Subgroups — #18090561

Order 4864.

882 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566119	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₉⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
6	#14563328	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₉⋊C₄	—	2	1	no	—
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926443	C₄	1	2	yes	complemented
14	#11926443	C₄	1	2	yes	complemented
15	#11926419	—	2	1	no	—
16	#11926419	—	2	1	no	—
17	C₄×Dic₁₉⋊C₄	—	2	2	no	—
18	C₄×Dic₁₉⋊C₄	—	2	2	no	—
19	C₄×C₄⋊Dic₁₉	—	2	2	no	—
20	C₂×C₁₉⋊#95	—	2	1	no	—
21	#11926305	—	2	2	no	—
22	#11926304	—	2	2	no	—
23	#11926303	—	2	2	no	—
24	#11926298	—	2	2	no	—
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#339	—	2	2	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
33	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
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	Q₈	1	2	yes	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	D₄	1	2	yes	—
44	C₁₉×#117	Q₈	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	D₄	1	2	yes	—
54	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	—	2	1	no	—
57	#10597372	—	2	1	no	—
58	#10597372	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	2	no	—
60	C₂×C₄⋊Dic₁₉	—	2	2	no	—
61	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×Dic₁₉⋊C₄	—	2	4	no	—
64	C₂×Dic₁₉⋊C₄	—	2	8	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	—	2	1	no	—
73	C₂×C₄×Dic₁₉	—	2	1	no	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
77	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
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	Q₈	1	2	yes	—
84	C₂²×C₁₉⋊C₈	—	2	1	no	—
85	C₁₉⋊#95	—	2	4	no	—
86	C₁₉⋊#95	—	2	2	no	—
87	C₁₉⋊#95	—	2	2	no	—
88	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×Dic₁₉	—	2	1	no	—
110	C₂²×Dic₁₉	—	2	1	no	—
111	C₂²×Dic₁₉	—	2	4	no	—
112	C₂²×Dic₁₉	—	2	4	no	—
113	C₂²×Dic₁₉	—	2	2	no	—
114	C₂²×Dic₁₉	—	2	1	no	—
115	C₂²×Dic₁₉	—	2	1	no	—
116	C₂²×Dic₁₉	—	2	1	no	—
117	C₂²×Dic₁₉	—	2	1	no	—
118	C₂²×Dic₁₉	—	4	2	no	—
119	C₂²×Dic₁₉	—	4	2	no	—
120	C₂²×Dic₁₉	—	4	1	no	—
121	C₂²×Dic₁₉	—	4	1	no	—
122	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
123	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
124	M₁₆×C₁₉	—	2	2	no	—
125	M₁₆×C₁₉	—	2	2	no	—
126	M₁₆×C₁₉	—	4	1	no	—
127	M₁₆×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	4	1	no	—
141	C₂²⋊Dic₁₉	—	4	1	no	—
142	C₂²⋊Dic₁₉	—	4	1	no	—
143	C₄⋊Dic₁₉	—	2	1	no	—
144	C₄⋊Dic₁₉	—	2	1	no	—
145	C₄⋊Dic₁₉	—	2	1	no	—
146	C₄⋊Dic₁₉	—	2	1	no	—
147	C₄⋊Dic₁₉	—	4	4	no	—
148	C₄⋊Dic₁₉	—	4	4	no	—
149	Dic₁₉⋊C₄	—	2	16	no	—
150	C₄×Dic₁₉	—	2	2	no	—
151	C₄×Dic₁₉	—	2	2	no	—
152	C₄×Dic₁₉	—	2	2	no	—
153	C₄×Dic₁₉	—	2	2	no	—
154	C₄×Dic₁₉	—	2	2	no	—
155	C₄×Dic₁₉	—	2	2	no	—
156	C₄×Dic₁₉	—	4	1	no	—
157	C₄×Dic₁₉	—	4	1	no	—
158	C₄×Dic₁₉	—	4	1	no	—
159	C₄×Dic₁₉	—	4	1	no	—
160	#64520	—	2	2	no	—
161	#64520	—	2	2	no	—
162	#64520	—	4	1	no	—
163	#64520	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	2	2	no	—
165	C₂×C₁₉⋊C₈	—	4	1	no	—
166	C₂×C₁₉⋊C₈	—	4	1	no	—
167	#11226	—	19	1	no	maximal, Sylow
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	C₂³×C₁₉	#121	1	1	yes	characteristic
173	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂³×C₁₉	#123	1	1	yes	characteristic
175	C₂³×C₁₉	#124	1	1	yes	characteristic
176	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄×D₄	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	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
213	C₂×Dic₁₉	—	2	4	no	—
214	C₂×Dic₁₉	—	2	4	no	—
215	C₂×Dic₁₉	—	2	2	no	—
216	C₂×Dic₁₉	—	2	2	no	—
217	C₂×Dic₁₉	—	2	4	no	—
218	C₂×Dic₁₉	—	2	2	no	—
219	C₂×Dic₁₉	—	2	2	no	—
220	C₂×Dic₁₉	—	2	2	no	—
221	C₂×Dic₁₉	—	4	4	no	—
222	C₂×Dic₁₉	—	4	2	no	—
223	C₂×Dic₁₉	—	4	4	no	—
224	C₂×Dic₁₉	—	4	2	no	—
225	C₂×Dic₁₉	—	4	2	no	—
226	C₂×Dic₁₉	—	4	2	no	—
227	C₂×Dic₁₉	—	4	1	no	—
228	C₂×Dic₁₉	—	4	1	no	—
229	C₂×Dic₁₉	—	4	2	no	—
230	C₂×Dic₁₉	—	4	2	no	—
231	C₂×Dic₁₉	#104	1	4	yes	—
232	C₈×C₁₉	—	4	2	no	—
233	C₁₉⋊C₈	—	4	2	no	—
234	#2296	—	19	1	no	—
235	C₂×C₄×C₄⋊C₄	—	19	1	no	—
236	C₂×#339	—	19	1	no	—
237	C₂×#339	—	19	1	no	—
238	C₂×#339	—	19	1	no	—
239	C₂×#339	D₁₉	1	1	yes	characteristic
240	#1728	—	19	1	no	—
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	2	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	#380	1	1	yes	characteristic
250	C₂²×C₁₉	#386	1	1	yes	characteristic
251	C₂²×C₁₉	#391	1	1	yes	characteristic
252	C₂²×C₁₉	#394	1	1	yes	characteristic
253	C₂²×C₁₉	#395	1	1	yes	characteristic
254	C₂²×C₁₉	#398	1	1	yes	characteristic
255	C₂²×C₁₉	#400	1	1	yes	characteristic
256	C₂²×C₁₉	C₂×#104	1	2	yes	—
257	C₂²×C₁₉	#421	1	2	yes	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	—	4	4	no	—
260	C₄×C₁₉	#387	1	1	yes	characteristic
261	C₄×C₁₉	#387	1	1	yes	characteristic
262	C₄×C₁₉	#389	1	1	yes	characteristic
263	C₄×C₁₉	#389	1	1	yes	characteristic
264	C₄×C₁₉	#396	1	1	yes	characteristic
265	C₄×C₁₉	#396	1	1	yes	characteristic
266	C₄×C₁₉	#398	1	1	yes	characteristic
267	C₄×C₁₉	#398	1	1	yes	characteristic
268	Dic₁₉	—	2	4	no	—
269	Dic₁₉	—	4	4	no	—
270	Dic₁₉	—	4	2	no	—
271	Dic₁₉	—	8	1	no	—
272	Dic₁₉	—	8	1	no	—
273	C₂²×M₁₆	—	19	1	no	—
274	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
275	C₂×#117	—	19	1	no	—
276	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	—	38	1	no	—
278	C₂²×C₄²	—	19	1	no	—
279	C₂²×C₄²	—	19	1	no	—
280	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
281	#389	—	19	2	no	—
282	#389	—	19	2	no	—
283	#385	—	38	1	no	—
284	#385	—	38	1	no	—
285	C₄×C₄⋊C₄	—	38	2	no	—
286	C₄×C₄⋊C₄	—	38	2	no	—
287	C₄×C₄⋊C₄	—	38	2	no	—
288	C₂×#95	—	38	1	no	—
289	#339	—	2	2	no	—
290	#339	—	38	2	no	—
291	#339	—	38	2	no	—
292	#339	—	38	2	no	—
293	#336	—	38	2	no	—
294	C₂×C₁₉	—	2	1	no	—
295	C₂×C₁₉	—	2	1	no	—
296	C₂×C₁₉	—	2	1	no	—
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	#1441	1	1	yes	characteristic
299	C₂×C₁₉	#1806	1	2	yes	—
300	C₂×C₁₉	#1896	1	1	yes	characteristic
301	C₂×C₁₉	#1897	1	1	yes	characteristic
302	C₂×C₁₉	#1986	1	2	yes	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	19	1	no	—
305	C₂³×C₄	—	19	1	no	—
306	C₂³×C₄	—	38	1	no	—
307	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	19	2	no	—
314	C₂×M₁₆	—	38	1	no	—
315	C₂×M₁₆	—	38	1	no	—
316	C₂×M₁₆	—	38	1	no	—
317	C₂×M₁₆	—	38	1	no	—
318	C₂×M₁₆	—	38	1	no	—
319	C₂×M₁₆	Dic₃₈	1	2	yes	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	38	1	no	—
322	#117	—	2	1	no	—
323	#117	—	2	1	no	—
324	#117	—	38	1	no	—
325	#117	—	38	1	no	—
326	#117	—	38	1	no	—
327	#117	—	38	1	no	—
328	#117	Dic₃₈	1	2	yes	—
329	#117	C₂²⋊D₁₉	1	2	yes	—
330	C₂×C₄⋊C₄	—	19	1	no	—
331	C₂×C₄⋊C₄	—	19	1	no	—
332	C₂×C₄⋊C₄	—	38	4	no	—
333	C₂×C₄⋊C₄	—	38	8	no	—
334	C₂×C₄⋊C₄	—	38	2	no	—
335	C₂×C₄⋊C₄	—	38	2	no	—
336	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	38	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	19	2	no	—
346	C₂×C₄²	—	19	2	no	—
347	C₂×C₄²	—	19	2	no	—
348	C₂×C₄²	—	38	1	no	—
349	C₂×C₄²	—	38	1	no	—
350	C₂×C₄²	—	38	1	no	—
351	C₂×C₄²	—	38	1	no	—
352	C₂×C₄²	—	38	1	no	—
353	C₂×C₄²	—	38	1	no	—
354	C₂×C₄²	—	38	1	no	—
355	C₂×C₄²	—	38	1	no	—
356	C₂×C₄²	—	38	1	no	—
357	C₂×C₄²	—	38	1	no	—
358	C₂×C₄²	D₇₆	1	2	yes	—
359	#95	—	38	2	no	—
360	#95	—	38	2	no	—
361	#95	—	38	4	no	—
362	C₁₉	#11226	1	1	yes	characteristic, complemented, Sylow
363	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	19	2	no	—
371	C₂²×C₄	—	19	2	no	—
372	C₂²×C₄	—	38	4	no	—
373	C₂²×C₄	—	38	1	no	—
374	C₂²×C₄	—	38	1	no	—
375	C₂²×C₄	—	38	4	no	—
376	C₂²×C₄	—	38	1	no	—
377	C₂²×C₄	—	38	2	no	—
378	C₂²×C₄	—	38	1	no	—
379	C₂²×C₄	—	38	1	no	—
380	C₂²×C₄	—	38	1	no	—
381	C₂²×C₄	—	76	2	no	—
382	C₂²×C₄	—	76	2	no	—
383	C₂²×C₄	—	76	1	no	—
384	C₂²×C₄	—	76	1	no	—
385	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
386	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
389	C₂²×C₄	#64541	1	1	yes	characteristic
390	C₂²×C₄	#64541	1	1	yes	characteristic
391	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
392	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
393	C₂²×C₄	#64543	1	1	yes	characteristic
394	C₂²×C₄	#64543	1	1	yes	characteristic
395	C₂²×C₄	#64543	1	1	yes	characteristic
396	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
397	C₂²×C₄	#64545	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	4	1	no	—
402	M₁₆	—	4	1	no	—
403	M₁₆	—	38	2	no	—
404	M₁₆	—	38	2	no	—
405	M₁₆	—	76	1	no	—
406	M₁₆	—	76	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	4	1	no	—
409	C₂×C₈	—	4	1	no	—
410	C₂×C₈	—	38	2	no	—
411	C₂×C₈	—	76	1	no	—
412	C₂×C₈	—	76	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	38	16	no	—
415	C₄⋊C₄	—	38	1	no	—
416	C₄⋊C₄	—	38	1	no	—
417	C₄⋊C₄	—	38	1	no	—
418	C₄⋊C₄	—	38	1	no	—
419	C₄⋊C₄	—	76	4	no	—
420	C₄⋊C₄	—	76	4	no	—
421	C₄⋊C₄	Dic₁₉⋊C₄	1	4	yes	complemented
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	76	1	no	—
425	C₂²⋊C₄	—	76	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₄²	—	38	2	no	—
433	C₄²	—	38	2	no	—
434	C₄²	—	38	2	no	—
435	C₄²	—	38	2	no	—
436	C₄²	—	38	2	no	—
437	C₄²	—	38	2	no	—
438	C₄²	—	76	1	no	—
439	C₄²	—	76	1	no	—
440	C₄²	—	76	1	no	—
441	C₄²	—	76	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	#10597324	1	1	yes	characteristic
445	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
446	C₂³	#10597328	1	1	yes	characteristic
447	C₂³	#10597331	1	1	yes	characteristic
448	C₂³	#10597334	1	1	yes	characteristic
449	C₂³	#10597340	1	1	yes	characteristic
450	C₂³	#10597385	1	1	yes	characteristic
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	19	4	no	—
460	C₂×C₄	—	38	4	no	—
461	C₂×C₄	—	38	4	no	—
462	C₂×C₄	—	38	2	no	—
463	C₂×C₄	—	38	2	no	—
464	C₂×C₄	—	38	4	no	—
465	C₂×C₄	—	38	2	no	—
466	C₂×C₄	—	38	2	no	—
467	C₂×C₄	—	38	2	no	—
468	C₂×C₄	—	76	4	no	—
469	C₂×C₄	—	76	4	no	—
470	C₂×C₄	—	76	2	no	—
471	C₂×C₄	—	76	2	no	—
472	C₂×C₄	—	76	2	no	—
473	C₂×C₄	—	76	2	no	—
474	C₂×C₄	—	76	2	no	—
475	C₂×C₄	—	76	2	no	—
476	C₂×C₄	—	76	1	no	—
477	C₂×C₄	—	76	1	no	—
478	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
479	C₂×C₄	#10597315	1	1	yes	characteristic
480	C₂×C₄	#10597316	1	1	yes	characteristic
481	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
482	C₂×C₄	#10597323	1	1	yes	characteristic
483	C₂×C₄	#10597324	1	1	yes	characteristic
484	C₂×C₄	#10597324	1	1	yes	characteristic
485	C₂×C₄	#10597324	1	1	yes	characteristic
486	C₂×C₄	#10597325	1	1	yes	characteristic
487	C₂×C₄	#10597329	1	1	yes	characteristic
488	C₂×C₄	#10597330	1	1	yes	characteristic
489	C₂×C₄	#10597332	1	1	yes	characteristic
490	C₂×C₄	#10597333	1	1	yes	characteristic
491	C₂×C₄	#10597334	1	1	yes	characteristic
492	C₂×C₄	#10597335	1	1	yes	characteristic
493	C₂×C₄	#10597336	1	1	yes	characteristic
494	C₂×C₄	#10597336	1	1	yes	characteristic
495	C₂×C₄	#10597339	1	1	yes	characteristic
496	C₂×C₄	#10597341	1	1	yes	characteristic
497	C₂×C₄	#10597342	1	1	yes	characteristic
498	C₂×C₄	#10597343	1	1	yes	characteristic
499	C₂×C₄	#10597344	1	1	yes	characteristic
500	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
501	C₂×C₄	#10597370	1	1	yes	characteristic
502	C₂×C₄	#10597376	1	1	yes	characteristic
503	C₂×C₄	#10597384	1	1	yes	characteristic
504	C₂×C₄	#10597385	1	1	yes	characteristic
505	C₂×C₄	#10597392	1	1	yes	characteristic
506	C₈	—	4	2	no	—
507	C₈	—	76	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	#11926402	1	1	yes	characteristic
517	C₂²	#11926422	1	1	yes	characteristic
518	C₂²	#11926448	1	1	yes	characteristic
519	C₂²	#11926460	1	1	yes	characteristic
520	C₂²	#11926465	1	1	yes	characteristic
521	C₂²	#11926477	1	1	yes	characteristic
522	C₂²	#11926486	1	1	yes	characteristic
523	C₂²	#104×D₁₉	1	2	yes	—
524	C₂²	#11926559	1	2	yes	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	38	4	no	—
528	C₄	—	76	4	no	—
529	C₄	—	76	2	no	—
530	C₄	—	152	1	no	—
531	C₄	—	152	1	no	—
532	C₄	#11926427	1	1	yes	characteristic
533	C₄	#11926429	1	1	yes	characteristic
534	C₄	#11926440	1	1	yes	characteristic
535	C₄	#11926442	1	1	yes	characteristic
536	C₄	#11926466	1	1	yes	characteristic
537	C₄	#11926467	1	1	yes	characteristic
538	C₄	#11926476	1	1	yes	characteristic
539	C₄	#11926478	1	1	yes	characteristic
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	#14561887	1	1	yes	characteristic
545	C₂	#14563653	1	2	yes	—
546	C₂	#14564077	1	1	yes	characteristic
547	C₂	#14564082	1	1	yes	characteristic
548	C₂	#14564577	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#11226
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #11926443	C₄	semidirect
14. #11926443	C₄	semidirect
132. C₄⋊C₄×C₁₉	C₄⋊C₄	semidirect
362. C₁₉	#11226	semidirect
421. C₄⋊C₄	Dic₁₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#14566119	2
C₂×C₄×Dic₁₉⋊C₄	2
C₂×#11926305	2
C₂×#11926304	2
C₂×#11926303	2
#14563328	2
C₂×C₁₉×#339	2
#11226	19