Subgroups — #18088060

Order 4864.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 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	#14572155	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926541	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926316	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563346	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563331	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	#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	C₂×M₁₆×D₁₉	—	2	2	no	—
17	C₂×#10597372	C₂²	1	1	yes	characteristic
18	C₂×#10597372	C₂²	1	1	yes	characteristic
19	#11926554	—	2	1	no	—
20	#11926550	—	2	1	no	—
21	#11926546	C₄	1	4	yes	complemented
22	#11926541	—	2	2	no	—
23	#11926541	—	2	2	no	—
24	#11926541	C₄	1	4	yes	complemented
25	C₂×#10597273	—	2	1	no	—
26	C₂×#10597278	—	2	1	no	—
27	#11926316	—	2	2	no	—
28	#11926305	—	2	2	no	—
29	#11926298	—	2	2	no	—
30	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#341	—	2	2	no	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₂²⋊D₁₉	—	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	C₂×C₄	1	2	yes	—
43	C₂×#64541	C₂×C₄	1	2	yes	—
44	C₂×#64541	C₂×C₄	1	2	yes	—
45	C₂×#64541	D₄	1	2	yes	—
46	C₂×#64541	D₄	1	2	yes	—
47	C₂×#64541	Q₈	1	2	yes	—
48	C₂²×D₇₆	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₉	—	2	1	no	—
50	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
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	—	2	1	no	—
59	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
62	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
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	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
73	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
74	#10597372	—	2	1	no	—
75	#10597372	—	2	1	no	—
76	#10597372	—	2	1	no	—
77	#10597372	—	2	1	no	—
78	#10597372	—	2	1	no	—
79	#10597372	—	2	1	no	—
80	#10597372	—	2	1	no	—
81	#10597372	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊Dic₁₉	—	2	1	no	—
83	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₄×Dic₁₉	—	2	1	no	—
85	C₂×C₄×Dic₁₉	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	—	2	1	no	—
88	C₂×#64520	—	2	1	no	—
89	C₂×#64520	—	2	1	no	—
90	C₂×#64520	C₂×C₄	1	2	yes	—
91	C₂×#64520	D₄	1	2	yes	—
92	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
93	#10597353	—	2	8	no	—
94	#10597353	—	2	8	no	—
95	M₁₆×D₁₉	—	2	8	no	—
96	M₁₆×D₁₉	—	2	8	no	—
97	#10597347	—	2	8	no	—
98	#10597347	—	2	8	no	—
99	C₂×#64515	—	2	4	no	—
100	C₂×C₈×D₁₉	—	2	4	no	—
101	#10597278	—	2	4	no	—
102	#10597278	—	2	4	no	—
103	#10597273	—	2	4	no	—
104	#10597273	—	2	4	no	—
105	C₂⁴×C₁₉	#41	1	1	yes	characteristic
106	C₂³×D₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂²×C₄	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×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
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	C₂×C₂²⋊D₁₉	—	2	2	no	—
127	C₂²×Dic₁₉	—	2	1	no	—
128	C₂²×Dic₁₉	—	2	2	no	—
129	C₂²×Dic₁₉	—	4	1	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	—	2	2	no	—
141	#64541	—	2	2	no	—
142	#64541	C₄²	1	4	yes	—
143	#64541	C₂²⋊C₄	1	4	yes	—
144	#64541	C₄⋊C₄	1	4	yes	—
145	#64541	C₄⋊C₄	1	4	yes	—
146	C₂×D₇₆	—	2	1	no	—
147	C₂×D₇₆	—	2	1	no	—
148	C₂×D₇₆	—	2	1	no	—
149	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
150	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
151	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
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×C₄×D₁₉	—	2	2	no	—
157	C₂×C₄×D₁₉	—	2	2	no	—
158	C₂×Dic₃₈	—	2	1	no	—
159	C₂×Dic₃₈	—	2	1	no	—
160	C₂×Dic₃₈	—	2	1	no	—
161	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
162	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
163	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	2	2	no	—
168	M₁₆×C₁₉	—	2	2	no	—
169	M₁₆×C₁₉	—	4	1	no	—
170	M₁₆×C₁₉	—	4	1	no	—
171	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	2	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₂×C₈×C₁₉	—	4	1	no	—
180	C₂×C₈×C₁₉	—	4	1	no	—
181	C₂×C₈×C₁₉	—	4	1	no	—
182	C₂×C₈×C₁₉	—	4	1	no	—
183	C₂×C₈×C₁₉	—	4	1	no	—
184	C₂×C₈×C₁₉	—	4	1	no	—
185	C₂²⋊Dic₁₉	—	2	2	no	—
186	C₂²⋊Dic₁₉	—	4	1	no	—
187	C₂²⋊Dic₁₉	—	4	1	no	—
188	C₂²⋊Dic₁₉	—	4	1	no	—
189	C₄⋊Dic₁₉	—	2	2	no	—
190	C₄⋊Dic₁₉	—	2	2	no	—
191	C₄⋊Dic₁₉	—	2	2	no	—
192	C₄⋊Dic₁₉	—	4	1	no	—
193	C₄×Dic₁₉	—	2	2	no	—
194	C₄×Dic₁₉	—	4	1	no	—
195	C₄×Dic₁₉	—	4	1	no	—
196	C₄×Dic₁₉	—	4	1	no	—
197	#64520	—	2	2	no	—
198	#64520	—	2	2	no	—
199	#64520	—	2	2	no	—
200	#64520	—	2	2	no	—
201	C₂×C₁₉⋊C₈	—	2	2	no	—
202	C₂×C₁₉⋊C₈	—	2	2	no	—
203	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
204	#64515	—	2	16	no	—
205	C₈×D₁₉	—	2	16	no	—
206	#10782	—	19	1	no	maximal, Sylow
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	#117	1	1	yes	characteristic
209	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
211	C₂³×C₁₉	#121	1	1	yes	characteristic
212	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₁₉	#123	1	1	yes	characteristic
214	C₂³×C₁₉	#123	1	1	yes	characteristic
215	C₂²×D₁₉	—	2	2	no	—
216	C₂²×D₁₉	—	2	2	no	—
217	C₂²×D₁₉	—	2	2	no	—
218	C₂²×D₁₉	—	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	4	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	8	2	no	—
258	D₇₆	—	2	2	no	—
259	D₇₆	—	2	2	no	—
260	D₇₆	—	2	2	no	—
261	D₇₆	#95	1	4	yes	—
262	C₄×D₁₉	—	2	4	no	—
263	C₄×D₁₉	—	2	4	no	—
264	C₄×D₁₉	—	2	4	no	—
265	C₄×D₁₉	—	2	4	no	—
266	Dic₃₈	—	2	2	no	—
267	Dic₃₈	—	2	2	no	—
268	Dic₃₈	—	2	2	no	—
269	Dic₃₈	#95	1	4	yes	—
270	C₈×C₁₉	—	2	4	no	—
271	C₈×C₁₉	—	4	2	no	—
272	C₈×C₁₉	—	4	2	no	—
273	C₁₉⋊C₈	—	2	4	no	—
274	C₂×#568	—	19	1	no	—
275	#2896	—	19	1	no	—
276	C₂×#416	—	19	1	no	—
277	C₂×#344	—	19	1	no	—
278	C₂×#341	D₁₉	1	1	yes	characteristic, complemented
279	#1733	—	19	1	no	—
280	#1729	—	19	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	2	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₁₉	#380	1	1	yes	characteristic
290	C₂²×C₁₉	#381	1	1	yes	characteristic
291	C₂²×C₁₉	#385	1	1	yes	characteristic
292	C₂²×C₁₉	#385	1	1	yes	characteristic
293	C₂²×C₁₉	#386	1	1	yes	characteristic
294	C₂²×C₁₉	#386	1	1	yes	characteristic
295	C₂×D₁₉	—	2	4	no	—
296	C₂×D₁₉	—	4	4	no	—
297	C₂×D₁₉	—	8	2	no	—
298	C₂×D₁₉	—	8	2	no	—
299	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
300	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×C₁₉	#379	1	1	yes	characteristic
302	C₄×C₁₉	#380	1	1	yes	characteristic
303	C₄×C₁₉	#385	1	1	yes	characteristic
304	C₄×C₁₉	#385	1	1	yes	characteristic
305	C₄×C₁₉	#386	1	1	yes	characteristic
306	C₄×C₁₉	#386	1	1	yes	characteristic
307	Dic₁₉	—	2	4	no	—
308	Dic₁₉	—	8	2	no	—
309	Dic₁₉	—	8	2	no	—
310	C₂²×#41	—	19	1	no	—
311	#568	—	19	4	no	—
312	#568	—	38	2	no	—
313	#568	—	38	2	no	—
314	#568	—	38	2	no	—
315	C₂×#131	—	38	2	no	—
316	C₂×#131	—	38	2	no	—
317	C₂²×M₁₆	—	19	1	no	—
318	C₂²×M₁₆	—	38	2	no	—
319	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
320	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
321	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
322	C₂×#117	—	19	1	no	—
323	C₂×#117	—	19	1	no	—
324	#419	—	38	1	no	—
325	#418	—	38	1	no	—
326	#417	—	19	4	no	—
327	#416	—	19	4	no	—
328	#416	—	38	2	no	—
329	#416	—	38	2	no	—
330	C₂×#103	—	38	1	no	—
331	C₂×#102	—	38	1	no	—
332	#344	—	38	2	no	—
333	#341	—	2	2	no	—
334	#339	—	38	2	no	—
335	#336	—	38	2	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	—	2	1	no	—
341	C₂×C₁₉	—	2	1	no	—
342	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
343	C₂×C₁₉	#1881	1	2	yes	—
344	D₁₉	—	4	4	no	—
345	C₂×#41	—	19	2	no	—
346	C₂×#41	—	19	2	no	—
347	C₂×#41	—	19	2	no	—
348	C₂×#41	—	19	2	no	—
349	C₂×#41	—	19	2	no	—
350	C₂×#41	—	19	2	no	—
351	C₂×#41	—	38	1	no	—
352	C₂×#41	—	38	1	no	—
353	C₂×#41	—	38	1	no	—
354	C₂×#41	—	38	1	no	—
355	C₂×#41	—	38	1	no	—
356	C₂×#41	—	38	1	no	—
357	C₂²×Q₈	—	19	1	no	—
358	C₂²×D₄	—	19	1	no	—
359	C₂²×D₄	—	38	1	no	—
360	C₂³×C₄	—	38	1	no	—
361	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
362	#131	—	38	8	no	—
363	#131	—	38	8	no	—
364	#131	—	38	8	no	—
365	#131	—	38	8	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	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	19	2	no	—
375	C₂×M₁₆	—	19	2	no	—
376	C₂×M₁₆	—	38	4	no	—
377	C₂×M₁₆	—	38	8	no	—
378	C₂×M₁₆	—	38	1	no	—
379	C₂×M₁₆	—	38	1	no	—
380	C₂×M₁₆	—	38	1	no	—
381	C₂×M₁₆	—	38	1	no	—
382	C₂×M₁₆	—	38	8	no	—
383	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
384	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
385	C₂×M₁₆	D₇₆	1	2	yes	—
386	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	19	2	no	—
396	C₂²×C₈	—	38	4	no	—
397	C₂²×C₈	C₄×D₁₉	1	2	yes	—
398	#117	—	19	2	no	—
399	#117	—	38	1	no	—
400	#117	—	38	1	no	—
401	#117	—	38	1	no	—
402	#117	—	38	1	no	—
403	#117	—	38	1	no	—
404	#117	—	38	1	no	—
405	#117	—	38	1	no	—
406	C₂×C₄⋊C₄	—	19	2	no	—
407	C₂×C₄⋊C₄	—	38	1	no	—
408	C₂×C₂²⋊C₄	—	38	1	no	—
409	C₂×C₂²⋊C₄	—	38	1	no	—
410	C₂×C₄²	—	38	1	no	—
411	C₂×C₄²	—	38	1	no	—
412	#103	—	38	4	no	—
413	#103	—	38	4	no	—
414	#102	—	38	4	no	—
415	#102	—	38	4	no	—
416	C₁₉	#10782	1	1	yes	characteristic, complemented, Sylow
417	C₂⁴	—	38	1	no	—
418	C₂⁴	#64545	1	1	yes	characteristic
419	#41	—	19	4	no	—
420	#41	—	19	4	no	—
421	#41	—	19	4	no	—
422	#41	—	19	4	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	#41	—	38	2	no	—
432	#41	—	38	2	no	—
433	#41	—	38	2	no	—
434	#41	—	38	2	no	—
435	C₂×Q₈	—	19	2	no	—
436	C₂×Q₈	—	19	2	no	—
437	C₂×Q₈	—	19	2	no	—
438	C₂×Q₈	—	38	1	no	—
439	C₂×Q₈	—	38	1	no	—
440	C₂×Q₈	—	38	1	no	—
441	C₂×D₄	—	19	2	no	—
442	C₂×D₄	—	19	2	no	—
443	C₂×D₄	—	19	2	no	—
444	C₂×D₄	—	38	2	no	—
445	C₂×D₄	—	38	2	no	—
446	C₂×D₄	—	38	2	no	—
447	C₂×D₄	—	38	2	no	—
448	C₂×D₄	—	38	2	no	—
449	C₂×D₄	—	38	2	no	—
450	C₂×D₄	—	38	1	no	—
451	C₂×D₄	—	38	1	no	—
452	C₂×D₄	—	38	1	no	—
453	C₂²×C₄	—	38	1	no	—
454	C₂²×C₄	—	38	2	no	—
455	C₂²×C₄	—	38	2	no	—
456	C₂²×C₄	—	38	2	no	—
457	C₂²×C₄	—	38	2	no	—
458	C₂²×C₄	—	38	2	no	—
459	C₂²×C₄	—	38	2	no	—
460	C₂²×C₄	—	38	2	no	—
461	C₂²×C₄	—	76	1	no	—
462	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
466	C₂²×C₄	#64541	1	1	yes	characteristic
467	C₂²×C₄	#64541	1	1	yes	characteristic
468	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
469	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
472	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
473	C₂²×C₄	#64543	1	1	yes	characteristic
474	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	4	1	no	—
482	M₁₆	—	4	1	no	—
483	M₁₆	—	38	16	no	—
484	M₁₆	—	38	2	no	—
485	M₁₆	—	38	2	no	—
486	M₁₆	—	38	2	no	—
487	M₁₆	—	38	2	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	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	4	1	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	4	1	no	—
499	C₂×C₈	—	4	1	no	—
500	C₂×C₈	—	4	1	no	—
501	C₂×C₈	—	4	1	no	—
502	C₂×C₈	—	19	4	no	—
503	C₂×C₈	—	38	16	no	—
504	C₂×C₈	—	38	2	no	—
505	C₂×C₈	—	38	2	no	—
506	C₄⋊C₄	—	38	2	no	—
507	C₄⋊C₄	—	38	2	no	—
508	C₄⋊C₄	—	38	2	no	—
509	C₄⋊C₄	—	76	1	no	—
510	C₂²⋊C₄	—	38	2	no	—
511	C₂²⋊C₄	—	76	1	no	—
512	C₂²⋊C₄	—	76	1	no	—
513	C₂²⋊C₄	—	76	1	no	—
514	C₄²	—	38	2	no	—
515	C₄²	—	76	1	no	—
516	C₄²	—	76	1	no	—
517	C₄²	—	76	1	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	38	2	no	—
520	C₂³	—	38	2	no	—
521	C₂³	—	38	2	no	—
522	C₂³	—	152	2	no	—
523	C₂³	#10597338	1	1	yes	characteristic
524	C₂³	#10597339	1	1	yes	characteristic
525	C₂³	#10597339	1	1	yes	characteristic
526	C₂³	#10597340	1	1	yes	characteristic
527	C₂³	#10597340	1	1	yes	characteristic
528	C₂³	#10597341	1	1	yes	characteristic
529	C₂³	#10597392	1	1	yes	characteristic
530	Q₈	—	19	4	no	—
531	Q₈	—	38	2	no	—
532	Q₈	—	38	2	no	—
533	Q₈	—	38	2	no	—
534	D₄	—	19	4	no	—
535	D₄	—	38	4	no	—
536	D₄	—	38	4	no	—
537	D₄	—	38	4	no	—
538	D₄	—	38	4	no	—
539	D₄	—	38	2	no	—
540	D₄	—	38	2	no	—
541	D₄	—	38	2	no	—
542	C₂×C₄	—	38	2	no	—
543	C₂×C₄	—	38	2	no	—
544	C₂×C₄	—	38	2	no	—
545	C₂×C₄	—	38	4	no	—
546	C₂×C₄	—	38	4	no	—
547	C₂×C₄	—	38	4	no	—
548	C₂×C₄	—	38	4	no	—
549	C₂×C₄	—	76	4	no	—
550	C₂×C₄	—	76	2	no	—
551	C₂×C₄	—	76	2	no	—
552	C₂×C₄	—	152	2	no	—
553	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
554	C₂×C₄	#10597318	1	1	yes	characteristic
555	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
556	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
557	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
558	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
559	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
560	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
561	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
562	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
563	C₂×C₄	#10597328	1	1	yes	characteristic
564	C₂×C₄	#10597328	1	1	yes	characteristic
565	C₂×C₄	#10597329	1	1	yes	characteristic
566	C₂×C₄	#10597329	1	1	yes	characteristic
567	C₂×C₄	#10597330	1	1	yes	characteristic
568	C₂×C₄	#10597330	1	1	yes	characteristic
569	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
570	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
571	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
572	C₂×C₄	#10597342	1	1	yes	characteristic
573	C₂×C₄	#10597342	1	1	yes	characteristic
574	C₂×C₄	#10597343	1	1	yes	characteristic
575	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
577	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
578	C₂×C₄	#10597383	1	1	yes	characteristic
579	C₂×C₄	#10597383	1	1	yes	characteristic
580	C₂×C₄	#10597384	1	1	yes	characteristic
581	C₈	—	2	4	no	—
582	C₈	—	4	2	no	—
583	C₈	—	4	2	no	—
584	C₈	—	38	4	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	38	4	no	—
593	C₂²	—	76	4	no	—
594	C₂²	—	152	2	no	—
595	C₂²	—	152	2	no	—
596	C₂²	#11926391	1	1	yes	characteristic
597	C₂²	#11926401	1	1	yes	characteristic
598	C₂²	#11926406	1	1	yes	characteristic
599	C₂²	#11926415	1	1	yes	characteristic
600	C₂²	#11926415	1	1	yes	characteristic
601	C₂²	#11926422	1	1	yes	characteristic
602	C₂²	#11926422	1	1	yes	characteristic
603	C₄	—	38	4	no	—
604	C₄	—	152	2	no	—
605	C₄	—	152	2	no	—
606	C₄	#95×D₁₉	1	1	yes	characteristic
607	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
608	C₄	#11926399	1	1	yes	characteristic
609	C₄	#11926403	1	1	yes	characteristic
610	C₄	#11926418	1	1	yes	characteristic
611	C₄	#11926418	1	1	yes	characteristic
612	C₄	#11926420	1	1	yes	characteristic
613	C₄	#11926420	1	1	yes	characteristic
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	76	4	no	—
621	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic
622	C₂	#14563998	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#341	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#341	D₁₉
hypocenter	C₁₉	#10782
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#341

Complements

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

N	H ≅ G/N	type
4. C₂×#11926316	C₂	semidirect
5. #14563346	C₂	semidirect
6. #14563331	C₂	semidirect
7. C₂×C₁₉×#341	C₂	semidirect
12. #11927310	C₄	semidirect
21. #11926546	C₄	semidirect
24. #11926541	C₄	semidirect
278. C₂×#341	D₁₉	semidirect
416. C₁₉	#10782	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
#14572155	2
C₂×#11926541	2
C₂×#11926316	2
#14563346	2
#14563331	2
C₂×C₁₉×#341	2
#10782	19