Subgroups — #18074904

Order 4864.

748 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564468	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562365	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562357	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562270	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562147	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562143	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic
8	#11926601	C₂²	1	1	yes	characteristic
9	#11926601	C₂²	1	1	yes	characteristic
10	#11926568	C₂²	1	1	yes	characteristic
11	C₂×#10597294	—	2	2	no	—
12	#11926390	C₂²	1	1	yes	characteristic
13	#11926293	—	2	1	no	—
14	#11926290	—	2	1	no	—
15	#11926290	—	2	1	no	—
16	#11926288	—	2	1	no	—
17	#11926284	—	2	2	no	—
18	#11926281	—	2	2	no	—
19	#11926278	—	2	2	no	—
20	C₁₉×#562	—	2	2	no	—
21	C₁₉×#554	—	2	1	no	—
22	C₁₉×#554	C₄	1	2	yes	complemented
23	C₁₉×#550	—	2	1	no	—
24	C₁₉×#550	C₄	1	2	yes	complemented
25	C₁₉×#547	—	2	1	no	—
26	C₁₉×#547	—	2	1	no	—
27	C₁₉×#540	—	2	2	no	—
28	C₁₉×#537	—	2	2	no	—
29	C₁₉×#537	—	2	2	no	—
30	C₁₉×#533	C₂²	1	1	yes	characteristic
31	C₁₉×#532	C₂²	1	1	yes	characteristic
32	C₁₉×#532	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	D₄	1	2	yes	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
39	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
41	C₁₉×#127	—	2	2	no	—
42	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
43	C₁₉×#127	D₄	1	1	yes	characteristic
44	C₁₉×#125	—	2	2	no	—
45	C₁₉×#125	—	2	1	no	—
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#124	D₄	1	2	yes	—
48	C₁₉×#123	—	2	4	no	—
49	C₁₉×#123	—	2	4	no	—
50	C₁₉×C₂²⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	4	no	—
52	C₁₉×C₂²⋊Q₈	—	2	2	no	—
53	C₁₉×C₂²⋊Q₈	—	2	4	no	—
54	C₁₉×C₂²⋊Q₈	—	2	1	no	—
55	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
56	C₁₉×#121	—	2	4	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	4	no	—
60	C₁₉×#121	—	2	4	no	—
61	C₁₉×#121	—	2	1	no	—
62	C₁₉×#121	—	2	1	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	D₄	1	2	yes	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	#10597294	—	4	4	no	—
81	C₁₉⋊#95	—	2	1	no	—
82	C₁₉⋊#95	—	2	1	no	—
83	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
84	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
85	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
86	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
87	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
88	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
89	#10597260	—	2	1	no	—
90	#10597260	—	2	1	no	—
91	#41×C₁₉	—	4	2	no	—
92	#41×C₁₉	—	4	2	no	—
93	#41×C₁₉	—	8	2	no	—
94	#41×C₁₉	—	8	4	no	—
95	#41×C₁₉	—	8	2	no	—
96	#41×C₁₉	—	8	2	no	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
110	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
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×D₄	1	1	yes	characteristic
118	C₂²×Dic₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	—	2	4	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₁₉	—	2	2	no	—
144	C₄×Dic₁₉	—	4	1	no	—
145	#64520	—	4	2	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	#8493	—	19	1	no	maximal, Sylow
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	#120	1	1	yes	characteristic
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	4	2	no	—
161	D₄×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	4	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	2	no	—
166	D₄×C₁₉	—	8	2	no	—
167	D₄×C₁₉	—	8	4	no	—
168	D₄×C₁₉	—	8	4	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	8	4	no	—
181	C₂×C₄×C₁₉	—	8	4	no	—
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
188	C₂×Dic₁₉	—	4	2	no	—
189	C₂×Dic₁₉	—	8	1	no	—
190	C₂×Dic₁₉	—	8	1	no	—
191	C₁₉⋊C₈	—	8	1	no	—
192	C₁₉⋊C₈	—	8	1	no	—
193	C₁₉⋊C₈	—	8	1	no	—
194	#3548	D₁₉	1	1	yes	characteristic
195	#1963	—	19	1	no	—
196	#1559	—	19	1	no	—
197	#1557	—	19	1	no	—
198	#1536	—	19	1	no	—
199	#1506	—	19	1	no	—
200	#1505	—	19	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	#379	1	1	yes	characteristic
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	#453	1	1	yes	characteristic
221	C₄×C₁₉	#455	1	1	yes	characteristic
222	Dic₁₉	—	8	2	no	—
223	#562	—	2	2	no	—
224	#554	—	2	1	no	—
225	#554	Dic₁₉	1	2	yes	complemented
226	#550	—	2	1	no	—
227	#550	Dic₁₉	1	2	yes	complemented
228	#547	—	2	1	no	—
229	#547	—	2	1	no	—
230	#540	—	2	2	no	—
231	#537	—	2	2	no	—
232	#537	—	2	2	no	—
233	#533	C₂×D₁₉	1	1	yes	characteristic
234	#532	C₂×D₁₉	1	1	yes	characteristic
235	#532	C₂×D₁₉	1	1	yes	characteristic
236	#432	—	19	1	no	—
237	#432	—	19	1	no	—
238	#423	—	19	1	no	—
239	C₂×#104	—	38	2	no	—
240	#376	—	19	1	no	—
241	#333	—	38	1	no	—
242	#332	—	38	1	no	—
243	#332	—	38	1	no	—
244	#331	—	38	1	no	—
245	#329	—	38	2	no	—
246	#328	—	38	2	no	—
247	#327	—	38	2	no	—
248	C₂×C₁₉	—	4	1	no	—
249	C₂×C₁₉	—	8	2	no	—
250	C₂×C₁₉	—	8	2	no	—
251	C₂×C₁₉	#1792	1	1	yes	characteristic
252	C₂×C₁₉	#1795	1	1	yes	characteristic
253	C₂×C₁₉	#1796	1	1	yes	characteristic
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	1	no	—
257	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
258	C₂×M₁₆	—	38	1	no	—
259	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
260	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
263	#127	—	2	2	no	—
264	#127	C₂×Dic₁₉	1	1	yes	characteristic
265	#127	C₂²⋊D₁₉	1	1	yes	characteristic
266	#125	—	2	2	no	—
267	#125	—	2	1	no	—
268	#124	—	2	1	no	—
269	#124	C₂²⋊D₁₉	1	2	yes	—
270	#123	—	2	4	no	—
271	#123	—	2	4	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
278	#121	—	2	4	no	—
279	#121	—	2	4	no	—
280	#121	—	2	2	no	—
281	#121	—	2	4	no	—
282	#121	—	2	4	no	—
283	#121	—	2	1	no	—
284	#121	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	—	2	2	no	—
287	#121	C₂²⋊D₁₉	1	2	yes	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	C₂×Dic₁₉	1	2	yes	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
296	#117	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	38	1	no	—
300	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
301	C₄⋊C₈	—	38	1	no	—
302	C₄⋊C₈	—	38	1	no	—
303	C₄⋊C₈	—	38	1	no	—
304	C₄⋊C₈	—	38	1	no	—
305	#104	—	76	4	no	—
306	C₂²⋊C₈	—	38	1	no	—
307	C₂²⋊C₈	—	38	1	no	—
308	#97	—	38	1	no	—
309	#97	—	38	1	no	—
310	#95	—	38	1	no	—
311	#95	—	38	1	no	—
312	C₁₉	#8493	1	1	yes	characteristic, complemented, Sylow
313	#41	—	4	2	no	—
314	#41	—	4	2	no	—
315	#41	—	8	2	no	—
316	#41	—	8	4	no	—
317	#41	—	8	2	no	—
318	#41	—	8	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
322	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
332	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	76	1	no	—
338	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
341	M₁₆	—	76	2	no	—
342	C₂×C₈	—	76	1	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
356	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	38	2	no	—
366	C₄²	—	76	1	no	—
367	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	#10597399	1	1	yes	characteristic
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	1	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	8	1	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	4	no	—
389	D₄	—	8	4	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	8	4	no	—
403	C₂×C₄	—	76	2	no	—
404	C₂×C₄	—	152	1	no	—
405	C₂×C₄	—	152	1	no	—
406	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
407	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
409	C₂×C₄	#10597399	1	1	yes	characteristic
410	C₂×C₄	#10597399	1	1	yes	characteristic
411	C₂×C₄	#10597399	1	1	yes	characteristic
412	C₈	—	152	1	no	—
413	C₈	—	152	1	no	—
414	C₈	—	152	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	#11926400	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	152	2	no	—
435	C₄	#11926712	1	1	yes	characteristic
436	C₄	#11926722	1	1	yes	characteristic
437	C₂	—	4	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	8	2	no	—
440	C₂	#14563589	1	1	yes	characteristic
441	C₂	#14563605	1	1	yes	characteristic
442	C₂	#14563610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3548	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3548	D₁₉
hypocenter	C₁₉	#8493
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3548

Complements

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

N	H ≅ G/N	type
1. #14564468	C₂	semidirect
2. #14562365	C₂	semidirect
3. #14562357	C₂	semidirect
4. #14562270	C₂	semidirect
5. #14562147	C₂	semidirect
6. #14562143	C₂	semidirect
22. C₁₉×#554	C₄	semidirect
24. C₁₉×#550	C₄	semidirect
225. #554	Dic₁₉	semidirect
227. #550	Dic₁₉	semidirect
312. C₁₉	#8493	semidirect

Maximal subgroups

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

subgroup	index
#14564468	2
#14562365	2
#14562357	2
#14562270	2
#14562147	2
#14562143	2
C₁₉×#3548	2
#8493	19