Subgroups — #18070697

Order 4864.

656 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	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563397	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561461	C₂	1	2	yes	maximal, complemented
4	#14561456	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×#10597260	—	2	1	no	—
10	#11926299	C₂²	1	2	yes	—
11	#11926299	C₂²	1	2	yes	—
12	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#391	C₄	1	1	yes	characteristic
16	C₁₉×#391	C₂²	1	1	yes	characteristic
17	C₁₉×#390	C₄	1	1	yes	characteristic
18	C₁₉×#390	C₂²	1	1	yes	characteristic
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#386	—	2	1	no	—
21	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂×#41×C₁₉	—	2	2	no	—
24	C₂×#41×C₁₉	—	2	2	no	—
25	C₂×#41×C₁₉	—	4	2	no	—
26	C₂×#41×C₁₉	—	4	2	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₁₉×#117	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	4	2	no	—
44	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
57	#10597260	—	4	2	no	—
58	C₂⁴×C₁₉	—	2	1	no	—
59	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	#41×C₁₉	—	4	8	no	—
61	#41×C₁₉	—	4	8	no	—
62	C₂×Q₈×C₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	—	4	1	no	—
64	C₂×Q₈×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
66	C₂×D₄×C₁₉	—	2	4	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	4	1	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	4	2	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₂²⋊C₄×C₁₉	—	4	2	no	—
99	C₂²⋊C₄×C₁₉	—	4	2	no	—
100	C₂²⋊C₄×C₁₉	—	4	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	2	no	—
102	C₂²⋊C₄×C₁₉	—	4	1	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	2	no	—
109	C₂×C₁₉⋊C₈	—	2	4	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	#7612	—	19	1	no	maximal, Sylow
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	#100	1	2	yes	—
130	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	Q₈×C₁₉	—	4	2	no	—
132	Q₈×C₁₉	—	4	2	no	—
133	D₄×C₁₉	—	4	2	no	—
134	D₄×C₁₉	—	4	2	no	—
135	D₄×C₁₉	—	4	8	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	8	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	#99	1	2	yes	—
165	C₂×C₄×C₁₉	#104	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#135	1	2	yes	—
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
171	C₁₉⋊C₈	—	4	4	no	—
172	C₁₉⋊C₈	—	8	2	no	—
173	#2297	D₁₉	1	1	yes	characteristic
174	#1797	—	19	1	no	—
175	#1749	—	19	1	no	—
176	#1272	—	19	2	no	—
177	#1270	—	19	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	1	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	2	no	—
186	C₂²×C₁₉	—	4	2	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	8	1	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	#407	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
194	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
195	C₂²×C₁₉	#416	1	1	yes	characteristic
196	C₂²×C₁₉	#417	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
198	C₂²×C₁₉	#421	1	1	yes	characteristic
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	1	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	—	8	1	no	—
210	C₂²×#41	Dic₁₉	1	1	yes	characteristic
211	C₂×#117	Dic₁₉	1	1	yes	characteristic
212	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	38	1	no	—
214	C₂×C₂²⋊C₈	—	38	1	no	—
215	C₂×C₂²⋊C₈	—	38	1	no	—
216	C₂×#97	—	38	1	no	—
217	#391	Dic₁₉	1	1	yes	characteristic
218	#391	C₂×D₁₉	1	1	yes	characteristic
219	#390	Dic₁₉	1	1	yes	characteristic
220	#390	C₂×D₁₉	1	1	yes	characteristic
221	#386	—	2	1	no	—
222	#386	—	2	1	no	—
223	C₄×C₂²⋊C₄	—	2	1	no	—
224	C₄×C₂²⋊C₄	—	2	1	no	—
225	#336	—	19	2	no	—
226	#336	—	19	2	no	—
227	C₂×C₁₉	—	4	2	no	—
228	C₂×C₁₉	—	8	2	no	—
229	C₂×C₁₉	#1462	1	1	yes	characteristic
230	C₂×C₁₉	#1488	1	1	yes	characteristic
231	C₂×C₁₉	#1489	1	1	yes	characteristic
232	C₂×C₁₉	#1501	1	1	yes	characteristic
233	C₂×C₁₉	#1513	1	1	yes	characteristic
234	C₂×C₁₉	#1530	1	1	yes	characteristic
235	C₂×C₁₉	#1551	1	1	yes	characteristic
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	4	2	no	—
239	C₂×#41	—	4	2	no	—
240	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
245	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂²×C₈	—	38	2	no	—
248	C₂²×C₈	—	38	2	no	—
249	#117	—	4	2	no	—
250	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	4	2	no	—
259	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	C₄⋊C₈	—	76	2	no	—
264	C₂²⋊C₈	—	38	4	no	—
265	C₂²⋊C₈	—	76	2	no	—
266	#97	—	76	2	no	—
267	#95	—	2	1	no	—
268	#95	—	2	1	no	—
269	#95	—	2	1	no	—
270	#95	—	2	1	no	—
271	C₁₉	#7612	1	1	yes	characteristic, complemented, Sylow
272	C₂⁴	—	2	1	no	—
273	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
274	#41	—	4	8	no	—
275	#41	—	4	8	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	#64520	1	2	yes	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	#64520	1	2	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
310	C₂×C₈	—	38	4	no	—
311	C₂×C₈	—	76	2	no	—
312	C₂×C₈	—	76	2	no	—
313	C₂×C₈	—	76	2	no	—
314	C₂×C₈	—	76	2	no	—
315	C₂×C₈	—	76	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	—	4	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	#10597290	1	2	yes	—
343	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	#10597291	1	2	yes	—
378	C₂×C₄	#10597294	1	2	yes	—
379	C₂×C₄	C₂×#64520	1	1	yes	characteristic
380	C₂×C₄	C₂×#64520	1	1	yes	characteristic
381	C₂×C₄	#10597395	1	1	yes	characteristic
382	C₂×C₄	#10597396	1	2	yes	—
383	C₂×C₄	#10597397	1	1	yes	characteristic
384	C₈	—	76	4	no	—
385	C₈	—	152	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	#11926508	1	1	yes	characteristic
401	C₂²	C₂×#10597291	1	1	yes	characteristic
402	C₂²	C₂×#10597290	1	1	yes	characteristic
403	C₂²	#11926540	1	1	yes	characteristic
404	C₂²	#11926545	1	1	yes	characteristic
405	C₂²	C₂×#10597294	1	1	yes	characteristic
406	C₂²	#11926561	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	1	no	—
418	C₂	—	4	2	no	—
419	C₂	—	8	2	no	—
420	C₂	#14561962	1	1	yes	characteristic
421	C₂	#14562069	1	1	yes	characteristic
422	C₂	#14562074	1	1	yes	characteristic
423	C₂	#14562126	1	1	yes	characteristic
424	C₂	#14562178	1	1	yes	characteristic
425	C₂	#14562246	1	1	yes	characteristic
426	C₂	#14562330	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2297	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2297	D₁₉
hypocenter	C₁₉	#7612
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2297

Complements

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

N	H ≅ G/N	type
1. #14563615	C₂	semidirect
2. #14563397	C₂	semidirect
3. #14561461	C₂	semidirect
4. #14561456	C₂	semidirect
271. C₁₉	#7612	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
#14563397	2
#14561461	2
#14561456	2
C₁₉×#2297	2
#7612	19