Subgroups — #14577455

Order 2432.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927272	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927271	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927271	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927269	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927253	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927253	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927252	C₂	1	2	yes	maximal, complemented
8	#11927251	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927249	C₂	1	2	yes	maximal, complemented
10	#11927248	C₂	1	2	yes	maximal, complemented
11	#11927248	C₂	1	2	yes	maximal, complemented
12	#11927174	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927173	C₂	1	2	yes	maximal, complemented
14	#11927173	C₂	1	2	yes	maximal, complemented
15	#11927171	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927096	C₂	1	2	yes	maximal, complemented
18	C₂×#10597335	C₂	1	2	yes	maximal, complemented
19	#125×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927023	C₂	1	1	yes	maximal, characteristic
21	#11927023	C₂	1	1	yes	maximal, characteristic
22	C₄×#64543	C₂	1	1	yes	maximal, characteristic
23	C₁₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64543	C₂²	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₁₉×#125	C₂²	1	1	yes	characteristic
28	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
36	#10597392	C₂²	1	1	yes	characteristic
37	#10597392	C₂²	1	2	yes	—
38	Q₈×Dic₁₉	C₂²	1	2	yes	—
39	#10597390	C₂²	1	2	yes	—
40	#10597390	C₂²	1	1	yes	characteristic
41	#10597390	C₂²	1	2	yes	—
42	#10597390	C₂²	1	2	yes	—
43	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
44	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
45	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
49	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
50	#10597370	C₂²	1	2	yes	—
51	#10597370	C₂²	1	2	yes	—
52	#10597370	C₂²	1	2	yes	—
53	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
54	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
55	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
56	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
57	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
58	#10597343	C₂²	1	1	yes	characteristic
59	#10597343	C₂²	1	2	yes	—
60	#10597342	C₂²	1	1	yes	characteristic
61	#10597342	C₂²	1	1	yes	characteristic
62	#10597342	C₂²	1	2	yes	—
63	#10597342	C₂²	1	2	yes	—
64	#10597338	C₂²	1	1	yes	characteristic
65	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
66	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
67	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
68	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
69	#10597336	C₂²	1	1	yes	characteristic
70	#10597336	C₂²	1	1	yes	characteristic
71	#10597336	C₂²	1	1	yes	characteristic
72	#10597336	C₂²	1	1	yes	characteristic
73	#10597335	C₂²	1	2	yes	—
74	#10597335	C₂²	1	2	yes	—
75	#10597335	C₂²	1	1	yes	characteristic
76	#10597335	C₂²	1	2	yes	—
77	#10597335	C₂²	1	2	yes	—
78	#10597335	C₂²	1	2	yes	—
79	#10597335	C₂²	1	2	yes	—
80	#10597335	C₂²	1	2	yes	—
81	#10597335	C₂²	1	2	yes	—
82	#10597335	C₂²	1	1	yes	characteristic
83	#10597335	C₂²	1	2	yes	—
84	#10597335	C₂²	1	2	yes	—
85	#10597335	C₂²	1	2	yes	—
86	#10597335	C₂²	1	2	yes	—
87	#10597334	C₂²	1	2	yes	—
88	#10597334	C₂²	1	1	yes	characteristic
89	#10597334	C₂²	1	1	yes	characteristic
90	#10597334	C₂²	1	2	yes	—
91	#10597334	C₂²	1	2	yes	—
92	#10597334	C₂²	1	1	yes	characteristic
93	#10597333	C₂²	1	2	yes	—
94	#10597333	C₂²	1	2	yes	—
95	#10597333	C₂²	1	2	yes	—
96	#10597333	C₂²	1	1	yes	characteristic
97	#10597333	C₂²	1	1	yes	characteristic
98	#10597333	C₂²	1	1	yes	characteristic
99	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
100	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
102	#10597324	C₂²	1	2	yes	—
103	#10597324	C₂²	1	2	yes	—
104	#10597324	C₂²	1	2	yes	—
105	#10597324	C₂²	1	2	yes	—
106	#10597324	C₂²	1	2	yes	—
107	#10597324	C₂²	1	2	yes	—
108	#10597323	C₂²	1	2	yes	—
109	#10597323	C₂²	1	2	yes	—
110	#10597323	C₂²	1	2	yes	—
111	#10597318	C₂²	1	1	yes	characteristic
112	#10597318	C₂²	1	1	yes	characteristic
113	C₄²×D₁₉	C₂²	1	1	yes	characteristic
114	#10597316	C₂²	1	1	yes	characteristic
115	#10597316	C₂²	1	1	yes	characteristic
116	#10597315	C₂²	1	1	yes	characteristic
117	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
118	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
119	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
130	C₂²×Dic₁₉	C₂³	1	2	yes	—
131	C₂²×Dic₁₉	C₂³	1	2	yes	—
132	C₂²×Dic₁₉	C₂³	1	2	yes	—
133	C₂²×Dic₁₉	C₂³	1	2	yes	—
134	#64543	Q₈	1	8	yes	complemented
135	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
140	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
141	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
142	C₂×Dic₃₈	C₂³	1	2	yes	—
143	C₂×Dic₃₈	C₂³	1	2	yes	—
144	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
145	C₂×Dic₃₈	C₂³	1	2	yes	—
146	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
152	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
161	C₄²×C₁₉	C₂³	1	1	yes	characteristic
162	C₄²×C₁₉	C₂³	1	1	yes	characteristic
163	C₄²×C₁₉	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
166	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
167	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
168	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
169	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
170	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₁₉	C₂³	1	2	yes	—
177	C₄⋊Dic₁₉	C₂³	1	2	yes	—
178	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₁₉	C₂³	1	2	yes	—
180	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₁₉	C₂³	1	2	yes	—
182	C₄⋊Dic₁₉	C₂³	1	2	yes	—
183	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
184	Dic₁₉⋊C₄	C₂³	1	2	yes	—
185	Dic₁₉⋊C₄	C₂³	1	2	yes	—
186	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
187	Dic₁₉⋊C₄	C₂³	1	2	yes	—
188	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
189	Dic₁₉⋊C₄	C₂³	1	2	yes	—
190	Dic₁₉⋊C₄	C₂³	1	2	yes	—
191	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
192	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
193	Dic₁₉⋊C₄	C₂³	1	2	yes	—
194	Dic₁₉⋊C₄	C₂³	1	2	yes	—
195	Dic₁₉⋊C₄	C₂³	1	2	yes	—
196	Dic₁₉⋊C₄	C₂³	1	2	yes	—
197	Dic₁₉⋊C₄	C₂³	1	2	yes	—
198	Dic₁₉⋊C₄	C₂³	1	2	yes	—
199	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₁₉⋊C₄	C₂³	1	2	yes	—
202	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
213	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₉	C₂³	1	2	yes	—
215	C₄×Dic₁₉	C₂³	1	2	yes	—
216	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₉	C₂³	1	2	yes	—
218	C₄×Dic₁₉	C₂³	1	2	yes	—
219	C₄×Dic₁₉	C₂³	1	2	yes	—
220	C₄×Dic₁₉	C₂³	1	2	yes	—
221	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₂³×C₁₉	C₂⁴	1	2	yes	—
224	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	D₄×C₁₉	C₂×Q₈	1	4	yes	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
234	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₁₉	C₂×Q₈	1	8	yes	—
242	C₂×Dic₁₉	—	4	2	no	—
243	C₂×Dic₁₉	—	4	2	no	—
244	C₂×Dic₁₉	—	4	2	no	—
245	C₂×Dic₁₉	C₂×Q₈	1	8	yes	—
246	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₉	C₂⁴	1	2	yes	—
251	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₉	C₂⁴	1	2	yes	—
253	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₉	C₂⁴	1	2	yes	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
257	C₄×D₁₉	—	4	1	no	—
258	C₄×D₁₉	—	4	2	no	—
259	C₄×D₁₉	—	4	2	no	—
260	C₄×D₁₉	—	4	1	no	—
261	C₄×D₁₉	C₂×Q₈	1	4	yes	—
262	Dic₃₈	—	4	1	no	—
263	Dic₃₈	—	4	2	no	—
264	Dic₃₈	—	4	2	no	—
265	Dic₃₈	—	4	1	no	—
266	Dic₃₈	—	4	1	no	—
267	Dic₃₈	—	4	2	no	—
268	Dic₃₈	C₂×Q₈	1	4	yes	—
269	#3504	—	19	1	no	maximal, Sylow
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	2	no	—
272	C₂²×C₁₉	C₂²×Q₈	1	4	yes	—
273	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
274	C₂×D₁₉	—	2	1	no	—
275	C₂×D₁₉	—	2	1	no	—
276	C₂×D₁₉	C₂²×Q₈	1	2	yes	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	C₂²×Q₈	1	2	yes	—
287	Dic₁₉	—	2	1	no	—
288	Dic₁₉	—	2	1	no	—
289	Dic₁₉	—	2	1	no	—
290	Dic₁₉	—	2	2	no	—
291	Dic₁₉	—	2	2	no	—
292	Dic₁₉	—	2	2	no	—
293	Dic₁₉	—	2	1	no	—
294	Dic₁₉	—	2	1	no	—
295	Dic₁₉	—	2	1	no	—
296	Dic₁₉	C₂²×Q₈	1	4	yes	—
297	Dic₁₉	C₂²×Q₈	1	2	yes	—
298	#557	—	19	1	no	—
299	#557	—	19	1	no	—
300	#557	—	19	1	no	—
301	#557	—	19	1	no	—
302	#554	—	19	2	no	—
303	#554	—	19	2	no	—
304	#554	—	19	2	no	—
305	#554	—	19	1	no	—
306	#554	—	19	1	no	—
307	#554	—	19	1	no	—
308	#554	—	19	2	no	—
309	#554	D₁₉	1	1	yes	characteristic, complemented
310	#544	—	19	1	no	—
311	#544	—	19	1	no	—
312	#544	—	19	2	no	—
313	#544	—	19	2	no	—
314	#533	—	19	2	no	—
315	#533	—	19	1	no	—
316	C₂×#125	—	19	1	no	—
317	C₂×#125	—	19	2	no	—
318	#520	—	19	1	no	—
319	#520	—	19	1	no	—
320	C₄×#41	—	19	1	no	—
321	C₂×C₁₉	—	2	4	no	—
322	C₂×C₁₉	C₂³×Q₈	1	1	yes	characteristic
323	C₂×C₁₉	#585	1	1	yes	characteristic
324	C₂×C₁₉	#585	1	1	yes	characteristic
325	D₁₉	—	2	2	no	—
326	C₂×#41	—	19	1	no	—
327	C₄⋊Q₈	—	19	2	no	—
328	C₄⋊Q₈	—	19	1	no	—
329	C₄⋊Q₈	—	19	2	no	—
330	C₄⋊Q₈	—	19	2	no	—
331	C₄⋊Q₈	—	19	2	no	—
332	C₄⋊Q₈	—	19	1	no	—
333	C₄⋊Q₈	—	19	2	no	—
334	C₄⋊Q₈	—	19	2	no	—
335	C₄⋊Q₈	—	19	1	no	—
336	C₄⋊Q₈	—	19	1	no	—
337	C₄⋊Q₈	—	19	1	no	—
338	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
339	#125	—	19	2	no	—
340	#125	—	19	1	no	—
341	#125	—	19	2	no	—
342	#125	—	19	2	no	—
343	#125	—	19	2	no	—
344	#125	—	19	2	no	—
345	#125	—	19	2	no	—
346	#125	—	19	2	no	—
347	#125	—	19	2	no	—
348	#125	—	19	1	no	—
349	#125	—	19	1	no	—
350	#125	—	19	1	no	—
351	#125	—	19	2	no	—
352	#125	—	19	2	no	—
353	#125	—	19	2	no	—
354	#125	—	19	2	no	—
355	#125	—	19	1	no	—
356	#125	—	19	1	no	—
357	#125	—	19	1	no	—
358	#125	—	19	1	no	—
359	#125	C₂×D₁₉	1	1	yes	characteristic
360	#125	C₂×D₁₉	1	1	yes	characteristic
361	C₂²⋊Q₈	—	19	1	no	—
362	C₂²⋊Q₈	—	19	2	no	—
363	C₂²⋊Q₈	—	19	2	no	—
364	C₂²⋊Q₈	—	19	2	no	—
365	C₂²⋊Q₈	—	19	2	no	—
366	C₂²⋊Q₈	—	19	1	no	—
367	C₂²⋊Q₈	—	19	1	no	—
368	C₂²⋊Q₈	—	19	1	no	—
369	C₂²⋊Q₈	—	19	2	no	—
370	C₂²⋊Q₈	—	19	2	no	—
371	C₂²⋊Q₈	—	19	2	no	—
372	C₂²⋊Q₈	—	19	2	no	—
373	C₂²⋊Q₈	—	19	2	no	—
374	C₂²⋊Q₈	—	19	2	no	—
375	C₂²⋊Q₈	—	19	2	no	—
376	C₂²⋊Q₈	—	19	2	no	—
377	C₂²⋊Q₈	—	19	2	no	—
378	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
379	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
380	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
381	C₄×Q₈	—	19	2	no	—
382	C₄×Q₈	—	19	1	no	—
383	C₄×Q₈	—	19	1	no	—
384	C₄×Q₈	—	19	1	no	—
385	C₄×Q₈	—	19	2	no	—
386	C₄×Q₈	—	19	2	no	—
387	C₄×Q₈	—	19	2	no	—
388	C₄×Q₈	—	19	1	no	—
389	C₄×Q₈	—	19	1	no	—
390	C₄×Q₈	—	19	1	no	—
391	C₄×Q₈	—	19	1	no	—
392	C₄×Q₈	—	19	1	no	—
393	C₄×Q₈	—	19	1	no	—
394	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
395	C₄×D₄	—	19	1	no	—
396	C₄×D₄	—	19	1	no	—
397	C₄×D₄	—	19	1	no	—
398	C₄×D₄	—	19	2	no	—
399	C₄×D₄	—	19	2	no	—
400	C₄×D₄	—	19	2	no	—
401	C₄×D₄	—	19	2	no	—
402	C₄×D₄	—	19	2	no	—
403	C₄×D₄	—	19	2	no	—
404	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
405	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
406	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
407	#117	—	19	1	no	—
408	#117	—	19	2	no	—
409	#117	—	19	2	no	—
410	#117	—	19	2	no	—
411	#117	—	19	1	no	—
412	#117	—	19	1	no	—
413	C₂×C₄⋊C₄	—	19	2	no	—
414	C₂×C₄⋊C₄	—	19	2	no	—
415	C₂×C₄⋊C₄	—	19	2	no	—
416	C₂×C₄⋊C₄	—	19	2	no	—
417	C₂×C₄⋊C₄	—	19	2	no	—
418	C₂×C₄⋊C₄	—	19	1	no	—
419	C₂×C₄⋊C₄	—	19	1	no	—
420	C₂×C₄⋊C₄	—	19	2	no	—
421	C₂×C₄⋊C₄	—	19	2	no	—
422	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
423	C₂×C₄²	—	19	2	no	—
424	C₂×C₄²	—	19	1	no	—
425	C₁₉	#3504	1	1	yes	characteristic, complemented, Sylow
426	#41	—	19	8	no	—
427	C₂×Q₈	—	19	1	no	—
428	C₂×Q₈	—	19	2	no	—
429	C₂×Q₈	—	19	1	no	—
430	C₂×Q₈	—	19	2	no	—
431	C₂×Q₈	—	19	1	no	—
432	C₂×Q₈	—	19	1	no	—
433	C₂×Q₈	—	19	2	no	—
434	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
435	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
436	C₂×D₄	—	19	2	no	—
437	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
438	C₂²×C₄	—	19	2	no	—
439	C₂²×C₄	—	19	1	no	—
440	C₂²×C₄	—	19	2	no	—
441	C₂²×C₄	—	19	2	no	—
442	C₂²×C₄	—	19	2	no	—
443	C₂²×C₄	—	19	1	no	—
444	C₂²×C₄	—	19	1	no	—
445	C₂²×C₄	—	19	2	no	—
446	C₂²×C₄	—	19	2	no	—
447	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
448	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
449	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
450	C₄⋊C₄	—	19	2	no	—
451	C₄⋊C₄	—	19	2	no	—
452	C₄⋊C₄	—	19	1	no	—
453	C₄⋊C₄	—	19	1	no	—
454	C₄⋊C₄	—	19	2	no	—
455	C₄⋊C₄	—	19	1	no	—
456	C₄⋊C₄	—	19	1	no	—
457	C₄⋊C₄	—	19	2	no	—
458	C₄⋊C₄	—	19	2	no	—
459	C₄⋊C₄	—	19	2	no	—
460	C₄⋊C₄	—	19	2	no	—
461	C₄⋊C₄	—	19	2	no	—
462	C₄⋊C₄	—	19	2	no	—
463	C₄⋊C₄	—	19	2	no	—
464	C₄⋊C₄	—	19	2	no	—
465	C₄⋊C₄	—	19	2	no	—
466	C₄⋊C₄	—	19	2	no	—
467	C₄⋊C₄	—	19	2	no	—
468	C₄⋊C₄	—	19	1	no	—
469	C₄⋊C₄	—	19	1	no	—
470	C₄⋊C₄	—	19	2	no	—
471	C₄⋊C₄	—	19	2	no	—
472	C₄⋊C₄	—	19	1	no	—
473	C₄⋊C₄	—	19	1	no	—
474	C₄⋊C₄	—	19	2	no	—
475	C₄⋊C₄	—	19	1	no	—
476	C₄⋊C₄	—	19	2	no	—
477	C₄⋊C₄	—	19	1	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	1	no	—
480	C₄⋊C₄	—	19	1	no	—
481	C₄⋊C₄	—	19	1	no	—
482	C₄⋊C₄	—	19	2	no	—
483	C₄⋊C₄	—	19	2	no	—
484	C₄⋊C₄	—	19	2	no	—
485	C₄⋊C₄	—	19	1	no	—
486	C₄⋊C₄	—	19	1	no	—
487	C₄⋊C₄	—	19	2	no	—
488	C₄⋊C₄	—	19	1	no	—
489	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
490	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
495	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
496	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	19	2	no	—
501	C₂²⋊C₄	—	19	2	no	—
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	1	no	—
504	C₂²⋊C₄	—	19	1	no	—
505	C₂²⋊C₄	—	19	2	no	—
506	C₂²⋊C₄	—	19	1	no	—
507	C₂²⋊C₄	—	19	1	no	—
508	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
511	C₄²	—	19	1	no	—
512	C₄²	—	19	2	no	—
513	C₄²	—	19	1	no	—
514	C₄²	—	19	2	no	—
515	C₄²	—	19	2	no	—
516	C₄²	—	19	1	no	—
517	C₄²	—	19	2	no	—
518	C₄²	—	19	2	no	—
519	C₄²	—	19	2	no	—
520	C₄²	—	19	2	no	—
521	C₄²	—	19	1	no	—
522	C₄²	—	19	1	no	—
523	C₄²	C₂²×D₁₉	1	1	yes	characteristic
524	C₄²	C₂²×D₁₉	1	1	yes	characteristic
525	C₄²	C₂²×D₁₉	1	1	yes	characteristic
526	C₂³	—	19	1	no	—
527	C₂³	C₂³×D₁₉	1	2	yes	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	19	4	no	—
531	Q₈	—	76	1	no	—
532	Q₈	—	76	2	no	—
533	Q₈	—	76	1	no	—
534	Q₈	—	76	2	no	—
535	Q₈	—	76	1	no	—
536	Q₈	—	76	2	no	—
537	D₄	—	19	8	no	—
538	D₄	Q₈×D₁₉	1	4	yes	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	19	8	no	—
543	C₂×C₄	—	19	2	no	—
544	C₂×C₄	—	19	1	no	—
545	C₂×C₄	—	19	4	no	—
546	C₂×C₄	—	19	1	no	—
547	C₂×C₄	—	19	1	no	—
548	C₂×C₄	—	19	1	no	—
549	C₂×C₄	—	19	1	no	—
550	C₂×C₄	—	19	2	no	—
551	C₂×C₄	—	19	2	no	—
552	C₂×C₄	—	19	1	no	—
553	C₂×C₄	—	19	2	no	—
554	C₂×C₄	—	19	1	no	—
555	C₂×C₄	—	76	1	no	—
556	C₂×C₄	—	76	2	no	—
557	C₂×C₄	—	76	2	no	—
558	C₂×C₄	—	76	1	no	—
559	C₂×C₄	—	76	2	no	—
560	C₂×C₄	—	76	2	no	—
561	C₂×C₄	—	76	2	no	—
562	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₁₉	1	2	yes	—
566	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₉	1	2	yes	—
568	C₂×C₄	C₂³×D₁₉	1	2	yes	—
569	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	19	2	no	—
575	C₂²	—	38	1	no	—
576	C₂²	—	38	1	no	—
577	C₂²	C₂×Q₈×D₁₉	1	4	yes	—
578	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	19	2	no	—
589	C₄	—	19	4	no	—
590	C₄	—	38	2	no	—
591	C₄	—	38	1	no	—
592	C₄	—	38	1	no	—
593	C₄	—	38	1	no	—
594	C₄	—	38	1	no	—
595	C₄	—	38	2	no	—
596	C₄	—	38	1	no	—
597	C₄	—	38	2	no	—
598	C₄	—	38	1	no	—
599	C₄	C₂×Q₈×D₁₉	1	2	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	38	2	no	—
602	C₂	C₂²×Q₈×D₁₉	1	1	yes	characteristic
603	C₂	#11927379	1	1	yes	characteristic
604	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#554	C₂
prime radical	C₂×#64543	C₂²
hypercenter	#554	D₁₉
hypocenter	C₁₉	#3504
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #11927272	C₂	semidirect
2. #11927271	C₂	semidirect
3. #11927271	C₂	semidirect
4. #11927269	C₂	semidirect
5. #11927253	C₂	semidirect
6. #11927253	C₂	semidirect
7. #11927252	C₂	semidirect
8. #11927251	C₂	semidirect
9. #11927249	C₂	semidirect
10. #11927248	C₂	semidirect
11. #11927248	C₂	semidirect
12. #11927174	C₂	semidirect
13. #11927173	C₂	semidirect
14. #11927173	C₂	semidirect
15. #11927171	C₂	semidirect
16. #11927098	C₂	semidirect
17. #11927096	C₂	semidirect
18. C₂×#10597335	C₂	semidirect
19. #125×D₁₉	C₂	semidirect
23. C₁₉×#554	C₂	semidirect
134. #64543	Q₈	semidirect
309. #554	D₁₉	semidirect
425. C₁₉	#3504	semidirect

Maximal subgroups

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

subgroup	index
#11927272	2
#11927271	2
#11927269	2
#11927253	2
#11927252	2
#11927251	2
#11927249	2
#11927248	2
#11927174	2
#11927173	2
#11927171	2
#11927098	2
#11927096	2
C₂×#10597335	2
#125×D₁₉	2
#11927023	2
C₄×#64543	2
C₁₉×#554	2
#3504	19