Subgroups — #18088634

Order 4864.

670 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926592	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926314	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926314	C₂	1	1	yes	maximal, characteristic
4	#14563361	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926309	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926309	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×#64520	C₂²	1	1	yes	characteristic
11	C₂²×#64520	C₂²	1	1	yes	characteristic
12	#11926592	—	2	2	no	—
13	#11926592	C₄	1	4	yes	complemented
14	C₂×#10597279	—	2	2	no	—
15	#11926314	—	2	2	no	—
16	#11926314	C₄	1	4	yes	—
17	#11926309	—	2	1	no	—
18	#11926309	—	2	1	no	—
19	#11926309	C₄	1	4	yes	complemented
20	#11926308	—	2	2	no	—
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#405	—	2	2	no	—
25	C₁₉×#405	—	2	2	no	—
26	C₂×C₁₉×#97	—	2	1	no	—
27	C₂×C₄×C₈×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
34	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	C₂×C₄	1	2	yes	—
47	C₁₉×#117	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×#64520	—	2	1	no	—
52	C₂×#64520	—	2	1	no	—
53	C₂×#64520	—	2	1	no	—
54	C₂×#64520	—	2	1	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂×#64520	—	2	1	no	—
59	C₂×#64520	—	2	1	no	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	—	2	1	no	—
69	C₂×#64520	C₂×C₄	1	2	yes	—
70	C₂×#64520	C₂×C₄	1	2	yes	—
71	C₂×#64520	C₂×C₄	1	2	yes	—
72	C₂×#64520	C₂×C₄	1	2	yes	—
73	C₂×#64520	C₂×C₄	1	2	yes	—
74	C₂×#64520	C₂×C₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	—	2	1	no	—
79	C₁₉×#97	—	2	4	no	—
80	C₄×C₈×C₁₉	—	2	4	no	—
81	#10597279	—	2	8	no	—
82	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	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×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	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	M₁₆×C₁₉	—	2	2	no	—
99	M₁₆×C₁₉	—	2	2	no	—
100	M₁₆×C₁₉	—	2	2	no	—
101	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
114	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
119	C₄²×C₁₉	—	2	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	#64520	—	2	2	no	—
122	#64520	—	2	2	no	—
123	#64520	—	2	2	no	—
124	#64520	—	2	2	no	—
125	#64520	—	2	2	no	—
126	#64520	—	2	2	no	—
127	#64520	—	2	2	no	—
128	#64520	—	2	2	no	—
129	#64520	—	2	2	no	—
130	#64520	—	4	1	no	—
131	#64520	—	4	1	no	—
132	#64520	—	4	1	no	—
133	#64520	—	4	1	no	—
134	#64520	—	4	1	no	—
135	#64520	—	4	1	no	—
136	#64520	C₄²	1	4	yes	—
137	C₂×C₁₉⋊C₈	—	2	2	no	—
138	C₂×C₁₉⋊C₈	—	2	2	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	2	2	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	#10898	—	19	1	no	maximal, Sylow
150	C₂³×C₁₉	—	4	2	no	—
151	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
153	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
154	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂³×C₁₉	#125	1	1	yes	characteristic
157	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
188	C₈×C₁₉	—	2	2	no	—
189	C₈×C₁₉	—	2	2	no	—
190	C₈×C₁₉	—	2	4	no	—
191	C₁₉⋊C₈	—	2	4	no	—
192	C₁₉⋊C₈	—	4	2	no	—
193	C₁₉⋊C₈	—	4	2	no	—
194	C₁₉⋊C₈	—	4	2	no	—
195	C₂×#430	—	19	1	no	—
196	C₂×#405	D₁₉	1	1	yes	characteristic
197	C₂×#344	—	19	1	no	—
198	C₂×#344	—	19	1	no	—
199	#1738	—	19	1	no	—
200	C₂×#341	—	19	1	no	—
201	C₂×#341	—	19	1	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
210	C₂²×C₁₉	#385	1	1	yes	characteristic
211	C₂²×C₁₉	#387	1	1	yes	characteristic
212	C₂²×C₁₉	#387	1	1	yes	characteristic
213	C₂²×C₁₉	#389	1	1	yes	characteristic
214	C₂²×C₁₉	#389	1	1	yes	characteristic
215	C₂²×C₁₉	#391	1	1	yes	characteristic
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
218	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
219	C₄×C₁₉	#385	1	1	yes	characteristic
220	C₄×C₁₉	#386	1	1	yes	characteristic
221	C₄×C₁₉	#387	1	1	yes	characteristic
222	C₄×C₁₉	#387	1	1	yes	characteristic
223	C₄×C₁₉	#388	1	1	yes	characteristic
224	C₄×C₁₉	#388	1	1	yes	characteristic
225	C₂²×M₁₆	—	19	1	no	—
226	C₂²×M₁₆	—	19	1	no	—
227	C₂²×M₁₆	—	19	1	no	—
228	C₂²×M₁₆	—	19	1	no	—
229	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
230	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
231	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
232	#430	—	19	4	no	—
233	#430	—	38	2	no	—
234	C₂×#108	—	38	2	no	—
235	#405	—	2	2	no	—
236	#405	—	2	2	no	—
237	C₂×#97	—	2	1	no	—
238	C₂×C₄×C₈	—	2	1	no	—
239	#344	—	19	4	no	—
240	#344	—	38	2	no	—
241	#341	—	19	4	no	—
242	#341	—	38	2	no	—
243	#341	—	38	1	no	—
244	#341	—	38	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	#1436	1	1	yes	characteristic
252	C₂×C₁₉	#1953	1	2	yes	—
253	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	19	2	no	—
258	C₂×M₁₆	—	19	2	no	—
259	C₂×M₁₆	—	19	2	no	—
260	C₂×M₁₆	—	19	2	no	—
261	C₂×M₁₆	—	19	2	no	—
262	C₂×M₁₆	—	19	2	no	—
263	C₂×M₁₆	—	38	1	no	—
264	C₂×M₁₆	—	38	1	no	—
265	C₂×M₁₆	—	38	1	no	—
266	C₂×M₁₆	—	38	1	no	—
267	C₂×M₁₆	—	38	1	no	—
268	C₂×M₁₆	—	38	1	no	—
269	C₂×M₁₆	—	38	1	no	—
270	C₂×M₁₆	—	38	1	no	—
271	C₂×M₁₆	—	38	1	no	—
272	C₂×M₁₆	—	38	1	no	—
273	C₂×M₁₆	—	38	1	no	—
274	C₂×M₁₆	—	38	1	no	—
275	C₂×M₁₆	—	38	1	no	—
276	C₂×M₁₆	—	38	1	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	—	38	1	no	—
279	C₂×M₁₆	—	38	1	no	—
280	C₂×M₁₆	—	38	1	no	—
281	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
282	C₂×M₁₆	D₇₆	1	2	yes	—
283	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	38	1	no	—
290	C₂²×C₈	—	38	1	no	—
291	C₂²×C₈	—	38	1	no	—
292	C₂²×C₈	—	38	1	no	—
293	C₂²×C₈	Dic₃₈	1	2	yes	—
294	C₂²×C₈	C₄×D₁₉	1	2	yes	—
295	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	#117	C₄×D₁₉	1	2	yes	—
300	#117	C₂²⋊D₁₉	1	2	yes	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
303	C₂×C₄²	—	2	1	no	—
304	#108	—	38	8	no	—
305	#97	—	2	4	no	—
306	C₄×C₈	—	2	4	no	—
307	C₁₉	#10898	1	1	yes	characteristic, complemented, Sylow
308	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
315	C₂²×C₄	#64541	1	1	yes	characteristic
316	C₂²×C₄	#64541	1	1	yes	characteristic
317	C₂²×C₄	#64541	1	1	yes	characteristic
318	C₂²×C₄	#64541	1	1	yes	characteristic
319	C₂²×C₄	#64541	1	1	yes	characteristic
320	C₂²×C₄	#64541	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	19	4	no	—
328	M₁₆	—	38	2	no	—
329	M₁₆	—	38	2	no	—
330	M₁₆	—	38	2	no	—
331	M₁₆	—	38	2	no	—
332	M₁₆	—	38	2	no	—
333	M₁₆	—	38	2	no	—
334	M₁₆	—	38	2	no	—
335	M₁₆	—	38	2	no	—
336	M₁₆	—	38	2	no	—
337	M₁₆	—	76	1	no	—
338	M₁₆	—	76	1	no	—
339	M₁₆	—	76	1	no	—
340	M₁₆	—	76	1	no	—
341	M₁₆	—	76	1	no	—
342	M₁₆	—	76	1	no	—
343	M₁₆	(C₂×D₁₉)⋊C₄	1	4	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	38	2	no	—
356	C₂×C₈	—	38	2	no	—
357	C₂×C₈	—	38	2	no	—
358	C₂×C₈	—	38	2	no	—
359	C₂×C₈	—	38	2	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	76	1	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₂×C₈	—	76	1	no	—
367	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
368	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
377	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
378	C₂³	#10597315	1	1	yes	characteristic
379	C₂³	#10597316	1	1	yes	characteristic
380	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
381	C₂³	#10597370	1	1	yes	characteristic
382	C₂³	#10597370	1	1	yes	characteristic
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
386	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
387	C₂×C₄	#10597316	1	1	yes	characteristic
388	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
389	C₂×C₄	#10597318	1	1	yes	characteristic
390	C₂×C₄	#10597318	1	1	yes	characteristic
391	C₂×C₄	#10597318	1	1	yes	characteristic
392	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
393	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
394	C₂×C₄	#10597321	1	1	yes	characteristic
395	C₂×C₄	#10597322	1	1	yes	characteristic
396	C₂×C₄	#10597322	1	1	yes	characteristic
397	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
398	C₂×C₄	#10597370	1	1	yes	characteristic
399	C₂×C₄	#10597370	1	1	yes	characteristic
400	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
401	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
402	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
403	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
404	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
406	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
407	C₂×C₄	#10597375	1	1	yes	characteristic
408	C₂×C₄	#10597375	1	1	yes	characteristic
409	C₂×C₄	#10597375	1	1	yes	characteristic
410	C₂×C₄	#10597376	1	1	yes	characteristic
411	C₂×C₄	#10597376	1	1	yes	characteristic
412	C₂×C₄	#10597399	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	4	no	—
416	C₈	—	38	4	no	—
417	C₈	—	76	2	no	—
418	C₈	—	76	2	no	—
419	C₈	—	76	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
428	C₂²	#11926417	1	1	yes	characteristic
429	C₂²	#11926428	1	1	yes	characteristic
430	C₂²	#11926428	1	1	yes	characteristic
431	C₂²	#11926442	1	1	yes	characteristic
432	C₂²	#11926442	1	1	yes	characteristic
433	C₂²	#11926450	1	1	yes	characteristic
434	C₄	—	4	4	no	—
435	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
436	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
437	C₄	#11926417	1	1	yes	characteristic
438	C₄	#11926423	1	1	yes	characteristic
439	C₄	#11926428	1	1	yes	characteristic
440	C₄	#11926428	1	1	yes	characteristic
441	C₄	#11926435	1	1	yes	characteristic
442	C₄	#11926435	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	#14561868	1	1	yes	characteristic
450	C₂	#14564425	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#405	C₂
socle	C₂²×C₁₉	#389
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#405	D₁₉
hypocenter	C₁₉	#10898
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
13. #11926592	C₄	semidirect
19. #11926309	C₄	semidirect
307. C₁₉	#10898	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926592	2
C₂×#11926314	2
#14563361	2
C₂×#11926309	2
C₂×C₁₉×#405	2
#10898	19