Subgroups — #18088137

Order 4864.

1164 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927311	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926561	C₂	1	1	yes	maximal, characteristic
3	#14563374	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926300	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic
8	#11927311	—	2	2	no	—
9	#11927311	—	2	2	no	—
10	#11927311	—	2	2	no	—
11	#11927311	—	2	2	no	—
12	C₂×#10597394	—	2	2	no	—
13	C₂×#10597394	C₄	1	4	yes	complemented
14	C₂²×#64520	—	2	2	no	—
15	C₂²×#64520	C₂²	1	1	yes	characteristic
16	C₂²×#64520	C₂²	1	1	yes	characteristic
17	C₂²×#64520	C₂²	1	1	yes	characteristic
18	C₂×#10597372	C₂²	1	1	yes	characteristic
19	#11926561	—	2	2	no	—
20	#11926561	—	2	2	no	—
21	C₂×#10597294	C₄	1	4	yes	complemented
22	#11926313	—	2	2	no	—
23	#11926312	—	2	2	no	—
24	C₁₉⋊#338	—	2	2	no	—
25	#11926300	—	2	2	no	—
26	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₁₉×#421	—	2	2	no	—
30	C₁₉×#421	—	2	2	no	—
31	C₂×C₁₉×#104	C₄	1	4	yes	complemented
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₁₉	D₄	1	2	yes	—
42	C₂×#41×C₁₉	D₄	1	2	yes	—
43	C₂×#41×C₁₉	D₄	1	2	yes	—
44	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
64	#10597394	—	2	8	no	—
65	#10597394	—	2	8	no	—
66	#10597394	—	2	8	no	—
67	#10597394	—	2	8	no	—
68	#10597372	—	2	1	no	—
69	#10597372	—	2	1	no	—
70	#10597372	—	2	1	no	—
71	#10597372	—	2	1	no	—
72	C₂×C₄⋊Dic₁₉	—	2	1	no	—
73	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
74	C₂×#64520	—	2	8	no	—
75	C₂×#64520	—	2	8	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	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	4	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	—	2	1	no	—
88	C₂×#64520	—	2	1	no	—
89	C₂×#64520	C₂×C₄	1	2	yes	—
90	C₂×#64520	C₂×C₄	1	2	yes	—
91	C₂×#64520	D₄	1	2	yes	—
92	C₂×#64520	D₄	1	2	yes	—
93	C₂×#64520	D₄	1	2	yes	—
94	C₂×#64520	D₄	1	2	yes	—
95	C₂²×C₁₉⋊C₈	—	2	1	no	—
96	C₂²×C₁₉⋊C₈	—	2	4	no	—
97	C₂²×C₁₉⋊C₈	—	2	1	no	—
98	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
99	C₁₉×#104	—	2	8	no	—
100	#10597294	—	2	8	no	—
101	C₂⁴×C₁₉	—	2	1	no	—
102	C₂⁴×C₁₉	#41	1	1	yes	characteristic
103	#41×C₁₉	—	2	2	no	—
104	#41×C₁₉	—	2	2	no	—
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	2	2	no	—
112	#41×C₁₉	—	2	2	no	—
113	#41×C₁₉	—	2	2	no	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	C₄²	1	4	yes	—
116	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
117	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
118	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
123	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
124	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
135	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
136	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
159	C₂²×Dic₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	4	1	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	4	1	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₂²⋊C₄×C₁₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₂²⋊Dic₁₉	—	4	1	no	—
174	C₂²⋊Dic₁₉	—	4	1	no	—
175	C₄⋊Dic₁₉	—	4	1	no	—
176	C₄⋊Dic₁₉	—	4	1	no	—
177	C₄×Dic₁₉	—	2	2	no	—
178	C₄×Dic₁₉	—	2	2	no	—
179	#64520	—	2	16	no	—
180	#64520	—	2	2	no	—
181	#64520	—	2	2	no	—
182	#64520	—	2	2	no	—
183	#64520	—	2	2	no	—
184	#64520	—	2	2	no	—
185	#64520	—	2	2	no	—
186	#64520	—	2	2	no	—
187	#64520	—	2	2	no	—
188	#64520	—	2	2	no	—
189	#64520	—	4	1	no	—
190	#64520	—	4	1	no	—
191	#64520	C₂²⋊C₄	1	4	yes	—
192	C₂×C₁₉⋊C₈	—	2	16	no	—
193	C₂×C₁₉⋊C₈	—	2	2	no	—
194	C₂×C₁₉⋊C₈	—	2	2	no	—
195	C₂×C₁₉⋊C₈	—	2	2	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	#10794	—	19	1	no	maximal, Sylow
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	8	1	no	—
207	C₂³×C₁₉	—	8	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	Q₈×C₁₉	—	2	2	no	—
216	Q₈×C₁₉	—	2	2	no	—
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	#95	1	4	yes	—
219	D₄×C₁₉	—	2	4	no	—
220	D₄×C₁₉	—	2	4	no	—
221	D₄×C₁₉	—	2	4	no	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	2	no	—
224	D₄×C₁₉	—	2	2	no	—
225	D₄×C₁₉	—	2	2	no	—
226	D₄×C₁₉	#95	1	4	yes	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	8	2	no	—
236	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
264	C₂×Dic₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	8	2	no	—
266	C₈×C₁₉	—	4	2	no	—
267	C₁₉⋊C₈	—	2	4	no	—
268	C₁₉⋊C₈	—	2	4	no	—
269	C₁₉⋊C₈	—	4	2	no	—
270	C₂×#568	—	19	1	no	—
271	C₂×#421	—	19	1	no	—
272	C₂×#421	D₁₉	1	1	yes	characteristic
273	#1742	—	19	1	no	—
274	#1742	—	19	1	no	—
275	C₂×#338	—	19	1	no	—
276	C₂×H(3,ℤ/4)	—	19	1	no	—
277	C₂²×C₁₉	—	2	4	no	—
278	C₂²×C₁₉	—	4	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	4	no	—
286	C₂²×C₁₉	—	8	2	no	—
287	C₂²×C₁₉	—	8	2	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	C₄×C₁₉	—	2	4	no	—
296	C₄×C₁₉	—	8	2	no	—
297	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
298	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
299	C₄×C₁₉	#379	1	1	yes	characteristic
300	C₄×C₁₉	#380	1	1	yes	characteristic
301	C₄×C₁₉	#385	1	1	yes	characteristic
302	C₄×C₁₉	#385	1	1	yes	characteristic
303	C₄×C₁₉	#386	1	1	yes	characteristic
304	C₄×C₁₉	#386	1	1	yes	characteristic
305	Dic₁₉	—	8	2	no	—
306	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
307	#568	—	38	2	no	—
308	#568	—	38	2	no	—
309	#568	—	38	2	no	—
310	#568	—	38	2	no	—
311	C₂×#131	—	19	4	no	—
312	C₂×#131	—	38	2	no	—
313	C₂²×M₁₆	—	19	1	no	—
314	C₂²×M₁₆	—	19	1	no	—
315	C₂²×M₁₆	—	19	1	no	—
316	C₂²×M₁₆	—	38	2	no	—
317	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
318	C₂×#117	—	19	1	no	—
319	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
320	#421	—	2	2	no	—
321	#421	—	2	2	no	—
322	#421	—	38	2	no	—
323	#421	—	38	2	no	—
324	C₂×#104	—	19	4	no	—
325	C₂×#104	Dic₁₉	1	4	yes	complemented
326	#343	—	38	2	no	—
327	#343	—	38	2	no	—
328	#338	—	38	2	no	—
329	H(3,ℤ/4)	—	38	2	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	2	1	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	—	4	4	no	—
338	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	C₄×D₁₉	1	2	yes	—
346	C₂×#41	C₄×D₁₉	1	2	yes	—
347	C₂×#41	D₇₆	1	2	yes	—
348	C₂×#41	C₂×Dic₁₉	1	2	yes	—
349	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
350	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
351	C₂²×Q₈	Dic₃₈	1	1	yes	characteristic
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
356	#131	—	38	8	no	—
357	#131	—	38	8	no	—
358	#131	—	38	8	no	—
359	#131	—	38	8	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	—	19	2	no	—
366	C₂×M₁₆	—	19	2	no	—
367	C₂×M₁₆	—	19	2	no	—
368	C₂×M₁₆	—	19	2	no	—
369	C₂×M₁₆	—	19	2	no	—
370	C₂×M₁₆	—	19	2	no	—
371	C₂×M₁₆	—	38	4	no	—
372	C₂×M₁₆	—	38	8	no	—
373	C₂×M₁₆	—	38	8	no	—
374	C₂×M₁₆	—	38	1	no	—
375	C₂×M₁₆	—	38	1	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	1	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	C₂×Dic₁₉	1	2	yes	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	19	2	no	—
389	C₂²×C₈	—	38	4	no	—
390	C₂²×C₈	—	38	1	no	—
391	C₂²×C₈	—	38	1	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	38	1	no	—
397	#117	—	38	1	no	—
398	#117	—	38	1	no	—
399	#117	—	38	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	38	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	38	1	no	—
404	C₂×C₄²	—	19	2	no	—
405	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
406	#104	—	2	8	no	—
407	#104	—	38	8	no	—
408	C₁₉	#10794	1	1	yes	characteristic, complemented, Sylow
409	C₂⁴	—	2	1	no	—
410	C₂⁴	#64543	1	1	yes	characteristic
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	C₄×Dic₁₉	1	4	yes	—
424	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
425	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
426	#41	C₂²⋊Dic₁₉	1	4	yes	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
431	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
432	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
443	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
444	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	38	2	no	—
454	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₇₆	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	D₄×D₁₉	1	1	yes	characteristic
462	C₂²×C₄	#64543	1	1	yes	characteristic
463	C₂²×C₄	#64543	1	1	yes	characteristic
464	C₂²×C₄	#64543	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	19	4	no	—
473	M₁₆	—	38	16	no	—
474	M₁₆	—	38	2	no	—
475	M₁₆	—	38	2	no	—
476	M₁₆	—	38	2	no	—
477	M₁₆	—	38	2	no	—
478	M₁₆	—	38	2	no	—
479	M₁₆	—	38	2	no	—
480	M₁₆	—	38	2	no	—
481	M₁₆	—	38	2	no	—
482	M₁₆	—	38	2	no	—
483	M₁₆	—	76	1	no	—
484	M₁₆	—	76	1	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	—	19	4	no	—
489	C₂×C₈	—	38	16	no	—
490	C₂×C₈	—	38	2	no	—
491	C₂×C₈	—	38	2	no	—
492	C₂×C₈	—	38	2	no	—
493	C₂×C₈	—	38	2	no	—
494	C₂×C₈	—	38	2	no	—
495	C₂×C₈	—	38	2	no	—
496	C₂×C₈	—	76	1	no	—
497	C₂×C₈	—	76	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	76	1	no	—
501	C₄⋊C₄	—	76	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	76	1	no	—
505	C₂²⋊C₄	—	76	1	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	38	2	no	—
509	C₄²	—	38	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	8	1	no	—
514	C₂³	—	8	2	no	—
515	C₂³	#10597323	1	1	yes	characteristic
516	C₂³	#10597324	1	1	yes	characteristic
517	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
518	C₂³	#10597332	1	1	yes	characteristic
519	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
520	C₂³	#10597381	1	1	yes	characteristic
521	C₂³	#10597385	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	C₁₉⋊#95	1	4	yes	—
526	D₄	—	2	4	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	2	2	no	—
533	D₄	C₁₉⋊#95	1	4	yes	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	76	2	no	—
544	C₂×C₄	—	152	2	no	—
545	C₂×C₄	#10597323	1	1	yes	characteristic
546	C₂×C₄	#10597324	1	1	yes	characteristic
547	C₂×C₄	#10597324	1	1	yes	characteristic
548	C₂×C₄	#10597324	1	1	yes	characteristic
549	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
551	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
552	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
553	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
554	C₂×C₄	#10597328	1	1	yes	characteristic
555	C₂×C₄	#10597328	1	1	yes	characteristic
556	C₂×C₄	#10597332	1	1	yes	characteristic
557	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
558	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
561	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
563	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
564	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
565	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
566	C₂×C₄	#10597381	1	1	yes	characteristic
567	C₂×C₄	#10597383	1	1	yes	characteristic
568	C₂×C₄	#10597383	1	1	yes	characteristic
569	C₂×C₄	#10597385	1	1	yes	characteristic
570	C₂×C₄	#10597385	1	1	yes	characteristic
571	C₂×C₄	#10597385	1	1	yes	characteristic
572	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
573	C₈	—	4	2	no	—
574	C₈	—	38	4	no	—
575	C₈	—	38	4	no	—
576	C₈	—	76	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
589	C₂²	#11926402	1	1	yes	characteristic
590	C₂²	#11926405	1	1	yes	characteristic
591	C₂²	#11926416	1	1	yes	characteristic
592	C₂²	#11926419	1	1	yes	characteristic
593	C₂²	#11926421	1	1	yes	characteristic
594	C₂²	#11926424	1	1	yes	characteristic
595	C₄	—	2	4	no	—
596	C₄	—	8	2	no	—
597	C₄	—	152	2	no	—
598	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
599	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
600	C₄	#11926399	1	1	yes	characteristic
601	C₄	#11926402	1	1	yes	characteristic
602	C₄	#11926416	1	1	yes	characteristic
603	C₄	#11926419	1	1	yes	characteristic
604	C₄	#11926421	1	1	yes	characteristic
605	C₄	#11926424	1	1	yes	characteristic
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	4	4	no	—
614	C₂	#14561857	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊C₄×Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#421	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#421	D₁₉
hypocenter	C₁₉	#10794
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
3. #14563374	C₂	semidirect
4. #14563373	C₂	semidirect
5. C₂×C₁₉⋊#338	C₂	semidirect
6. C₂×#11926300	C₂	semidirect
13. C₂×#10597394	C₄	semidirect
21. C₂×#10597294	C₄	semidirect
31. C₂×C₁₉×#104	C₄	semidirect
325. C₂×#104	Dic₁₉	semidirect
408. C₁₉	#10794	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927311	2
C₂×#11926561	2
#14563374	2
#14563373	2
C₂×C₁₉⋊#338	2
C₂×#11926300	2
C₂×C₁₉×#421	2
#10794	19