Subgroups — #18079401

Order 4864.

580 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572746	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564563	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562303	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561536	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561509	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3038	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₁₉⋊C₈	—	2	1	no	—
9	D₄×C₁₉⋊C₈	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	1	no	—
11	#11926597	—	2	1	no	—
12	#11926597	C₂²	1	1	yes	characteristic
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#10597294	—	2	1	no	—
17	C₂×#10597289	—	2	2	no	—
18	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
19	#11926303	—	2	1	no	—
20	#11926288	—	2	1	no	—
21	#11926288	—	2	1	no	—
22	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#460	—	2	1	no	—
26	C₁₉×#460	C₄	1	2	yes	complemented
27	C₁₉×#459	—	2	1	no	—
28	C₁₉×#459	C₄	1	2	yes	complemented
29	C₁₉×#423	C₂²	1	1	yes	characteristic
30	C₁₉×#418	—	2	1	no	—
31	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
36	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
37	C₂×SD₁₆×C₁₉	—	2	2	no	—
38	C₂×D₈×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂²×C₁₉⋊C₈	—	2	2	no	—
58	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₉×#102	—	2	2	no	—
62	C₁₉×#102	—	2	2	no	—
63	#10597294	—	4	2	no	—
64	#10597289	—	4	4	no	—
65	C₁₉⋊#95	—	2	1	no	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
74	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
75	C₄×C₁₉⋊C₈	—	2	2	no	—
76	C₄×C₁₉⋊C₈	—	2	1	no	—
77	C₂⁴×C₁₉	—	4	1	no	—
78	#41×C₁₉	—	2	1	no	—
79	#41×C₁₉	—	2	1	no	—
80	#41×C₁₉	D₈	1	2	yes	—
81	#41×C₁₉	SD₁₆	1	2	yes	—
82	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	8	2	no	—
97	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×Dic₁₉	—	4	1	no	—
105	SD₁₆×C₁₉	—	4	4	no	—
106	D₈×C₁₉	—	4	4	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	C₄²×C₁₉	—	2	1	no	—
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	C₄⋊Dic₁₉	—	2	2	no	—
125	C₄⋊Dic₁₉	—	4	1	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	#64520	—	4	1	no	—
129	#64520	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	2	1	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	1	no	—
133	C₂×C₁₉⋊C₈	—	4	2	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	8	2	no	—
136	#9318	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	8	2	no	—
140	C₂³×C₁₉	—	8	2	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	#121	1	1	yes	characteristic
144	Q₈×C₁₉	—	2	1	no	—
145	Q₈×C₁₉	#102	1	2	yes	complemented
146	D₄×C₁₉	—	2	2	no	—
147	D₄×C₁₉	—	2	2	no	—
148	D₄×C₁₉	—	2	1	no	—
149	D₄×C₁₉	—	4	4	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	8	2	no	—
153	D₄×C₁₉	—	8	2	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	8	1	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	#102	1	2	yes	complemented
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×Dic₁₉	—	4	2	no	—
181	C₂×Dic₁₉	—	8	1	no	—
182	C₂×Dic₁₉	—	8	1	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₁₉⋊C₈	—	4	2	no	—
185	C₁₉⋊C₈	—	4	1	no	—
186	C₁₉⋊C₈	—	4	1	no	—
187	C₁₉⋊C₈	—	8	1	no	—
188	#3038	D₁₉	1	1	yes	characteristic
189	#2988	—	19	1	no	—
190	#1982	—	19	1	no	—
191	#1806	—	19	1	no	—
192	#1545	—	19	1	no	—
193	#1303	—	19	1	no	—
194	#1292	—	19	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	16	2	no	—
204	C₂²×C₁₉	—	16	2	no	—
205	C₂²×C₁₉	#386	1	1	yes	characteristic
206	C₂²×C₁₉	#465	1	1	yes	characteristic
207	C₂²×C₁₉	#466	1	1	yes	characteristic
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	4	1	no	—
213	C₄×C₁₉	—	4	1	no	—
214	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
215	C₄×C₁₉	#416	1	1	yes	characteristic
216	C₄×C₁₉	#453	1	1	yes	characteristic
217	C₄×C₁₉	#454	1	1	yes	characteristic
218	C₄×C₁₉	#465	1	1	yes	characteristic
219	C₄×C₁₉	#466	1	1	yes	characteristic
220	Dic₁₉	—	8	2	no	—
221	C₂×AGL(1,ℤ/8)	—	2	1	no	—
222	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
223	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
224	#460	—	2	1	no	—
225	#460	Dic₁₉	1	2	yes	complemented
226	#459	—	2	1	no	—
227	#459	Dic₁₉	1	2	yes	complemented
228	C₈×Q₈	—	38	1	no	—
229	C₈×D₄	—	38	2	no	—
230	C₈×D₄	—	38	1	no	—
231	#431	—	19	1	no	—
232	#431	—	38	1	no	—
233	#423	—	19	1	no	—
234	#423	C₂×D₁₉	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	19	1	no	—
236	C₂×C₄⋊C₈	—	38	1	no	—
237	C₂×#104	—	38	1	no	—
238	#418	—	2	1	no	—
239	C₂×#102	—	38	2	no	—
240	C₄×C₄⋊C₄	—	19	1	no	—
241	#339	—	38	1	no	—
242	#331	—	38	1	no	—
243	#331	—	38	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	4	2	no	—
247	C₂×C₁₉	—	16	2	no	—
248	C₂×C₁₉	#1883	1	1	yes	characteristic
249	C₂×C₁₉	#1893	1	1	yes	characteristic
250	C₂×C₁₉	#1903	1	1	yes	characteristic
251	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	AGL(1,ℤ/8)	—	4	2	no	—
256	AGL(1,ℤ/8)	—	4	2	no	—
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	38	1	no	—
261	C₂²×C₈	—	19	2	no	—
262	C₂²×C₈	—	38	2	no	—
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	—	2	1	no	—
266	#127	C₂×Dic₁₉	1	2	yes	—
267	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
268	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
272	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
273	#117	—	2	1	no	—
274	#117	C₂²⋊D₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	—	38	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	38	1	no	—
278	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	19	1	no	—
281	C₄⋊C₈	—	19	1	no	—
282	C₄⋊C₈	—	38	2	no	—
283	C₄⋊C₈	—	38	1	no	—
284	C₄⋊C₈	—	38	1	no	—
285	C₄⋊C₈	—	38	1	no	—
286	C₄⋊C₈	—	38	1	no	—
287	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
288	#104	—	76	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	76	4	no	—
292	C₂²⋊C₈	—	38	2	no	—
293	C₂²⋊C₈	—	38	1	no	—
294	C₄×C₈	—	38	2	no	—
295	C₄×C₈	—	38	1	no	—
296	#95	—	38	1	no	—
297	C₁₉	#9318	1	1	yes	characteristic, complemented, Sylow
298	C₂⁴	—	4	1	no	—
299	#41	—	2	1	no	—
300	#41	—	2	1	no	—
301	#41	#64525	1	2	yes	—
302	#41	#64526	1	2	yes	—
303	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	8	2	no	—
318	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	#64543	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
326	SD₁₆	—	4	4	no	—
327	D₈	—	4	4	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	76	1	no	—
331	M₁₆	—	76	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	38	1	no	—
334	C₂×C₈	—	38	1	no	—
335	C₂×C₈	—	38	2	no	—
336	C₂×C₈	—	76	2	no	—
337	C₂×C₈	—	76	1	no	—
338	C₂×C₈	—	152	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	38	2	no	—
342	C₄⋊C₄	—	76	1	no	—
343	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
344	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	76	1	no	—
352	C₄²	—	76	1	no	—
353	C₄²	D₄×D₁₉	1	1	yes	characteristic
354	C₄²	#64543	1	1	yes	characteristic
355	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
356	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
357	C₂³	—	2	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	1	no	—
363	C₂³	#10597385	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	#10597289	1	2	yes	complemented
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	D₄	#10597289	1	2	yes	complemented
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	76	2	no	—
391	C₂×C₄	—	152	1	no	—
392	C₂×C₄	—	152	1	no	—
393	C₂×C₄	C₂×#64525	1	1	yes	characteristic
394	C₂×C₄	C₂×#64526	1	1	yes	characteristic
395	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
396	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
397	C₂×C₄	#10597381	1	1	yes	characteristic
398	C₂×C₄	#10597383	1	1	yes	characteristic
399	C₂×C₄	#10597385	1	1	yes	characteristic
400	C₂×C₄	#10597396	1	1	yes	characteristic
401	C₂×C₄	#10597396	1	1	yes	characteristic
402	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	76	2	no	—
405	C₈	—	76	1	no	—
406	C₈	—	76	1	no	—
407	C₈	—	152	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	16	2	no	—
417	C₂²	—	16	2	no	—
418	C₂²	#11926424	1	1	yes	characteristic
419	C₂²	#11926771	1	1	yes	characteristic
420	C₂²	#11926778	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	152	2	no	—
428	C₄	C₂×#10597289	1	1	yes	characteristic
429	C₄	#11926540	1	1	yes	characteristic
430	C₄	#11926710	1	1	yes	characteristic
431	C₄	#11926715	1	1	yes	characteristic
432	C₄	#11926771	1	1	yes	characteristic
433	C₄	#11926778	1	1	yes	characteristic
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	4	2	no	—
437	C₂	—	16	2	no	—
438	C₂	#14564013	1	1	yes	characteristic
439	C₂	#14564064	1	1	yes	characteristic
440	C₂	#14564117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3038	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3038	D₁₉
hypocenter	C₁₉	#9318
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3038

Complements

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

N	H ≅ G/N	type
1. #14572746	C₂	semidirect
2. #14564563	C₂	semidirect
3. #14563655	C₂	semidirect
4. #14562303	C₂	semidirect
5. #14561536	C₂	semidirect
6. #14561509	C₂	semidirect
26. C₁₉×#460	C₄	semidirect
28. C₁₉×#459	C₄	semidirect
145. Q₈×C₁₉	#102	semidirect
158. D₄×C₁₉	#102	semidirect
225. #460	Dic₁₉	semidirect
227. #459	Dic₁₉	semidirect
297. C₁₉	#9318	semidirect
365. Q₈	#10597289	semidirect
378. D₄	#10597289	semidirect

Maximal subgroups

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

subgroup	index
#14572746	2
#14564563	2
#14563655	2
#14562303	2
#14561536	2
#14561509	2
C₁₉×#3038	2
#9318	19