Subgroups — #18077435

Order 4864.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572301	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562034	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562017	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3035	C₂	1	1	yes	maximal, characteristic
8	#11926605	—	2	2	no	—
9	#11926601	—	2	1	no	—
10	#11926597	—	2	1	no	—
11	#11926597	C₂²	1	1	yes	characteristic
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	#11926511	—	2	1	no	—
15	#11926500	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
18	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₂×C₁₉×#135	—	2	1	no	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#464	—	2	1	no	—
26	C₁₉×#463	—	2	1	no	—
27	C₁₉×#462	C₄	1	1	yes	characteristic
28	C₁₉×#461	C₄	1	1	yes	characteristic
29	C₁₉×#460	C₄	1	1	yes	characteristic
30	C₁₉×#459	C₄	1	1	yes	characteristic
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₉×#416	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
35	C₁₉×#135	—	4	2	no	—
36	C₁₉×#135	—	4	2	no	—
37	C₂×Q₁₆×C₁₉	—	2	1	no	—
38	C₂×SD₁₆×C₁₉	—	2	1	no	—
39	C₂×SD₁₆×C₁₉	—	2	1	no	—
40	C₂×D₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
43	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
44	C₁₉×#124	—	2	1	no	—
45	C₁₉×#121	—	2	1	no	—
46	C₁₉×#121	—	2	1	no	—
47	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	—	2	1	no	—
50	C₄×D₄×C₁₉	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×#64520	—	2	1	no	—
60	C₂²×C₁₉⋊C₈	—	2	1	no	—
61	C₂²×C₁₉⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
70	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	1	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)	D₄	1	1	yes	characteristic
76	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
77	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
78	#10597260	—	2	2	no	—
79	C₄×C₁₉⋊C₈	—	2	2	no	—
80	C₄×C₁₉⋊C₈	—	2	1	no	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	#41×C₁₉	—	2	1	no	—
84	#41×C₁₉	—	2	1	no	—
85	#41×C₁₉	—	2	1	no	—
86	#41×C₁₉	—	2	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	#41×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	Q₁₆×C₁₉	—	4	2	no	—
107	SD₁₆×C₁₉	—	4	2	no	—
108	SD₁₆×C₁₉	—	4	2	no	—
109	D₈×C₁₉	—	4	2	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	2	1	no	—
126	C₄²×C₁₉	—	2	1	no	—
127	C₄²×C₁₉	—	2	1	no	—
128	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	#64520	—	4	1	no	—
133	#64520	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	1	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	2	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	#8996	—	19	1	no	maximal, Sylow
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	#123	1	1	yes	characteristic
147	Q₈×C₁₉	—	2	1	no	—
148	Q₈×C₁₉	—	2	1	no	—
149	Q₈×C₁₉	—	4	1	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	2	1	no	—
152	D₄×C₁₉	—	2	1	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
184	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₈×C₁₉	—	4	1	no	—
187	C₈×C₁₉	—	4	1	no	—
188	C₁₉⋊C₈	—	4	2	no	—
189	C₁₉⋊C₈	—	4	1	no	—
190	C₁₉⋊C₈	—	4	1	no	—
191	C₁₉⋊C₈	—	4	2	no	—
192	C₁₉⋊C₈	—	8	1	no	—
193	#3035	D₁₉	1	1	yes	characteristic
194	#2925	—	19	1	no	—
195	#1492	—	19	1	no	—
196	#1480	—	19	1	no	—
197	#1476	—	19	1	no	—
198	#1301	—	19	1	no	—
199	#1277	—	19	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	#386	1	1	yes	characteristic
209	C₂²×C₁₉	#482	1	1	yes	characteristic
210	C₂²×C₁₉	#482	1	1	yes	characteristic
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	4	1	no	—
215	C₄×C₁₉	—	4	1	no	—
216	C₄×C₁₉	—	4	1	no	—
217	C₄×C₁₉	—	8	1	no	—
218	C₄×C₁₉	#416	1	1	yes	characteristic
219	C₄×C₁₉	#418	1	1	yes	characteristic
220	C₄×C₁₉	#443	1	1	yes	characteristic
221	C₄×C₁₉	#444	1	1	yes	characteristic
222	C₄×C₁₉	#449	1	1	yes	characteristic
223	C₄×C₁₉	#449	1	1	yes	characteristic
224	C₂×#135	—	2	1	no	—
225	#532	C₂×D₁₉	1	1	yes	characteristic
226	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
227	#464	—	2	1	no	—
228	#463	—	2	1	no	—
229	#462	Dic₁₉	1	1	yes	characteristic
230	#461	Dic₁₉	1	1	yes	characteristic
231	#460	Dic₁₉	1	1	yes	characteristic
232	#459	Dic₁₉	1	1	yes	characteristic
233	#433	—	38	2	no	—
234	#432	—	38	1	no	—
235	#431	—	19	1	no	—
236	#431	—	38	1	no	—
237	#423	—	19	1	no	—
238	C₂×C₄⋊C₈	—	19	1	no	—
239	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
240	#416	—	2	1	no	—
241	#408	—	38	1	no	—
242	#405	—	38	1	no	—
243	C₂×C₄×C₈	—	19	1	no	—
244	Q₈⋊C₈	—	38	1	no	—
245	D₄⋊C₈	—	38	1	no	—
246	D₄⋊C₈	—	38	1	no	—
247	D₄⋊C₈	—	38	2	no	—
248	D₄⋊C₈	—	38	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	8	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	#1875	1	1	yes	characteristic
254	C₂×C₁₉	#1876	1	1	yes	characteristic
255	C₂×C₁₉	#1881	1	1	yes	characteristic
256	C₂×#41	—	2	1	no	—
257	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
258	#135	—	4	2	no	—
259	#135	—	4	2	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×SD₁₆	—	2	1	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×M₁₆	—	38	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	38	1	no	—
267	C₂²×C₈	—	38	1	no	—
268	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
269	#127	C₂×Dic₁₉	1	1	yes	characteristic
270	#124	—	2	1	no	—
271	#121	—	2	1	no	—
272	#121	—	2	1	no	—
273	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
274	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
280	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	19	1	no	—
287	C₄⋊C₈	—	19	1	no	—
288	C₄⋊C₈	—	19	2	no	—
289	C₄⋊C₈	—	38	1	no	—
290	C₄⋊C₈	—	38	1	no	—
291	C₄⋊C₈	—	38	1	no	—
292	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
293	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
294	#103	—	2	1	no	—
295	#103	—	2	1	no	—
296	#102	—	2	1	no	—
297	#102	—	2	1	no	—
298	C₂²⋊C₈	—	38	2	no	—
299	C₂²⋊C₈	—	38	2	no	—
300	C₂²⋊C₈	—	38	1	no	—
301	#97	—	38	2	no	—
302	C₄×C₈	—	38	2	no	—
303	C₄×C₈	—	38	1	no	—
304	C₄×C₈	—	38	1	no	—
305	C₄×C₈	—	38	1	no	—
306	C₁₉	#8996	1	1	yes	characteristic, complemented, Sylow
307	#41	—	2	1	no	—
308	#41	—	2	1	no	—
309	#41	—	2	1	no	—
310	#41	—	2	1	no	—
311	#41	—	4	1	no	—
312	#41	—	4	1	no	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	#64543	1	1	yes	characteristic
328	C₂²×C₄	#64543	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
330	Q₁₆	—	4	2	no	—
331	SD₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	D₈	—	4	2	no	—
334	M₁₆	—	76	1	no	—
335	M₁₆	—	76	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	38	2	no	—
341	C₂×C₈	—	38	1	no	—
342	C₂×C₈	—	38	2	no	—
343	C₂×C₈	—	38	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	—	76	1	no	—
346	C₂×C₈	—	76	1	no	—
347	C₂×C₈	—	76	1	no	—
348	C₂×C₈	—	76	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
354	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	D₄×D₁₉	1	1	yes	characteristic
364	C₄²	D₄×D₁₉	1	1	yes	characteristic
365	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	#10597381	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	—	2	1	no	—
372	Q₈	—	4	1	no	—
373	Q₈	—	4	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	1	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	8	1	no	—
397	C₂×C₄	—	8	1	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	#10597378	1	1	yes	characteristic
400	C₂×C₄	#10597378	1	1	yes	characteristic
401	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
402	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
403	C₂×C₄	#10597383	1	1	yes	characteristic
404	C₂×C₄	#10597385	1	1	yes	characteristic
405	C₂×C₄	#10597385	1	1	yes	characteristic
406	C₂×C₄	#10597396	1	1	yes	characteristic
407	C₂×C₄	#10597396	1	1	yes	characteristic
408	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	76	2	no	—
412	C₈	—	76	1	no	—
413	C₈	—	76	1	no	—
414	C₈	—	76	2	no	—
415	C₈	—	152	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	#11926424	1	1	yes	characteristic
425	C₂²	#11926865	1	1	yes	characteristic
426	C₂²	#11926865	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	8	1	no	—
434	C₄	#11926540	1	1	yes	characteristic
435	C₄	#11926549	1	1	yes	characteristic
436	C₄	#11926661	1	1	yes	characteristic
437	C₄	#11926666	1	1	yes	characteristic
438	C₄	#11926687	1	1	yes	characteristic
439	C₄	#11926687	1	1	yes	characteristic
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	8	1	no	—
443	C₂	—	16	1	no	—
444	C₂	#14563958	1	1	yes	characteristic
445	C₂	#14563964	1	1	yes	characteristic
446	C₂	#14563999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3035	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3035	D₁₉
hypocenter	C₁₉	#8996
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. #14572301	C₂	semidirect
2. #14562086	C₂	semidirect
3. #14562034	C₂	semidirect
4. #14562017	C₂	semidirect
5. #14561532	C₂	semidirect
6. #14561469	C₂	semidirect
306. C₁₉	#8996	semidirect

Maximal subgroups

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

subgroup	index
#14572301	2
#14562086	2
#14562034	2
#14562017	2
#14561532	2
#14561469	2
C₁₉×#3035	2
#8996	19