Subgroups — #14577624

Order 2432.

1012 conjugacy classes of subgroups.

The subgroup lattice has 628 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	#11927267	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927261	C₂	1	2	yes	maximal, complemented
4	#11927251	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927248	C₂	1	2	yes	maximal, complemented
6	#11927240	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927237	C₂	1	2	yes	maximal, complemented
8	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927230	C₂	1	2	yes	maximal, complemented
10	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927203	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927203	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927165	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927158	C₂	1	2	yes	maximal, complemented
15	#11927156	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927153	C₂	1	2	yes	maximal, complemented
17	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927071	C₂	1	2	yes	maximal, complemented
19	#11927071	C₂	1	2	yes	maximal, complemented
20	#11927024	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927021	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64541	C₂²	1	1	yes	characteristic
25	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
26	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
27	C₁₉×#126	C₂²	1	1	yes	characteristic
28	C₁₉×#126	C₂²	1	1	yes	characteristic
29	C₁₉×#125	C₂²	1	1	yes	characteristic
30	C₁₉×#124	C₂²	1	1	yes	characteristic
31	C₁₉×#123	C₂²	1	1	yes	characteristic
32	C₁₉×#123	C₂²	1	1	yes	characteristic
33	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#117	C₂²	1	1	yes	characteristic
40	C₁₉×#117	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
42	#10597392	C₂²	1	2	yes	—
43	#10597390	C₂²	1	2	yes	—
44	#10597385	C₂²	1	2	yes	—
45	#10597385	C₂²	1	2	yes	—
46	#10597385	C₂²	1	2	yes	—
47	#10597381	C₂²	1	2	yes	—
48	D₄×Dic₁₉	C₂²	1	2	yes	—
49	D₄×Dic₁₉	C₂²	1	2	yes	—
50	#10597376	C₂²	1	1	yes	characteristic
51	#10597376	C₂²	1	1	yes	characteristic
52	#10597375	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
54	#10597372	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
57	#10597370	C₂²	1	1	yes	characteristic
58	#10597370	C₂²	1	1	yes	characteristic
59	#10597370	C₂²	1	1	yes	characteristic
60	#10597370	C₂²	1	1	yes	characteristic
61	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
62	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
63	#10597344	C₂²	1	2	yes	—
64	#10597344	C₂²	1	2	yes	—
65	#10597344	C₂²	1	2	yes	—
66	#10597344	C₂²	1	2	yes	—
67	#10597342	C₂²	1	2	yes	—
68	#10597342	C₂²	1	2	yes	—
69	#10597342	C₂²	1	2	yes	—
70	#10597338	C₂²	1	2	yes	—
71	#10597338	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
73	#10597336	C₂²	1	2	yes	—
74	#10597335	C₂²	1	2	yes	—
75	#10597335	C₂²	1	2	yes	—
76	#10597335	C₂²	1	2	yes	—
77	#10597335	C₂²	1	2	yes	—
78	#10597335	C₂²	1	2	yes	—
79	#10597334	C₂²	1	2	yes	—
80	#10597333	C₂²	1	2	yes	—
81	#10597333	C₂²	1	2	yes	—
82	#10597333	C₂²	1	2	yes	—
83	#10597331	C₂²	1	2	yes	—
84	#10597331	C₂²	1	2	yes	—
85	#10597331	C₂²	1	2	yes	—
86	#10597329	C₂²	1	2	yes	—
87	#10597329	C₂²	1	2	yes	—
88	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
89	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
90	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
91	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
93	#10597325	C₂²	1	2	yes	—
94	#10597325	C₂²	1	2	yes	—
95	#10597325	C₂²	1	2	yes	—
96	#10597324	C₂²	1	2	yes	—
97	#10597324	C₂²	1	2	yes	—
98	#10597324	C₂²	1	2	yes	—
99	#10597324	C₂²	1	2	yes	—
100	#10597323	C₂²	1	2	yes	—
101	#10597323	C₂²	1	2	yes	—
102	#10597323	C₂²	1	2	yes	—
103	#10597322	C₂²	1	2	yes	—
104	#10597321	C₂²	1	1	yes	characteristic
105	#10597321	C₂²	1	1	yes	characteristic
106	C₄×D₇₆	C₂²	1	1	yes	characteristic
107	C₄×D₇₆	C₂²	1	1	yes	characteristic
108	#10597318	C₂²	1	2	yes	—
109	#10597316	C₂²	1	1	yes	characteristic
110	#10597316	C₂²	1	1	yes	characteristic
111	#10597315	C₂²	1	1	yes	characteristic
112	#10597315	C₂²	1	1	yes	characteristic
113	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
114	C₄×Dic₃₈	C₂²	1	2	yes	—
115	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
116	C₄×Dic₃₈	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	2	yes	—
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×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
135	C₂²×Dic₁₉	C₂³	1	2	yes	—
136	C₂²×Dic₁₉	C₂³	1	2	yes	—
137	C₂²×Dic₁₉	C₂³	1	2	yes	—
138	C₂²×Dic₁₉	C₂³	1	2	yes	—
139	#64541	—	2	4	no	—
140	C₂×D₇₆	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₉	C₂³	1	2	yes	—
142	C₂×C₄×D₁₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₉	C₂³	1	2	yes	—
144	C₂×Dic₃₈	—	2	4	no	—
145	C₂×Dic₃₈	—	2	4	no	—
146	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
147	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
148	C₂×Dic₃₈	C₂³	1	2	yes	—
149	C₂×Dic₃₈	C₂³	1	2	yes	—
150	C₂×Dic₃₈	C₂³	1	2	yes	—
151	C₂×Dic₃₈	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	1	yes	characteristic
157	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
162	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₄²×C₁₉	C₂³	1	1	yes	characteristic
173	C₄²×C₁₉	C₂³	1	1	yes	characteristic
174	C₄²×C₁₉	C₂³	1	1	yes	characteristic
175	C₄²×C₁₉	C₂³	1	1	yes	characteristic
176	C₄²×C₁₉	C₂³	1	1	yes	characteristic
177	C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₉	C₂³	1	2	yes	—
194	C₄⋊Dic₁₉	C₂³	1	2	yes	—
195	C₄⋊Dic₁₉	C₂³	1	2	yes	—
196	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₉	C₂³	1	2	yes	—
200	Dic₁₉⋊C₄	C₂³	1	2	yes	—
201	Dic₁₉⋊C₄	C₂³	1	2	yes	—
202	Dic₁₉⋊C₄	C₂³	1	2	yes	—
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₁₉	C₂³	1	2	yes	—
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	2	yes	—
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₉	C₂⁴	1	2	yes	—
229	Q₈×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	2	2	no	—
231	D₄×C₁₉	—	2	2	no	—
232	D₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
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	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₁₉	—	2	4	no	—
251	C₂²⋊D₁₉	—	2	4	no	—
252	C₂²⋊D₁₉	—	4	2	no	—
253	C₂×Dic₁₉	—	2	4	no	—
254	C₂×Dic₁₉	—	2	4	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	—	4	2	no	—
257	C₂×Dic₁₉	C₂⁴	1	2	yes	—
258	C₂×Dic₁₉	C₂⁴	1	2	yes	—
259	C₂×Dic₁₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₉	C₂⁴	1	2	yes	—
261	C₂×Dic₁₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₉	C₂⁴	1	2	yes	—
263	C₂×Dic₁₉	C₂⁴	1	2	yes	—
264	D₇₆	—	2	2	no	—
265	C₄×D₁₉	—	2	4	no	—
266	C₄×D₁₉	—	4	2	no	—
267	C₄×D₁₉	—	4	2	no	—
268	Dic₃₈	—	2	2	no	—
269	Dic₃₈	—	2	2	no	—
270	Dic₃₈	—	2	4	no	—
271	Dic₃₈	—	2	4	no	—
272	Dic₃₈	—	4	2	no	—
273	Dic₃₈	#41	1	4	yes	—
274	#3516	—	19	1	no	maximal, Sylow
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
284	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
285	C₂×D₁₉	—	2	2	no	—
286	C₂×D₁₉	—	2	2	no	—
287	C₂×D₁₉	—	2	2	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	C₂×#41	1	2	yes	—
300	Dic₁₉	—	2	2	no	—
301	Dic₁₉	—	2	2	no	—
302	Dic₁₉	—	2	2	no	—
303	Dic₁₉	—	2	2	no	—
304	Dic₁₉	—	2	2	no	—
305	Dic₁₉	—	2	2	no	—
306	Dic₁₉	C₂×#41	1	4	yes	—
307	#557	—	19	1	no	—
308	#556	—	19	2	no	—
309	#556	—	19	1	no	—
310	#554	—	19	2	no	—
311	#554	—	19	1	no	—
312	#553	—	19	2	no	—
313	#553	—	19	1	no	—
314	#552	—	19	2	no	—
315	#552	—	19	1	no	—
316	D₄×Q₈	—	19	1	no	—
317	#548	—	19	1	no	—
318	#548	—	19	1	no	—
319	#542	—	19	2	no	—
320	#542	—	19	1	no	—
321	#541	—	19	2	no	—
322	#541	—	19	1	no	—
323	#529	—	19	2	no	—
324	#529	—	19	2	no	—
325	#529	—	19	1	no	—
326	#529	D₁₉	1	1	yes	characteristic, complemented
327	#520	—	19	1	no	—
328	#519	—	19	1	no	—
329	C₂×C₄×Q₈	—	19	1	no	—
330	C₂×C₁₉	—	2	2	no	—
331	C₂×C₁₉	—	4	1	no	—
332	C₂×C₁₉	—	4	1	no	—
333	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
334	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×C₁₉	#585	1	1	yes	characteristic
336	D₁₉	—	4	2	no	—
337	C₂×#41	—	19	1	no	—
338	C₂²×Q₈	—	19	1	no	—
339	C₂²×Q₈	—	19	1	no	—
340	C₄⋊Q₈	—	19	2	no	—
341	C₄⋊Q₈	—	19	2	no	—
342	C₄⋊Q₈	—	19	1	no	—
343	C₄⋊Q₈	—	19	1	no	—
344	#126	—	19	2	no	—
345	#126	—	19	2	no	—
346	#126	—	19	2	no	—
347	#126	—	19	2	no	—
348	#126	—	19	2	no	—
349	#126	—	19	2	no	—
350	#126	—	19	2	no	—
351	#126	—	19	2	no	—
352	#126	C₂×D₁₉	1	1	yes	characteristic
353	#126	C₂×D₁₉	1	1	yes	characteristic
354	#125	—	19	2	no	—
355	#125	—	19	2	no	—
356	#125	—	19	2	no	—
357	#125	—	19	2	no	—
358	#125	—	19	2	no	—
359	#125	—	19	2	no	—
360	#125	—	19	1	no	—
361	#125	—	19	1	no	—
362	#125	C₂×D₁₉	1	1	yes	characteristic
363	#124	—	19	2	no	—
364	#124	—	19	2	no	—
365	#124	—	19	2	no	—
366	#124	—	19	1	no	—
367	#124	—	19	1	no	—
368	#124	C₂×D₁₉	1	1	yes	characteristic
369	#123	—	19	2	no	—
370	#123	—	19	2	no	—
371	#123	—	19	2	no	—
372	#123	—	19	2	no	—
373	#123	C₂×D₁₉	1	1	yes	characteristic
374	#123	C₂×D₁₉	1	1	yes	characteristic
375	C₂²⋊Q₈	—	19	2	no	—
376	C₂²⋊Q₈	—	19	1	no	—
377	C₂²⋊Q₈	—	19	1	no	—
378	C₂²⋊Q₈	—	19	1	no	—
379	C₂²⋊Q₈	—	19	1	no	—
380	C₂²⋊Q₈	—	19	2	no	—
381	C₂²⋊Q₈	—	19	2	no	—
382	C₂²⋊Q₈	—	19	2	no	—
383	C₂²⋊Q₈	—	19	2	no	—
384	C₂²⋊Q₈	—	19	2	no	—
385	C₂²⋊Q₈	—	19	2	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
388	#121	—	19	2	no	—
389	#121	—	19	2	no	—
390	#121	—	19	2	no	—
391	#121	—	19	1	no	—
392	#121	—	19	1	no	—
393	#121	C₂×D₁₉	1	1	yes	characteristic
394	C₄×Q₈	—	19	2	no	—
395	C₄×Q₈	—	19	2	no	—
396	C₄×Q₈	—	19	2	no	—
397	C₄×Q₈	—	19	1	no	—
398	C₄×Q₈	—	19	2	no	—
399	C₄×Q₈	—	19	1	no	—
400	C₄×Q₈	—	19	1	no	—
401	C₄×Q₈	—	19	1	no	—
402	C₄×Q₈	—	19	2	no	—
403	C₄×Q₈	—	19	1	no	—
404	C₄×Q₈	—	19	1	no	—
405	C₄×Q₈	—	19	1	no	—
406	C₄×Q₈	—	19	1	no	—
407	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
408	C₄×D₄	—	19	2	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	2	no	—
413	C₄×D₄	—	19	2	no	—
414	C₄×D₄	—	19	2	no	—
415	C₄×D₄	—	19	2	no	—
416	C₄×D₄	—	19	1	no	—
417	C₄×D₄	—	19	1	no	—
418	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
419	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
420	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
421	#117	—	19	1	no	—
422	#117	—	19	2	no	—
423	#117	—	19	2	no	—
424	#117	—	19	2	no	—
425	#117	—	19	2	no	—
426	#117	—	19	2	no	—
427	#117	—	19	2	no	—
428	#117	C₂×D₁₉	1	1	yes	characteristic
429	#117	C₂×D₁₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	—	19	2	no	—
431	C₂×C₄⋊C₄	—	19	1	no	—
432	C₂×C₄⋊C₄	—	19	1	no	—
433	C₂×C₄⋊C₄	—	19	2	no	—
434	C₂×C₄²	—	19	2	no	—
435	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
436	C₁₉	#3516	1	1	yes	characteristic, complemented, Sylow
437	#41	—	38	4	no	—
438	C₂×Q₈	—	19	1	no	—
439	C₂×Q₈	—	19	2	no	—
440	C₂×Q₈	—	19	2	no	—
441	C₂×Q₈	—	19	1	no	—
442	C₂×Q₈	—	19	1	no	—
443	C₂×Q₈	—	19	2	no	—
444	C₂×Q₈	—	38	4	no	—
445	C₂×Q₈	—	38	4	no	—
446	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
447	C₂×D₄	—	19	2	no	—
448	C₂×D₄	—	19	2	no	—
449	C₂×D₄	—	19	2	no	—
450	C₂×D₄	—	19	1	no	—
451	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
452	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
453	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
454	C₂²×C₄	—	19	2	no	—
455	C₂²×C₄	—	19	2	no	—
456	C₂²×C₄	—	19	2	no	—
457	C₂²×C₄	—	19	2	no	—
458	C₂²×C₄	—	19	2	no	—
459	C₂²×C₄	—	19	2	no	—
460	C₂²×C₄	—	19	2	no	—
461	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
466	C₄⋊C₄	—	19	2	no	—
467	C₄⋊C₄	—	19	2	no	—
468	C₄⋊C₄	—	19	2	no	—
469	C₄⋊C₄	—	19	2	no	—
470	C₄⋊C₄	—	19	2	no	—
471	C₄⋊C₄	—	19	2	no	—
472	C₄⋊C₄	—	19	2	no	—
473	C₄⋊C₄	—	19	2	no	—
474	C₄⋊C₄	—	19	2	no	—
475	C₄⋊C₄	—	19	2	no	—
476	C₄⋊C₄	—	19	2	no	—
477	C₄⋊C₄	—	19	2	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	2	no	—
481	C₄⋊C₄	—	19	2	no	—
482	C₄⋊C₄	—	19	1	no	—
483	C₄⋊C₄	—	19	2	no	—
484	C₄⋊C₄	—	19	1	no	—
485	C₄⋊C₄	—	19	1	no	—
486	C₄⋊C₄	—	19	2	no	—
487	C₄⋊C₄	—	19	1	no	—
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	2	no	—
491	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	19	2	no	—
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	2	no	—
504	C₂²⋊C₄	—	19	2	no	—
505	C₂²⋊C₄	—	19	2	no	—
506	C₂²⋊C₄	—	19	2	no	—
507	C₂²⋊C₄	—	19	2	no	—
508	C₂²⋊C₄	—	19	2	no	—
509	C₂²⋊C₄	—	19	2	no	—
510	C₂²⋊C₄	—	19	2	no	—
511	C₂²⋊C₄	—	19	2	no	—
512	C₂²⋊C₄	—	19	2	no	—
513	C₂²⋊C₄	—	19	2	no	—
514	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
515	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
516	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
517	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
518	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
522	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
524	C₄²	—	19	2	no	—
525	C₄²	—	19	2	no	—
526	C₄²	—	19	2	no	—
527	C₄²	—	19	2	no	—
528	C₄²	—	19	2	no	—
529	C₄²	—	19	2	no	—
530	C₄²	—	19	2	no	—
531	C₄²	—	19	2	no	—
532	C₄²	—	19	2	no	—
533	C₄²	C₂²×D₁₉	1	1	yes	characteristic
534	C₄²	C₂²×D₁₉	1	1	yes	characteristic
535	C₄²	C₂²×D₁₉	1	1	yes	characteristic
536	C₄²	C₂²×D₁₉	1	1	yes	characteristic
537	C₄²	C₂²×D₁₉	1	1	yes	characteristic
538	C₄²	C₂²×D₁₉	1	1	yes	characteristic
539	C₂³	—	19	2	no	—
540	C₂³	C₂³×D₁₉	1	1	yes	characteristic
541	C₂³	C₂³×D₁₉	1	1	yes	characteristic
542	C₂³	C₂³×D₁₉	1	1	yes	characteristic
543	Q₈	—	4	1	no	—
544	Q₈	—	19	4	no	—
545	Q₈	—	38	4	no	—
546	Q₈	—	38	4	no	—
547	Q₈	—	38	2	no	—
548	Q₈	—	38	2	no	—
549	Q₈	—	76	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	4	1	no	—
553	D₄	—	38	4	no	—
554	D₄	—	38	4	no	—
555	D₄	—	38	2	no	—
556	D₄	—	76	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	19	2	no	—
563	C₂×C₄	—	19	2	no	—
564	C₂×C₄	—	19	2	no	—
565	C₂×C₄	—	19	2	no	—
566	C₂×C₄	—	19	2	no	—
567	C₂×C₄	—	19	2	no	—
568	C₂×C₄	—	19	2	no	—
569	C₂×C₄	—	38	4	no	—
570	C₂×C₄	—	38	4	no	—
571	C₂×C₄	—	38	4	no	—
572	C₂×C₄	—	76	2	no	—
573	C₂×C₄	—	76	2	no	—
574	C₂×C₄	—	76	2	no	—
575	C₂×C₄	—	76	2	no	—
576	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	38	2	no	—
597	C₂²	—	38	2	no	—
598	C₂²	—	38	2	no	—
599	C₂²	#10597436	1	2	yes	—
600	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	19	4	no	—
613	C₄	—	38	2	no	—
614	C₄	—	38	2	no	—
615	C₄	—	38	2	no	—
616	C₄	—	38	2	no	—
617	C₄	—	38	2	no	—
618	C₄	—	38	2	no	—
619	C₄	#41×D₁₉	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	4	1	no	—
622	C₂	—	4	1	no	—
623	C₂	—	76	2	no	—
624	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
625	C₂	C₂×#10597436	1	1	yes	characteristic
626	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#529	C₂
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3516
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #11927272	C₂	semidirect
2. #11927267	C₂	semidirect
3. #11927261	C₂	semidirect
4. #11927251	C₂	semidirect
5. #11927248	C₂	semidirect
6. #11927240	C₂	semidirect
7. #11927237	C₂	semidirect
8. #11927234	C₂	semidirect
9. #11927230	C₂	semidirect
10. D₄×Dic₃₈	C₂	semidirect
11. #11927203	C₂	semidirect
12. #11927203	C₂	semidirect
13. #11927165	C₂	semidirect
14. #11927158	C₂	semidirect
15. #11927156	C₂	semidirect
16. #11927153	C₂	semidirect
17. #11927078	C₂	semidirect
18. #11927071	C₂	semidirect
19. #11927071	C₂	semidirect
20. #11927024	C₂	semidirect
21. #11927021	C₂	semidirect
22. C₂×C₄×Dic₃₈	C₂	semidirect
23. C₁₉×#529	C₂	semidirect
326. #529	D₁₉	semidirect
436. C₁₉	#3516	semidirect

Maximal subgroups

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

subgroup	index
#11927272	2
#11927267	2
#11927261	2
#11927251	2
#11927248	2
#11927240	2
#11927237	2
#11927234	2
#11927230	2
D₄×Dic₃₈	2
#11927203	2
#11927165	2
#11927158	2
#11927156	2
#11927153	2
#11927078	2
#11927071	2
#11927024	2
#11927021	2
C₂×C₄×Dic₃₈	2
C₁₉×#529	2
#3516	19