Subgroups — #18091212

Order 4864.

790 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572224	C₂	1	1	yes	maximal, characteristic
2	#14566119	C₂	1	1	yes	maximal, characteristic
3	#14566117	C₂	1	1	yes	maximal, characteristic
4	#14563346	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926300	C₂	1	1	yes	maximal, characteristic
6	#14563328	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	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	#11926587	—	2	2	no	—
13	#11926584	—	2	2	no	—
14	#11926580	—	2	2	no	—
15	#11926443	—	2	2	no	—
16	#11926440	—	2	2	no	—
17	#11926419	—	2	2	no	—
18	#11926416	—	2	2	no	—
19	C₄×Dic₁₉⋊C₄	—	2	2	no	—
20	C₄×C₄⋊Dic₁₉	—	2	2	no	—
21	#11926305	—	2	2	no	—
22	#11926300	C₄	1	4	yes	complemented
23	#11926298	—	2	2	no	—
24	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₁₉×#339	—	2	2	no	—
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂³×Dic₁₉	D₄	1	2	yes	—
30	C₂×M₁₆×C₁₉	—	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	Q₈	1	2	yes	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	—	2	1	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×#117	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	C₂×C₄	1	2	yes	—
44	C₁₉×#117	Q₈	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	D₄	1	2	yes	—
51	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
52	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
53	#10597372	—	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	—	2	1	no	—
59	#10597372	C₂×C₄	1	2	yes	—
60	#10597372	Q₈	1	2	yes	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	4	no	—
63	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
64	C₂×Dic₁₉⋊C₄	—	2	4	no	—
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	D₄	1	2	yes	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	C₂×C₄	1	2	yes	—
78	C₂×#64520	Q₈	1	2	yes	—
79	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
80	C₁₉⋊#95	—	2	4	no	—
81	C₁₉⋊#95	—	2	4	no	—
82	#10597265	—	2	4	no	—
83	#10597264	—	2	4	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	C₂²×C₄	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×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	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×Q₈	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×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	2	2	no	—
102	C₂²×Dic₁₉	—	2	2	no	—
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂²×Dic₁₉	—	2	2	no	—
106	C₂²×Dic₁₉	—	4	4	no	—
107	M₁₆×C₁₉	—	2	2	no	—
108	M₁₆×C₁₉	—	2	2	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	M₁₆×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂²⋊C₄×C₁₉	—	2	2	no	—
120	C₂²⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	1	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	C₄⋊C₄	1	4	yes	complemented
126	C₂²⋊Dic₁₉	—	2	2	no	—
127	C₂²⋊Dic₁₉	—	2	2	no	—
128	C₂²⋊Dic₁₉	—	4	1	no	—
129	C₂²⋊Dic₁₉	—	4	1	no	—
130	C₄⋊Dic₁₉	—	2	2	no	—
131	C₄⋊Dic₁₉	—	2	2	no	—
132	C₄⋊Dic₁₉	—	2	2	no	—
133	C₄⋊Dic₁₉	—	2	2	no	—
134	C₄⋊Dic₁₉	—	4	8	no	—
135	Dic₁₉⋊C₄	—	4	8	no	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	4	1	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	C₄×Dic₁₉	—	4	1	no	—
140	C₄×Dic₁₉	—	4	1	no	—
141	C₄×Dic₁₉	—	4	1	no	—
142	C₄×Dic₁₉	—	4	1	no	—
143	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	complemented
144	#64520	—	2	2	no	—
145	#64520	—	2	2	no	—
146	#64520	—	2	2	no	—
147	#64520	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	2	no	—
150	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	complemented
151	#11335	—	19	1	no	maximal, Sylow
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂³×C₁₉	#120	1	1	yes	characteristic
155	C₂³×C₁₉	#120	1	1	yes	characteristic
156	C₂³×C₁₉	#121	1	1	yes	characteristic
157	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₄⋊C₄	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×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#123	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	#125	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
192	C₂×Dic₁₉	—	2	4	no	—
193	C₂×Dic₁₉	—	2	4	no	—
194	C₂×Dic₁₉	—	2	4	no	—
195	C₂×Dic₁₉	—	2	4	no	—
196	C₂×Dic₁₉	—	4	4	no	—
197	C₂×Dic₁₉	—	4	2	no	—
198	C₂×Dic₁₉	—	4	2	no	—
199	C₂×Dic₁₉	—	4	2	no	—
200	C₂×Dic₁₉	—	4	2	no	—
201	C₂×Dic₁₉	—	4	4	no	—
202	C₂×Dic₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₁₉⋊C₈	—	2	4	no	—
205	#2911	—	19	1	no	—
206	#2296	—	19	1	no	—
207	#2296	—	19	1	no	—
208	#1733	—	19	1	no	—
209	#1733	D₁₉	1	1	yes	characteristic
210	C₂×H(3,ℤ/4)	—	19	1	no	—
211	#1728	—	19	1	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	#385	1	1	yes	characteristic
220	C₂²×C₁₉	#385	1	1	yes	characteristic
221	C₂²×C₁₉	#389	1	1	yes	characteristic
222	C₂²×C₁₉	#392	1	1	yes	characteristic
223	C₂²×C₁₉	#395	1	1	yes	characteristic
224	C₂²×C₁₉	#395	1	1	yes	characteristic
225	C₂²×C₁₉	#398	1	1	yes	characteristic
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	#384	1	1	yes	characteristic
229	C₄×C₁₉	#385	1	1	yes	characteristic
230	C₄×C₁₉	#389	1	1	yes	characteristic
231	C₄×C₁₉	#389	1	1	yes	characteristic
232	C₄×C₁₉	#395	1	1	yes	characteristic
233	C₄×C₁₉	#398	1	1	yes	characteristic
234	C₄×C₁₉	#398	1	1	yes	characteristic
235	C₄×C₁₉	#399	1	1	yes	characteristic
236	Dic₁₉	—	4	4	no	—
237	Dic₁₉	—	4	4	no	—
238	Dic₁₉	—	8	2	no	—
239	C₂²×M₁₆	—	19	1	no	—
240	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
241	C₂×#117	—	19	1	no	—
242	C₂×#117	—	19	1	no	—
243	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
244	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
245	C₂²×C₄²	—	19	1	no	—
246	#428	—	38	2	no	—
247	#428	—	38	2	no	—
248	#427	—	38	2	no	—
249	#389	—	38	2	no	—
250	#389	—	38	2	no	—
251	#385	—	38	2	no	—
252	#385	—	38	2	no	—
253	C₄×C₄⋊C₄	—	38	2	no	—
254	C₄×C₄⋊C₄	—	38	2	no	—
255	#339	—	2	2	no	—
256	#339	—	38	2	no	—
257	H(3,ℤ/4)	—	19	4	no	—
258	#336	—	38	2	no	—
259	C₂×C₁₉	—	2	1	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	—	2	1	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	#1444	1	1	yes	characteristic
266	C₂×C₁₉	#2010	1	2	yes	—
267	C₂³×C₄	—	19	2	no	—
268	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	19	2	no	—
275	C₂×M₁₆	—	19	2	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	Dic₃₈	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	19	2	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	19	2	no	—
290	#117	—	19	2	no	—
291	#117	—	38	1	no	—
292	#117	—	38	1	no	—
293	#117	—	38	1	no	—
294	#117	—	38	1	no	—
295	#117	—	38	1	no	—
296	#117	—	38	1	no	—
297	#117	Dic₃₈	1	2	yes	—
298	#117	C₄×D₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	19	2	no	—
301	C₂×C₄⋊C₄	—	38	1	no	—
302	C₂×C₄⋊C₄	—	38	4	no	—
303	C₂×C₄⋊C₄	—	38	4	no	—
304	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	38	1	no	—
308	C₂×C₂²⋊C₄	—	38	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	19	2	no	—
311	C₂×C₄²	—	38	1	no	—
312	C₂×C₄²	—	38	1	no	—
313	C₂×C₄²	—	38	1	no	—
314	C₂×C₄²	—	38	1	no	—
315	C₂×C₄²	—	38	1	no	—
316	C₂×C₄²	—	38	1	no	—
317	C₂×C₄²	—	38	1	no	—
318	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
319	#107	—	38	4	no	—
320	#106	—	38	4	no	—
321	#95	—	38	4	no	—
322	#95	—	38	4	no	—
323	C₁₉	#11335	1	1	yes	characteristic, complemented, Sylow
324	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	38	2	no	—
328	C₂²×C₄	—	38	2	no	—
329	C₂²×C₄	—	38	2	no	—
330	C₂²×C₄	—	38	2	no	—
331	C₂²×C₄	—	38	2	no	—
332	C₂²×C₄	—	76	4	no	—
333	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
334	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
337	C₂²×C₄	#64541	1	1	yes	characteristic
338	C₂²×C₄	#64541	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
341	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
342	C₂²×C₄	#64543	1	1	yes	characteristic
343	C₂²×C₄	#64543	1	1	yes	characteristic
344	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
345	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	4	1	no	—
350	M₁₆	—	4	1	no	—
351	M₁₆	—	38	2	no	—
352	M₁₆	—	38	2	no	—
353	M₁₆	—	38	2	no	—
354	M₁₆	—	38	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	19	4	no	—
359	C₂×C₈	—	38	2	no	—
360	C₂×C₈	—	38	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	38	2	no	—
366	C₄⋊C₄	—	38	2	no	—
367	C₄⋊C₄	—	38	2	no	—
368	C₄⋊C₄	—	38	2	no	—
369	C₄⋊C₄	—	76	8	no	—
370	C₄⋊C₄	—	76	8	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	38	2	no	—
376	C₂²⋊C₄	—	38	2	no	—
377	C₂²⋊C₄	—	76	1	no	—
378	C₂²⋊C₄	—	76	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	4	1	no	—
381	C₄²	—	4	1	no	—
382	C₄²	—	19	4	no	—
383	C₄²	—	38	2	no	—
384	C₄²	—	76	1	no	—
385	C₄²	—	76	1	no	—
386	C₄²	—	76	1	no	—
387	C₄²	—	76	1	no	—
388	C₄²	—	76	1	no	—
389	C₄²	—	76	1	no	—
390	C₄²	Dic₁₉⋊C₄	1	4	yes	complemented
391	C₂³	—	4	2	no	—
392	C₂³	#10597324	1	1	yes	characteristic
393	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
394	C₂³	#10597328	1	1	yes	characteristic
395	C₂³	#10597330	1	1	yes	characteristic
396	C₂³	#10597334	1	1	yes	characteristic
397	C₂³	#10597342	1	1	yes	characteristic
398	C₂³	#10597383	1	1	yes	characteristic
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	38	4	no	—
404	C₂×C₄	—	38	4	no	—
405	C₂×C₄	—	38	4	no	—
406	C₂×C₄	—	38	4	no	—
407	C₂×C₄	—	76	4	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	76	2	no	—
410	C₂×C₄	—	76	2	no	—
411	C₂×C₄	—	76	2	no	—
412	C₂×C₄	—	76	4	no	—
413	C₂×C₄	—	76	2	no	—
414	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
415	C₂×C₄	#10597315	1	1	yes	characteristic
416	C₂×C₄	#10597316	1	1	yes	characteristic
417	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
418	C₂×C₄	#10597324	1	1	yes	characteristic
419	C₂×C₄	#10597324	1	1	yes	characteristic
420	C₂×C₄	#10597324	1	1	yes	characteristic
421	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
422	C₂×C₄	#10597328	1	1	yes	characteristic
423	C₂×C₄	#10597329	1	1	yes	characteristic
424	C₂×C₄	#10597329	1	1	yes	characteristic
425	C₂×C₄	#10597330	1	1	yes	characteristic
426	C₂×C₄	#10597334	1	1	yes	characteristic
427	C₂×C₄	#10597334	1	1	yes	characteristic
428	C₂×C₄	#10597334	1	1	yes	characteristic
429	C₂×C₄	#10597335	1	1	yes	characteristic
430	C₂×C₄	#10597335	1	1	yes	characteristic
431	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
432	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
433	C₂×C₄	#10597342	1	1	yes	characteristic
434	C₂×C₄	#10597343	1	1	yes	characteristic
435	C₂×C₄	#10597343	1	1	yes	characteristic
436	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
437	C₂×C₄	#10597370	1	1	yes	characteristic
438	C₂×C₄	#10597376	1	1	yes	characteristic
439	C₂×C₄	#10597381	1	1	yes	characteristic
440	C₂×C₄	#10597386	1	1	yes	characteristic
441	C₂×C₄	#10597390	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	38	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	#11926416	1	1	yes	characteristic
452	C₂²	#11926418	1	1	yes	characteristic
453	C₂²	#11926441	1	1	yes	characteristic
454	C₂²	#11926453	1	1	yes	characteristic
455	C₂²	#11926464	1	1	yes	characteristic
456	C₂²	#11926465	1	1	yes	characteristic
457	C₂²	#11926478	1	1	yes	characteristic
458	C₄	—	4	4	no	—
459	C₄	—	8	2	no	—
460	C₄	—	76	4	no	—
461	C₄	—	76	4	no	—
462	C₄	—	152	2	no	—
463	C₄	#11926413	1	1	yes	characteristic
464	C₄	#11926418	1	1	yes	characteristic
465	C₄	#11926441	1	1	yes	characteristic
466	C₄	#11926442	1	1	yes	characteristic
467	C₄	#11926465	1	1	yes	characteristic
468	C₄	#11926474	1	1	yes	characteristic
469	C₄	#11926478	1	1	yes	characteristic
470	C₄	#11926480	1	1	yes	characteristic
471	C₂	—	2	1	no	—
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	#14561899	1	1	yes	characteristic
478	C₂	#14564701	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1733	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1733	D₁₉
hypocenter	C₁₉	#11335
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
22. #11926300	C₄	semidirect
125. C₄²×C₁₉	C₄⋊C₄	semidirect
143. C₄×Dic₁₉	C₄⋊C₄	semidirect
150. C₂×C₁₉⋊C₈	C₄⋊C₄	semidirect
323. C₁₉	#11335	semidirect
390. C₄²	Dic₁₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#14572224	2
#14566119	2
#14566117	2
#14563346	2
C₂×#11926300	2
#14563328	2
C₁₉×#1733	2
#11335	19