×Dic₁₉	#95	1	1	yes	characteristic
157	C₂×Dic₁₉	#95	1	1	yes	characteristic
158	C₂×Dic₁₉	#95	1	1	yes	characteristic
159	C₂×Dic₁₉	#95	1	1	yes	characteristic
160	C₄×D₁₉	—	2	2	no	—
161	C₄×D₁₉	—	2	2	no	—
162	C₄×D₁₉	—	2	1	no	—
163	C₄×D₁₉	—	2	1	no	—
164	C₄×D₁₉	—	2	1	no	—
165	C₄×D₁₉	—	2	1	no	—
166	C₄×D₁₉	—	2	2	no	—
167	C₄×D₁₉	—	2	2	no	—
168	C₄×D₁₉	—	2	2	no	—
169	C₄×D₁₉	—	2	2	no	—
170	C₄×D₁₉	—	4	1	no	—
171	C₄×D₁₉	—	4	1	no	—
172	C₄×D₁₉	—	4	1	no	—
173	C₄×D₁₉	—	4	1	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₈×C₁₉	—	4	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₁₉⋊C₈	—	4	2	no	—
178	C₁₉⋊C₈	—	4	2	no	—
179	C₁₉⋊C₈	—	4	2	no	—
180	#2920	—	19	1	no	—
181	#2920	—	19	1	no	—
182	C₂×#431	—	19	1	no	—
183	#1283	—	19	1	no	—
184	#1283	—	19	1	no	—
185	#1283	—	19	1	no	—
186	#1283	D₁₉	1	1	yes	characteristic, complemented
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
190	C₂²×C₁₉	#405	1	1	yes	characteristic
191	C₂²×C₁₉	#405	1	1	yes	characteristic
192	C₂×D₁₉	—	2	1	no	—
193	C₂×D₁₉	—	2	1	no	—
194	C₂×D₁₉	—	2	1	no	—
195	C₂×D₁₉	—	2	1	no	—
196	C₂×D₁₉	—	2	1	no	—
197	C₂×D₁₉	—	2	1	no	—
198	C₂×D₁₉	—	4	2	no	—
199	C₂×D₁₉	—	4	2	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	#408	1	2	yes	—
204	C₄×C₁₉	#413	1	1	yes	characteristic
205	C₄×C₁₉	#413	1	1	yes	characteristic
206	C₄×C₁₉	#424	1	2	yes	—
207	Dic₁₉	—	2	1	no	—
208	Dic₁₉	—	2	1	no	—
209	Dic₁₉	—	2	1	no	—
210	Dic₁₉	—	2	1	no	—
211	Dic₁₉	—	2	1	no	—
212	Dic₁₉	#344	1	2	yes	—
213	C₂²×C₄²	—	19	1	no	—
214	#432	—	19	2	no	—
215	#432	—	38	1	no	—
216	#432	—	38	1	no	—
217	#432	—	38	1	no	—
218	#431	—	19	1	no	—
219	#431	—	38	1	no	—
220	#431	—	38	1	no	—
221	#431	—	38	1	no	—
222	#431	—	38	1	no	—
223	#431	—	38	1	no	—
224	#431	—	38	1	no	—
225	#431	—	38	1	no	—
226	#431	C₂×D₁₉	1	1	yes	characteristic
227	#423	—	19	2	no	—
228	#423	—	38	1	no	—
229	C₂×C₄⋊C₈	—	19	1	no	—
230	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
231	#407	—	19	2	no	—
232	#407	—	19	2	no	—
233	C₂×C₂²⋊C₈	—	19	2	no	—
234	C₄×M₁₆	—	19	1	no	—
235	C₄×M₁₆	—	38	1	no	—
236	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
237	C₂×C₄×C₈	—	19	2	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	#1729	1	1	yes	characteristic
241	C₂×C₁₉	#1742	1	1	yes	characteristic
242	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
243	D₁₉	—	4	1	no	—
244	D₁₉	—	4	1	no	—
245	C₂³×C₄	—	19	1	no	—
246	C₂³×C₄	—	19	1	no	—
247	C₂³×C₄	—	19	1	no	—
248	C₂×M₁₆	—	19	2	no	—
249	C₂×M₁₆	—	38	2	no	—
250	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
251	C₂²×C₈	—	19	2	no	—
252	C₂²×C₈	C₄×D₁₉	1	2	yes	—
253	C₂×C₄²	—	19	1	no	—
254	C₂×C₄²	—	19	1	no	—
255	C₂×C₄²	—	19	1	no	—
256	C₂×C₄²	—	19	1	no	—
257	C₂×C₄²	—	19	1	no	—
258	C₂×C₄²	—	19	1	no	—
259	C₂×C₄²	—	19	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	C₂²×D₁₉	1	1	yes	characteristic
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	38	2	no	—
269	C₄⋊C₈	—	38	2	no	—
270	C₄⋊C₈	—	38	2	no	—
271	C₄⋊C₈	—	38	1	no	—
272	C₄⋊C₈	—	38	1	no	—
273	C₄⋊C₈	—	38	1	no	—
274	C₂²⋊C₈	—	19	2	no	—
275	C₂²⋊C₈	—	38	2	no	—
276	C₂²⋊C₈	—	38	2	no	—
277	C₂²⋊C₈	—	38	2	no	—
278	C₂²⋊C₈	—	38	2	no	—
279	C₂²⋊C₈	—	38	2	no	—
280	C₂²⋊C₈	C₄×D₁₉	1	2	yes	—
281	#97	—	2	1	no	—
282	#97	—	38	2	no	—
283	#97	—	38	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	38	2	no	—
287	C₄×C₈	—	38	2	no	—
288	C₄×C₈	—	38	1	no	—
289	C₄×C₈	—	38	1	no	—
290	C₁₉	#7936	1	1	yes	characteristic, complemented, Sylow
291	C₂⁴	—	19	1	no	—
292	C₂²×C₄	—	19	1	no	—
293	C₂²×C₄	—	19	1	no	—
294	C₂²×C₄	—	19	1	no	—
295	C₂²×C₄	—	19	1	no	—
296	C₂²×C₄	—	19	1	no	—
297	C₂²×C₄	—	19	1	no	—
298	C₂²×C₄	—	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	—	38	2	no	—
308	C₂²×C₄	—	38	2	no	—
309	C₂²×C₄	—	76	1	no	—
310	C₂²×C₄	—	76	1	no	—
311	C₂²×C₄	—	76	2	no	—
312	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	38	2	no	—
318	M₁₆	—	38	2	no	—
319	M₁₆	—	76	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	38	2	no	—
325	C₂×C₈	—	38	2	no	—
326	C₂×C₈	—	38	2	no	—
327	C₂×C₈	—	76	2	no	—
328	C₄²	—	19	1	no	—
329	C₄²	—	19	1	no	—
330	C₄²	—	19	1	no	—
331	C₄²	—	19	1	no	—
332	C₄²	—	19	1	no	—
333	C₄²	—	19	1	no	—
334	C₄²	—	19	1	no	—
335	C₄²	—	19	1	no	—
336	C₄²	—	19	1	no	—
337	C₄²	—	19	1	no	—
338	C₄²	—	19	1	no	—
339	C₄²	—	19	1	no	—
340	C₄²	D₄×D₁₉	1	1	yes	characteristic
341	C₄²	D₄×D₁₉	1	1	yes	characteristic
342	C₄²	D₄×D₁₉	1	1	yes	characteristic
343	C₄²	Q₈×D₁₉	1	1	yes	characteristic
344	C₂³	—	19	1	no	—
345	C₂³	—	19	1	no	—
346	C₂³	—	38	1	no	—
347	C₂³	—	38	1	no	—
348	C₂³	—	76	1	no	—
349	C₂³	—	76	1	no	—
350	C₂³	C₄²×D₁₉	1	1	yes	characteristic
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	19	1	no	—
355	C₂×C₄	—	19	1	no	—
356	C₂×C₄	—	19	1	no	—
357	C₂×C₄	—	19	1	no	—
358	C₂×C₄	—	19	1	no	—
359	C₂×C₄	—	19	1	no	—
360	C₂×C₄	—	38	2	no	—
361	C₂×C₄	—	38	2	no	—
362	C₂×C₄	—	38	2	no	—
363	C₂×C₄	—	38	1	no	—
364	C₂×C₄	—	38	1	no	—
365	C₂×C₄	—	38	2	no	—
366	C₂×C₄	—	38	2	no	—
367	C₂×C₄	—	38	2	no	—
368	C₂×C₄	—	38	2	no	—
369	C₂×C₄	—	38	1	no	—
370	C₂×C₄	—	38	1	no	—
371	C₂×C₄	—	38	1	no	—
372	C₂×C₄	—	38	1	no	—
373	C₂×C₄	—	76	1	no	—
374	C₂×C₄	—	76	1	no	—
375	C₂×C₄	—	76	1	no	—
376	C₂×C₄	—	76	1	no	—
377	C₂×C₄	—	76	1	no	—
378	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
380	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
381	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
382	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
383	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
384	C₂×C₄	#10597347	1	2	yes	—
385	C₂×C₄	#10597353	1	2	yes	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	76	2	no	—
390	C₈	—	76	2	no	—
391	C₈	—	76	2	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	38	1	no	—
395	C₂²	—	38	1	no	—
396	C₂²	—	38	1	no	—
397	C₂²	—	38	1	no	—
398	C₂²	—	38	1	no	—
399	C₂²	—	38	1	no	—
400	C₂²	—	76	2	no	—
401	C₂²	—	76	2	no	—
402	C₂²	#95×D₁₉	1	1	yes	characteristic
403	C₂²	#11926498	1	1	yes	characteristic
404	C₂²	#11926501	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	19	2	no	—
409	C₄	—	38	1	no	—
410	C₄	—	38	1	no	—
411	C₄	—	38	1	no	—
412	C₄	—	38	1	no	—
413	C₄	—	38	1	no	—
414	C₄	#11926509	1	2	yes	—
415	C₄	#11926525	1	1	yes	characteristic
416	C₄	#11926527	1	1	yes	characteristic
417	C₄	#11926569	1	2	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	76	1	no	—
421	C₂	—	76	1	no	—
422	C₂	#14563330	1	1	yes	characteristic
423	C₂	#14563372	1	1	yes	characteristic
424	C₂	D₁₉×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1283	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂³×D₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1283	D₁₉
hypocenter	C₁₉	#7936
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1283

Complements

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

N	H ≅ G/N	type
4. #14561486	C₂	semidirect
5. #14561485	C₂	semidirect
6. #14561484	C₂	semidirect
7. C₁₉×#1283	C₂	semidirect
186. #1283	D₁₉	semidirect
290. C₁₉	#7936	semidirect

Maximal subgroups

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

subgroup	index
#14572266	2
#14572263	2
C₂×#11926596	2
#14561486	2
#14561485	2
#14561484	2
C₁₉×#1283	2
#7936	19