Subgroups — #18076398

Order 4864.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926600	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926297	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926294	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	#11926600	—	2	2	no	—
10	#11926600	—	2	2	no	—
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	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
17	C₂×#10597272	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926298	—	2	1	no	—
20	#11926298	C₄	1	1	yes	characteristic
21	#11926298	C₄	1	1	yes	characteristic
22	#11926297	—	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	C₄²×D₁₉	—	2	1	no	—
43	C₄²×D₁₉	—	2	1	no	—
44	C₄²×D₁₉	—	2	1	no	—
45	C₄²×D₁₉	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	—	2	1	no	—
48	C₁₉×C₄⋊C₈	—	2	1	no	—
49	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	(C₂×D₁₉)⋊C₈	—	2	4	no	—
53	(C₂×D₁₉)⋊C₈	—	2	2	no	—
54	(C₂×D₁₉)⋊C₈	—	2	2	no	—
55	(C₂×D₁₉)⋊C₈	—	4	2	no	—
56	#10597272	—	2	4	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
61	C₄×C₁₉⋊C₈	—	2	1	no	—
62	C₄×C₁₉⋊C₈	—	2	1	no	—
63	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
67	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×D₁₉	—	2	2	no	—
71	C₂×C₄×D₁₉	—	2	1	no	—
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	—	2	1	no	—
74	C₂×C₄×D₁₉	—	2	1	no	—
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	—	4	1	no	—
86	C₂×C₈×C₁₉	—	2	1	no	—
87	C₂×C₈×C₁₉	—	2	1	no	—
88	C₂×C₈×C₁₉	—	2	1	no	—
89	C₂×C₈×C₁₉	—	2	2	no	—
90	C₂×C₈×C₁₉	—	2	1	no	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
98	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₉	#41	1	1	yes	characteristic
101	C₄²×C₁₉	#41	1	1	yes	characteristic
102	C₄×Dic₁₉	—	2	1	no	—
103	C₄×Dic₁₉	—	2	1	no	—
104	C₄×Dic₁₉	—	2	1	no	—
105	C₄×Dic₁₉	—	2	1	no	—
106	C₄×Dic₁₉	—	2	1	no	—
107	C₄×Dic₁₉	—	2	1	no	—
108	C₂×C₁₉⋊C₈	—	2	1	no	—
109	C₂×C₁₉⋊C₈	—	2	1	no	—
110	C₂×C₁₉⋊C₈	—	2	1	no	—
111	C₂×C₁₉⋊C₈	—	2	2	no	—
112	C₂×C₁₉⋊C₈	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	2	1	no	—
114	C₂×C₁₉⋊C₈	—	4	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	M₁₆	1	2	yes	—
120	#8834	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂²×D₁₉	—	2	1	no	—
123	C₂²×D₁₉	—	2	1	no	—
124	C₂²×D₁₉	—	2	1	no	—
125	C₂²×D₁₉	—	2	1	no	—
126	C₂²×D₁₉	—	2	1	no	—
127	C₂²×D₁₉	—	2	1	no	—
128	C₂²×D₁₉	#108	1	2	yes	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
145	C₂×Dic₁₉	—	2	1	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	—	2	1	no	—
148	C₂×Dic₁₉	—	2	1	no	—
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₄×D₁₉	—	4	2	no	—
155	C₄×D₁₉	—	4	2	no	—
156	C₄×D₁₉	—	4	1	no	—
157	C₄×D₁₉	—	4	1	no	—
158	C₄×D₁₉	—	4	1	no	—
159	C₄×D₁₉	—	4	1	no	—
160	C₄×D₁₉	—	4	1	no	—
161	C₄×D₁₉	—	4	1	no	—
162	C₄×D₁₉	—	4	1	no	—
163	C₄×D₁₉	—	4	1	no	—
164	C₈×C₁₉	—	2	2	no	—
165	C₈×C₁₉	—	4	1	no	—
166	C₈×C₁₉	—	4	2	no	—
167	C₈×C₁₉	—	8	1	no	—
168	C₁₉⋊C₈	—	2	2	no	—
169	C₁₉⋊C₈	—	4	1	no	—
170	C₁₉⋊C₈	—	4	2	no	—
171	C₁₉⋊C₈	—	8	1	no	—
172	C₂×#432	—	19	1	no	—
173	#1797	—	19	1	no	—
174	C₄×C₂²⋊C₈	—	19	1	no	—
175	C₂×#335	—	19	1	no	—
176	C₂×#334	—	19	1	no	—
177	#1277	—	19	1	no	—
178	#1277	D₁₉	1	1	yes	characteristic, complemented
179	C₂²×C₁₉	#385	1	1	yes	characteristic
180	C₂²×C₁₉	#423	1	1	yes	characteristic
181	C₂²×C₁₉	#424	1	1	yes	characteristic
182	C₂²×C₁₉	#427	1	1	yes	characteristic
183	C₂²×C₁₉	#428	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
185	C₂²×C₁₉	#430	1	1	yes	characteristic
186	C₂×D₁₉	—	2	2	no	—
187	C₂×D₁₉	—	2	2	no	—
188	C₂×D₁₉	—	2	2	no	—
189	C₂×D₁₉	—	4	1	no	—
190	C₂×D₁₉	—	4	1	no	—
191	C₂×D₁₉	—	4	1	no	—
192	C₂×D₁₉	—	4	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	#435	1	1	yes	characteristic
196	C₄×C₁₉	#435	1	1	yes	characteristic
197	C₄×C₁₉	#436	1	1	yes	characteristic
198	C₄×C₁₉	#436	1	1	yes	characteristic
199	C₄×C₁₉	#449	1	1	yes	characteristic
200	C₄×C₁₉	#452	1	1	yes	characteristic
201	C₄×C₁₉	#482	1	1	yes	characteristic
202	C₄×C₁₉	#485	1	1	yes	characteristic
203	Dic₁₉	—	4	1	no	—
204	Dic₁₉	—	4	1	no	—
205	Dic₁₉	—	4	1	no	—
206	C₂²×C₄²	—	19	1	no	—
207	#432	—	38	2	no	—
208	#432	—	38	2	no	—
209	C₂×C₄⋊C₈	—	19	1	no	—
210	C₂×C₄⋊C₈	—	19	1	no	—
211	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	—	19	1	no	—
214	C₂×C₂²⋊C₈	—	19	1	no	—
215	C₂×C₂²⋊C₈	—	38	1	no	—
216	C₂×C₂²⋊C₈	—	38	1	no	—
217	C₂×#97	—	38	1	no	—
218	C₂×C₄×C₈	—	19	1	no	—
219	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
220	#336	—	19	1	no	—
221	#336	—	19	1	no	—
222	#336	—	38	1	no	—
223	#335	—	38	2	no	—
224	#334	—	38	2	no	—
225	C₂×C₁₉	#1568	1	1	yes	characteristic
226	C₂×C₁₉	#1569	1	1	yes	characteristic
227	C₂×C₁₉	#1572	1	1	yes	characteristic
228	C₂×C₁₉	#1573	1	1	yes	characteristic
229	C₂×C₁₉	#1851	1	1	yes	characteristic
230	C₂×C₁₉	#1854	1	1	yes	characteristic
231	C₂×C₁₉	#1855	1	1	yes	characteristic
232	D₁₉	—	4	2	no	—
233	C₂³×C₄	—	19	1	no	—
234	C₂³×C₄	—	19	1	no	—
235	C₂³×C₄	—	19	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	19	1	no	—
239	C₂²×C₈	—	19	1	no	—
240	C₂²×C₈	—	38	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
243	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
244	C₂×C₄²	—	19	1	no	—
245	C₂×C₄²	—	19	1	no	—
246	C₂×C₄²	—	19	1	no	—
247	C₂×C₄²	—	38	1	no	—
248	C₂×C₄²	—	38	1	no	—
249	C₂×C₄²	—	38	1	no	—
250	C₂×C₄²	—	38	1	no	—
251	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	19	2	no	—
256	C₄⋊C₈	—	38	1	no	—
257	C₄⋊C₈	—	38	1	no	—
258	C₄⋊C₈	—	38	1	no	—
259	C₄⋊C₈	D₇₆	1	2	yes	—
260	C₂²⋊C₈	—	38	2	no	—
261	C₂²⋊C₈	—	38	4	no	—
262	C₂²⋊C₈	—	38	2	no	—
263	C₂²⋊C₈	—	76	2	no	—
264	#97	—	38	4	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	38	1	no	—
268	C₄×C₈	—	38	1	no	—
269	C₁₉	#8834	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴	—	19	1	no	—
271	C₂²×C₄	—	19	1	no	—
272	C₂²×C₄	—	19	1	no	—
273	C₂²×C₄	—	19	1	no	—
274	C₂²×C₄	—	38	2	no	—
275	C₂²×C₄	—	38	1	no	—
276	C₂²×C₄	—	38	1	no	—
277	C₂²×C₄	—	38	1	no	—
278	C₂²×C₄	—	38	1	no	—
279	C₂²×C₄	—	38	1	no	—
280	C₂²×C₄	—	38	1	no	—
281	C₂²×C₄	—	38	1	no	—
282	C₂²×C₄	—	38	1	no	—
283	C₂²×C₄	—	38	1	no	—
284	C₂²×C₄	—	38	1	no	—
285	C₂²×C₄	—	38	1	no	—
286	C₂²×C₄	—	38	1	no	—
287	C₂²×C₄	—	38	1	no	—
288	C₂²×C₄	—	38	1	no	—
289	C₂²×C₄	—	76	1	no	—
290	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	19	2	no	—
305	C₂×C₈	—	38	1	no	—
306	C₂×C₈	—	38	1	no	—
307	C₂×C₈	—	38	1	no	—
308	C₂×C₈	—	38	2	no	—
309	C₂×C₈	—	38	1	no	—
310	C₂×C₈	—	38	1	no	—
311	C₂×C₈	—	76	1	no	—
312	C₂×C₈	—	76	1	no	—
313	C₂×C₈	—	76	1	no	—
314	C₂×C₈	—	76	1	no	—
315	C₂×C₈	—	76	1	no	—
316	C₂×C₈	#64515	1	2	yes	—
317	C₄²	—	38	1	no	—
318	C₄²	—	38	1	no	—
319	C₄²	—	38	1	no	—
320	C₄²	—	38	1	no	—
321	C₄²	—	38	1	no	—
322	C₄²	—	38	1	no	—
323	C₄²	C₂×D₇₆	1	1	yes	characteristic
324	C₄²	#64541	1	1	yes	characteristic
325	C₄²	D₄×D₁₉	1	1	yes	characteristic
326	C₄²	#64543	1	1	yes	characteristic
327	C₂³	—	19	2	no	—
328	C₂³	—	38	1	no	—
329	C₂³	—	38	1	no	—
330	C₂³	—	38	1	no	—
331	C₂³	—	38	1	no	—
332	C₂³	—	38	1	no	—
333	C₂³	—	38	1	no	—
334	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	38	1	no	—
338	C₂×C₄	—	38	1	no	—
339	C₂×C₄	—	38	1	no	—
340	C₂×C₄	—	38	1	no	—
341	C₂×C₄	—	38	1	no	—
342	C₂×C₄	—	38	1	no	—
343	C₂×C₄	—	38	1	no	—
344	C₂×C₄	—	38	1	no	—
345	C₂×C₄	—	38	1	no	—
346	C₂×C₄	—	76	2	no	—
347	C₂×C₄	—	76	2	no	—
348	C₂×C₄	—	76	1	no	—
349	C₂×C₄	—	76	1	no	—
350	C₂×C₄	—	76	1	no	—
351	C₂×C₄	—	76	1	no	—
352	C₂×C₄	—	76	1	no	—
353	C₂×C₄	—	76	1	no	—
354	C₂×C₄	—	76	1	no	—
355	C₂×C₄	—	76	1	no	—
356	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
357	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	#10597328	1	1	yes	characteristic
359	C₂×C₄	#10597329	1	1	yes	characteristic
360	C₂×C₄	#10597342	1	1	yes	characteristic
361	C₂×C₄	#10597343	1	1	yes	characteristic
362	C₂×C₄	C₂×#64515	1	1	yes	characteristic
363	C₂×C₄	#10597347	1	1	yes	characteristic
364	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
365	C₂×C₄	#10597353	1	1	yes	characteristic
366	C₂×C₄	#10597358	1	1	yes	characteristic
367	C₂×C₄	#10597360	1	1	yes	characteristic
368	C₂×C₄	#10597361	1	1	yes	characteristic
369	C₂×C₄	#10597365	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	8	1	no	—
374	C₈	—	38	2	no	—
375	C₈	—	76	1	no	—
376	C₈	—	76	2	no	—
377	C₈	—	152	1	no	—
378	C₂²	—	38	2	no	—
379	C₂²	—	38	2	no	—
380	C₂²	—	38	2	no	—
381	C₂²	—	76	1	no	—
382	C₂²	—	76	1	no	—
383	C₂²	—	76	1	no	—
384	C₂²	—	76	1	no	—
385	C₂²	#11926418	1	1	yes	characteristic
386	C₂²	#11926566	1	1	yes	characteristic
387	C₂²	#11926569	1	1	yes	characteristic
388	C₂²	#11926581	1	1	yes	characteristic
389	C₂²	#11926583	1	1	yes	characteristic
390	C₂²	#108×D₁₉	1	1	yes	characteristic
391	C₂²	#11926591	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	76	1	no	—
395	C₄	—	76	1	no	—
396	C₄	—	76	1	no	—
397	C₄	#11926612	1	1	yes	characteristic
398	C₄	#11926617	1	1	yes	characteristic
399	C₄	#11926619	1	1	yes	characteristic
400	C₄	#11926623	1	1	yes	characteristic
401	C₄	#11926692	1	1	yes	characteristic
402	C₄	#11926707	1	1	yes	characteristic
403	C₄	#11926866	1	1	yes	characteristic
404	C₄	#11926884	1	1	yes	characteristic
405	C₂	—	76	2	no	—
406	C₂	#14562397	1	1	yes	characteristic
407	C₂	#14562399	1	1	yes	characteristic
408	C₂	#14562414	1	1	yes	characteristic
409	C₂	#14562417	1	1	yes	characteristic
410	C₂	#14563819	1	1	yes	characteristic
411	C₂	#14563837	1	1	yes	characteristic
412	C₂	#14563841	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
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	#8834
LCS	G ▷ C₂²×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×#11926297	C₂	semidirect
5. C₂×#11926294	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₁₉×#1277	C₂	semidirect
178. #1277	D₁₉	semidirect
269. C₁₉	#8834	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926600	2
#14563612	2
C₄×(C₂×D₁₉)⋊C₈	2
C₂×#11926297	2
C₂×#11926294	2
#14561469	2
C₁₉×#1277	2
#8834	19