Subgroups — #18075381

Order 4864.

546 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64515	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926294	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64515	C₄	1	1	yes	characteristic
9	C₂²×#64515	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
14	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
15	C₄×#64515	—	2	2	no	—
16	C₄×#64515	—	2	2	no	—
17	C₂×#10597272	C₄	1	1	yes	characteristic
18	C₂×#10597272	C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926298	—	2	1	no	—
21	#11926298	—	2	1	no	—
22	#11926296	—	2	2	no	—
23	#11926294	—	2	2	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	—	2	1	no	—
40	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×#64515	—	2	2	no	—
43	C₂×#64515	—	2	2	no	—
44	C₂×#64515	—	2	2	no	—
45	C₂×#64515	—	2	2	no	—
46	C₂×#64515	—	2	2	no	—
47	C₂×#64515	C₈	1	4	yes	complemented
48	C₄²×D₁₉	—	2	1	no	—
49	C₄²×D₁₉	—	2	1	no	—
50	C₄²×D₁₉	—	2	1	no	—
51	C₄²×D₁₉	—	2	1	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	(C₂×D₁₉)⋊C₈	—	4	2	no	—
59	(C₂×D₁₉)⋊C₈	—	4	2	no	—
60	#10597272	—	2	2	no	—
61	#10597272	—	2	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
67	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
68	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
72	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₉	—	2	1	no	—
76	C₂×C₄×D₁₉	—	2	1	no	—
77	C₂×C₄×D₁₉	—	2	1	no	—
78	C₂×C₄×D₁₉	—	2	1	no	—
79	C₂×C₄×D₁₉	—	2	1	no	—
80	C₂×C₄×D₁₉	—	2	1	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	2	1	no	—
84	C₂×C₄×D₁₉	—	2	1	no	—
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	4	1	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
90	C₂×C₄×D₁₉	M₁₆	1	2	yes	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	2	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
102	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	C₄×Dic₁₉	—	2	1	no	—
108	C₄×Dic₁₉	—	2	1	no	—
109	C₄×Dic₁₉	—	2	1	no	—
110	C₄×Dic₁₉	—	2	1	no	—
111	C₄×Dic₁₉	—	2	1	no	—
112	C₄×Dic₁₉	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	2	1	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
122	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
123	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
124	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
125	#64515	—	2	8	no	—
126	#64515	—	2	8	no	—
127	#8597	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂²×D₁₉	—	2	1	no	—
130	C₂²×D₁₉	—	2	1	no	—
131	C₂²×D₁₉	—	2	1	no	—
132	C₂²×D₁₉	—	2	1	no	—
133	C₂²×D₁₉	—	2	1	no	—
134	C₂²×D₁₉	—	2	1	no	—
135	C₂²×D₁₉	C₄⋊C₈	1	2	yes	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	—	2	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	2	1	no	—
159	C₂×Dic₁₉	—	2	1	no	—
160	C₂×Dic₁₉	C₄⋊C₈	1	2	yes	—
161	C₄×D₁₉	—	2	2	no	—
162	C₄×D₁₉	—	2	2	no	—
163	C₄×D₁₉	—	2	2	no	—
164	C₄×D₁₉	—	2	2	no	—
165	C₄×D₁₉	—	4	2	no	—
166	C₄×D₁₉	—	4	2	no	—
167	C₄×D₁₉	—	4	1	no	—
168	C₄×D₁₉	—	4	1	no	—
169	C₄×D₁₉	—	4	1	no	—
170	C₄×D₁₉	—	4	1	no	—
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	—	2	2	no	—
173	C₈×C₁₉	—	8	1	no	—
174	C₈×C₁₉	—	8	1	no	—
175	C₁₉⋊C₈	—	2	2	no	—
176	C₁₉⋊C₈	—	8	1	no	—
177	C₁₉⋊C₈	—	8	1	no	—
178	C₁₉⋊C₈	C₂²⋊C₈	1	4	yes	complemented
179	C₂×C₄×M₁₆	—	19	1	no	—
180	#1797	—	19	1	no	—
181	#1797	—	19	1	no	—
182	C₂×#335	—	19	1	no	—
183	C₂×#334	—	19	1	no	—
184	#1277	—	19	1	no	—
185	#1277	D₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	#380	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
188	C₂²×C₁₉	#423	1	1	yes	characteristic
189	C₂²×C₁₉	#428	1	1	yes	characteristic
190	C₂²×C₁₉	#428	1	1	yes	characteristic
191	C₂²×C₁₉	#430	1	1	yes	characteristic
192	C₂²×C₁₉	#430	1	1	yes	characteristic
193	C₂×D₁₉	—	2	2	no	—
194	C₂×D₁₉	—	2	2	no	—
195	C₂×D₁₉	—	2	2	no	—
196	C₂×D₁₉	—	4	1	no	—
197	C₂×D₁₉	—	4	1	no	—
198	C₂×D₁₉	—	4	1	no	—
199	C₂×D₁₉	—	4	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
203	C₄×C₁₉	#407	1	1	yes	characteristic
204	C₄×C₁₉	#431	1	1	yes	characteristic
205	C₄×C₁₉	#432	1	1	yes	characteristic
206	C₄×C₁₉	#468	1	1	yes	characteristic
207	C₄×C₁₉	#468	1	1	yes	characteristic
208	C₄×C₁₉	#469	1	1	yes	characteristic
209	C₄×C₁₉	#470	1	1	yes	characteristic
210	Dic₁₉	—	2	2	no	—
211	Dic₁₉	—	4	1	no	—
212	Dic₁₉	—	4	1	no	—
213	C₂²×M₁₆	—	19	1	no	—
214	C₂²×M₁₆	—	19	1	no	—
215	C₂²×C₄²	—	19	1	no	—
216	C₂×C₄⋊C₈	—	19	1	no	—
217	C₂×C₄⋊C₈	—	19	1	no	—
218	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	—	38	1	no	—
221	C₂×C₂²⋊C₈	—	38	1	no	—
222	C₄×M₁₆	—	38	2	no	—
223	C₄×M₁₆	—	38	2	no	—
224	C₂×#97	—	19	1	no	—
225	C₂×#97	—	19	1	no	—
226	C₂×C₄×C₈	—	19	1	no	—
227	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
228	#336	—	38	1	no	—
229	#336	—	38	1	no	—
230	#335	—	38	2	no	—
231	#334	—	38	2	no	—
232	C₂×C₁₉	#1565	1	1	yes	characteristic
233	C₂×C₁₉	#1565	1	1	yes	characteristic
234	C₂×C₁₉	#1569	1	1	yes	characteristic
235	C₂×C₁₉	#1569	1	1	yes	characteristic
236	C₂×C₁₉	#1797	1	1	yes	characteristic
237	C₂×C₁₉	#1809	1	1	yes	characteristic
238	C₂×C₁₉	#1811	1	1	yes	characteristic
239	D₁₉	—	4	2	no	—
240	C₂³×C₄	—	19	1	no	—
241	C₂³×C₄	—	19	1	no	—
242	C₂³×C₄	—	19	1	no	—
243	C₂×M₁₆	—	19	4	no	—
244	C₂×M₁₆	—	38	2	no	—
245	C₂×M₁₆	—	38	2	no	—
246	C₂×M₁₆	—	38	2	no	—
247	C₂×M₁₆	—	38	2	no	—
248	C₂×M₁₆	—	38	2	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	19	1	no	—
252	C₂²×C₈	—	19	1	no	—
253	C₂²×C₈	—	38	1	no	—
254	C₂²×C₈	—	38	1	no	—
255	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
256	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
257	C₂×C₄²	—	19	1	no	—
258	C₂×C₄²	—	19	1	no	—
259	C₂×C₄²	—	19	1	no	—
260	C₂×C₄²	—	38	1	no	—
261	C₂×C₄²	—	38	1	no	—
262	C₂×C₄²	—	38	1	no	—
263	C₂×C₄²	—	38	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	—	2	1	no	—
269	C₄⋊C₈	—	38	1	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	C₄⋊C₈	—	38	1	no	—
273	C₂²⋊C₈	—	76	2	no	—
274	C₂²⋊C₈	—	76	2	no	—
275	#97	—	38	2	no	—
276	#97	—	38	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	19	2	no	—
280	C₄×C₈	—	19	2	no	—
281	C₁₉	#8597	1	1	yes	characteristic, complemented, Sylow
282	C₂⁴	—	19	1	no	—
283	C₂²×C₄	—	19	1	no	—
284	C₂²×C₄	—	19	2	no	—
285	C₂²×C₄	—	19	2	no	—
286	C₂²×C₄	—	19	1	no	—
287	C₂²×C₄	—	19	1	no	—
288	C₂²×C₄	—	38	1	no	—
289	C₂²×C₄	—	38	1	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	38	1	no	—
292	C₂²×C₄	—	38	1	no	—
293	C₂²×C₄	—	38	1	no	—
294	C₂²×C₄	—	38	1	no	—
295	C₂²×C₄	—	38	1	no	—
296	C₂²×C₄	—	38	1	no	—
297	C₂²×C₄	—	38	1	no	—
298	C₂²×C₄	—	38	1	no	—
299	C₂²×C₄	—	38	1	no	—
300	C₂²×C₄	—	76	1	no	—
301	C₂²×C₄	—	76	1	no	—
302	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
303	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
304	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
305	M₁₆	—	38	8	no	—
306	M₁₆	—	38	8	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	19	2	no	—
318	C₂×C₈	—	19	2	no	—
319	C₂×C₈	—	19	2	no	—
320	C₂×C₈	—	19	2	no	—
321	C₂×C₈	—	38	1	no	—
322	C₂×C₈	—	38	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	C₈×D₁₉	1	2	yes	—
330	C₂×C₈	#64515	1	2	yes	—
331	C₄²	—	38	1	no	—
332	C₄²	—	38	1	no	—
333	C₄²	—	38	1	no	—
334	C₄²	—	38	1	no	—
335	C₄²	—	38	1	no	—
336	C₄²	—	38	1	no	—
337	C₄²	#64541	1	1	yes	characteristic
338	C₄²	#64541	1	1	yes	characteristic
339	C₄²	D₄×D₁₉	1	1	yes	characteristic
340	C₄²	D₄×D₁₉	1	1	yes	characteristic
341	C₂³	—	19	2	no	—
342	C₂³	—	38	1	no	—
343	C₂³	—	38	1	no	—
344	C₂³	—	38	1	no	—
345	C₂³	—	38	1	no	—
346	C₂³	—	38	1	no	—
347	C₂³	—	38	1	no	—
348	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	19	2	no	—
352	C₂×C₄	—	38	1	no	—
353	C₂×C₄	—	38	1	no	—
354	C₂×C₄	—	38	2	no	—
355	C₂×C₄	—	38	2	no	—
356	C₂×C₄	—	38	2	no	—
357	C₂×C₄	—	38	2	no	—
358	C₂×C₄	—	38	1	no	—
359	C₂×C₄	—	38	1	no	—
360	C₂×C₄	—	38	1	no	—
361	C₂×C₄	—	38	1	no	—
362	C₂×C₄	—	38	1	no	—
363	C₂×C₄	—	38	1	no	—
364	C₂×C₄	—	76	2	no	—
365	C₂×C₄	—	76	2	no	—
366	C₂×C₄	—	76	1	no	—
367	C₂×C₄	—	76	1	no	—
368	C₂×C₄	—	76	1	no	—
369	C₂×C₄	—	76	1	no	—
370	C₂×C₄	#10597318	1	1	yes	characteristic
371	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
372	C₂×C₄	#10597330	1	1	yes	characteristic
373	C₂×C₄	#10597330	1	1	yes	characteristic
374	C₂×C₄	#10597342	1	1	yes	characteristic
375	C₂×C₄	#10597342	1	1	yes	characteristic
376	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂×#64515	1	1	yes	characteristic
378	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
379	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
380	C₂×C₄	#10597357	1	1	yes	characteristic
381	C₂×C₄	#10597360	1	1	yes	characteristic
382	C₂×C₄	#10597361	1	1	yes	characteristic
383	C₂×C₄	#10597364	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	2	no	—
386	C₈	—	8	1	no	—
387	C₈	—	8	1	no	—
388	C₈	—	19	4	no	—
389	C₈	—	38	2	no	—
390	C₈	—	152	1	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	38	2	no	—
393	C₂²	—	38	2	no	—
394	C₂²	—	38	2	no	—
395	C₂²	—	76	1	no	—
396	C₂²	—	76	1	no	—
397	C₂²	—	76	1	no	—
398	C₂²	—	76	1	no	—
399	C₂²	#11926403	1	1	yes	characteristic
400	C₂²	C₄⋊C₈×D₁₉	1	1	yes	characteristic
401	C₂²	#11926566	1	1	yes	characteristic
402	C₂²	#11926583	1	1	yes	characteristic
403	C₂²	#11926585	1	1	yes	characteristic
404	C₂²	#11926591	1	1	yes	characteristic
405	C₂²	#11926591	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	38	2	no	—
409	C₄	—	76	1	no	—
410	C₄	—	76	1	no	—
411	C₄	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
412	C₄	#11926506	1	1	yes	characteristic
413	C₄	#11926595	1	1	yes	characteristic
414	C₄	#11926599	1	1	yes	characteristic
415	C₄	#11926789	1	1	yes	characteristic
416	C₄	#11926793	1	1	yes	characteristic
417	C₄	#11926796	1	1	yes	characteristic
418	C₄	#11926801	1	1	yes	characteristic
419	C₂	—	76	2	no	—
420	C₂	#14562384	1	1	yes	characteristic
421	C₂	#14562386	1	1	yes	characteristic
422	C₂	#14562399	1	1	yes	characteristic
423	C₂	#14562401	1	1	yes	characteristic
424	C₂	#14563614	1	1	yes	characteristic
425	C₂	#14563667	1	1	yes	characteristic
426	C₂	#14563676	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	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#8597
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
4. C₂×#11926296	C₂	semidirect
5. C₂×#11926294	C₂	semidirect
6. #14561470	C₂	semidirect
7. C₁₉×#1277	C₂	semidirect
47. C₂×#64515	C₈	semidirect
178. C₁₉⋊C₈	C₂²⋊C₈	semidirect
185. #1277	D₁₉	semidirect
281. C₁₉	#8597	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64515	2
#14563612	2
C₂×#11926296	2
C₂×#11926294	2
#14561470	2
C₁₉×#1277	2
#8597	19