Subgroups — #18084879

Order 4864.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 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, complemented
2	#14568548	C₂	1	1	yes	maximal, characteristic
3	#14564438	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597376	—	2	1	no	—
9	C₂×#10597384	—	2	1	no	—
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#11926831	—	2	2	no	—
12	#11926831	—	2	2	no	—
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	#11926460	—	2	2	no	—
19	#11926414	C₂²	1	1	yes	characteristic
20	#11926404	—	2	1	no	—
21	#11926401	—	2	1	no	—
22	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
23	#11926271	—	2	2	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#476	—	2	2	no	—
27	C₁₉×#476	—	2	2	no	—
28	C₂×C₁₉×#106	—	2	1	no	—
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₂²⋊D₁₉	—	2	2	no	—
35	C₂²×D₇₆	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	D₄	1	2	yes	complemented
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
52	#10597384	—	4	2	no	—
53	#10597384	—	4	2	no	—
54	#10597376	—	4	2	no	—
55	#10597376	—	4	2	no	—
56	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₁₉)⋊C₄	—	2	1	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	C₂²×C₁₉⋊C₈	—	2	1	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₄×D₇₆	—	2	1	no	—
65	C₄×D₇₆	—	2	1	no	—
66	C₄×D₇₆	—	2	1	no	—
67	C₄×D₇₆	—	2	1	no	—
68	C₁₉×#106	—	2	4	no	—
69	C₁₉×C₄⋊C₈	—	2	1	no	—
70	C₁₉×C₄⋊C₈	D₄	1	2	yes	complemented
71	C₁₉×#102	—	2	4	no	—
72	#10597292	—	4	4	no	—
73	C₁₉⋊#95	—	2	2	no	—
74	#10597266	—	2	4	no	—
75	#10597265	—	2	4	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	complemented
78	C₄×C₁₉⋊C₈	—	2	1	no	—
79	C₄×C₁₉⋊C₈	—	2	1	no	—
80	C₂⁴×C₁₉	—	2	1	no	—
81	C₂³×D₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	—	4	2	no	—
85	C₂×Q₈×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₂²⋊D₁₉	—	4	4	no	—
104	C₂×C₂²⋊D₁₉	—	4	4	no	—
105	C₂×C₂²⋊D₁₉	—	8	2	no	—
106	C₂²×Dic₁₉	—	2	1	no	—
107	C₂²×Dic₁₉	—	2	2	no	—
108	C₂×D₇₆	—	2	1	no	—
109	C₂×D₇₆	—	2	1	no	—
110	C₂×D₇₆	—	2	1	no	—
111	C₂×D₇₆	—	2	1	no	—
112	C₂×D₇₆	—	2	1	no	—
113	C₂×D₇₆	SD₁₆	1	2	yes	—
114	C₂×C₄×D₁₉	—	4	1	no	—
115	C₂×C₄×D₁₉	—	4	1	no	—
116	C₂×C₄×D₁₉	—	4	1	no	—
117	C₂×C₄×D₁₉	—	4	1	no	—
118	C₂×C₄×D₁₉	—	4	1	no	—
119	C₂×C₄×D₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	#41	1	1	yes	characteristic
135	C₂²⋊Dic₁₉	—	4	4	no	—
136	(C₂×D₁₉)⋊C₄	—	4	4	no	—
137	(C₂×D₁₉)⋊C₄	—	4	1	no	—
138	(C₂×D₁₉)⋊C₄	—	4	1	no	—
139	C₄⋊Dic₁₉	—	2	1	no	—
140	C₄⋊Dic₁₉	—	2	1	no	—
141	C₄⋊Dic₁₉	—	4	1	no	—
142	C₄⋊Dic₁₉	—	4	1	no	—
143	C₄⋊Dic₁₉	—	4	1	no	—
144	C₄⋊Dic₁₉	—	4	1	no	—
145	C₄⋊Dic₁₉	—	4	2	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	—	4	1	no	—
152	#10235	—	19	1	no	maximal, Sylow
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	#120	1	1	yes	characteristic
161	C₂²×D₁₉	—	2	2	no	—
162	C₂²×D₁₉	—	4	1	no	—
163	C₂²×D₁₉	—	4	1	no	—
164	C₂²×D₁₉	—	4	1	no	—
165	C₂²×D₁₉	—	4	1	no	—
166	C₂²×D₁₉	—	4	1	no	—
167	C₂²×D₁₉	—	4	1	no	—
168	Q₈×C₁₉	—	4	4	no	—
169	Q₈×C₁₉	—	8	2	no	—
170	D₄×C₁₉	—	2	2	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	8	1	no	—
181	C₂×C₄×C₁₉	—	8	1	no	—
182	C₂×C₄×C₁₉	—	8	1	no	—
183	C₂×C₄×C₁₉	—	8	1	no	—
184	C₂×C₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	8	1	no	—
186	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
196	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
200	C₂²⋊D₁₉	—	8	8	no	—
201	C₂×Dic₁₉	—	4	1	no	—
202	C₂×Dic₁₉	—	4	2	no	—
203	C₂×Dic₁₉	—	4	2	no	—
204	C₂×Dic₁₉	—	4	1	no	—
205	C₂×Dic₁₉	—	4	1	no	—
206	C₂×Dic₁₉	—	4	2	no	—
207	D₇₆	—	2	2	no	—
208	D₇₆	—	2	2	no	—
209	D₇₆	—	4	1	no	—
210	D₇₆	—	4	1	no	—
211	C₄×D₁₉	—	8	1	no	—
212	C₄×D₁₉	—	8	1	no	—
213	C₄×D₁₉	—	8	1	no	—
214	C₄×D₁₉	—	8	1	no	—
215	C₈×C₁₉	—	4	2	no	—
216	C₁₉⋊C₈	—	4	2	no	—
217	C₁₉⋊C₈	—	4	2	no	—
218	C₂×#476	—	19	1	no	—
219	C₂×#476	D₁₉	1	1	yes	characteristic, complemented
220	#2537	—	19	1	no	—
221	#1956	—	19	1	no	—
222	C₂×D₄⋊C₈	—	19	1	no	—
223	C₂×D₄⋊C₈	—	19	1	no	—
224	#1296	—	19	1	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	8	1	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	#392	1	1	yes	characteristic
233	C₂²×C₁₉	#450	1	1	yes	characteristic
234	C₂²×C₁₉	#450	1	1	yes	characteristic
235	C₂²×C₁₉	#452	1	1	yes	characteristic
236	C₂²×C₁₉	#452	1	1	yes	characteristic
237	C₂²×C₁₉	#453	1	1	yes	characteristic
238	C₂²×C₁₉	#454	1	1	yes	characteristic
239	C₂×D₁₉	—	4	2	no	—
240	C₂×D₁₉	—	4	2	no	—
241	C₂×D₁₉	—	4	2	no	—
242	C₂×D₁₉	—	8	1	no	—
243	C₂×D₁₉	—	8	1	no	—
244	C₂×D₁₉	—	8	1	no	—
245	C₂×D₁₉	—	8	1	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	8	1	no	—
249	C₄×C₁₉	—	8	2	no	—
250	C₄×C₁₉	#448	1	1	yes	characteristic
251	C₄×C₁₉	#448	1	1	yes	characteristic
252	C₄×C₁₉	#449	1	1	yes	characteristic
253	C₄×C₁₉	#449	1	1	yes	characteristic
254	C₄×C₁₉	#465	1	1	yes	characteristic
255	C₄×C₁₉	#465	1	1	yes	characteristic
256	C₄×C₁₉	#468	1	1	yes	characteristic
257	C₄×C₁₉	#468	1	1	yes	characteristic
258	Dic₁₉	—	8	2	no	—
259	Dic₁₉	—	8	1	no	—
260	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
261	C₂×#121	—	38	1	no	—
262	C₂×#121	—	38	1	no	—
263	C₂×C₄×D₄	—	19	1	no	—
264	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
265	#476	—	2	2	no	—
266	#476	—	2	2	no	—
267	#476	—	38	2	no	—
268	#476	—	38	2	no	—
269	C₂×#106	—	2	1	no	—
270	C₂×#106	—	38	1	no	—
271	C₂×C₄⋊C₈	—	19	1	no	—
272	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
273	C₂×#103	—	38	2	no	—
274	C₂×#102	—	2	1	no	—
275	C₂×#102	—	38	1	no	—
276	C₂×C₄×C₈	—	19	1	no	—
277	#394	—	38	2	no	—
278	#384	—	19	1	no	—
279	#380	—	38	1	no	—
280	#380	—	38	1	no	—
281	D₄⋊C₈	—	38	2	no	—
282	D₄⋊C₈	—	38	2	no	—
283	C₂×C₁₉	—	8	2	no	—
284	C₂×C₁₉	#1629	1	1	yes	characteristic
285	C₂×C₁₉	#1634	1	1	yes	characteristic
286	C₂×C₁₉	#1635	1	1	yes	characteristic
287	C₂×C₁₉	#1635	1	1	yes	characteristic
288	C₂×C₁₉	#2000	1	1	yes	characteristic
289	C₂×C₁₉	#2000	1	1	yes	characteristic
290	C₂×C₁₉	#2006	1	1	yes	characteristic
291	D₁₉	—	8	2	no	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×D₄	—	19	1	no	—
294	C₂²×D₄	—	38	2	no	—
295	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	38	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	38	1	no	—
300	C₂²×C₈	—	38	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	complemented
305	#121	—	76	2	no	—
306	#121	—	76	2	no	—
307	#121	—	76	2	no	—
308	#121	—	76	2	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	38	1	no	—
314	C₄×D₄	—	38	1	no	—
315	C₄×D₄	—	38	1	no	—
316	C₄×D₄	—	38	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	19	1	no	—
320	C₂×C₄⋊C₄	—	19	2	no	—
321	C₂×C₄⋊C₄	—	38	1	no	—
322	C₂×C₄⋊C₄	—	38	1	no	—
323	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	38	2	no	—
326	C₂×C₂²⋊C₄	—	38	2	no	—
327	C₂×C₂²⋊C₄	—	38	1	no	—
328	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
329	#106	—	2	4	no	—
330	#106	—	38	4	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	19	2	no	—
333	C₄⋊C₈	—	38	1	no	—
334	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	complemented
335	#103	—	76	4	no	—
336	#102	—	2	4	no	—
337	#102	—	38	4	no	—
338	C₄×C₈	—	38	1	no	—
339	C₄×C₈	—	38	1	no	—
340	#95	—	38	2	no	—
341	C₁₉	#10235	1	1	yes	characteristic, complemented, Sylow
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	38	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	19	2	no	—
354	C₂×D₄	—	38	1	no	—
355	C₂×D₄	—	38	1	no	—
356	C₂×D₄	—	38	1	no	—
357	C₂×D₄	—	38	1	no	—
358	C₂×D₄	—	38	1	no	—
359	C₂×D₄	—	76	4	no	—
360	C₂×D₄	—	76	4	no	—
361	C₂×D₄	—	152	2	no	—
362	C₂×D₄	#64527	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	—	38	1	no	—
372	C₂²×C₄	—	38	2	no	—
373	C₂²×C₄	—	76	1	no	—
374	C₂²×C₄	—	76	1	no	—
375	C₂²×C₄	—	76	1	no	—
376	C₂²×C₄	—	76	1	no	—
377	C₂²×C₄	—	76	1	no	—
378	C₂²×C₄	—	76	1	no	—
379	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
380	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	4	1	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	38	2	no	—
386	C₂×C₈	—	38	2	no	—
387	C₂×C₈	—	76	1	no	—
388	C₂×C₈	—	76	1	no	—
389	C₂×C₈	—	76	1	no	—
390	C₂×C₈	—	76	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	38	1	no	—
398	C₄⋊C₄	—	38	1	no	—
399	C₄⋊C₄	—	76	2	no	—
400	C₄⋊C₄	—	76	1	no	—
401	C₄⋊C₄	—	76	1	no	—
402	C₄⋊C₄	—	76	1	no	—
403	C₄⋊C₄	—	76	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	4	1	no	—
406	C₂²⋊C₄	—	76	4	no	—
407	C₂²⋊C₄	—	76	4	no	—
408	C₂²⋊C₄	—	76	1	no	—
409	C₂²⋊C₄	—	76	1	no	—
410	C₄²	D₄×D₁₉	1	1	yes	characteristic
411	C₄²	#64543	1	1	yes	characteristic
412	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
413	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	38	2	no	—
422	C₂³	—	76	1	no	—
423	C₂³	—	76	1	no	—
424	C₂³	—	76	1	no	—
425	C₂³	—	76	1	no	—
426	C₂³	—	76	1	no	—
427	C₂³	—	76	1	no	—
428	C₂³	#10597383	1	1	yes	characteristic
429	Q₈	—	4	4	no	—
430	Q₈	—	8	2	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	38	2	no	—
436	D₄	—	38	2	no	—
437	D₄	—	76	1	no	—
438	D₄	—	76	1	no	—
439	D₄	—	152	8	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	8	1	no	—
448	C₂×C₄	—	8	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	76	2	no	—
453	C₂×C₄	—	76	1	no	—
454	C₂×C₄	—	76	2	no	—
455	C₂×C₄	—	76	1	no	—
456	C₂×C₄	—	76	1	no	—
457	C₂×C₄	—	76	2	no	—
458	C₂×C₄	—	152	1	no	—
459	C₂×C₄	—	152	1	no	—
460	C₂×C₄	—	152	1	no	—
461	C₂×C₄	—	152	1	no	—
462	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
463	C₂×C₄	#10597360	1	1	yes	characteristic
464	C₂×C₄	#10597361	1	1	yes	characteristic
465	C₂×C₄	#10597362	1	1	yes	characteristic
466	C₂×C₄	#10597383	1	1	yes	characteristic
467	C₂×C₄	#10597384	1	1	yes	characteristic
468	C₂×C₄	#10597385	1	1	yes	characteristic
469	C₂×C₄	#10597385	1	1	yes	characteristic
470	C₂×C₄	#10597386	1	1	yes	characteristic
471	C₂×C₄	C₂×#64527	1	1	yes	characteristic
472	C₂×C₄	#10597388	1	1	yes	characteristic
473	C₂×C₄	#10597395	1	1	yes	characteristic
474	C₂×C₄	#10597396	1	1	yes	characteristic
475	C₂×C₄	#10597399	1	1	yes	characteristic
476	C₈	—	4	2	no	—
477	C₈	—	76	2	no	—
478	C₈	—	76	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	76	2	no	—
487	C₂²	—	76	2	no	—
488	C₂²	—	76	2	no	—
489	C₂²	—	152	1	no	—
490	C₂²	—	152	1	no	—
491	C₂²	—	152	1	no	—
492	C₂²	—	152	1	no	—
493	C₂²	#11926452	1	1	yes	characteristic
494	C₂²	#11926693	1	1	yes	characteristic
495	C₂²	#11926694	1	1	yes	characteristic
496	C₂²	#11926703	1	1	yes	characteristic
497	C₂²	#11926704	1	1	yes	characteristic
498	C₂²	#11926710	1	1	yes	characteristic
499	C₂²	#11926715	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	8	1	no	—
503	C₄	—	8	2	no	—
504	C₄	—	152	1	no	—
505	C₄	—	152	2	no	—
506	C₄	#11926681	1	1	yes	characteristic
507	C₄	#11926683	1	1	yes	characteristic
508	C₄	#11926688	1	1	yes	characteristic
509	C₄	#11926689	1	1	yes	characteristic
510	C₄	#11926770	1	1	yes	characteristic
511	C₄	#11926775	1	1	yes	characteristic
512	C₄	#11926787	1	1	yes	characteristic
513	C₄	#11926792	1	1	yes	characteristic
514	C₂	—	8	2	no	—
515	C₂	—	152	2	no	—
516	C₂	#14562750	1	1	yes	characteristic
517	C₂	#14562779	1	1	yes	characteristic
518	C₂	#14562784	1	1	yes	characteristic
519	C₂	#14562785	1	1	yes	characteristic
520	C₂	#14564635	1	1	yes	characteristic
521	C₂	#14564636	1	1	yes	characteristic
522	C₂	#14564675	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#476	C₂
socle	C₂³×C₁₉	#120
prime radical	#14568548	C₂
hypercenter	C₂×#476	D₁₉
hypocenter	C₁₉	#10235
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#476

Complements

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

N	H ≅ G/N	type
1. C₂×#11926831	C₂	semidirect
3. #14564438	C₂	semidirect
4. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
5. C₂×#11926271	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₂×C₁₉×#476	C₂	semidirect
41. C₁₉×C₄⋊Q₈	D₄	semidirect
70. C₁₉×C₄⋊C₈	D₄	semidirect
77. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
219. C₂×#476	D₁₉	semidirect
304. C₄⋊Q₈	C₂²⋊D₁₉	semidirect
334. C₄⋊C₈	C₂²⋊D₁₉	semidirect
341. C₁₉	#10235	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
#14568548	2
#14564438	2
C₂×D₄⋊(C₁₉⋊C₈)	2
C₂×#11926271	2
#14561519	2
C₂×C₁₉×#476	2
#10235	19