Subgroups — #18088095

Order 4864.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927310	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926562	C₂	1	1	yes	maximal, characteristic
3	#14572155	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926316	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926300	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	#11927310	—	2	2	no	—
10	#11927310	—	2	2	no	—
11	#11927310	—	2	2	no	—
12	#11927310	C₄	1	4	yes	complemented
13	C₂×#10597353	—	2	2	no	—
14	C₂×#10597347	—	2	2	no	—
15	C₂²×#64520	C₂²	1	1	yes	characteristic
16	C₂²×#64520	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₁₉	—	2	2	no	—
18	C₂×#10597372	C₂²	1	1	yes	characteristic
19	#11926562	—	2	2	no	—
20	#11926562	—	2	2	no	—
21	C₂×#10597262	C₄	1	4	yes	complemented
22	#11926554	C₄	1	2	yes	complemented
23	#11926550	C₄	1	2	yes	complemented
24	#11926546	—	2	2	no	—
25	#11926541	—	2	2	no	—
26	#11926316	—	2	2	no	—
27	#11926308	—	2	2	no	—
28	#11926300	—	2	2	no	—
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₁₉×#343	—	2	2	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₉	—	2	1	no	—
35	C₂×#64541	—	2	1	no	—
36	C₂×#64541	—	2	1	no	—
37	C₂×#64541	—	2	1	no	—
38	C₂×#64541	—	2	1	no	—
39	C₂×#64541	—	2	1	no	—
40	C₂×#64541	—	2	1	no	—
41	C₂×#64541	C₂×C₄	1	2	yes	—
42	C₂×#64541	C₂×C₄	1	2	yes	—
43	C₂×#64541	D₄	1	2	yes	—
44	C₂×#64541	D₄	1	2	yes	—
45	C₂×#64541	D₄	1	2	yes	—
46	C₂×#64541	Q₈	1	2	yes	—
47	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₉	—	2	1	no	—
49	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
61	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
72	#10597372	—	2	1	no	—
73	#10597372	—	2	1	no	—
74	#10597372	—	2	1	no	—
75	#10597372	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊Dic₁₉	—	2	1	no	—
77	C₂×C₄×Dic₁₉	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	C₂×C₄	1	2	yes	—
88	C₂×#64520	C₂×C₄	1	2	yes	—
89	C₂×#64520	D₄	1	2	yes	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
92	#10597353	—	2	8	no	—
93	#10597353	—	2	8	no	—
94	M₁₆×D₁₉	—	2	8	no	—
95	M₁₆×D₁₉	—	2	8	no	—
96	#10597347	—	2	8	no	—
97	#10597347	—	2	8	no	—
98	C₂×#64515	—	2	4	no	—
99	C₂×C₈×D₁₉	—	2	4	no	—
100	#10597278	—	2	4	no	—
101	#10597273	—	2	4	no	—
102	#10597262	—	2	8	no	—
103	C₂⁴×C₁₉	#41	1	1	yes	characteristic
104	C₂³×D₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₉	—	2	2	no	—
121	C₂×C₂²⋊D₁₉	—	2	2	no	—
122	C₂×C₂²⋊D₁₉	—	2	2	no	—
123	C₂×C₂²⋊D₁₉	—	2	2	no	—
124	C₂×C₂²⋊D₁₉	—	2	2	no	—
125	C₂×C₂²⋊D₁₉	—	2	2	no	—
126	C₂²×Dic₁₉	—	2	1	no	—
127	C₂²×Dic₁₉	—	4	1	no	—
128	#64541	—	2	2	no	—
129	#64541	—	2	2	no	—
130	#64541	—	2	2	no	—
131	#64541	—	2	2	no	—
132	#64541	—	2	2	no	—
133	#64541	—	2	2	no	—
134	#64541	—	2	2	no	—
135	#64541	—	2	2	no	—
136	#64541	—	2	2	no	—
137	#64541	—	2	2	no	—
138	#64541	—	2	2	no	—
139	#64541	—	2	2	no	—
140	#64541	C₂²⋊C₄	1	4	yes	—
141	#64541	C₂²⋊C₄	1	4	yes	—
142	#64541	C₄⋊C₄	1	4	yes	—
143	#64541	C₄⋊C₄	1	4	yes	—
144	C₂×D₇₆	—	2	1	no	—
145	C₂×D₇₆	—	2	1	no	—
146	C₂×D₇₆	—	2	1	no	—
147	C₂×D₇₆	C₄²	1	2	yes	—
148	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
149	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
150	C₂×C₄×D₁₉	—	2	2	no	—
151	C₂×C₄×D₁₉	—	2	2	no	—
152	C₂×C₄×D₁₉	—	2	2	no	—
153	C₂×C₄×D₁₉	—	2	2	no	—
154	C₂×C₄×D₁₉	—	2	2	no	—
155	C₂×C₄×D₁₉	—	2	2	no	—
156	C₂×Dic₃₈	—	2	1	no	—
157	C₂×Dic₃₈	—	2	1	no	—
158	C₂×Dic₃₈	—	2	1	no	—
159	C₂×Dic₃₈	C₄²	1	2	yes	—
160	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
161	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	4	1	no	—
168	M₁₆×C₁₉	—	4	1	no	—
169	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	4	1	no	—
175	C₂×C₈×C₁₉	—	4	1	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₂²⋊Dic₁₉	—	2	2	no	—
183	C₂²⋊Dic₁₉	—	4	1	no	—
184	C₄⋊Dic₁₉	—	2	2	no	—
185	C₄⋊Dic₁₉	—	4	1	no	—
186	C₄×Dic₁₉	—	2	2	no	—
187	C₄×Dic₁₉	—	4	1	no	—
188	#64520	—	2	2	no	—
189	#64520	—	2	2	no	—
190	#64520	—	2	2	no	—
191	#64520	—	2	2	no	—
192	#64520	—	2	2	no	—
193	#64520	—	2	2	no	—
194	#64520	—	4	1	no	—
195	#64520	—	4	1	no	—
196	C₂×C₁₉⋊C₈	—	2	2	no	—
197	C₂×C₁₉⋊C₈	—	2	2	no	—
198	C₂×C₁₉⋊C₈	—	2	2	no	—
199	C₂×C₁₉⋊C₈	—	4	1	no	—
200	C₂×C₁₉⋊C₈	—	4	1	no	—
201	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
202	#64515	—	2	16	no	—
203	C₈×D₁₉	—	2	16	no	—
204	#10787	—	19	1	no	maximal, Sylow
205	C₂³×C₁₉	—	8	1	no	—
206	C₂³×C₁₉	#117	1	1	yes	characteristic
207	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₁₉	#121	1	1	yes	characteristic
210	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂³×C₁₉	#123	1	1	yes	characteristic
212	C₂³×C₁₉	#123	1	1	yes	characteristic
213	C₂²×D₁₉	—	2	2	no	—
214	C₂²×D₁₉	—	2	2	no	—
215	C₂²×D₁₉	—	2	2	no	—
216	C₂²×D₁₉	—	8	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	8	2	no	—
219	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
247	C₂²⋊D₁₉	—	2	4	no	—
248	C₂²⋊D₁₉	—	2	4	no	—
249	C₂²⋊D₁₉	—	2	4	no	—
250	C₂²⋊D₁₉	—	2	4	no	—
251	C₂×Dic₁₉	—	2	2	no	—
252	C₂×Dic₁₉	—	2	2	no	—
253	C₂×Dic₁₉	—	2	2	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	8	2	no	—
256	D₇₆	—	2	2	no	—
257	D₇₆	—	2	2	no	—
258	D₇₆	—	2	2	no	—
259	D₇₆	#95	1	4	yes	—
260	C₄×D₁₉	—	2	4	no	—
261	C₄×D₁₉	—	2	4	no	—
262	C₄×D₁₉	—	2	4	no	—
263	C₄×D₁₉	—	2	4	no	—
264	Dic₃₈	—	2	2	no	—
265	Dic₃₈	—	2	2	no	—
266	Dic₃₈	—	2	2	no	—
267	Dic₃₈	#95	1	4	yes	—
268	C₈×C₁₉	—	2	4	no	—
269	C₈×C₁₉	—	4	2	no	—
270	C₁₉⋊C₈	—	2	4	no	—
271	C₁₉⋊C₈	—	4	2	no	—
272	C₂×#568	—	19	1	no	—
273	C₂×#421	—	19	1	no	—
274	#2896	—	19	1	no	—
275	C₂×#344	—	19	1	no	—
276	#1742	D₁₉	1	1	yes	characteristic, complemented
277	#1738	—	19	1	no	—
278	C₂×H(3,ℤ/4)	—	19	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₁₉	#380	1	1	yes	characteristic
288	C₂²×C₁₉	#381	1	1	yes	characteristic
289	C₂²×C₁₉	#385	1	1	yes	characteristic
290	C₂²×C₁₉	#385	1	1	yes	characteristic
291	C₂²×C₁₉	#386	1	1	yes	characteristic
292	C₂²×C₁₉	#386	1	1	yes	characteristic
293	C₂×D₁₉	—	2	4	no	—
294	C₂×D₁₉	—	4	4	no	—
295	C₂×D₁₉	—	8	2	no	—
296	C₂×D₁₉	—	8	2	no	—
297	C₄×C₁₉	—	8	2	no	—
298	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
299	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₁₉	#379	1	1	yes	characteristic
301	C₄×C₁₉	#380	1	1	yes	characteristic
302	C₄×C₁₉	#385	1	1	yes	characteristic
303	C₄×C₁₉	#385	1	1	yes	characteristic
304	C₄×C₁₉	#386	1	1	yes	characteristic
305	C₄×C₁₉	#386	1	1	yes	characteristic
306	Dic₁₉	—	2	4	no	—
307	Dic₁₉	—	8	2	no	—
308	C₂²×#41	—	19	1	no	—
309	#568	—	19	4	no	—
310	#568	—	38	2	no	—
311	#568	—	38	2	no	—
312	#568	—	38	2	no	—
313	C₂×#131	—	38	2	no	—
314	C₂×#131	—	38	2	no	—
315	C₂²×M₁₆	—	19	1	no	—
316	C₂²×M₁₆	—	19	1	no	—
317	C₂²×M₁₆	—	38	2	no	—
318	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
319	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
320	C₂×#117	—	19	1	no	—
321	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
322	#421	—	38	2	no	—
323	#421	—	38	2	no	—
324	C₂×#104	—	19	4	no	—
325	#419	—	19	2	no	—
326	#418	—	19	2	no	—
327	#417	—	38	2	no	—
328	#416	—	38	2	no	—
329	#344	—	38	2	no	—
330	#343	—	2	2	no	—
331	#341	—	38	2	no	—
332	H(3,ℤ/4)	—	38	2	no	—
333	C₂×C₁₉	—	2	1	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	—	2	1	no	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
341	D₁₉	—	4	4	no	—
342	C₂×#41	—	19	2	no	—
343	C₂×#41	—	19	2	no	—
344	C₂×#41	—	19	2	no	—
345	C₂×#41	—	19	2	no	—
346	C₂×#41	—	19	2	no	—
347	C₂×#41	—	19	2	no	—
348	C₂×#41	—	38	1	no	—
349	C₂×#41	—	38	1	no	—
350	C₂×#41	—	38	1	no	—
351	C₂×#41	—	38	1	no	—
352	C₂×#41	—	38	1	no	—
353	C₂×#41	—	38	1	no	—
354	C₂²×Q₈	—	19	1	no	—
355	C₂²×D₄	—	19	1	no	—
356	C₂²×D₄	—	38	1	no	—
357	C₂³×C₄	—	38	1	no	—
358	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
359	#131	—	38	8	no	—
360	#131	—	38	8	no	—
361	#131	—	38	8	no	—
362	#131	—	38	8	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	19	2	no	—
372	C₂×M₁₆	—	19	2	no	—
373	C₂×M₁₆	—	19	2	no	—
374	C₂×M₁₆	—	38	4	no	—
375	C₂×M₁₆	—	38	8	no	—
376	C₂×M₁₆	—	38	1	no	—
377	C₂×M₁₆	—	38	1	no	—
378	C₂×M₁₆	—	38	1	no	—
379	C₂×M₁₆	—	38	1	no	—
380	C₂×M₁₆	—	38	8	no	—
381	C₂×M₁₆	—	38	1	no	—
382	C₂×M₁₆	—	38	1	no	—
383	C₂×M₁₆	—	38	1	no	—
384	C₂×M₁₆	—	38	1	no	—
385	C₂×M₁₆	—	38	1	no	—
386	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
387	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
388	C₂×M₁₆	D₇₆	1	2	yes	—
389	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	19	2	no	—
393	C₂²×C₈	—	38	4	no	—
394	C₂²×C₈	—	38	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	19	2	no	—
400	#117	—	38	1	no	—
401	#117	—	38	1	no	—
402	#117	—	38	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	38	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	38	1	no	—
407	C₂×C₄²	—	38	1	no	—
408	C₂×C₄²	C₄×D₁₉	1	2	yes	—
409	#104	—	38	8	no	—
410	#103	—	38	4	no	—
411	#102	—	38	4	no	—
412	C₁₉	#10787	1	1	yes	characteristic, complemented, Sylow
413	C₂⁴	—	38	1	no	—
414	C₂⁴	#64541	1	1	yes	characteristic
415	#41	—	19	4	no	—
416	#41	—	19	4	no	—
417	#41	—	19	4	no	—
418	#41	—	19	4	no	—
419	#41	—	38	2	no	—
420	#41	—	38	2	no	—
421	#41	—	38	2	no	—
422	#41	—	38	2	no	—
423	#41	—	38	2	no	—
424	#41	—	38	2	no	—
425	#41	—	38	2	no	—
426	#41	—	38	2	no	—
427	#41	—	38	2	no	—
428	#41	—	38	2	no	—
429	#41	—	38	2	no	—
430	#41	—	38	2	no	—
431	C₂×Q₈	—	19	2	no	—
432	C₂×Q₈	—	19	2	no	—
433	C₂×Q₈	—	19	2	no	—
434	C₂×Q₈	—	38	1	no	—
435	C₂×Q₈	—	38	1	no	—
436	C₂×Q₈	—	38	1	no	—
437	C₂×D₄	—	19	2	no	—
438	C₂×D₄	—	19	2	no	—
439	C₂×D₄	—	19	2	no	—
440	C₂×D₄	—	38	2	no	—
441	C₂×D₄	—	38	2	no	—
442	C₂×D₄	—	38	2	no	—
443	C₂×D₄	—	38	2	no	—
444	C₂×D₄	—	38	2	no	—
445	C₂×D₄	—	38	2	no	—
446	C₂×D₄	—	38	1	no	—
447	C₂×D₄	—	38	1	no	—
448	C₂×D₄	—	38	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	38	1	no	—
451	C₂²×C₄	—	38	2	no	—
452	C₂²×C₄	—	38	2	no	—
453	C₂²×C₄	—	38	2	no	—
454	C₂²×C₄	—	38	2	no	—
455	C₂²×C₄	—	38	2	no	—
456	C₂²×C₄	—	38	2	no	—
457	C₂²×C₄	—	76	1	no	—
458	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
462	C₂²×C₄	#64541	1	1	yes	characteristic
463	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
464	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
465	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
466	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
467	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
468	C₂²×C₄	#64543	1	1	yes	characteristic
469	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
470	C₂²×C₄	#64545	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	4	1	no	—
478	M₁₆	—	4	1	no	—
479	M₁₆	—	38	16	no	—
480	M₁₆	—	38	2	no	—
481	M₁₆	—	38	2	no	—
482	M₁₆	—	38	2	no	—
483	M₁₆	—	38	2	no	—
484	M₁₆	—	38	2	no	—
485	M₁₆	—	38	2	no	—
486	M₁₆	—	76	1	no	—
487	M₁₆	—	76	1	no	—
488	M₁₆	(C₂×D₁₉)⋊C₄	1	4	yes	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	19	4	no	—
496	C₂×C₈	—	38	16	no	—
497	C₂×C₈	—	38	2	no	—
498	C₂×C₈	—	38	2	no	—
499	C₂×C₈	—	38	2	no	—
500	C₂×C₈	—	76	1	no	—
501	C₂×C₈	—	76	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	38	2	no	—
505	C₄⋊C₄	—	76	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	38	2	no	—
509	C₂²⋊C₄	—	76	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	38	2	no	—
513	C₄²	—	76	1	no	—
514	C₂³	—	8	1	no	—
515	C₂³	—	38	2	no	—
516	C₂³	—	38	2	no	—
517	C₂³	—	38	2	no	—
518	C₂³	—	152	2	no	—
519	C₂³	#10597318	1	1	yes	characteristic
520	C₂³	C₄×D₇₆	1	1	yes	characteristic
521	C₂³	#10597329	1	1	yes	characteristic
522	C₂³	#10597330	1	1	yes	characteristic
523	C₂³	#10597340	1	1	yes	characteristic
524	C₂³	#10597342	1	1	yes	characteristic
525	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
526	Q₈	—	19	4	no	—
527	Q₈	—	38	2	no	—
528	Q₈	—	38	2	no	—
529	Q₈	—	38	2	no	—
530	D₄	—	19	4	no	—
531	D₄	—	38	4	no	—
532	D₄	—	38	4	no	—
533	D₄	—	38	4	no	—
534	D₄	—	38	4	no	—
535	D₄	—	38	2	no	—
536	D₄	—	38	2	no	—
537	D₄	—	38	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	38	2	no	—
541	C₂×C₄	—	38	2	no	—
542	C₂×C₄	—	38	2	no	—
543	C₂×C₄	—	38	4	no	—
544	C₂×C₄	—	38	4	no	—
545	C₂×C₄	—	38	4	no	—
546	C₂×C₄	—	38	4	no	—
547	C₂×C₄	—	76	2	no	—
548	C₂×C₄	—	152	2	no	—
549	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
550	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
551	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
552	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
554	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
555	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
556	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
557	C₂×C₄	#10597328	1	1	yes	characteristic
558	C₂×C₄	#10597328	1	1	yes	characteristic
559	C₂×C₄	#10597329	1	1	yes	characteristic
560	C₂×C₄	#10597330	1	1	yes	characteristic
561	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
562	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
563	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
564	C₂×C₄	#10597338	1	1	yes	characteristic
565	C₂×C₄	#10597339	1	1	yes	characteristic
566	C₂×C₄	#10597339	1	1	yes	characteristic
567	C₂×C₄	#10597340	1	1	yes	characteristic
568	C₂×C₄	#10597341	1	1	yes	characteristic
569	C₂×C₄	#10597342	1	1	yes	characteristic
570	C₂×C₄	#10597343	1	1	yes	characteristic
571	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
573	C₂×C₄	#10597383	1	1	yes	characteristic
574	C₂×C₄	#10597383	1	1	yes	characteristic
575	C₂×C₄	#10597384	1	1	yes	characteristic
576	C₂×C₄	#10597392	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	4	2	no	—
579	C₈	—	38	4	no	—
580	C₈	—	76	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	38	4	no	—
589	C₂²	—	76	4	no	—
590	C₂²	—	152	2	no	—
591	C₂²	—	152	2	no	—
592	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
593	C₂²	#11926403	1	1	yes	characteristic
594	C₂²	#11926406	1	1	yes	characteristic
595	C₂²	#11926415	1	1	yes	characteristic
596	C₂²	#11926418	1	1	yes	characteristic
597	C₂²	#11926420	1	1	yes	characteristic
598	C₂²	#11926422	1	1	yes	characteristic
599	C₄	—	8	2	no	—
600	C₄	—	38	4	no	—
601	C₄	—	152	2	no	—
602	C₄	#95×D₁₉	1	1	yes	characteristic
603	C₄	#11926391	1	1	yes	characteristic
604	C₄	#11926399	1	1	yes	characteristic
605	C₄	#11926401	1	1	yes	characteristic
606	C₄	#11926415	1	1	yes	characteristic
607	C₄	#11926418	1	1	yes	characteristic
608	C₄	#11926420	1	1	yes	characteristic
609	C₄	#11926422	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	76	4	no	—
618	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926422
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1742	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1742	D₁₉
hypocenter	C₁₉	#10787
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1742

Complements

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

N	H ≅ G/N	type
4. C₂×#11926316	C₂	semidirect
5. #14563361	C₂	semidirect
6. C₂×#11926300	C₂	semidirect
7. C₁₉×#1742	C₂	semidirect
12. #11927310	C₄	semidirect
21. C₂×#10597262	C₄	semidirect
22. #11926554	C₄	semidirect
23. #11926550	C₄	semidirect
276. #1742	D₁₉	semidirect
412. C₁₉	#10787	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927310	2
C₂×#11926562	2
#14572155	2
C₂×#11926316	2
#14563361	2
C₂×#11926300	2
C₁₉×#1742	2
#10787	19