Subgroups — #18077275

Order 4864.

664 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	C₂×#11926831	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₇₆	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	—	2	1	no	—
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×D₁₉	—	2	1	no	—
11	#11926831	—	2	2	no	—
12	#11926831	C₄	1	4	yes	complemented
13	C₂×#10597265	—	2	1	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#10597292	—	2	2	no	—
16	C₂×#10597266	—	2	1	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	#11926442	—	2	1	no	—
19	#11926418	—	2	2	no	—
20	#11926414	C₂²	1	1	yes	characteristic
21	#11926401	—	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×C₄×D₁₉	—	2	2	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×(C₂×D₁₉)⋊C₄	—	2	1	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×Dic₁₉⋊C₄	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₄⋊C₄×D₁₉	—	4	2	no	—
53	C₄⋊C₄×D₁₉	—	4	2	no	—
54	C₄×D₇₆	—	2	1	no	—
55	C₄×D₇₆	—	2	1	no	—
56	C₄×D₇₆	—	4	2	no	—
57	C₄×D₇₆	—	4	2	no	—
58	C₄×D₇₆	C₂×C₄	1	2	yes	—
59	C₄×D₇₆	D₄	1	2	yes	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	#10597292	—	4	4	no	—
64	C₁₉⋊#95	—	2	2	no	—
65	#10597266	—	2	4	no	—
66	#10597265	—	2	4	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₂³×D₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	2	no	—
73	C₂×Q₈×C₁₉	—	4	2	no	—
74	C₂×Q₈×C₁₉	—	4	2	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	—	2	1	no	—
83	C₂²×Dic₁₉	—	2	2	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×D₇₆	SD₁₆	1	2	yes	—
89	C₂×D₇₆	Q₁₆	1	2	yes	—
90	C₂×C₄×D₁₉	—	2	2	no	—
91	C₂×C₄×D₁₉	—	2	2	no	—
92	C₂×C₄×D₁₉	—	4	1	no	—
93	C₂×C₄×D₁₉	—	4	1	no	—
94	C₂×C₄×D₁₉	—	4	1	no	—
95	C₂×C₄×D₁₉	—	4	1	no	—
96	C₂×C₄×D₁₉	—	4	4	no	—
97	C₂×C₄×D₁₉	—	4	4	no	—
98	C₂×C₄×D₁₉	—	8	2	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	C₄²×C₁₉	#41	1	1	yes	characteristic
116	(C₂×D₁₉)⋊C₄	—	2	2	no	—
117	(C₂×D₁₉)⋊C₄	—	2	2	no	—
118	(C₂×D₁₉)⋊C₄	—	4	4	no	—
119	C₄⋊Dic₁₉	—	2	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	1	no	—
122	C₄⋊Dic₁₉	—	4	1	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄⋊Dic₁₉	—	4	2	no	—
125	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
126	Dic₁₉⋊C₄	—	4	4	no	—
127	C₂×C₁₉⋊C₈	—	2	2	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	#8973	—	19	1	no	maximal, Sylow
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	C₂²×D₁₉	—	2	2	no	—
136	C₂²×D₁₉	—	2	2	no	—
137	C₂²×D₁₉	—	2	2	no	—
138	C₂²×D₁₉	—	4	1	no	—
139	C₂²×D₁₉	—	4	1	no	—
140	C₂²×D₁₉	—	4	1	no	—
141	C₂²×D₁₉	—	4	1	no	—
142	Q₈×C₁₉	—	4	4	no	—
143	Q₈×C₁₉	—	8	2	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	8	1	no	—
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
165	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
169	C₂×Dic₁₉	—	2	2	no	—
170	C₂×Dic₁₉	—	4	1	no	—
171	C₂×Dic₁₉	—	4	1	no	—
172	C₂×Dic₁₉	—	4	2	no	—
173	C₂×Dic₁₉	—	4	2	no	—
174	C₂×Dic₁₉	—	4	2	no	—
175	D₇₆	—	2	2	no	—
176	D₇₆	—	2	2	no	—
177	D₇₆	—	2	2	no	—
178	D₇₆	#103	1	4	yes	complemented
179	C₄×D₁₉	—	4	2	no	—
180	C₄×D₁₉	—	4	2	no	—
181	C₄×D₁₉	—	4	2	no	—
182	C₄×D₁₉	—	4	2	no	—
183	C₄×D₁₉	—	8	8	no	—
184	C₈×C₁₉	—	8	1	no	—
185	C₁₉⋊C₈	—	4	2	no	—
186	C₁₉⋊C₈	—	4	2	no	—
187	C₂×#476	—	19	1	no	—
188	D₄×C₄⋊C₄	—	19	1	no	—
189	#1987	D₁₉	1	1	yes	characteristic, complemented
190	#1956	—	19	1	no	—
191	C₂×D₄⋊C₈	—	19	1	no	—
192	#1296	—	19	1	no	—
193	#1279	—	19	1	no	—
194	C₂²×C₁₉	#386	1	1	yes	characteristic
195	C₂²×C₁₉	#450	1	1	yes	characteristic
196	C₂²×C₁₉	#450	1	1	yes	characteristic
197	C₂²×C₁₉	#451	1	1	yes	characteristic
198	C₂²×C₁₉	#452	1	1	yes	characteristic
199	C₂²×C₁₉	#453	1	1	yes	characteristic
200	C₂²×C₁₉	#454	1	1	yes	characteristic
201	C₂×D₁₉	—	2	4	no	—
202	C₂×D₁₉	—	4	2	no	—
203	C₂×D₁₉	—	4	2	no	—
204	C₂×D₁₉	—	4	2	no	—
205	C₂×D₁₉	—	4	2	no	—
206	C₂×D₁₉	—	4	2	no	—
207	C₂×D₁₉	—	4	2	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
214	C₄×C₁₉	#417	1	1	yes	characteristic
215	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
216	C₄×C₁₉	#440	1	1	yes	characteristic
217	C₄×C₁₉	#461	1	1	yes	characteristic
218	C₄×C₁₉	#463	1	1	yes	characteristic
219	C₄×C₁₉	#483	1	1	yes	characteristic
220	C₄×C₁₉	#484	1	1	yes	characteristic
221	Dic₁₉	—	4	2	no	—
222	Dic₁₉	—	8	2	no	—
223	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
224	C₂×C₄×D₄	—	19	1	no	—
225	C₂×C₄×D₄	—	38	1	no	—
226	C₂²×C₄⋊C₄	—	38	1	no	—
227	#476	—	19	4	no	—
228	#476	—	38	2	no	—
229	C₂×#106	—	38	1	no	—
230	C₂×C₄⋊C₈	—	19	1	no	—
231	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
232	C₂×#103	—	38	2	no	—
233	C₂×#102	—	38	1	no	—
234	C₂×C₄×C₈	—	19	1	no	—
235	#389	—	38	1	no	—
236	#385	—	38	2	no	—
237	#384	—	19	1	no	—
238	#380	—	38	1	no	—
239	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
240	#340	—	2	1	no	—
241	#340	—	2	1	no	—
242	D₄⋊C₈	—	38	2	no	—
243	C₂×C₁₉	#1629	1	1	yes	characteristic
244	C₂×C₁₉	#1632	1	1	yes	characteristic
245	C₂×C₁₉	#1635	1	1	yes	characteristic
246	C₂×C₁₉	#1637	1	1	yes	characteristic
247	C₂×C₁₉	#1872	1	1	yes	characteristic
248	C₂×C₁₉	#1877	1	1	yes	characteristic
249	C₂×C₁₉	#1883	1	1	yes	characteristic
250	D₁₉	—	4	4	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	19	1	no	—
253	C₂³×C₄	—	38	2	no	—
254	C₂³×C₄	—	38	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	38	1	no	—
257	C₂²×C₈	—	38	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	C₄×D₁₉	1	2	yes	complemented
262	C₄×D₄	—	19	2	no	—
263	C₄×D₄	—	19	2	no	—
264	C₄×D₄	—	38	1	no	—
265	C₄×D₄	—	38	1	no	—
266	C₄×D₄	—	76	2	no	—
267	C₄×D₄	—	76	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	19	1	no	—
271	C₂×C₄⋊C₄	—	19	2	no	—
272	C₂×C₄⋊C₄	—	38	2	no	—
273	C₂×C₄⋊C₄	—	38	1	no	—
274	C₂×C₄⋊C₄	—	38	1	no	—
275	C₂×C₄⋊C₄	—	76	2	no	—
276	C₂×C₄⋊C₄	—	76	2	no	—
277	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	38	1	no	—
280	C₂×C₂²⋊C₄	—	38	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
283	#106	—	38	4	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	19	2	no	—
287	C₄⋊C₈	—	38	1	no	—
288	#103	—	76	4	no	—
289	#102	—	38	4	no	—
290	C₄×C₈	—	38	1	no	—
291	C₄×C₈	—	38	1	no	—
292	#95	—	2	1	no	—
293	#95	—	38	2	no	—
294	C₁₉	#8973	1	1	yes	characteristic, complemented, Sylow
295	C₂⁴	—	38	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×D₄	—	19	2	no	—
301	C₂×D₄	—	19	2	no	—
302	C₂×D₄	—	19	2	no	—
303	C₂×D₄	—	38	1	no	—
304	C₂×D₄	—	38	1	no	—
305	C₂×D₄	—	38	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	2	no	—
311	C₂²×C₄	—	38	2	no	—
312	C₂²×C₄	—	38	2	no	—
313	C₂²×C₄	—	76	4	no	—
314	C₂²×C₄	—	76	4	no	—
315	C₂²×C₄	—	76	1	no	—
316	C₂²×C₄	—	76	1	no	—
317	C₂²×C₄	—	76	1	no	—
318	C₂²×C₄	—	76	1	no	—
319	C₂²×C₄	—	152	2	no	—
320	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	38	2	no	—
327	C₂×C₈	—	38	2	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	—	76	1	no	—
330	C₂×C₈	—	76	1	no	—
331	C₂×C₈	—	76	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	19	2	no	—
340	C₄⋊C₄	—	38	1	no	—
341	C₄⋊C₄	—	76	2	no	—
342	C₄⋊C₄	—	76	4	no	—
343	C₄⋊C₄	—	76	1	no	—
344	C₄⋊C₄	—	76	1	no	—
345	C₄⋊C₄	—	76	1	no	—
346	C₄⋊C₄	—	76	1	no	—
347	C₄⋊C₄	#64527	1	2	yes	—
348	C₂²⋊C₄	—	38	2	no	—
349	C₂²⋊C₄	—	38	2	no	—
350	C₂²⋊C₄	—	76	4	no	—
351	C₄²	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
354	C₄²	#64541	1	1	yes	characteristic
355	C₄²	D₄×D₁₉	1	1	yes	characteristic
356	C₄²	#64543	1	1	yes	characteristic
357	C₂³	—	38	2	no	—
358	C₂³	—	38	2	no	—
359	C₂³	—	38	2	no	—
360	C₂³	—	76	1	no	—
361	C₂³	—	76	1	no	—
362	C₂³	—	76	1	no	—
363	C₂³	—	76	1	no	—
364	C₂³	#10597383	1	1	yes	characteristic
365	Q₈	—	4	4	no	—
366	Q₈	—	8	2	no	—
367	D₄	—	19	4	no	—
368	D₄	—	38	2	no	—
369	D₄	—	38	2	no	—
370	D₄	—	38	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	8	1	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	38	2	no	—
383	C₂×C₄	—	76	1	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	—	76	2	no	—
386	C₂×C₄	—	76	2	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	2	no	—
389	C₂×C₄	—	76	2	no	—
390	C₂×C₄	—	76	2	no	—
391	C₂×C₄	—	76	2	no	—
392	C₂×C₄	—	152	8	no	—
393	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
394	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	#10597329	1	1	yes	characteristic
396	C₂×C₄	#10597330	1	1	yes	characteristic
397	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
398	C₂×C₄	#10597360	1	1	yes	characteristic
399	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
400	C₂×C₄	#10597364	1	1	yes	characteristic
401	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
402	C₂×C₄	#10597384	1	1	yes	characteristic
403	C₂×C₄	C₂×#64527	1	1	yes	characteristic
404	C₂×C₄	#10597388	1	1	yes	characteristic
405	C₂×C₄	#10597395	1	1	yes	characteristic
406	C₂×C₄	#10597396	1	1	yes	characteristic
407	C₈	—	8	1	no	—
408	C₈	—	76	2	no	—
409	C₈	—	76	2	no	—
410	C₂²	—	38	4	no	—
411	C₂²	—	76	2	no	—
412	C₂²	—	76	2	no	—
413	C₂²	—	76	2	no	—
414	C₂²	—	76	2	no	—
415	C₂²	—	76	2	no	—
416	C₂²	—	76	2	no	—
417	C₂²	#11926420	1	1	yes	characteristic
418	C₂²	#11926693	1	1	yes	characteristic
419	C₂²	#11926694	1	1	yes	characteristic
420	C₂²	#11926698	1	1	yes	characteristic
421	C₂²	#11926704	1	1	yes	characteristic
422	C₂²	#11926710	1	1	yes	characteristic
423	C₂²	#11926715	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	76	2	no	—
430	C₄	—	152	2	no	—
431	C₄	#103×D₁₉	1	1	yes	characteristic
432	C₄	#11926544	1	1	yes	characteristic
433	C₄	C₄×#64527	1	1	yes	characteristic
434	C₄	#11926642	1	1	yes	characteristic
435	C₄	#11926746	1	1	yes	characteristic
436	C₄	#11926756	1	1	yes	characteristic
437	C₄	#11926873	1	1	yes	characteristic
438	C₄	#11926878	1	1	yes	characteristic
439	C₂	—	76	4	no	—
440	C₂	#14562750	1	1	yes	characteristic
441	C₂	#14562768	1	1	yes	characteristic
442	C₂	#14562785	1	1	yes	characteristic
443	C₂	#14562798	1	1	yes	characteristic
444	C₂	#14563939	1	1	yes	characteristic
445	C₂	#14563972	1	1	yes	characteristic
446	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	#8973
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
12. #11926831	C₄	semidirect
36. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
68. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
178. D₇₆	#103	semidirect
189. #1987	D₁₉	semidirect
261. C₄⋊Q₈	C₄×D₁₉	semidirect
294. C₁₉	#8973	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
C₄⋊C₄×D₇₆	2
#14564438	2
C₂×#11926271	2
#14561519	2
#14561476	2
C₁₉×#1987	2
#8973	19