Subgroups — #18090363

Order 4864.

886 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	C₂²×#10597282	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926541	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926512	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×#10597282	—	2	2	no	—
13	C₂×#10597282	—	2	2	no	—
14	C₂×#10597282	—	2	2	no	—
15	#11926541	—	2	2	no	—
16	#11926541	—	2	2	no	—
17	C₂×#10597273	C₄	1	2	yes	complemented
18	C₂×#10597278	C₄	1	2	yes	complemented
19	#11926512	—	2	2	no	—
20	#11926512	—	2	2	no	—
21	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
22	#11926305	—	2	2	no	—
23	#11926298	—	2	2	no	—
24	#11926298	—	2	2	no	—
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#341	—	2	2	no	—
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₂²⋊D₁₉	—	2	1	no	—
31	C₂³×Dic₁₉	—	2	1	no	—
32	C₂×#64541	—	2	1	no	—
33	C₂×#64541	—	2	1	no	—
34	C₂×#64541	—	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	—	2	1	no	—
42	C₂×#64541	D₄	1	2	yes	—
43	C₂×#64541	D₄	1	2	yes	—
44	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₉	—	2	1	no	—
46	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
58	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
69	#10597372	—	2	1	no	—
70	#10597372	—	2	1	no	—
71	#10597372	—	2	1	no	—
72	#10597372	—	2	1	no	—
73	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	—	2	1	no	—
76	C₂×C₄×Dic₁₉	—	2	1	no	—
77	C₂×C₄×Dic₁₉	—	2	1	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×C₄×Dic₁₉	—	2	1	no	—
80	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
81	C₂²×C₁₉⋊C₈	—	2	1	no	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	C₂²×C₁₉⋊C₈	—	2	1	no	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
88	#10597282	—	2	8	no	—
89	#10597278	—	2	4	no	—
90	(C₂×D₁₉)⋊C₈	—	2	8	no	—
91	#10597273	—	2	4	no	—
92	C₂⁴×C₁₉	#41	1	1	yes	characteristic
93	C₂³×D₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂×C₂²⋊D₁₉	—	2	2	no	—
109	C₂×C₂²⋊D₁₉	—	2	2	no	—
110	C₂×C₂²⋊D₁₉	—	4	1	no	—
111	C₂×C₂²⋊D₁₉	—	4	1	no	—
112	C₂×C₂²⋊D₁₉	—	4	1	no	—
113	C₂×C₂²⋊D₁₉	—	4	1	no	—
114	C₂²×Dic₁₉	—	2	4	no	—
115	C₂²×Dic₁₉	—	2	1	no	—
116	C₂²×Dic₁₉	—	2	2	no	—
117	C₂²×Dic₁₉	—	2	2	no	—
118	C₂²×Dic₁₉	—	4	2	no	—
119	C₂²×Dic₁₉	—	4	1	no	—
120	C₂²×Dic₁₉	—	4	1	no	—
121	#64541	—	2	2	no	—
122	#64541	—	2	2	no	—
123	#64541	—	2	2	no	—
124	#64541	—	2	2	no	—
125	#64541	—	2	2	no	—
126	#64541	—	2	2	no	—
127	#64541	—	2	2	no	—
128	#64541	—	2	2	no	—
129	#64541	—	4	1	no	—
130	#64541	—	4	1	no	—
131	#64541	—	4	1	no	—
132	#64541	—	4	1	no	—
133	#64541	—	4	1	no	—
134	#64541	—	4	1	no	—
135	#64541	—	4	1	no	—
136	#64541	—	4	1	no	—
137	C₂×D₇₆	—	2	1	no	—
138	C₂×D₇₆	—	2	1	no	—
139	C₂×D₇₆	—	2	1	no	—
140	C₂×D₇₆	—	2	1	no	—
141	C₂×D₇₆	—	2	1	no	—
142	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×D₁₉	—	2	2	no	—
144	C₂×C₄×D₁₉	—	2	2	no	—
145	C₂×C₄×D₁₉	—	4	1	no	—
146	C₂×C₄×D₁₉	—	4	1	no	—
147	C₂×C₄×D₁₉	—	4	1	no	—
148	C₂×C₄×D₁₉	—	4	1	no	—
149	C₂×Dic₃₈	—	2	1	no	—
150	C₂×Dic₃₈	—	2	1	no	—
151	C₂×Dic₃₈	—	2	1	no	—
152	C₂×Dic₃₈	—	2	1	no	—
153	C₂×Dic₃₈	—	2	1	no	—
154	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	2	2	no	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	4	1	no	—
160	M₁₆×C₁₉	—	4	1	no	—
161	M₁₆×C₁₉	—	4	1	no	—
162	M₁₆×C₁₉	—	4	1	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	4	1	no	—
169	C₂×C₈×C₁₉	—	4	1	no	—
170	C₂×C₈×C₁₉	—	4	1	no	—
171	C₂×C₈×C₁₉	—	4	1	no	—
172	C₂×C₈×C₁₉	—	4	1	no	—
173	C₂×C₈×C₁₉	—	4	1	no	—
174	C₂×C₈×C₁₉	—	4	1	no	—
175	C₂×C₈×C₁₉	—	4	1	no	—
176	C₂²⋊Dic₁₉	—	4	1	no	—
177	C₂²⋊Dic₁₉	—	4	1	no	—
178	C₄⋊Dic₁₉	—	2	2	no	—
179	C₄⋊Dic₁₉	—	2	2	no	—
180	C₄×Dic₁₉	—	2	2	no	—
181	C₄×Dic₁₉	—	2	2	no	—
182	C₄×Dic₁₉	—	4	1	no	—
183	C₄×Dic₁₉	—	4	1	no	—
184	C₄×Dic₁₉	—	4	1	no	—
185	C₄×Dic₁₉	—	4	1	no	—
186	C₂×C₁₉⋊C₈	—	2	2	no	—
187	C₂×C₁₉⋊C₈	—	2	2	no	—
188	C₂×C₁₉⋊C₈	—	2	2	no	—
189	C₂×C₁₉⋊C₈	—	4	1	no	—
190	C₂×C₁₉⋊C₈	—	4	1	no	—
191	C₂×C₁₉⋊C₈	—	4	1	no	—
192	C₂×C₁₉⋊C₈	—	4	1	no	—
193	#11191	—	19	1	no	maximal, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
197	C₂³×C₁₉	#121	1	1	yes	characteristic
198	C₂³×C₁₉	#123	1	1	yes	characteristic
199	C₂³×C₁₉	#123	1	1	yes	characteristic
200	C₂³×C₁₉	#124	1	1	yes	characteristic
201	C₂³×C₁₉	#126	1	1	yes	characteristic
202	C₂³×C₁₉	#126	1	1	yes	characteristic
203	C₂²×D₁₉	—	2	2	no	—
204	C₂²×D₁₉	—	4	1	no	—
205	C₂²×D₁₉	—	4	1	no	—
206	C₂²×D₁₉	—	4	2	no	—
207	C₂²×D₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
236	C₂²⋊D₁₉	—	4	2	no	—
237	C₂²⋊D₁₉	—	4	2	no	—
238	C₂²⋊D₁₉	—	4	2	no	—
239	C₂²⋊D₁₉	—	4	2	no	—
240	C₂×Dic₁₉	—	2	4	no	—
241	C₂×Dic₁₉	—	2	2	no	—
242	C₂×Dic₁₉	—	4	4	no	—
243	C₂×Dic₁₉	—	4	4	no	—
244	C₂×Dic₁₉	—	4	2	no	—
245	C₂×Dic₁₉	—	4	1	no	—
246	C₂×Dic₁₉	—	4	1	no	—
247	C₂×Dic₁₉	—	4	2	no	—
248	C₂×Dic₁₉	—	4	2	no	—
249	C₂×Dic₁₉	—	4	2	no	—
250	C₂×Dic₁₉	—	4	2	no	—
251	D₇₆	—	2	2	no	—
252	D₇₆	—	2	2	no	—
253	D₇₆	—	4	1	no	—
254	D₇₆	—	4	1	no	—
255	C₄×D₁₉	—	4	2	no	—
256	C₄×D₁₉	—	4	2	no	—
257	C₄×D₁₉	—	4	2	no	—
258	C₄×D₁₉	—	4	2	no	—
259	Dic₃₈	—	2	2	no	—
260	Dic₃₈	—	2	2	no	—
261	Dic₃₈	—	4	1	no	—
262	Dic₃₈	—	4	1	no	—
263	C₈×C₁₉	—	4	2	no	—
264	C₈×C₁₉	—	4	2	no	—
265	C₈×C₁₉	—	4	2	no	—
266	C₁₉⋊C₈	—	4	2	no	—
267	C₂²×#104	—	19	1	no	—
268	C₂×#416	—	19	1	no	—
269	C₂×#408	—	19	1	no	—
270	C₂×#341	D₁₉	1	1	yes	characteristic, complemented
271	C₂×#339	—	19	1	no	—
272	#1729	—	19	1	no	—
273	C₂×#336	—	19	1	no	—
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	#386	1	1	yes	characteristic
283	C₂²×C₁₉	#388	1	1	yes	characteristic
284	C₂²×C₁₉	#388	1	1	yes	characteristic
285	C₂²×C₁₉	#394	1	1	yes	characteristic
286	C₂²×C₁₉	#397	1	1	yes	characteristic
287	C₂²×C₁₉	#397	1	1	yes	characteristic
288	C₂²×C₁₉	#397	1	1	yes	characteristic
289	C₂²×C₁₉	#443	1	2	yes	—
290	C₂²×C₁₉	#444	1	2	yes	—
291	C₂×D₁₉	—	4	4	no	—
292	C₂×D₁₉	—	4	2	no	—
293	C₂×D₁₉	—	8	2	no	—
294	C₂×D₁₉	—	8	1	no	—
295	C₂×D₁₉	—	8	1	no	—
296	C₄×C₁₉	#381	1	1	yes	characteristic
297	C₄×C₁₉	#386	1	1	yes	characteristic
298	C₄×C₁₉	#388	1	1	yes	characteristic
299	C₄×C₁₉	#388	1	1	yes	characteristic
300	C₄×C₁₉	#394	1	1	yes	characteristic
301	C₄×C₁₉	#394	1	1	yes	characteristic
302	C₄×C₁₉	#394	1	1	yes	characteristic
303	C₄×C₁₉	#397	1	1	yes	characteristic
304	Dic₁₉	—	4	4	no	—
305	Dic₁₉	—	4	2	no	—
306	Dic₁₉	—	8	2	no	—
307	C₂²×#41	—	19	1	no	—
308	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
309	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
310	C₂³×C₈	—	19	1	no	—
311	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
312	C₂×#117	—	19	1	no	—
313	C₂²×C₄²	—	19	1	no	—
314	C₂×#104	—	38	2	no	—
315	C₂×#104	—	38	2	no	—
316	C₂×#104	—	38	2	no	—
317	#416	—	38	2	no	—
318	#416	—	38	2	no	—
319	C₂×#103	—	19	2	no	—
320	C₂×#102	—	19	2	no	—
321	#408	—	38	2	no	—
322	#408	—	38	2	no	—
323	C₂×C₂²⋊C₈	—	38	2	no	—
324	#341	—	2	2	no	—
325	#339	—	38	2	no	—
326	#336	—	38	2	no	—
327	#336	—	38	2	no	—
328	C₂×C₁₉	—	2	1	no	—
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	#1440	1	1	yes	characteristic
333	C₂×C₁₉	#1876	1	2	yes	—
334	C₂×C₁₉	#1929	1	2	yes	—
335	C₂×C₁₉	#1937	1	1	yes	characteristic
336	C₂×C₁₉	#1938	1	1	yes	characteristic
337	D₁₉	—	8	2	no	—
338	C₂×#41	—	19	2	no	—
339	C₂×#41	—	19	2	no	—
340	C₂×#41	—	38	1	no	—
341	C₂×#41	—	38	1	no	—
342	C₂×#41	—	38	1	no	—
343	C₂×#41	—	38	1	no	—
344	C₂×#41	—	38	1	no	—
345	C₂×#41	—	38	1	no	—
346	C₂×#41	—	38	1	no	—
347	C₂×#41	—	38	1	no	—
348	C₂×#41	—	38	1	no	—
349	C₂×#41	—	38	1	no	—
350	C₂²×Q₈	—	19	1	no	—
351	C₂²×D₄	—	19	1	no	—
352	C₂²×D₄	—	38	1	no	—
353	C₂³×C₄	—	38	1	no	—
354	C₂³×C₄	—	38	1	no	—
355	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	D₇₆	1	2	yes	—
367	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	19	2	no	—
377	C₂²×C₈	—	38	1	no	—
378	C₂²×C₈	—	38	1	no	—
379	C₂²×C₈	—	38	1	no	—
380	C₂²×C₈	—	38	1	no	—
381	C₂²×C₈	—	38	1	no	—
382	C₂²×C₈	—	38	1	no	—
383	C₂²×C₈	C₄×D₁₉	1	2	yes	—
384	#117	—	38	1	no	—
385	#117	—	38	1	no	—
386	#117	—	38	1	no	—
387	#117	—	38	1	no	—
388	C₂×C₄⋊C₄	—	19	2	no	—
389	C₂×C₂²⋊C₄	—	38	1	no	—
390	C₂×C₄²	—	19	2	no	—
391	C₂×C₄²	—	38	1	no	—
392	C₂×C₄²	—	38	1	no	—
393	C₂×C₄²	—	38	1	no	—
394	C₂×C₄²	—	38	1	no	—
395	C₂×C₄²	—	38	1	no	—
396	C₂×C₄²	—	38	1	no	—
397	#104	—	38	8	no	—
398	#103	—	38	4	no	—
399	#102	—	38	4	no	—
400	C₂²⋊C₈	—	38	8	no	—
401	C₁₉	#11191	1	1	yes	characteristic, complemented, Sylow
402	C₂⁴	—	38	1	no	—
403	C₂⁴	#64545	1	1	yes	characteristic
404	#41	—	38	2	no	—
405	#41	—	38	2	no	—
406	#41	—	38	2	no	—
407	#41	—	38	2	no	—
408	#41	—	38	2	no	—
409	#41	—	38	2	no	—
410	#41	—	38	2	no	—
411	#41	—	38	2	no	—
412	#41	—	76	1	no	—
413	#41	—	76	1	no	—
414	#41	—	76	1	no	—
415	#41	—	76	1	no	—
416	#41	—	76	1	no	—
417	#41	—	76	1	no	—
418	#41	—	76	1	no	—
419	#41	—	76	1	no	—
420	C₂×Q₈	—	19	2	no	—
421	C₂×Q₈	—	38	1	no	—
422	C₂×Q₈	—	38	1	no	—
423	C₂×Q₈	—	38	1	no	—
424	C₂×Q₈	—	38	1	no	—
425	C₂×Q₈	—	38	1	no	—
426	C₂×D₄	—	19	2	no	—
427	C₂×D₄	—	38	2	no	—
428	C₂×D₄	—	38	2	no	—
429	C₂×D₄	—	38	1	no	—
430	C₂×D₄	—	38	1	no	—
431	C₂×D₄	—	38	1	no	—
432	C₂×D₄	—	38	1	no	—
433	C₂×D₄	—	38	1	no	—
434	C₂×D₄	—	76	1	no	—
435	C₂×D₄	—	76	1	no	—
436	C₂×D₄	—	76	1	no	—
437	C₂×D₄	—	76	1	no	—
438	C₂²×C₄	—	38	4	no	—
439	C₂²×C₄	—	38	1	no	—
440	C₂²×C₄	—	38	2	no	—
441	C₂²×C₄	—	38	2	no	—
442	C₂²×C₄	—	38	2	no	—
443	C₂²×C₄	—	38	2	no	—
444	C₂²×C₄	—	76	2	no	—
445	C₂²×C₄	—	76	1	no	—
446	C₂²×C₄	—	76	1	no	—
447	C₂²×C₄	—	76	1	no	—
448	C₂²×C₄	—	76	1	no	—
449	C₂²×C₄	—	76	1	no	—
450	C₂²×C₄	—	76	1	no	—
451	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
453	C₂²×C₄	#64541	1	1	yes	characteristic
454	C₂²×C₄	#64541	1	1	yes	characteristic
455	C₂²×C₄	#64541	1	1	yes	characteristic
456	C₂²×C₄	#64541	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
461	C₂²×C₄	#64543	1	1	yes	characteristic
462	C₂²×C₄	#64543	1	1	yes	characteristic
463	C₂²×C₄	#64545	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	38	2	no	—
487	C₂×C₈	—	38	2	no	—
488	C₂×C₈	—	38	2	no	—
489	C₂×C₈	—	76	1	no	—
490	C₂×C₈	—	76	1	no	—
491	C₂×C₈	—	76	1	no	—
492	C₂×C₈	—	76	1	no	—
493	C₄⋊C₄	—	38	2	no	—
494	C₄⋊C₄	—	38	2	no	—
495	C₂²⋊C₄	—	76	1	no	—
496	C₂²⋊C₄	—	76	1	no	—
497	C₄²	—	38	2	no	—
498	C₄²	—	38	2	no	—
499	C₄²	—	76	1	no	—
500	C₄²	—	76	1	no	—
501	C₄²	—	76	1	no	—
502	C₄²	—	76	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	38	2	no	—
506	C₂³	—	76	2	no	—
507	C₂³	—	76	2	no	—
508	C₂³	—	76	1	no	—
509	C₂³	—	76	1	no	—
510	C₂³	#10597339	1	1	yes	characteristic
511	C₂³	#10597340	1	1	yes	characteristic
512	C₂³	#10597340	1	1	yes	characteristic
513	C₂³	#10597341	1	1	yes	characteristic
514	C₂³	#10597344	1	1	yes	characteristic
515	C₂³	#10597344	1	1	yes	characteristic
516	C₂³	#10597393	1	1	yes	characteristic
517	Q₈	—	38	2	no	—
518	Q₈	—	38	2	no	—
519	Q₈	—	76	1	no	—
520	Q₈	—	76	1	no	—
521	D₄	—	38	2	no	—
522	D₄	—	38	2	no	—
523	D₄	—	76	2	no	—
524	D₄	—	76	2	no	—
525	D₄	—	76	2	no	—
526	D₄	—	76	2	no	—
527	D₄	—	76	1	no	—
528	D₄	—	76	1	no	—
529	C₂×C₄	—	38	4	no	—
530	C₂×C₄	—	38	2	no	—
531	C₂×C₄	—	76	4	no	—
532	C₂×C₄	—	76	4	no	—
533	C₂×C₄	—	76	2	no	—
534	C₂×C₄	—	76	1	no	—
535	C₂×C₄	—	76	1	no	—
536	C₂×C₄	—	76	2	no	—
537	C₂×C₄	—	76	2	no	—
538	C₂×C₄	—	76	2	no	—
539	C₂×C₄	—	76	2	no	—
540	C₂×C₄	—	76	2	no	—
541	C₂×C₄	—	76	2	no	—
542	C₂×C₄	—	76	2	no	—
543	C₂×C₄	—	76	2	no	—
544	C₂×C₄	#10597318	1	1	yes	characteristic
545	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
546	C₂×C₄	#10597321	1	1	yes	characteristic
547	C₂×C₄	#10597322	1	1	yes	characteristic
548	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
549	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
550	C₂×C₄	#10597328	1	1	yes	characteristic
551	C₂×C₄	#10597329	1	1	yes	characteristic
552	C₂×C₄	#10597329	1	1	yes	characteristic
553	C₂×C₄	#10597329	1	1	yes	characteristic
554	C₂×C₄	#10597330	1	1	yes	characteristic
555	C₂×C₄	#10597330	1	1	yes	characteristic
556	C₂×C₄	#10597330	1	1	yes	characteristic
557	C₂×C₄	#10597331	1	1	yes	characteristic
558	C₂×C₄	#10597331	1	1	yes	characteristic
559	C₂×C₄	#10597332	1	1	yes	characteristic
560	C₂×C₄	#10597338	1	1	yes	characteristic
561	C₂×C₄	#10597340	1	1	yes	characteristic
562	C₂×C₄	#10597340	1	1	yes	characteristic
563	C₂×C₄	#10597340	1	1	yes	characteristic
564	C₂×C₄	#10597341	1	1	yes	characteristic
565	C₂×C₄	#10597344	1	1	yes	characteristic
566	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
567	C₂×C₄	#10597375	1	1	yes	characteristic
568	C₂×C₄	#10597376	1	1	yes	characteristic
569	C₂×C₄	#10597383	1	1	yes	characteristic
570	C₂×C₄	#10597384	1	1	yes	characteristic
571	C₂×C₄	#10597385	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₈	—	4	2	no	—
575	C₈	—	76	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	76	2	no	—
585	C₂²	—	76	4	no	—
586	C₂²	—	152	2	no	—
587	C₂²	—	152	1	no	—
588	C₂²	—	152	1	no	—
589	C₂²	#11926422	1	1	yes	characteristic
590	C₂²	#11926433	1	1	yes	characteristic
591	C₂²	#11926434	1	1	yes	characteristic
592	C₂²	#11926461	1	1	yes	characteristic
593	C₂²	#11926470	1	1	yes	characteristic
594	C₂²	#11926471	1	1	yes	characteristic
595	C₂²	#11926473	1	1	yes	characteristic
596	C₂²	#11926660	1	2	yes	—
597	C₂²	#11926665	1	2	yes	—
598	C₄	—	76	4	no	—
599	C₄	—	76	2	no	—
600	C₄	—	152	2	no	—
601	C₄	#11926406	1	1	yes	characteristic
602	C₄	#11926420	1	1	yes	characteristic
603	C₄	#11926435	1	1	yes	characteristic
604	C₄	#11926436	1	1	yes	characteristic
605	C₄	#11926459	1	1	yes	characteristic
606	C₄	#11926460	1	1	yes	characteristic
607	C₄	#11926462	1	1	yes	characteristic
608	C₄	#11926473	1	1	yes	characteristic
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	152	2	no	—
614	C₂	#14561883	1	1	yes	characteristic
615	C₂	#14563963	1	2	yes	—
616	C₂	#14564282	1	2	yes	—
617	C₂	#14564337	1	1	yes	characteristic
618	C₂	#14564344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#341	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#341	D₁₉
hypocenter	C₁₉	#11191
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#341

Complements

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

N	H ≅ G/N	type
4. C₂×#11926305	C₂	semidirect
5. #14563333	C₂	semidirect
6. C₂×#11926298	C₂	semidirect
7. C₂×C₁₉×#341	C₂	semidirect
17. C₂×#10597273	C₄	semidirect
18. C₂×#10597278	C₄	semidirect
270. C₂×#341	D₁₉	semidirect
401. C₁₉	#11191	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597282	2
C₂×#11926541	2
C₂×#11926512	2
C₂×#11926305	2
#14563333	2
C₂×#11926298	2
C₂×C₁₉×#341	2
#11191	19