Subgroups — #18077296

Order 4864.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926831	C₂	1	1	yes	maximal, characteristic
2	#14566582	C₂	1	1	yes	maximal, characteristic
3	#14564438	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×#10597338	—	2	1	no	—
10	#11926831	—	2	2	no	—
11	#11926831	C₄	1	4	yes	complemented
12	C₂×#10597265	—	2	1	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597292	—	2	2	no	—
15	C₂×#10597266	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926446	—	2	1	no	—
18	#11926436	—	2	2	no	—
19	#11926414	C₂²	1	1	yes	characteristic
20	#11926401	—	2	1	no	—
21	C₄×C₄⋊Dic₁₉	—	2	1	no	—
22	#11926271	—	2	2	no	—
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#340	—	2	1	no	—
27	C₁₉×#340	—	2	1	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×D₇₆	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
43	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
45	C₂×C₄⋊Dic₁₉	—	2	1	no	—
46	C₂×C₄⋊Dic₁₉	—	2	1	no	—
47	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
49	C₂×C₄×Dic₁₉	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	#10597338	—	4	2	no	—
53	#10597338	—	4	2	no	—
54	C₄×D₇₆	—	2	1	no	—
55	C₄×D₇₆	—	2	1	no	—
56	C₄×D₇₆	C₂×C₄	1	2	yes	—
57	C₄×D₇₆	D₄	1	2	yes	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×#95	—	2	1	no	—
61	#10597292	—	4	4	no	—
62	C₁₉⋊#95	—	2	2	no	—
63	#10597266	—	2	4	no	—
64	#10597265	—	2	4	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₂³×D₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	2	no	—
71	C₂×Q₈×C₁₉	—	4	2	no	—
72	C₂×Q₈×C₁₉	—	4	2	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	—	2	2	no	—
82	C₂×D₇₆	—	2	1	no	—
83	C₂×D₇₆	—	2	1	no	—
84	C₂×D₇₆	—	2	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×D₁₉	—	2	2	no	—
89	C₂×C₄×D₁₉	—	2	2	no	—
90	C₂×C₄×D₁₉	—	4	1	no	—
91	C₂×C₄×D₁₉	—	4	1	no	—
92	C₂×C₄×D₁₉	—	4	1	no	—
93	C₂×C₄×D₁₉	—	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	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	(C₂×D₁₉)⋊C₄	—	2	2	no	—
112	(C₂×D₁₉)⋊C₄	—	2	2	no	—
113	(C₂×D₁₉)⋊C₄	—	4	4	no	—
114	(C₂×D₁₉)⋊C₄	—	8	2	no	—
115	C₄⋊Dic₁₉	—	2	1	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	4	1	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	2	no	—
121	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
122	C₄×Dic₁₉	—	4	4	no	—
123	C₂×C₁₉⋊C₈	—	2	2	no	—
124	C₂×C₁₉⋊C₈	—	2	2	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	#8976	—	19	1	no	maximal, Sylow
130	C₂³×C₁₉	#120	1	1	yes	characteristic
131	C₂²×D₁₉	—	2	2	no	—
132	C₂²×D₁₉	—	4	1	no	—
133	C₂²×D₁₉	—	4	1	no	—
134	C₂²×D₁₉	—	4	1	no	—
135	C₂²×D₁₉	—	4	1	no	—
136	C₂²×D₁₉	—	4	1	no	—
137	C₂²×D₁₉	—	4	1	no	—
138	Q₈×C₁₉	—	4	4	no	—
139	Q₈×C₁₉	—	8	2	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	8	1	no	—
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
165	C₂×Dic₁₉	—	2	2	no	—
166	C₂×Dic₁₉	—	4	1	no	—
167	C₂×Dic₁₉	—	4	1	no	—
168	C₂×Dic₁₉	—	4	2	no	—
169	C₂×Dic₁₉	—	4	2	no	—
170	C₂×Dic₁₉	—	4	2	no	—
171	D₇₆	—	2	2	no	—
172	D₇₆	—	2	2	no	—
173	D₇₆	—	4	1	no	—
174	D₇₆	—	4	1	no	—
175	C₄×D₁₉	—	4	2	no	—
176	C₄×D₁₉	—	4	2	no	—
177	C₄×D₁₉	—	4	2	no	—
178	C₄×D₁₉	—	4	2	no	—
179	C₈×C₁₉	—	8	1	no	—
180	C₁₉⋊C₈	—	4	2	no	—
181	C₁₉⋊C₈	—	4	2	no	—
182	C₂×#476	—	19	1	no	—
183	#2354	—	19	1	no	—
184	#1987	D₁₉	1	1	yes	characteristic, complemented
185	#1956	—	19	1	no	—
186	C₂×D₄⋊C₈	—	19	1	no	—
187	#1296	—	19	1	no	—
188	#1279	—	19	1	no	—
189	C₂²×C₁₉	#386	1	1	yes	characteristic
190	C₂²×C₁₉	#450	1	1	yes	characteristic
191	C₂²×C₁₉	#452	1	1	yes	characteristic
192	C₂²×C₁₉	#452	1	1	yes	characteristic
193	C₂²×C₁₉	#452	1	1	yes	characteristic
194	C₂²×C₁₉	#453	1	1	yes	characteristic
195	C₂²×C₁₉	#454	1	1	yes	characteristic
196	C₂×D₁₉	—	4	2	no	—
197	C₂×D₁₉	—	4	2	no	—
198	C₂×D₁₉	—	4	2	no	—
199	C₂×D₁₉	—	8	1	no	—
200	C₂×D₁₉	—	8	1	no	—
201	C₂×D₁₉	—	8	1	no	—
202	C₂×D₁₉	—	8	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	#416	1	1	yes	characteristic
209	C₄×C₁₉	#419	1	1	yes	characteristic
210	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
211	C₄×C₁₉	#440	1	1	yes	characteristic
212	C₄×C₁₉	#461	1	1	yes	characteristic
213	C₄×C₁₉	#463	1	1	yes	characteristic
214	C₄×C₁₉	#485	1	1	yes	characteristic
215	C₄×C₁₉	#485	1	1	yes	characteristic
216	Dic₁₉	—	4	2	no	—
217	Dic₁₉	—	8	2	no	—
218	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
219	C₂×C₄×D₄	—	19	1	no	—
220	C₂×#117	—	38	1	no	—
221	#476	—	19	4	no	—
222	#476	—	38	2	no	—
223	C₂×#106	—	38	1	no	—
224	C₂×C₄⋊C₈	—	19	1	no	—
225	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
226	C₂×#103	—	38	2	no	—
227	C₂×#102	—	38	1	no	—
228	C₂×C₄×C₈	—	19	1	no	—
229	#390	—	38	1	no	—
230	#388	—	38	2	no	—
231	#384	—	19	1	no	—
232	#380	—	38	1	no	—
233	C₄×C₄⋊C₄	—	38	1	no	—
234	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
235	#340	—	2	1	no	—
236	#340	—	2	1	no	—
237	D₄⋊C₈	—	38	2	no	—
238	C₂×C₁₉	#1631	1	1	yes	characteristic
239	C₂×C₁₉	#1634	1	1	yes	characteristic
240	C₂×C₁₉	#1635	1	1	yes	characteristic
241	C₂×C₁₉	#1638	1	1	yes	characteristic
242	C₂×C₁₉	#1873	1	1	yes	characteristic
243	C₂×C₁₉	#1877	1	1	yes	characteristic
244	C₂×C₁₉	#1883	1	1	yes	characteristic
245	D₁₉	—	8	2	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	19	1	no	—
248	C₂³×C₄	—	38	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	38	1	no	—
251	C₂²×C₈	—	38	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
256	C₄×D₄	—	19	2	no	—
257	C₄×D₄	—	19	2	no	—
258	C₄×D₄	—	38	1	no	—
259	C₄×D₄	—	38	1	no	—
260	#117	—	76	2	no	—
261	#117	—	76	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	19	1	no	—
265	C₂×C₄⋊C₄	—	19	2	no	—
266	C₂×C₄⋊C₄	—	38	1	no	—
267	C₂×C₄⋊C₄	—	38	1	no	—
268	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	38	1	no	—
271	C₂×C₂²⋊C₄	—	38	2	no	—
272	C₂×C₂²⋊C₄	—	38	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	38	2	no	—
275	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
276	#106	—	38	4	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	19	2	no	—
280	C₄⋊C₈	—	38	1	no	—
281	#103	—	76	4	no	—
282	#102	—	38	4	no	—
283	C₄×C₈	—	38	1	no	—
284	C₄×C₈	—	38	1	no	—
285	#95	—	2	1	no	—
286	#95	—	38	2	no	—
287	C₁₉	#8976	1	1	yes	characteristic, complemented, Sylow
288	C₂⁴	—	38	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	19	2	no	—
294	C₂×D₄	—	38	1	no	—
295	C₂×D₄	—	38	1	no	—
296	C₂×D₄	—	38	1	no	—
297	C₂×D₄	—	38	1	no	—
298	C₂×D₄	—	38	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	38	1	no	—
303	C₂²×C₄	—	38	2	no	—
304	C₂²×C₄	—	38	2	no	—
305	C₂²×C₄	—	38	2	no	—
306	C₂²×C₄	—	76	1	no	—
307	C₂²×C₄	—	76	1	no	—
308	C₂²×C₄	—	76	1	no	—
309	C₂²×C₄	—	76	1	no	—
310	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	38	2	no	—
317	C₂×C₈	—	38	2	no	—
318	C₂×C₈	—	76	1	no	—
319	C₂×C₈	—	76	1	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	19	2	no	—
330	C₄⋊C₄	—	38	1	no	—
331	C₄⋊C₄	—	76	2	no	—
332	C₄⋊C₄	—	76	1	no	—
333	C₄⋊C₄	—	76	1	no	—
334	C₄⋊C₄	—	76	1	no	—
335	C₄⋊C₄	—	76	1	no	—
336	C₄⋊C₄	#64527	1	2	yes	—
337	C₂²⋊C₄	—	38	2	no	—
338	C₂²⋊C₄	—	38	2	no	—
339	C₂²⋊C₄	—	76	4	no	—
340	C₂²⋊C₄	—	152	2	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	76	4	no	—
344	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
345	C₄²	#64541	1	1	yes	characteristic
346	C₄²	D₄×D₁₉	1	1	yes	characteristic
347	C₄²	#64543	1	1	yes	characteristic
348	C₂³	—	38	2	no	—
349	C₂³	—	76	1	no	—
350	C₂³	—	76	1	no	—
351	C₂³	—	76	1	no	—
352	C₂³	—	76	1	no	—
353	C₂³	—	76	1	no	—
354	C₂³	—	76	1	no	—
355	C₂³	#10597383	1	1	yes	characteristic
356	Q₈	—	4	4	no	—
357	Q₈	—	8	2	no	—
358	D₄	—	38	2	no	—
359	D₄	—	38	2	no	—
360	D₄	—	76	1	no	—
361	D₄	—	76	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	38	2	no	—
374	C₂×C₄	—	76	1	no	—
375	C₂×C₄	—	76	1	no	—
376	C₂×C₄	—	76	2	no	—
377	C₂×C₄	—	76	2	no	—
378	C₂×C₄	—	76	2	no	—
379	C₂×C₄	—	76	2	no	—
380	C₂×C₄	—	76	2	no	—
381	C₂×C₄	—	76	2	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
384	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
385	C₂×C₄	#10597329	1	1	yes	characteristic
386	C₂×C₄	#10597330	1	1	yes	characteristic
387	C₂×C₄	#10597361	1	1	yes	characteristic
388	C₂×C₄	#10597362	1	1	yes	characteristic
389	C₂×C₄	#10597364	1	1	yes	characteristic
390	C₂×C₄	#10597365	1	1	yes	characteristic
391	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
392	C₂×C₄	#10597384	1	1	yes	characteristic
393	C₂×C₄	C₂×#64527	1	1	yes	characteristic
394	C₂×C₄	#10597388	1	1	yes	characteristic
395	C₂×C₄	#10597395	1	1	yes	characteristic
396	C₂×C₄	#10597396	1	1	yes	characteristic
397	C₈	—	8	1	no	—
398	C₈	—	76	2	no	—
399	C₈	—	76	2	no	—
400	C₂²	—	76	2	no	—
401	C₂²	—	76	2	no	—
402	C₂²	—	76	2	no	—
403	C₂²	—	152	1	no	—
404	C₂²	—	152	1	no	—
405	C₂²	—	152	1	no	—
406	C₂²	—	152	1	no	—
407	C₂²	#11926420	1	1	yes	characteristic
408	C₂²	#11926694	1	1	yes	characteristic
409	C₂²	#11926703	1	1	yes	characteristic
410	C₂²	#11926704	1	1	yes	characteristic
411	C₂²	#11926705	1	1	yes	characteristic
412	C₂²	#11926710	1	1	yes	characteristic
413	C₂²	#11926715	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	76	2	no	—
420	C₄	—	152	2	no	—
421	C₄	#11926539	1	1	yes	characteristic
422	C₄	#11926551	1	1	yes	characteristic
423	C₄	C₄×#64527	1	1	yes	characteristic
424	C₄	#11926642	1	1	yes	characteristic
425	C₄	#11926746	1	1	yes	characteristic
426	C₄	#11926756	1	1	yes	characteristic
427	C₄	#11926883	1	1	yes	characteristic
428	C₄	#11926884	1	1	yes	characteristic
429	C₂	—	152	2	no	—
430	C₂	#14562760	1	1	yes	characteristic
431	C₂	#14562779	1	1	yes	characteristic
432	C₂	#14562784	1	1	yes	characteristic
433	C₂	#14562806	1	1	yes	characteristic
434	C₂	#14563944	1	1	yes	characteristic
435	C₂	#14563972	1	1	yes	characteristic
436	C₂	#14564008	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1987	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1987	D₁₉
hypocenter	C₁₉	#8976
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1987

Complements

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

N	H ≅ G/N	type
3. #14564438	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#1987	C₂	semidirect
11. #11926831	C₄	semidirect
184. #1987	D₁₉	semidirect
287. C₁₉	#8976	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926831	2
#14566582	2
#14564438	2
C₂×#11926271	2
#14561519	2
#14561476	2
C₁₉×#1987	2
#8976	19