Subgroups — #18081502

Order 4864.

584 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597393	C₂	1	1	yes	maximal, characteristic
2	#14563490	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597393	C₄	1	1	yes	characteristic
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	1	no	—
12	C₂×#10597272	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926451	C₄	1	1	yes	characteristic
15	#11926445	C₄	1	1	yes	characteristic
16	#11926434	—	2	1	no	—
17	#11926434	—	2	1	no	—
18	#11926409	C₄	1	1	yes	characteristic
19	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
20	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
21	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
22	#11926298	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
25	#11926273	—	2	2	no	—
26	#11926271	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	#10597393	—	2	2	no	—
45	#10597393	—	2	2	no	—
46	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
47	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
48	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
49	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
50	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₄×D₇₆	—	2	1	no	—
61	C₄×D₇₆	—	2	1	no	—
62	C₄×D₇₆	—	2	1	no	—
63	C₄×D₇₆	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
66	C₄×C₈×C₁₉	—	2	1	no	—
67	C₄×C₈×C₁₉	—	2	1	no	—
68	C₁₉⋊#95	—	2	1	no	—
69	C₁₉⋊#95	—	2	1	no	—
70	C₁₉⋊#95	—	2	1	no	—
71	C₁₉⋊#95	—	2	1	no	—
72	#10597272	—	4	2	no	—
73	Dic₁₉⋊C₈	—	2	4	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
76	C₄×C₁₉⋊C₈	—	2	1	no	—
77	C₄×C₁₉⋊C₈	—	2	1	no	—
78	C₂³×D₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₁₉	—	2	1	no	—
91	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×D₇₆	—	2	1	no	—
96	C₂×D₇₆	—	2	1	no	—
97	C₂×D₇₆	—	2	1	no	—
98	C₂×D₇₆	—	2	1	no	—
99	C₂×D₇₆	—	2	1	no	—
100	C₂×D₇₆	M₁₆	1	2	yes	—
101	C₂×C₄×D₁₉	—	4	1	no	—
102	C₂×C₄×D₁₉	—	4	1	no	—
103	C₂×C₄×D₁₉	—	4	1	no	—
104	C₂×C₄×D₁₉	—	4	1	no	—
105	C₂×C₄×D₁₉	—	4	1	no	—
106	C₂×C₄×D₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	#41	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	(C₂×D₁₉)⋊C₄	—	2	4	no	—
124	(C₂×D₁₉)⋊C₄	—	2	4	no	—
125	(C₂×D₁₉)⋊C₄	—	4	2	no	—
126	(C₂×D₁₉)⋊C₄	—	4	1	no	—
127	(C₂×D₁₉)⋊C₄	—	4	1	no	—
128	(C₂×D₁₉)⋊C₄	—	4	2	no	—
129	C₄⋊Dic₁₉	—	2	1	no	—
130	C₄⋊Dic₁₉	—	2	1	no	—
131	C₄×Dic₁₉	—	2	1	no	—
132	C₄×Dic₁₉	—	2	1	no	—
133	C₄×Dic₁₉	—	2	1	no	—
134	C₄×Dic₁₉	—	2	1	no	—
135	C₄×Dic₁₉	—	2	1	no	—
136	C₄×Dic₁₉	—	2	1	no	—
137	C₄×Dic₁₉	—	2	1	no	—
138	C₄×Dic₁₉	—	2	1	no	—
139	C₄×Dic₁₉	—	2	2	no	—
140	C₄×Dic₁₉	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	#9676	—	19	1	no	maximal, Sylow
148	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×D₁₉	—	2	2	no	—
150	C₂²×D₁₉	—	4	1	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	Q₈×C₁₉	—	2	2	no	—
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	4	1	no	—
159	Q₈×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
182	C₂×Dic₁₉	—	2	1	no	—
183	C₂×Dic₁₉	—	2	1	no	—
184	C₂×Dic₁₉	—	2	1	no	—
185	C₂×Dic₁₉	—	2	1	no	—
186	C₂×Dic₁₉	—	2	1	no	—
187	C₂×Dic₁₉	—	2	1	no	—
188	C₂×Dic₁₉	—	2	1	no	—
189	C₂×Dic₁₉	—	2	1	no	—
190	C₂×Dic₁₉	—	2	1	no	—
191	C₂×Dic₁₉	—	2	1	no	—
192	C₂×Dic₁₉	—	2	1	no	—
193	C₂×Dic₁₉	—	4	1	no	—
194	C₂×Dic₁₉	—	4	1	no	—
195	C₂×Dic₁₉	—	4	1	no	—
196	C₂×Dic₁₉	#104	1	2	yes	—
197	D₇₆	—	2	2	no	—
198	D₇₆	—	2	2	no	—
199	D₇₆	—	4	1	no	—
200	D₇₆	—	4	1	no	—
201	C₄×D₁₉	—	8	1	no	—
202	C₄×D₁₉	—	8	1	no	—
203	C₄×D₁₉	—	8	1	no	—
204	C₄×D₁₉	—	8	1	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₈×C₁₉	—	4	2	no	—
207	C₁₉⋊C₈	—	4	2	no	—
208	C₁₉⋊C₈	—	4	2	no	—
209	C₄×#124	—	19	1	no	—
210	#1767	—	19	1	no	—
211	C₄×C₄⋊C₈	—	19	1	no	—
212	C₂×Q₈⋊C₈	—	19	1	no	—
213	C₂×Q₈⋊C₈	D₁₉	1	1	yes	characteristic, complemented
214	C₂×D₄⋊C₈	—	19	1	no	—
215	C₂×D₄⋊C₈	—	19	1	no	—
216	C₂²×C₁₉	#390	1	1	yes	characteristic
217	C₂²×C₁₉	#407	1	1	yes	characteristic
218	C₂²×C₁₉	#408	1	1	yes	characteristic
219	C₂²×C₁₉	#416	1	1	yes	characteristic
220	C₂²×C₁₉	#417	1	1	yes	characteristic
221	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
222	C₂²×C₁₉	#421	1	1	yes	characteristic
223	C₂×D₁₉	—	4	2	no	—
224	C₂×D₁₉	—	4	2	no	—
225	C₂×D₁₉	—	4	2	no	—
226	C₂×D₁₉	—	8	1	no	—
227	C₂×D₁₉	—	8	1	no	—
228	C₂×D₁₉	—	8	1	no	—
229	C₂×D₁₉	—	8	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	#435	1	1	yes	characteristic
235	C₄×C₁₉	#435	1	1	yes	characteristic
236	C₄×C₁₉	#435	1	1	yes	characteristic
237	C₄×C₁₉	#435	1	1	yes	characteristic
238	C₄×C₁₉	#463	1	1	yes	characteristic
239	C₄×C₁₉	#463	1	1	yes	characteristic
240	C₄×C₁₉	#464	1	1	yes	characteristic
241	C₄×C₁₉	#464	1	1	yes	characteristic
242	Dic₁₉	—	2	2	no	—
243	Dic₁₉	—	4	1	no	—
244	Dic₁₉	—	4	1	no	—
245	Dic₁₉	—	4	1	no	—
246	Dic₁₉	—	8	1	no	—
247	C₂×#124	—	19	1	no	—
248	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
249	C₂×C₄×D₄	—	19	1	no	—
250	C₂×C₄⋊C₈	—	19	1	no	—
251	C₂×C₄⋊C₈	—	38	1	no	—
252	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
253	C₂×#97	—	38	1	no	—
254	C₂×C₄×C₈	—	19	1	no	—
255	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
256	#391	—	19	1	no	—
257	#390	—	19	1	no	—
258	#388	—	38	1	no	—
259	#388	—	38	1	no	—
260	#382	—	19	1	no	—
261	C₄×C₂²⋊C₄	—	38	1	no	—
262	C₄×C₂²⋊C₄	—	38	1	no	—
263	C₄³	—	19	1	no	—
264	#336	—	38	1	no	—
265	#336	—	38	1	no	—
266	Q₈⋊C₈	—	2	2	no	—
267	Q₈⋊C₈	—	38	2	no	—
268	D₄⋊C₈	—	38	2	no	—
269	D₄⋊C₈	—	38	2	no	—
270	C₂×C₁₉	#1488	1	1	yes	characteristic
271	C₂×C₁₉	#1489	1	1	yes	characteristic
272	C₂×C₁₉	#1494	1	1	yes	characteristic
273	C₂×C₁₉	#1495	1	1	yes	characteristic
274	C₂×C₁₉	#1955	1	1	yes	characteristic
275	C₂×C₁₉	#1980	1	1	yes	characteristic
276	C₂×C₁₉	#1983	1	1	yes	characteristic
277	D₁₉	—	8	2	no	—
278	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
279	C₂²×D₄	—	19	1	no	—
280	C₂³×C₄	—	38	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	38	1	no	—
284	C₂²×C₈	—	38	1	no	—
285	#124	—	38	2	no	—
286	#124	—	38	2	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×D₄	—	38	1	no	—
292	C₄×D₄	—	38	1	no	—
293	C₄×D₄	—	38	1	no	—
294	C₄×D₄	—	38	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	19	1	no	—
297	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	38	1	no	—
299	C₂×C₂²⋊C₄	—	38	1	no	—
300	C₂×C₂²⋊C₄	—	38	1	no	—
301	C₂×C₂²⋊C₄	—	38	1	no	—
302	C₂×C₂²⋊C₄	—	38	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	19	1	no	—
305	C₂×C₄²	—	19	1	no	—
306	C₂×C₄²	—	19	1	no	—
307	C₂×C₄²	—	19	1	no	—
308	C₂×C₄²	—	19	1	no	—
309	C₂×C₄²	—	19	1	no	—
310	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	19	2	no	—
313	C₄⋊C₈	—	38	4	no	—
314	C₄⋊C₈	—	38	1	no	—
315	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
316	#97	—	76	2	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	38	1	no	—
320	C₄×C₈	—	38	1	no	—
321	#95	—	38	1	no	—
322	#95	—	38	1	no	—
323	#95	—	38	1	no	—
324	#95	—	38	1	no	—
325	C₁₉	#9676	1	1	yes	characteristic, complemented, Sylow
326	C₂⁴	—	38	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	#64515	1	2	yes	—
333	C₂×D₄	—	19	2	no	—
334	C₂×D₄	—	38	1	no	—
335	C₂×D₄	—	38	1	no	—
336	C₂×D₄	—	38	1	no	—
337	C₂×D₄	—	38	1	no	—
338	C₂×D₄	—	38	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	19	1	no	—
342	C₂²×C₄	—	19	1	no	—
343	C₂²×C₄	—	19	1	no	—
344	C₂²×C₄	—	19	1	no	—
345	C₂²×C₄	—	38	1	no	—
346	C₂²×C₄	—	76	1	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	C₂×C₄×D₁₉	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	38	2	no	—
362	C₂×C₈	—	38	2	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₂×C₈	—	76	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	38	1	no	—
372	C₄⋊C₄	—	38	1	no	—
373	C₂²⋊C₄	—	38	4	no	—
374	C₂²⋊C₄	—	38	4	no	—
375	C₂²⋊C₄	—	76	2	no	—
376	C₂²⋊C₄	—	76	2	no	—
377	C₂²⋊C₄	—	76	1	no	—
378	C₂²⋊C₄	—	76	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	—	38	2	no	—
382	C₄²	—	38	1	no	—
383	C₄²	—	38	1	no	—
384	C₄²	—	38	1	no	—
385	C₄²	—	38	1	no	—
386	C₄²	—	38	1	no	—
387	C₄²	—	38	1	no	—
388	C₄²	—	38	1	no	—
389	C₄²	—	38	1	no	—
390	C₄²	—	76	1	no	—
391	C₄²	#64541	1	1	yes	characteristic
392	C₄²	D₄×D₁₉	1	1	yes	characteristic
393	C₄²	#64543	1	1	yes	characteristic
394	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
395	C₂³	—	38	2	no	—
396	C₂³	—	76	1	no	—
397	C₂³	—	76	1	no	—
398	C₂³	—	76	1	no	—
399	C₂³	—	76	1	no	—
400	C₂³	—	76	1	no	—
401	C₂³	—	76	1	no	—
402	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	D₄	—	38	2	no	—
408	D₄	—	38	2	no	—
409	D₄	—	76	1	no	—
410	D₄	—	76	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	19	2	no	—
420	C₂×C₄	—	38	1	no	—
421	C₂×C₄	—	38	1	no	—
422	C₂×C₄	—	38	1	no	—
423	C₂×C₄	—	38	1	no	—
424	C₂×C₄	—	38	1	no	—
425	C₂×C₄	—	38	1	no	—
426	C₂×C₄	—	38	1	no	—
427	C₂×C₄	—	38	1	no	—
428	C₂×C₄	—	38	1	no	—
429	C₂×C₄	—	38	1	no	—
430	C₂×C₄	—	38	1	no	—
431	C₂×C₄	—	76	1	no	—
432	C₂×C₄	—	76	1	no	—
433	C₂×C₄	—	76	1	no	—
434	C₂×C₄	—	152	1	no	—
435	C₂×C₄	—	152	1	no	—
436	C₂×C₄	—	152	1	no	—
437	C₂×C₄	—	152	1	no	—
438	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
439	C₂×C₄	#10597330	1	1	yes	characteristic
440	C₂×C₄	#10597331	1	1	yes	characteristic
441	C₂×C₄	C₂×#64515	1	1	yes	characteristic
442	C₂×C₄	#10597347	1	1	yes	characteristic
443	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
444	C₂×C₄	#10597353	1	1	yes	characteristic
445	C₂×C₄	#10597360	1	1	yes	characteristic
446	C₂×C₄	#10597362	1	1	yes	characteristic
447	C₂×C₄	#10597364	1	1	yes	characteristic
448	C₂×C₄	#10597365	1	1	yes	characteristic
449	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
450	C₂×C₄	#10597385	1	1	yes	characteristic
451	C₂×C₄	#10597386	1	1	yes	characteristic
452	C₈	—	4	2	no	—
453	C₈	—	4	2	no	—
454	C₈	—	76	2	no	—
455	C₈	—	76	2	no	—
456	C₂²	—	76	2	no	—
457	C₂²	—	76	2	no	—
458	C₂²	—	76	2	no	—
459	C₂²	—	152	1	no	—
460	C₂²	—	152	1	no	—
461	C₂²	—	152	1	no	—
462	C₂²	—	152	1	no	—
463	C₂²	#11926444	1	1	yes	characteristic
464	C₂²	#11926506	1	1	yes	characteristic
465	C₂²	#11926509	1	1	yes	characteristic
466	C₂²	#11926539	1	1	yes	characteristic
467	C₂²	#11926544	1	1	yes	characteristic
468	C₂²	#104×D₁₉	1	1	yes	characteristic
469	C₂²	#11926559	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	1	no	—
474	C₄	—	38	2	no	—
475	C₄	—	76	1	no	—
476	C₄	—	76	1	no	—
477	C₄	—	76	1	no	—
478	C₄	—	152	1	no	—
479	C₄	#11926612	1	1	yes	characteristic
480	C₄	#11926613	1	1	yes	characteristic
481	C₄	#11926615	1	1	yes	characteristic
482	C₄	#11926618	1	1	yes	characteristic
483	C₄	#11926761	1	1	yes	characteristic
484	C₄	#11926762	1	1	yes	characteristic
485	C₄	#11926768	1	1	yes	characteristic
486	C₄	#11926769	1	1	yes	characteristic
487	C₂	—	152	2	no	—
488	C₂	#14562068	1	1	yes	characteristic
489	C₂	#14562073	1	1	yes	characteristic
490	C₂	#14562094	1	1	yes	characteristic
491	C₂	#14562099	1	1	yes	characteristic
492	C₂	#14564431	1	1	yes	characteristic
493	C₂	#14564552	1	1	yes	characteristic
494	C₂	#14564564	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#9676
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #14563490	C₂	semidirect
3. C₄×Dic₁₉⋊C₈	C₂	semidirect
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
7. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
213. C₂×Q₈⋊C₈	D₁₉	semidirect
325. C₁₉	#9676	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597393	2
#14563490	2
C₄×Dic₁₉⋊C₈	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×#11926273	2
C₂×#11926271	2
C₂×C₁₉×Q₈⋊C₈	2
#9676	19