Subgroups — #18084859

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926746	C₂	1	1	yes	maximal, characteristic
2	#14568553	C₂	1	1	yes	maximal, characteristic
3	#14564597	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂×#10597392	—	2	1	no	—
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#11926746	—	2	2	no	—
12	#11926746	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597292	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926466	—	2	2	no	—
17	#11926446	—	2	1	no	—
18	#11926442	—	2	1	no	—
19	#11926414	C₂²	1	1	yes	characteristic
20	#11926401	—	2	1	no	—
21	#11926306	—	2	2	no	—
22	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
23	#11926271	—	2	2	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#475	—	2	2	no	—
27	C₁₉×#475	—	2	2	no	—
28	C₂×C₁₉×#106	—	2	1	no	—
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₇₆	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	#10597392	—	4	2	no	—
51	#10597392	—	4	2	no	—
52	C₂×#64527	—	2	4	no	—
53	C₂×#64527	—	4	2	no	—
54	C₂×#64527	—	4	2	no	—
55	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
57	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
62	C₂×Dic₁₉⋊C₄	—	2	2	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₄×D₇₆	—	2	1	no	—
66	C₄×D₇₆	—	2	1	no	—
67	C₄×D₇₆	—	2	1	no	—
68	C₄×D₇₆	—	2	1	no	—
69	C₁₉×#106	—	2	4	no	—
70	C₁₉×C₄⋊C₈	—	2	1	no	—
71	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
72	C₁₉×#103	—	2	4	no	—
73	#10597292	—	2	4	no	—
74	C₁₉⋊#95	—	2	2	no	—
75	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₄×C₁₉⋊C₈	—	2	1	no	—
79	C₂³×D₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	4	1	no	—
87	C₂×Q₈×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	complemented
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₁₉	—	2	1	no	—
99	C₂²×Dic₁₉	—	2	2	no	—
100	C₂×D₇₆	—	2	1	no	—
101	C₂×D₇₆	—	2	1	no	—
102	C₂×D₇₆	—	2	1	no	—
103	C₂×D₇₆	—	2	1	no	—
104	C₂×D₇₆	—	2	1	no	—
105	C₂×D₇₆	SD₁₆	1	2	yes	—
106	C₂×C₄×D₁₉	—	4	1	no	—
107	C₂×C₄×D₁₉	—	4	1	no	—
108	C₂×C₄×D₁₉	—	4	1	no	—
109	C₂×C₄×D₁₉	—	4	1	no	—
110	C₂×C₄×D₁₉	—	4	1	no	—
111	C₂×C₄×D₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₉	#41	1	1	yes	characteristic
129	#64527	—	4	8	no	—
130	(C₂×D₁₉)⋊C₄	—	4	4	no	—
131	(C₂×D₁₉)⋊C₄	—	4	1	no	—
132	(C₂×D₁₉)⋊C₄	—	4	1	no	—
133	(C₂×D₁₉)⋊C₄	—	8	2	no	—
134	C₄⋊Dic₁₉	—	2	1	no	—
135	C₄⋊Dic₁₉	—	2	1	no	—
136	C₄⋊Dic₁₉	—	4	1	no	—
137	C₄⋊Dic₁₉	—	4	1	no	—
138	C₄⋊Dic₁₉	—	4	1	no	—
139	C₄⋊Dic₁₉	—	4	1	no	—
140	C₄⋊Dic₁₉	—	4	2	no	—
141	Dic₁₉⋊C₄	—	4	4	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	2	2	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	#10232	—	19	1	no	maximal, Sylow
149	C₂³×C₁₉	#120	1	1	yes	characteristic
150	C₂²×D₁₉	—	2	2	no	—
151	C₂²×D₁₉	—	4	1	no	—
152	C₂²×D₁₉	—	4	1	no	—
153	C₂²×D₁₉	—	4	1	no	—
154	C₂²×D₁₉	—	4	1	no	—
155	C₂²×D₁₉	—	4	1	no	—
156	C₂²×D₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	2	no	—
159	Q₈×C₁₉	—	4	1	no	—
160	Q₈×C₁₉	—	4	1	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	8	1	no	—
164	Q₈×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	2	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	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
186	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
190	C₂×Dic₁₉	—	4	1	no	—
191	C₂×Dic₁₉	—	4	2	no	—
192	C₂×Dic₁₉	—	4	1	no	—
193	C₂×Dic₁₉	—	4	2	no	—
194	C₂×Dic₁₉	—	4	1	no	—
195	C₂×Dic₁₉	—	4	2	no	—
196	D₇₆	—	2	2	no	—
197	D₇₆	—	2	2	no	—
198	D₇₆	—	4	1	no	—
199	D₇₆	—	4	1	no	—
200	C₄×D₁₉	—	8	1	no	—
201	C₄×D₁₉	—	8	1	no	—
202	C₄×D₁₉	—	8	1	no	—
203	C₄×D₁₉	—	8	1	no	—
204	C₈×C₁₉	—	4	2	no	—
205	C₁₉⋊C₈	—	4	2	no	—
206	C₁₉⋊C₈	—	4	2	no	—
207	C₂×#475	D₁₉	1	1	yes	characteristic, complemented
208	C₂×#461	—	19	1	no	—
209	#2538	—	19	1	no	—
210	#1990	—	19	1	no	—
211	C₂×Q₈⋊C₈	—	19	1	no	—
212	C₂×D₄⋊C₈	—	19	1	no	—
213	#1296	—	19	1	no	—
214	C₂²×C₁₉	#392	1	1	yes	characteristic
215	C₂²×C₁₉	#448	1	1	yes	characteristic
216	C₂²×C₁₉	#449	1	1	yes	characteristic
217	C₂²×C₁₉	#450	1	1	yes	characteristic
218	C₂²×C₁₉	#452	1	1	yes	characteristic
219	C₂²×C₁₉	#455	1	1	yes	characteristic
220	C₂²×C₁₉	#456	1	1	yes	characteristic
221	C₂×D₁₉	—	4	2	no	—
222	C₂×D₁₉	—	4	2	no	—
223	C₂×D₁₉	—	4	2	no	—
224	C₂×D₁₉	—	8	1	no	—
225	C₂×D₁₉	—	8	1	no	—
226	C₂×D₁₉	—	8	1	no	—
227	C₂×D₁₉	—	8	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	#448	1	1	yes	characteristic
234	C₄×C₁₉	#449	1	1	yes	characteristic
235	C₄×C₁₉	#450	1	1	yes	characteristic
236	C₄×C₁₉	#452	1	1	yes	characteristic
237	C₄×C₁₉	#465	1	1	yes	characteristic
238	C₄×C₁₉	#465	1	1	yes	characteristic
239	C₄×C₁₉	#468	1	1	yes	characteristic
240	C₄×C₁₉	#468	1	1	yes	characteristic
241	Dic₁₉	—	8	2	no	—
242	Dic₁₉	—	8	1	no	—
243	C₂²×SD₁₆	—	38	1	no	—
244	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	—	38	1	no	—
246	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
247	C₂×C₄×D₄	—	19	1	no	—
248	#475	—	2	2	no	—
249	#475	—	2	2	no	—
250	#461	—	38	2	no	—
251	#461	—	38	2	no	—
252	C₂×#106	—	2	1	no	—
253	C₂×C₄⋊C₈	—	19	1	no	—
254	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
255	C₂×#103	—	2	1	no	—
256	C₂×#103	—	38	1	no	—
257	C₂×C₄×C₈	—	19	1	no	—
258	#396	—	38	2	no	—
259	#390	—	38	1	no	—
260	#389	—	38	1	no	—
261	#384	—	19	1	no	—
262	#380	—	38	1	no	—
263	#340	—	38	2	no	—
264	Q₈⋊C₈	—	38	2	no	—
265	D₄⋊C₈	—	38	2	no	—
266	C₂×C₁₉	#1642	1	1	yes	characteristic
267	C₂×C₁₉	#1643	1	1	yes	characteristic
268	C₂×C₁₉	#1650	1	1	yes	characteristic
269	C₂×C₁₉	#1651	1	1	yes	characteristic
270	C₂×C₁₉	#2000	1	1	yes	characteristic
271	C₂×C₁₉	#2000	1	1	yes	characteristic
272	C₂×C₁₉	#2007	1	1	yes	characteristic
273	D₁₉	—	8	2	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
276	C₂²×D₄	—	19	1	no	—
277	C₂³×C₄	—	38	1	no	—
278	C₂×SD₁₆	—	38	4	no	—
279	C₂×SD₁₆	—	76	2	no	—
280	C₂×SD₁₆	—	76	2	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	38	1	no	—
283	C₂²×C₈	—	38	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
288	C₂²⋊Q₈	—	76	2	no	—
289	C₂²⋊Q₈	—	76	2	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×D₄	—	38	1	no	—
295	C₄×D₄	—	38	1	no	—
296	C₄×D₄	—	38	1	no	—
297	C₄×D₄	—	38	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	19	1	no	—
302	C₂×C₄⋊C₄	—	19	2	no	—
303	C₂×C₄⋊C₄	—	38	2	no	—
304	C₂×C₄⋊C₄	—	38	1	no	—
305	C₂×C₄⋊C₄	—	38	1	no	—
306	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	38	2	no	—
308	C₂×C₂²⋊C₄	—	38	1	no	—
309	C₂×C₂²⋊C₄	—	38	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
312	#106	—	2	4	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	19	2	no	—
315	C₄⋊C₈	—	38	1	no	—
316	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
317	#103	—	2	4	no	—
318	#103	—	38	4	no	—
319	C₄×C₈	—	38	1	no	—
320	C₄×C₈	—	38	1	no	—
321	#95	—	38	2	no	—
322	C₁₉	#10232	1	1	yes	characteristic, complemented, Sylow
323	C₂⁴	—	38	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	#64527	1	2	yes	complemented
336	C₂×D₄	—	19	2	no	—
337	C₂×D₄	—	38	1	no	—
338	C₂×D₄	—	38	1	no	—
339	C₂×D₄	—	38	1	no	—
340	C₂×D₄	—	38	1	no	—
341	C₂×D₄	—	38	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	38	1	no	—
346	C₂²×C₄	—	38	2	no	—
347	C₂²×C₄	—	76	1	no	—
348	C₂²×C₄	—	76	1	no	—
349	C₂²×C₄	—	76	1	no	—
350	C₂²×C₄	—	76	1	no	—
351	C₂²×C₄	—	76	1	no	—
352	C₂²×C₄	—	76	1	no	—
353	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
356	SD₁₆	—	76	8	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	38	2	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	38	1	no	—
375	C₄⋊C₄	—	38	1	no	—
376	C₄⋊C₄	—	76	2	no	—
377	C₄⋊C₄	—	76	4	no	—
378	C₄⋊C₄	—	76	1	no	—
379	C₄⋊C₄	—	76	1	no	—
380	C₄⋊C₄	—	76	1	no	—
381	C₄⋊C₄	—	76	1	no	—
382	C₂²⋊C₄	—	76	4	no	—
383	C₂²⋊C₄	—	76	1	no	—
384	C₂²⋊C₄	—	76	1	no	—
385	C₂²⋊C₄	—	152	2	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	D₄×D₁₉	1	1	yes	characteristic
389	C₄²	#64543	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
391	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
392	C₂³	—	38	2	no	—
393	C₂³	—	76	1	no	—
394	C₂³	—	76	1	no	—
395	C₂³	—	76	1	no	—
396	C₂³	—	76	1	no	—
397	C₂³	—	76	1	no	—
398	C₂³	—	76	1	no	—
399	C₂³	#10597383	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	8	1	no	—
407	Q₈	—	8	1	no	—
408	D₄	—	38	2	no	—
409	D₄	—	38	2	no	—
410	D₄	—	76	1	no	—
411	D₄	—	76	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	—	76	2	no	—
424	C₂×C₄	—	76	2	no	—
425	C₂×C₄	—	76	1	no	—
426	C₂×C₄	—	76	1	no	—
427	C₂×C₄	—	76	1	no	—
428	C₂×C₄	—	76	2	no	—
429	C₂×C₄	—	152	1	no	—
430	C₂×C₄	—	152	1	no	—
431	C₂×C₄	—	152	1	no	—
432	C₂×C₄	—	152	1	no	—
433	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
434	C₂×C₄	#10597360	1	1	yes	characteristic
435	C₂×C₄	#10597361	1	1	yes	characteristic
436	C₂×C₄	#10597362	1	1	yes	characteristic
437	C₂×C₄	#10597383	1	1	yes	characteristic
438	C₂×C₄	#10597384	1	1	yes	characteristic
439	C₂×C₄	#10597385	1	1	yes	characteristic
440	C₂×C₄	#10597385	1	1	yes	characteristic
441	C₂×C₄	#10597386	1	1	yes	characteristic
442	C₂×C₄	C₂×#64527	1	1	yes	characteristic
443	C₂×C₄	#10597388	1	1	yes	characteristic
444	C₂×C₄	#10597395	1	1	yes	characteristic
445	C₂×C₄	#10597396	1	1	yes	characteristic
446	C₂×C₄	#10597399	1	1	yes	characteristic
447	C₈	—	4	2	no	—
448	C₈	—	76	2	no	—
449	C₈	—	76	2	no	—
450	C₂²	—	76	2	no	—
451	C₂²	—	76	2	no	—
452	C₂²	—	76	2	no	—
453	C₂²	—	152	1	no	—
454	C₂²	—	152	1	no	—
455	C₂²	—	152	1	no	—
456	C₂²	—	152	1	no	—
457	C₂²	#11926452	1	1	yes	characteristic
458	C₂²	#11926681	1	1	yes	characteristic
459	C₂²	#11926688	1	1	yes	characteristic
460	C₂²	#11926694	1	1	yes	characteristic
461	C₂²	#11926704	1	1	yes	characteristic
462	C₂²	#11926720	1	1	yes	characteristic
463	C₂²	#11926725	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	152	2	no	—
470	C₄	—	152	1	no	—
471	C₄	#11926683	1	1	yes	characteristic
472	C₄	#11926689	1	1	yes	characteristic
473	C₄	#11926693	1	1	yes	characteristic
474	C₄	#11926703	1	1	yes	characteristic
475	C₄	#11926770	1	1	yes	characteristic
476	C₄	#11926775	1	1	yes	characteristic
477	C₄	#11926787	1	1	yes	characteristic
478	C₄	#11926792	1	1	yes	characteristic
479	C₂	—	152	2	no	—
480	C₂	#14562834	1	1	yes	characteristic
481	C₂	#14562841	1	1	yes	characteristic
482	C₂	#14562890	1	1	yes	characteristic
483	C₂	#14562897	1	1	yes	characteristic
484	C₂	#14564635	1	1	yes	characteristic
485	C₂	#14564636	1	1	yes	characteristic
486	C₂	#14564680	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#475	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
hypercenter	C₂×#475	D₁₉
hypocenter	C₁₉	#10232
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#475

Complements

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

N	H ≅ G/N	type
3. #14564597	C₂	semidirect
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₂×C₁₉×#475	C₂	semidirect
91. C₂×Q₈×C₁₉	SD₁₆	semidirect
207. C₂×#475	D₁₉	semidirect
322. C₁₉	#10232	semidirect
335. C₂×Q₈	#64527	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926746	2
#14568553	2
#14564597	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×#11926271	2
#14561519	2
C₂×C₁₉×#475	2
#10232	19