Subgroups — #18088481

Order 4864.

730 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597279	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926580	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926500	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926315	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926314	C₂	1	1	yes	maximal, characteristic
6	#14563344	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	C₂×#10597279	—	2	2	no	—
13	C₂×#10597279	—	2	1	no	—
14	C₂×#10597279	—	2	1	no	—
15	C₂×#10597279	C₄	1	4	yes	complemented
16	#11926580	—	2	2	no	—
17	#11926580	C₄	1	4	yes	complemented
18	C₂×#10597264	—	2	1	no	—
19	C₂×#10597265	—	2	1	no	—
20	#11926500	—	2	1	no	—
21	#11926500	—	2	1	no	—
22	#11926500	C₄	1	2	yes	complemented
23	#11926500	C₄	1	2	yes	complemented
24	C₂×#10597260	—	2	1	no	—
25	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
26	#11926315	—	2	2	no	—
27	#11926314	—	2	2	no	—
28	#11926303	—	2	2	no	—
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₁₉×#339	—	2	2	no	—
33	C₂³×C₄×C₁₉	C₂³	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	C₂×C₄	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	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	C₂×C₄	1	2	yes	—
47	C₁₉×#117	C₂×C₄	1	2	yes	—
48	C₁₉×#117	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₄²×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊Dic₁₉	—	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	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄×Dic₁₉	—	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	—	2	1	no	—
70	C₂×#64520	C₂×C₄	1	2	yes	—
71	C₂×#64520	C₂×C₄	1	2	yes	—
72	C₂×#64520	D₄	1	2	yes	—
73	C₂×#64520	Q₈	1	2	yes	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
77	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
78	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
81	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
82	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
83	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
84	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
85	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
86	#10597279	—	2	4	no	—
87	#10597279	—	2	4	no	—
88	#10597265	—	2	4	no	—
89	#10597264	—	2	4	no	—
90	#10597260	—	2	2	no	—
91	#10597260	—	2	2	no	—
92	C₄×C₁₉⋊C₈	—	2	2	no	—
93	C₄×C₁₉⋊C₈	—	2	2	no	—
94	C₂⁴×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×Dic₁₉	—	4	1	no	—
112	M₁₆×C₁₉	—	2	2	no	—
113	M₁₆×C₁₉	—	2	2	no	—
114	M₁₆×C₁₉	—	4	1	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
123	C₂²⋊C₄×C₁₉	—	2	2	no	—
124	C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	C₂²⋊Dic₁₉	—	2	2	no	—
132	C₂²⋊Dic₁₉	—	4	1	no	—
133	C₄⋊Dic₁₉	—	2	2	no	—
134	C₄⋊Dic₁₉	—	4	1	no	—
135	C₄×Dic₁₉	—	2	2	no	—
136	C₄×Dic₁₉	—	4	1	no	—
137	#64520	—	2	2	no	—
138	#64520	—	2	2	no	—
139	#64520	—	2	2	no	—
140	#64520	—	2	2	no	—
141	#64520	—	2	2	no	—
142	#64520	—	4	1	no	—
143	#64520	—	4	1	no	—
144	#64520	C₄⋊C₄	1	4	yes	—
145	C₂×C₁₉⋊C₈	—	2	2	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
152	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
153	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
158	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
159	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
160	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
161	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
162	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
163	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
164	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
165	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
166	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
167	#10872	—	19	1	no	maximal, Sylow
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	#117	1	1	yes	characteristic
170	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
172	C₂³×C₁₉	#121	1	1	yes	characteristic
173	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂³×C₁₉	#124	1	1	yes	characteristic
175	C₂³×C₁₉	#125	1	1	yes	characteristic
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	4	4	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	8	2	no	—
180	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#121	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	#124	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
208	C₂×Dic₁₉	—	4	2	no	—
209	C₂×Dic₁₉	—	8	2	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₁₉⋊C₈	—	2	4	no	—
212	C₁₉⋊C₈	—	4	2	no	—
213	C₁₉⋊C₈	#95	1	2	yes	—
214	C₁₉⋊C₈	#95	1	2	yes	—
215	C₁₉⋊C₈	#95	1	2	yes	—
216	C₁₉⋊C₈	#95	1	2	yes	—
217	C₂²×#108	—	19	1	no	—
218	C₂×#427	—	19	1	no	—
219	C₂×#405	—	19	1	no	—
220	C₂×#344	—	19	1	no	—
221	C₂×#344	—	19	1	no	—
222	#1733	—	19	1	no	—
223	#1733	D₁₉	1	1	yes	characteristic
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	4	1	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₁₉	#380	1	1	yes	characteristic
233	C₂²×C₁₉	#382	1	1	yes	characteristic
234	C₂²×C₁₉	#389	1	1	yes	characteristic
235	C₂²×C₁₉	#389	1	1	yes	characteristic
236	C₂²×C₁₉	#390	1	1	yes	characteristic
237	C₂²×C₁₉	#391	1	1	yes	characteristic
238	C₄×C₁₉	—	4	4	no	—
239	C₄×C₁₉	—	8	2	no	—
240	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
241	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
242	C₄×C₁₉	#380	1	1	yes	characteristic
243	C₄×C₁₉	#384	1	1	yes	characteristic
244	C₄×C₁₉	#389	1	1	yes	characteristic
245	C₄×C₁₉	#389	1	1	yes	characteristic
246	C₄×C₁₉	#390	1	1	yes	characteristic
247	C₄×C₁₉	#391	1	1	yes	characteristic
248	Dic₁₉	—	8	2	no	—
249	C₂²×M₁₆	—	19	1	no	—
250	C₂²×M₁₆	—	19	1	no	—
251	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
252	C₂³×C₈	—	19	1	no	—
253	C₂×#117	—	19	1	no	—
254	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
255	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
256	C₂×#108	—	19	4	no	—
257	C₂×#108	—	38	1	no	—
258	C₂×#108	—	38	1	no	—
259	C₂×#108	—	38	2	no	—
260	#427	—	19	4	no	—
261	#427	—	38	2	no	—
262	C₂×#107	—	38	1	no	—
263	C₂×#106	—	38	1	no	—
264	#405	—	19	2	no	—
265	#405	—	19	2	no	—
266	#405	—	38	1	no	—
267	#405	—	38	1	no	—
268	C₂×#97	—	38	1	no	—
269	C₂×C₄×C₈	—	38	1	no	—
270	#344	—	38	2	no	—
271	#344	—	38	2	no	—
272	#339	—	2	2	no	—
273	#339	—	38	2	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	2	1	no	—
276	C₂×C₁₉	—	2	1	no	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	2	1	no	—
280	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
281	C₂×C₁₉	#1814	1	2	yes	—
282	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	19	2	no	—
289	C₂×M₁₆	—	19	2	no	—
290	C₂×M₁₆	—	19	2	no	—
291	C₂×M₁₆	—	19	2	no	—
292	C₂×M₁₆	—	38	1	no	—
293	C₂×M₁₆	—	38	1	no	—
294	C₂×M₁₆	—	38	1	no	—
295	C₂×M₁₆	—	38	1	no	—
296	C₂×M₁₆	—	38	1	no	—
297	C₂×M₁₆	—	38	1	no	—
298	C₂×M₁₆	—	38	1	no	—
299	C₂×M₁₆	—	38	1	no	—
300	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	19	1	no	—
303	C₂²×C₈	—	19	1	no	—
304	C₂²×C₈	—	19	2	no	—
305	C₂²×C₈	—	19	2	no	—
306	C₂²×C₈	—	19	1	no	—
307	C₂²×C₈	—	19	1	no	—
308	C₂²×C₈	—	19	1	no	—
309	C₂²×C₈	—	19	1	no	—
310	C₂²×C₈	—	19	2	no	—
311	C₂²×C₈	—	19	2	no	—
312	C₂²×C₈	—	38	1	no	—
313	C₂²×C₈	—	38	1	no	—
314	#117	—	2	1	no	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	2	1	no	—
318	#117	—	2	1	no	—
319	#117	—	19	2	no	—
320	#117	—	38	1	no	—
321	#117	—	38	1	no	—
322	#117	—	38	1	no	—
323	#117	C₄×D₁₉	1	2	yes	—
324	#117	C₄×D₁₉	1	2	yes	—
325	#117	C₂²⋊D₁₉	1	2	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	38	1	no	—
328	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	38	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	38	1	no	—
335	#108	—	38	4	no	—
336	#108	—	38	4	no	—
337	#107	—	38	4	no	—
338	#106	—	38	4	no	—
339	#97	—	38	2	no	—
340	#97	—	38	2	no	—
341	C₄×C₈	—	38	2	no	—
342	C₄×C₈	—	38	2	no	—
343	C₁₉	#10872	1	1	yes	characteristic, complemented, Sylow
344	C₂⁴	#64543	1	1	yes	characteristic
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	76	1	no	—
348	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	#64541	1	1	yes	characteristic
353	C₂²×C₄	#64541	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
357	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
358	C₂²×C₄	#64543	1	1	yes	characteristic
359	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	1	no	—
365	M₁₆	—	4	1	no	—
366	M₁₆	—	19	4	no	—
367	M₁₆	—	38	2	no	—
368	M₁₆	—	38	2	no	—
369	M₁₆	—	38	2	no	—
370	M₁₆	—	38	2	no	—
371	M₁₆	—	38	2	no	—
372	M₁₆	—	76	1	no	—
373	M₁₆	—	76	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	19	2	no	—
378	C₂×C₈	—	19	2	no	—
379	C₂×C₈	—	19	1	no	—
380	C₂×C₈	—	19	1	no	—
381	C₂×C₈	—	19	1	no	—
382	C₂×C₈	—	19	1	no	—
383	C₂×C₈	—	19	2	no	—
384	C₂×C₈	—	19	2	no	—
385	C₂×C₈	—	19	2	no	—
386	C₂×C₈	—	19	2	no	—
387	C₂×C₈	—	19	2	no	—
388	C₂×C₈	—	19	2	no	—
389	C₂×C₈	—	19	2	no	—
390	C₂×C₈	—	19	2	no	—
391	C₂×C₈	—	19	2	no	—
392	C₂×C₈	—	19	2	no	—
393	C₂×C₈	—	38	2	no	—
394	C₂×C₈	—	38	2	no	—
395	C₂×C₈	—	38	2	no	—
396	C₂×C₈	—	38	2	no	—
397	C₂×C₈	—	76	1	no	—
398	C₂×C₈	—	76	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	38	2	no	—
403	C₄⋊C₄	—	76	1	no	—
404	C₄⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	4	1	no	—
409	C₂²⋊C₄	—	38	2	no	—
410	C₂²⋊C₄	—	76	1	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	38	2	no	—
416	C₄²	—	76	1	no	—
417	C₂³	—	4	2	no	—
418	C₂³	#10597323	1	1	yes	characteristic
419	C₂³	#10597324	1	1	yes	characteristic
420	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
421	C₂³	#10597331	1	1	yes	characteristic
422	C₂³	#10597333	1	1	yes	characteristic
423	C₂³	#10597335	1	1	yes	characteristic
424	C₂³	#10597385	1	1	yes	characteristic
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	76	2	no	—
430	C₂×C₄	—	152	2	no	—
431	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
432	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
433	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
434	C₂×C₄	#10597318	1	1	yes	characteristic
435	C₂×C₄	#10597324	1	1	yes	characteristic
436	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
439	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
440	C₂×C₄	#10597330	1	1	yes	characteristic
441	C₂×C₄	#10597330	1	1	yes	characteristic
442	C₂×C₄	#10597331	1	1	yes	characteristic
443	C₂×C₄	#10597333	1	1	yes	characteristic
444	C₂×C₄	#10597334	1	1	yes	characteristic
445	C₂×C₄	#10597334	1	1	yes	characteristic
446	C₂×C₄	#10597335	1	1	yes	characteristic
447	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
448	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
449	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
450	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
451	C₂×C₄	#10597342	1	1	yes	characteristic
452	C₂×C₄	#10597342	1	1	yes	characteristic
453	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
454	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
455	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
456	C₂×C₄	#10597385	1	1	yes	characteristic
457	C₂×C₄	#10597386	1	1	yes	characteristic
458	C₂×C₄	#10597390	1	1	yes	characteristic
459	C₈	—	4	2	no	—
460	C₈	—	19	2	no	—
461	C₈	—	19	2	no	—
462	C₈	—	19	2	no	—
463	C₈	—	19	2	no	—
464	C₈	—	38	4	no	—
465	C₈	—	76	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	#11926395	1	1	yes	characteristic
474	C₂²	#11926402	1	1	yes	characteristic
475	C₂²	#11926408	1	1	yes	characteristic
476	C₂²	#11926439	1	1	yes	characteristic
477	C₂²	#11926441	1	1	yes	characteristic
478	C₂²	#11926444	1	1	yes	characteristic
479	C₂²	#11926448	1	1	yes	characteristic
480	C₄	—	4	4	no	—
481	C₄	—	8	2	no	—
482	C₄	—	152	2	no	—
483	C₄	#95×D₁₉	1	1	yes	characteristic
484	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
485	C₄	#11926403	1	1	yes	characteristic
486	C₄	#11926413	1	1	yes	characteristic
487	C₄	#11926439	1	1	yes	characteristic
488	C₄	#11926441	1	1	yes	characteristic
489	C₄	#11926444	1	1	yes	characteristic
490	C₄	#11926448	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
498	C₂	#14563687	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1733	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1733	D₁₉
hypocenter	C₁₉	#10872
LCS	G ▷ C₂×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
15. C₂×#10597279	C₄	semidirect
17. #11926580	C₄	semidirect
22. #11926500	C₄	semidirect
23. #11926500	C₄	semidirect
343. C₁₉	#10872	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597279	2
C₂×#11926580	2
C₂×#11926500	2
C₂×#11926315	2
C₂×#11926314	2
#14563344	2
C₁₉×#1733	2
#10872	19