Subgroups — #14578009

Order 2432.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927284	C₂	1	4	yes	maximal, complemented
2	#11927267	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927247	C₂	1	2	yes	maximal, complemented
4	#11927216	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927215	C₂	1	2	yes	maximal, complemented
6	#11927199	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927190	C₂	1	2	yes	maximal, complemented
8	#11927187	C₂	1	2	yes	maximal, complemented
9	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927165	C₂	1	2	yes	maximal, complemented
11	#11927133	C₂	1	4	yes	maximal, complemented
12	#11927124	C₂	1	2	yes	maximal, complemented
13	#11927113	C₂	1	2	yes	maximal, complemented
14	#11927110	C₂	1	2	yes	maximal, complemented
15	#11927094	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927094	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#64545	C₂²	1	2	yes	complemented
19	C₂×D₄×D₁₉	C₂²	1	2	yes	—
20	C₂×#64541	C₂²	1	2	yes	complemented
21	C₂×#64541	C₂²	1	2	yes	complemented
22	C₂×#64541	C₂²	1	2	yes	complemented
23	C₂²×D₇₆	C₂²	1	2	yes	—
24	C₁₉×#126	C₂²	1	2	yes	complemented
25	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#124	C₂²	1	1	yes	characteristic
27	C₁₉×#123	C₂²	1	2	yes	complemented
28	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#121	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
33	C₁₉×#117	C₂²	1	2	yes	complemented
34	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
35	#10597392	C₂²	1	2	yes	complemented
36	#10597386	C₂²	1	4	yes	complemented
37	#10597384	C₂²	1	2	yes	—
38	#10597383	C₂²	1	4	yes	complemented
39	#10597376	C₂²	1	1	yes	characteristic
40	#10597376	C₂²	1	2	yes	—
41	#10597376	C₂²	1	2	yes	complemented
42	#10597376	C₂²	1	1	yes	characteristic, complemented
43	#10597376	C₂²	1	2	yes	complemented
44	#10597376	C₂²	1	2	yes	complemented
45	#10597370	C₂²	1	2	yes	complemented
46	#10597344	C₂²	1	4	yes	complemented
47	#10597344	C₂²	1	4	yes	complemented
48	#10597342	C₂²	1	4	yes	complemented
49	#10597341	C₂²	1	2	yes	—
50	#10597341	C₂²	1	2	yes	complemented
51	#10597341	C₂²	1	4	yes	complemented
52	#10597341	C₂²	1	4	yes	complemented
53	#10597341	C₂²	1	4	yes	complemented
54	#10597340	C₂²	1	4	yes	complemented
55	#10597339	C₂²	1	4	yes	complemented
56	#10597338	C₂²	1	2	yes	complemented
57	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
58	#10597331	C₂²	1	4	yes	complemented
59	#10597330	C₂²	1	4	yes	complemented
60	#10597330	C₂²	1	4	yes	complemented
61	#10597330	C₂²	1	4	yes	complemented
62	#10597329	C₂²	1	4	yes	complemented
63	#10597329	C₂²	1	4	yes	complemented
64	#10597328	C₂²	1	4	yes	—
65	#10597328	C₂²	1	4	yes	complemented
66	#10597328	C₂²	1	4	yes	complemented
67	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
68	#10597321	C₂²	1	2	yes	—
69	#10597321	C₂²	1	2	yes	complemented
70	#10597321	C₂²	1	2	yes	complemented
71	#10597320	C₂²	1	1	yes	characteristic
72	#10597320	C₂²	1	1	yes	characteristic
73	#10597320	C₂²	1	2	yes	complemented
74	C₄×D₇₆	C₂²	1	1	yes	characteristic
75	C₄×D₇₆	C₂²	1	2	yes	complemented
76	C₄×D₇₆	C₂²	1	2	yes	complemented
77	C₄×D₇₆	C₂²	1	2	yes	complemented
78	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₇₆	C₂²	1	2	yes	complemented
80	#10597315	C₂²	1	1	yes	characteristic, complemented
81	#10597315	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₃₈	C₂²	1	2	yes	complemented
83	C₂³×D₁₉	C₂³	1	4	yes	—
84	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₉	C₂³	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
96	#64545	—	4	4	no	—
97	D₄×D₁₉	—	4	4	no	—
98	#64541	—	4	4	no	—
99	#64541	—	4	4	no	—
100	#64541	—	4	4	no	—
101	C₂×D₇₆	—	4	4	no	—
102	C₂×D₇₆	C₂³	1	1	yes	characteristic
103	C₂×D₇₆	C₂³	1	2	yes	—
104	C₂×D₇₆	C₂³	1	1	yes	characteristic
105	C₂×D₇₆	C₂³	1	2	yes	—
106	C₂×D₇₆	C₂³	1	2	yes	—
107	C₂×D₇₆	C₂³	1	2	yes	—
108	C₂×D₇₆	C₂³	1	4	yes	—
109	C₂×D₇₆	C₂³	1	4	yes	—
110	C₂×D₇₆	C₂³	1	2	yes	—
111	C₂×D₇₆	C₂³	1	4	yes	—
112	C₂×C₄×D₁₉	C₂³	1	2	yes	—
113	C₂×C₄×D₁₉	C₂³	1	2	yes	—
114	C₂×C₄×D₁₉	C₂³	1	4	yes	—
115	C₂×C₄×D₁₉	C₂³	1	4	yes	—
116	C₂×C₄×D₁₉	C₂³	1	4	yes	—
117	C₂×Dic₃₈	C₂³	1	2	yes	—
118	C₂×Dic₃₈	C₂³	1	2	yes	—
119	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
121	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
130	C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₄²×C₁₉	C₂³	1	1	yes	characteristic
133	C₄²×C₁₉	C₂³	1	1	yes	characteristic
134	C₄²×C₁₉	C₂³	1	2	yes	—
135	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
136	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
137	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
139	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
141	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
142	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
143	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
144	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
145	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
146	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₉	C₂³	1	2	yes	—
151	Dic₁₉⋊C₄	C₂³	1	4	yes	—
152	Dic₁₉⋊C₄	C₂³	1	4	yes	—
153	C₄×Dic₁₉	C₂³	1	4	yes	—
154	C₂³×C₁₉	C₂⁴	1	2	yes	—
155	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
156	C₂²×D₁₉	—	4	4	no	—
157	C₂²×D₁₉	—	4	4	no	—
158	C₂²×D₁₉	—	4	4	no	—
159	C₂²×D₁₉	C₂⁴	1	2	yes	—
160	C₂²×D₁₉	C₂⁴	1	4	yes	—
161	C₂²×D₁₉	C₂⁴	1	2	yes	—
162	Q₈×C₁₉	—	2	2	no	—
163	D₄×C₁₉	—	2	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₁₉	—	4	4	no	—
179	C₂²⋊D₁₉	—	4	4	no	—
180	C₂²⋊D₁₉	—	4	2	no	—
181	C₂²⋊D₁₉	—	4	2	no	—
182	C₂²⋊D₁₉	—	4	4	no	—
183	C₂×Dic₁₉	C₂⁴	1	2	yes	—
184	C₂×Dic₁₉	C₂⁴	1	4	yes	—
185	C₂×Dic₁₉	C₂⁴	1	2	yes	—
186	D₇₆	—	2	2	no	—
187	D₇₆	—	2	4	no	—
188	D₇₆	—	2	2	no	—
189	D₇₆	—	2	4	no	—
190	D₇₆	—	4	4	no	—
191	D₇₆	—	4	2	no	—
192	D₇₆	—	4	2	no	—
193	D₇₆	—	4	4	no	—
194	D₇₆	—	4	2	no	—
195	D₇₆	—	4	4	no	—
196	C₄×D₁₉	—	2	4	no	—
197	C₄×D₁₉	—	2	4	no	—
198	C₄×D₁₉	—	4	4	no	—
199	C₄×D₁₉	—	4	4	no	—
200	C₄×D₁₉	—	4	4	no	—
201	Dic₃₈	—	2	4	no	—
202	Dic₃₈	—	4	2	no	—
203	#3546	—	19	1	no	maximal, Sylow
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
211	C₂×D₁₉	—	2	2	no	—
212	C₂×D₁₉	—	2	2	no	—
213	C₂×D₁₉	—	2	2	no	—
214	C₂×D₁₉	—	2	4	no	—
215	C₂×D₁₉	—	2	4	no	—
216	C₂×D₁₉	—	2	2	no	—
217	C₂×D₁₉	—	2	2	no	—
218	C₂×D₁₉	—	2	4	no	—
219	C₂×D₁₉	—	2	2	no	—
220	C₂×D₁₉	—	8	8	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	2	no	—
228	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
229	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
230	Dic₁₉	—	2	4	no	—
231	Dic₁₉	—	2	2	no	—
232	Dic₁₉	—	2	2	no	—
233	#560	—	19	4	no	—
234	#556	—	19	1	no	—
235	#553	—	19	2	no	—
236	#550	—	19	1	no	—
237	#550	—	19	2	no	—
238	#547	—	19	1	no	—
239	#546	—	19	2	no	—
240	#546	—	19	2	no	—
241	D₄²	—	19	1	no	—
242	#542	—	19	2	no	—
243	#538	—	19	4	no	—
244	#537	—	19	2	no	—
245	#535	—	19	2	no	—
246	#535	—	19	2	no	—
247	#532	—	19	1	no	—
248	#532	—	19	1	no	—
249	#529	D₁₉	1	1	yes	characteristic, complemented
250	C₂×C₁₉	—	4	2	no	—
251	C₂×C₁₉	—	4	1	no	—
252	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₁₉	#585	1	1	yes	characteristic
255	D₁₉	—	4	2	no	—
256	D₁₉	—	4	4	no	—
257	D₁₉	—	4	2	no	—
258	C₂×#41	—	19	2	no	—
259	C₂×#41	—	19	2	no	—
260	C₂×#41	—	19	2	no	—
261	C₂×#41	—	19	2	no	—
262	C₂²×D₄	—	19	2	no	—
263	C₂²×D₄	—	19	2	no	—
264	C₄⋊Q₈	—	19	1	no	—
265	C₄⋊Q₈	—	19	1	no	—
266	#127	—	19	4	no	—
267	#127	—	19	1	no	—
268	#127	—	19	1	no	—
269	#127	—	19	2	no	—
270	#126	—	19	4	no	—
271	#126	—	19	4	no	—
272	#126	C₂×D₁₉	1	2	yes	complemented
273	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
274	#124	—	19	4	no	—
275	#124	—	19	2	no	—
276	#124	—	19	2	no	—
277	#124	—	19	2	no	—
278	#124	C₂×D₁₉	1	1	yes	characteristic
279	#123	—	19	4	no	—
280	#123	—	19	4	no	—
281	#123	—	19	4	no	—
282	#123	C₂×D₁₉	1	2	yes	complemented
283	C₂²⋊Q₈	—	19	2	no	—
284	C₂²⋊Q₈	—	19	2	no	—
285	C₂²⋊Q₈	—	19	4	no	—
286	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
287	#121	—	19	2	no	—
288	#121	—	19	1	no	—
289	#121	—	19	2	no	—
290	#121	—	19	2	no	—
291	#121	—	19	1	no	—
292	#121	—	19	2	no	—
293	#121	—	19	2	no	—
294	#121	—	19	4	no	—
295	#121	—	19	2	no	—
296	#121	—	19	4	no	—
297	#121	—	19	2	no	—
298	#121	—	19	4	no	—
299	#121	—	19	4	no	—
300	#121	—	19	4	no	—
301	#121	—	19	4	no	—
302	#121	C₂×D₁₉	1	1	yes	characteristic
303	#120	—	19	4	no	—
304	#120	—	19	4	no	—
305	#120	—	19	4	no	—
306	#120	—	19	4	no	—
307	C₄×Q₈	—	19	2	no	—
308	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
309	C₄×D₄	—	19	4	no	—
310	C₄×D₄	—	19	2	no	—
311	C₄×D₄	—	19	1	no	—
312	C₄×D₄	—	19	2	no	—
313	C₄×D₄	—	19	2	no	—
314	C₄×D₄	—	19	1	no	—
315	C₄×D₄	—	19	2	no	—
316	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
317	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
318	#117	—	19	2	no	—
319	#117	C₂×D₁₉	1	2	yes	complemented
320	C₂×C₄⋊C₄	—	19	2	no	—
321	C₂×C₂²⋊C₄	—	19	4	no	—
322	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
323	C₁₉	#3546	1	1	yes	characteristic, complemented, Sylow
324	C₂⁴	—	19	4	no	—
325	#41	—	76	4	no	—
326	#41	—	76	4	no	—
327	#41	—	76	4	no	—
328	#41	—	76	4	no	—
329	C₂×Q₈	—	19	2	no	—
330	C₂×Q₈	—	19	2	no	—
331	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
332	C₂×D₄	—	19	2	no	—
333	C₂×D₄	—	19	4	no	—
334	C₂×D₄	—	19	4	no	—
335	C₂×D₄	—	19	4	no	—
336	C₂×D₄	—	19	2	no	—
337	C₂×D₄	—	19	2	no	—
338	C₂×D₄	—	19	1	no	—
339	C₂×D₄	—	19	2	no	—
340	C₂×D₄	—	19	1	no	—
341	C₂×D₄	—	19	2	no	—
342	C₂×D₄	—	19	2	no	—
343	C₂×D₄	—	19	4	no	—
344	C₂×D₄	—	19	2	no	—
345	C₂×D₄	—	19	4	no	—
346	C₂×D₄	—	19	4	no	—
347	C₂×D₄	—	76	4	no	—
348	C₂×D₄	—	76	4	no	—
349	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
350	C₂×D₄	C₂²×D₁₉	1	2	yes	—
351	C₂²×C₄	—	19	2	no	—
352	C₂²×C₄	—	19	2	no	—
353	C₂²×C₄	—	19	4	no	—
354	C₂²×C₄	—	19	4	no	—
355	C₂²×C₄	—	19	4	no	—
356	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
359	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
360	C₄⋊C₄	—	19	4	no	—
361	C₄⋊C₄	—	19	4	no	—
362	C₄⋊C₄	—	19	2	no	—
363	C₄⋊C₄	—	19	1	no	—
364	C₄⋊C₄	—	19	1	no	—
365	C₄⋊C₄	—	19	2	no	—
366	C₄⋊C₄	—	19	2	no	—
367	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
370	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
371	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
372	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
373	C₂²⋊C₄	—	19	4	no	—
374	C₂²⋊C₄	—	19	2	no	—
375	C₂²⋊C₄	—	19	4	no	—
376	C₂²⋊C₄	—	19	4	no	—
377	C₂²⋊C₄	—	19	2	no	—
378	C₂²⋊C₄	—	19	2	no	—
379	C₂²⋊C₄	—	19	4	no	—
380	C₂²⋊C₄	—	19	4	no	—
381	C₂²⋊C₄	—	19	4	no	—
382	C₂²⋊C₄	—	19	4	no	—
383	C₂²⋊C₄	—	19	2	no	—
384	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
387	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
388	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
389	C₄²	—	19	4	no	—
390	C₄²	C₂²×D₁₉	1	1	yes	characteristic
391	C₄²	C₂²×D₁₉	1	1	yes	characteristic
392	C₄²	C₂²×D₁₉	1	1	yes	characteristic
393	C₄²	C₂²×D₁₉	1	1	yes	characteristic
394	C₄²	C₂²×D₁₉	1	2	yes	—
395	C₂³	—	19	2	no	—
396	C₂³	—	19	4	no	—
397	C₂³	—	19	2	no	—
398	C₂³	—	76	4	no	—
399	C₂³	—	76	4	no	—
400	C₂³	—	76	4	no	—
401	C₂³	C₂³×D₁₉	1	2	yes	—
402	C₂³	C₂³×D₁₉	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	38	4	no	—
405	Q₈	—	76	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	38	2	no	—
409	D₄	—	38	4	no	—
410	D₄	—	38	4	no	—
411	D₄	—	38	2	no	—
412	D₄	—	76	4	no	—
413	D₄	—	76	2	no	—
414	D₄	—	76	4	no	—
415	D₄	—	76	2	no	—
416	D₄	—	76	2	no	—
417	D₄	—	76	4	no	—
418	D₄	—	76	4	no	—
419	D₄	—	76	2	no	—
420	D₄	—	76	2	no	—
421	D₄	—	76	4	no	—
422	D₄	—	76	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	19	2	no	—
428	C₂×C₄	—	19	4	no	—
429	C₂×C₄	—	19	2	no	—
430	C₂×C₄	—	38	4	no	—
431	C₂×C₄	—	38	4	no	—
432	C₂×C₄	—	76	4	no	—
433	C₂×C₄	—	76	4	no	—
434	C₂×C₄	—	76	4	no	—
435	C₂×C₄	C₂³×D₁₉	1	2	yes	—
436	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₉	1	2	yes	—
441	C₂×C₄	C₂³×D₁₉	1	2	yes	—
442	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	38	2	no	—
451	C₂²	—	38	2	no	—
452	C₂²	—	38	2	no	—
453	C₂²	—	38	4	no	—
454	C₂²	—	38	4	no	—
455	C₂²	—	38	2	no	—
456	C₂²	—	38	2	no	—
457	C₂²	—	38	4	no	—
458	C₂²	—	38	2	no	—
459	C₂²	—	152	8	no	—
460	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	2	no	—
468	C₄	—	38	2	no	—
469	C₄	—	38	2	no	—
470	C₄	—	38	4	no	—
471	C₄	#10597435	1	2	yes	—
472	C₄	#10597435	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	76	2	no	—
476	C₂	—	76	4	no	—
477	C₂	—	76	2	no	—
478	C₂	C₂×#10597435	1	1	yes	characteristic
479	C₂	C₂×#10597435	1	1	yes	characteristic
480	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	#3546
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. #11927284	C₂	semidirect
2. #11927267	C₂	semidirect
3. #11927247	C₂	semidirect
4. #11927216	C₂	semidirect
5. #11927215	C₂	semidirect
6. #11927199	C₂	semidirect
7. #11927190	C₂	semidirect
8. #11927187	C₂	semidirect
9. D₄×D₇₆	C₂	semidirect
10. #11927165	C₂	semidirect
11. #11927133	C₂	semidirect
12. #11927124	C₂	semidirect
13. #11927113	C₂	semidirect
14. #11927110	C₂	semidirect
15. #11927094	C₂	semidirect
16. #11927094	C₂	semidirect
17. C₁₉×#529	C₂	semidirect
18. C₂×#64545	C₂²	semidirect
20. C₂×#64541	C₂²	semidirect
21. C₂×#64541	C₂²	semidirect
22. C₂×#64541	C₂²	semidirect
24. C₁₉×#126	C₂²	semidirect
25. C₁₉×#125	C₂²	semidirect
27. C₁₉×#123	C₂²	semidirect
28. C₁₉×C₂²⋊Q₈	C₂²	semidirect
30. C₄×Q₈×C₁₉	C₂²	semidirect
32. C₄×D₄×C₁₉	C₂²	semidirect
33. C₁₉×#117	C₂²	semidirect
34. C₂×C₄²×C₁₉	C₂²	semidirect
35. #10597392	C₂²	semidirect
36. #10597386	C₂²	semidirect
38. #10597383	C₂²	semidirect
41. #10597376	C₂²	semidirect
42. #10597376	C₂²	semidirect
43. #10597376	C₂²	semidirect
44. #10597376	C₂²	semidirect
45. #10597370	C₂²	semidirect
46. #10597344	C₂²	semidirect
47. #10597344	C₂²	semidirect
48. #10597342	C₂²	semidirect
50. #10597341	C₂²	semidirect
51. #10597341	C₂²	semidirect
52. #10597341	C₂²	semidirect
53. #10597341	C₂²	semidirect
54. #10597340	C₂²	semidirect
55. #10597339	C₂²	semidirect
56. #10597338	C₂²	semidirect
57. C₄⋊C₄×D₁₉	C₂²	semidirect
58. #10597331	C₂²	semidirect
59. #10597330	C₂²	semidirect
60. #10597330	C₂²	semidirect
61. #10597330	C₂²	semidirect
62. #10597329	C₂²	semidirect
63. #10597329	C₂²	semidirect
65. #10597328	C₂²	semidirect
66. #10597328	C₂²	semidirect
67. C₂²⋊C₄×D₁₉	C₂²	semidirect
69. #10597321	C₂²	semidirect
70. #10597321	C₂²	semidirect
73. #10597320	C₂²	semidirect
75. C₄×D₇₆	C₂²	semidirect
76. C₄×D₇₆	C₂²	semidirect
77. C₄×D₇₆	C₂²	semidirect
78. C₄×D₇₆	C₂²	semidirect
79. C₄×D₇₆	C₂²	semidirect
80. #10597315	C₂²	semidirect
81. #10597315	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
249. #529	D₁₉	semidirect
272. #126	C₂×D₁₉	semidirect
273. #125	C₂×D₁₉	semidirect
282. #123	C₂×D₁₉	semidirect
286. C₂²⋊Q₈	C₂×D₁₉	semidirect
308. C₄×Q₈	C₂×D₁₉	semidirect
317. C₄×D₄	C₂×D₁₉	semidirect
319. #117	C₂×D₁₉	semidirect
322. C₂×C₄²	C₂×D₁₉	semidirect
323. C₁₉	#3546	semidirect

Maximal subgroups

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

subgroup	index
#11927284	2
#11927267	2
#11927247	2
#11927216	2
#11927215	2
#11927199	2
#11927190	2
#11927187	2
D₄×D₇₆	2
#11927165	2
#11927133	2
#11927124	2
#11927113	2
#11927110	2
#11927094	2
C₁₉×#529	2
#3546	19