Subgroups — #18088566

Order 4864.

754 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926572	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926502	C₂	1	1	yes	maximal, characteristic
3	#14563352	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926572	—	2	2	no	—
13	#11926572	C₄	1	4	yes	complemented
14	C₂×Dic₁₉⋊C₈	—	2	1	no	—
15	C₂×Dic₁₉⋊C₈	—	2	1	no	—
16	#11926502	—	2	2	no	—
17	#11926502	—	2	2	no	—
18	C₂×#10597272	—	2	1	no	—
19	C₂×C₈×Dic₁₉	—	2	1	no	—
20	#11926307	C₄	1	2	yes	complemented
21	#11926307	C₄	1	2	yes	complemented
22	#11926305	—	2	2	no	—
23	#11926305	C₄	1	4	yes	complemented
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	C₂³×Dic₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
42	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
43	C₂²×C₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₂²×C₈×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
53	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	—	2	1	no	—
57	#10597372	—	2	1	no	—
58	#10597372	C₂×C₄	1	2	yes	—
59	#10597372	C₂×C₄	1	2	yes	—
60	#10597372	D₄	1	2	yes	—
61	#10597372	Q₈	1	2	yes	—
62	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₁₉	—	2	1	no	—
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×C₄×Dic₁₉	—	2	1	no	—
68	C₂×C₄×Dic₁₉	—	2	1	no	—
69	C₂×C₄×Dic₁₉	—	2	1	no	—
70	C₂×C₄×Dic₁₉	—	2	1	no	—
71	C₂×C₄×Dic₁₉	—	2	1	no	—
72	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
78	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
80	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
81	#10597272	—	2	4	no	—
82	Dic₁₉⋊C₈	—	2	4	no	—
83	Dic₁₉⋊C₈	—	2	4	no	—
84	C₈×Dic₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×Dic₁₉	—	2	4	no	—
101	C₂²×Dic₁₉	—	2	1	no	—
102	C₂²×Dic₁₉	—	2	1	no	—
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂²×Dic₁₉	—	4	2	no	—
106	C₂²×Dic₁₉	—	4	1	no	—
107	C₂²×Dic₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	2	2	no	—
109	M₁₆×C₁₉	—	2	2	no	—
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	2	2	no	—
112	M₁₆×C₁₉	—	2	2	no	—
113	M₁₆×C₁₉	—	4	1	no	—
114	M₁₆×C₁₉	—	4	1	no	—
115	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₂×C₈×C₁₉	—	4	1	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂²⋊Dic₁₉	—	2	2	no	—
130	C₂²⋊Dic₁₉	—	2	2	no	—
131	C₂²⋊Dic₁₉	—	2	2	no	—
132	C₂²⋊Dic₁₉	—	2	2	no	—
133	C₄⋊Dic₁₉	—	2	1	no	—
134	C₄⋊Dic₁₉	—	2	1	no	—
135	C₄⋊Dic₁₉	—	2	2	no	—
136	C₄⋊Dic₁₉	C₄²	1	2	yes	—
137	C₄⋊Dic₁₉	C₄²	1	2	yes	—
138	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
139	C₄×Dic₁₉	—	2	2	no	—
140	C₄×Dic₁₉	—	2	2	no	—
141	C₄×Dic₁₉	—	2	2	no	—
142	C₄×Dic₁₉	—	2	2	no	—
143	C₄×Dic₁₉	—	2	2	no	—
144	C₄×Dic₁₉	—	2	2	no	—
145	C₄×Dic₁₉	—	4	1	no	—
146	C₄×Dic₁₉	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	1	no	—
150	C₂×C₁₉⋊C₈	—	2	1	no	—
151	C₂×C₁₉⋊C₈	—	2	2	no	—
152	C₂×C₁₉⋊C₈	—	2	2	no	—
153	C₂×C₁₉⋊C₈	—	2	1	no	—
154	C₂×C₁₉⋊C₈	—	2	1	no	—
155	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
156	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
157	#10887	—	19	1	no	maximal, Sylow
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	#117	1	1	yes	characteristic
161	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂³×C₁₉	#123	1	1	yes	characteristic
165	C₂³×C₁₉	#125	1	1	yes	characteristic
166	C₂³×C₁₉	#126	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
195	C₂×Dic₁₉	—	2	4	no	—
196	C₂×Dic₁₉	—	2	2	no	—
197	C₂×Dic₁₉	—	2	2	no	—
198	C₂×Dic₁₉	—	2	4	no	—
199	C₂×Dic₁₉	—	4	4	no	—
200	C₂×Dic₁₉	—	4	4	no	—
201	C₂×Dic₁₉	—	4	2	no	—
202	C₂×Dic₁₉	—	4	2	no	—
203	C₂×Dic₁₉	—	4	2	no	—
204	C₂×Dic₁₉	—	4	2	no	—
205	C₂×Dic₁₉	—	4	2	no	—
206	C₂×Dic₁₉	—	4	2	no	—
207	C₈×C₁₉	—	2	4	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	2	no	—
210	C₁₉⋊C₈	—	2	2	no	—
211	C₁₉⋊C₈	—	2	2	no	—
212	C₂×#424	—	19	1	no	—
213	C₂×#405	—	19	1	no	—
214	C₂×#341	D₁₉	1	1	yes	characteristic
215	#1735	—	19	1	no	—
216	C₂×#339	—	19	1	no	—
217	C₂×#339	—	19	1	no	—
218	C₂×#336	—	19	1	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₉	#385	1	1	yes	characteristic
229	C₂²×C₁₉	#387	1	1	yes	characteristic
230	C₂²×C₁₉	#387	1	1	yes	characteristic
231	C₂²×C₁₉	#387	1	1	yes	characteristic
232	C₂²×C₁₉	#388	1	1	yes	characteristic
233	C₂²×C₁₉	#389	1	1	yes	characteristic
234	C₂²×C₁₉	#443	1	2	yes	—
235	C₂²×C₁₉	#444	1	2	yes	—
236	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₁₉	#385	1	1	yes	characteristic
239	C₄×C₁₉	#386	1	1	yes	characteristic
240	C₄×C₁₉	#387	1	1	yes	characteristic
241	C₄×C₁₉	#388	1	1	yes	characteristic
242	C₄×C₁₉	#389	1	1	yes	characteristic
243	C₄×C₁₉	#391	1	1	yes	characteristic
244	Dic₁₉	—	4	4	no	—
245	Dic₁₉	—	4	4	no	—
246	Dic₁₉	—	4	2	no	—
247	Dic₁₉	—	4	2	no	—
248	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
249	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
250	C₂³×C₈	—	19	1	no	—
251	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
252	C₂×#117	—	19	1	no	—
253	C₂×#117	—	19	1	no	—
254	C₂²×C₄²	—	19	1	no	—
255	#424	—	19	4	no	—
256	#424	—	38	2	no	—
257	C₂×C₄⋊C₈	—	38	1	no	—
258	C₂×C₄⋊C₈	—	38	1	no	—
259	#405	—	38	2	no	—
260	#405	—	38	2	no	—
261	C₂×#97	—	38	1	no	—
262	C₂×C₄×C₈	—	38	1	no	—
263	#341	—	2	2	no	—
264	#340	—	19	2	no	—
265	#340	—	19	2	no	—
266	#339	—	19	4	no	—
267	#339	—	38	2	no	—
268	#336	—	38	2	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	—	2	1	no	—
273	C₂×C₁₉	#1436	1	1	yes	characteristic
274	C₂×C₁₉	#1764	1	1	yes	characteristic
275	C₂×C₁₉	#1765	1	1	yes	characteristic
276	C₂×C₁₉	#1866	1	2	yes	—
277	C₂×C₁₉	#1922	1	2	yes	—
278	C₂³×C₄	—	38	1	no	—
279	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	Dic₃₈	1	2	yes	—
289	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
290	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
291	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	19	2	no	—
301	C₂²×C₈	—	19	2	no	—
302	C₂²×C₈	—	19	1	no	—
303	C₂²×C₈	—	19	1	no	—
304	C₂²×C₈	—	38	1	no	—
305	C₂²×C₈	—	38	1	no	—
306	C₂²×C₈	—	38	1	no	—
307	C₂²×C₈	—	38	1	no	—
308	C₂²×C₈	C₄×D₁₉	1	2	yes	—
309	#117	—	19	2	no	—
310	#117	—	19	2	no	—
311	#117	—	19	2	no	—
312	#117	—	19	2	no	—
313	#117	—	38	1	no	—
314	#117	—	38	1	no	—
315	#117	—	38	1	no	—
316	#117	—	38	1	no	—
317	C₂×C₄⋊C₄	—	19	1	no	—
318	C₂×C₄⋊C₄	—	19	1	no	—
319	C₂×C₄⋊C₄	—	19	2	no	—
320	C₂×C₂²⋊C₄	—	38	1	no	—
321	C₂×C₂²⋊C₄	—	38	1	no	—
322	C₂×C₄²	—	19	2	no	—
323	C₂×C₄²	—	38	1	no	—
324	C₂×C₄²	—	38	1	no	—
325	C₂×C₄²	—	38	1	no	—
326	C₂×C₄²	—	38	1	no	—
327	C₂×C₄²	—	38	1	no	—
328	C₂×C₄²	—	38	1	no	—
329	C₂×C₄²	—	38	1	no	—
330	C₄⋊C₈	—	38	4	no	—
331	C₄⋊C₈	—	38	4	no	—
332	#97	—	38	4	no	—
333	C₄×C₈	—	38	4	no	—
334	C₁₉	#10887	1	1	yes	characteristic, complemented, Sylow
335	C₂⁴	#64545	1	1	yes	characteristic
336	C₂²×C₄	—	38	4	no	—
337	C₂²×C₄	—	38	2	no	—
338	C₂²×C₄	—	38	1	no	—
339	C₂²×C₄	—	38	1	no	—
340	C₂²×C₄	—	38	2	no	—
341	C₂²×C₄	—	76	2	no	—
342	C₂²×C₄	—	76	1	no	—
343	C₂²×C₄	—	76	1	no	—
344	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
348	C₂²×C₄	#64541	1	1	yes	characteristic
349	C₂²×C₄	#64541	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
353	C₂²×C₄	#64543	1	1	yes	characteristic
354	C₂²×C₄	#64543	1	1	yes	characteristic
355	C₂²×C₄	#64543	1	1	yes	characteristic
356	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	4	1	no	—
364	M₁₆	—	4	1	no	—
365	M₁₆	Dic₁₉⋊C₄	1	4	yes	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	19	2	no	—
380	C₂×C₈	—	19	2	no	—
381	C₂×C₈	—	38	1	no	—
382	C₂×C₈	—	38	1	no	—
383	C₂×C₈	—	38	2	no	—
384	C₂×C₈	—	38	2	no	—
385	C₂×C₈	—	38	1	no	—
386	C₂×C₈	—	38	1	no	—
387	C₂×C₈	—	38	2	no	—
388	C₂×C₈	—	38	2	no	—
389	C₄⋊C₄	—	19	2	no	—
390	C₄⋊C₄	—	19	2	no	—
391	C₄⋊C₄	—	19	4	no	—
392	C₄⋊C₄	—	38	1	no	—
393	C₄⋊C₄	—	38	1	no	—
394	C₄⋊C₄	—	38	2	no	—
395	C₂²⋊C₄	—	38	2	no	—
396	C₂²⋊C₄	—	38	2	no	—
397	C₂²⋊C₄	—	38	2	no	—
398	C₂²⋊C₄	—	38	2	no	—
399	C₄²	—	38	2	no	—
400	C₄²	—	38	2	no	—
401	C₄²	—	38	2	no	—
402	C₄²	—	38	2	no	—
403	C₄²	—	38	2	no	—
404	C₄²	—	38	2	no	—
405	C₄²	—	76	1	no	—
406	C₄²	—	76	1	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	#10597336	1	1	yes	characteristic
410	C₂³	#10597338	1	1	yes	characteristic
411	C₂³	#10597339	1	1	yes	characteristic
412	C₂³	#10597339	1	1	yes	characteristic
413	C₂³	#10597340	1	1	yes	characteristic
414	C₂³	#10597344	1	1	yes	characteristic
415	C₂³	#10597392	1	1	yes	characteristic
416	C₂×C₄	—	38	4	no	—
417	C₂×C₄	—	38	2	no	—
418	C₂×C₄	—	38	2	no	—
419	C₂×C₄	—	38	4	no	—
420	C₂×C₄	—	76	4	no	—
421	C₂×C₄	—	76	4	no	—
422	C₂×C₄	—	76	2	no	—
423	C₂×C₄	—	76	2	no	—
424	C₂×C₄	—	76	2	no	—
425	C₂×C₄	—	76	2	no	—
426	C₂×C₄	—	76	2	no	—
427	C₂×C₄	—	76	2	no	—
428	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
429	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
430	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
431	C₂×C₄	#10597318	1	1	yes	characteristic
432	C₂×C₄	#10597323	1	1	yes	characteristic
433	C₂×C₄	#10597324	1	1	yes	characteristic
434	C₂×C₄	#10597324	1	1	yes	characteristic
435	C₂×C₄	#10597325	1	1	yes	characteristic
436	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
437	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
438	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
439	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
440	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
441	C₂×C₄	#10597329	1	1	yes	characteristic
442	C₂×C₄	#10597330	1	1	yes	characteristic
443	C₂×C₄	#10597331	1	1	yes	characteristic
444	C₂×C₄	#10597333	1	1	yes	characteristic
445	C₂×C₄	#10597333	1	1	yes	characteristic
446	C₂×C₄	#10597334	1	1	yes	characteristic
447	C₂×C₄	#10597335	1	1	yes	characteristic
448	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
449	C₂×C₄	#10597342	1	1	yes	characteristic
450	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
451	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
452	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
453	C₂×C₄	#10597381	1	1	yes	characteristic
454	C₂×C₄	#10597383	1	1	yes	characteristic
455	C₂×C₄	#10597384	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	38	2	no	—
460	C₈	—	38	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	#11926391	1	1	yes	characteristic
470	C₂²	#11926415	1	1	yes	characteristic
471	C₂²	#11926425	1	1	yes	characteristic
472	C₂²	#11926427	1	1	yes	characteristic
473	C₂²	#11926431	1	1	yes	characteristic
474	C₂²	#11926433	1	1	yes	characteristic
475	C₂²	#11926440	1	1	yes	characteristic
476	C₂²	#11926660	1	2	yes	—
477	C₂²	#11926665	1	2	yes	—
478	C₄	—	76	4	no	—
479	C₄	—	76	4	no	—
480	C₄	—	76	2	no	—
481	C₄	—	76	2	no	—
482	C₄	#11926395	1	1	yes	characteristic
483	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
484	C₄	#11926416	1	1	yes	characteristic
485	C₄	#11926420	1	1	yes	characteristic
486	C₄	#11926426	1	1	yes	characteristic
487	C₄	#11926432	1	1	yes	characteristic
488	C₄	#11926441	1	1	yes	characteristic
489	C₄	#11926448	1	1	yes	characteristic
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	#14561866	1	1	yes	characteristic
495	C₂	#14563471	1	1	yes	characteristic
496	C₂	#14563478	1	1	yes	characteristic
497	C₂	#14563907	1	2	yes	—
498	C₂	#14564233	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#341	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#341	D₁₉
hypocenter	C₁₉	#10887
LCS	G ▷ C₂×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
13. #11926572	C₄	semidirect
20. #11926307	C₄	semidirect
21. #11926307	C₄	semidirect
23. #11926305	C₄	semidirect
334. C₁₉	#10887	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926572	2
C₂×#11926502	2
#14563352	2
C₂×#11926305	2
C₂×#11926298	2
C₂×C₁₉×#341	2
#10887	19