Subgroups — #14577684

Order 2432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927249	C₂	1	2	yes	maximal, complemented
3	#11927234	C₂	1	2	yes	maximal, complemented
4	#11927220	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927203	C₂	1	2	yes	maximal, complemented
7	#11927199	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927198	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927188	C₂	1	2	yes	maximal, complemented
10	#11927159	C₂	1	2	yes	maximal, complemented
11	#11927136	C₂	1	4	yes	maximal, complemented
12	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927055	C₂	1	2	yes	maximal, complemented
15	C₂×#10597370	C₂	1	2	yes	maximal, complemented
16	#11927023	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
20	C₂×#64543	C₂²	1	2	yes	—
21	C₂×#64541	C₂²	1	2	yes	complemented
22	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
23	C₄×D₄×C₁₉	C₂²	1	2	yes	—
24	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
32	#10597399	C₂²	1	4	yes	—
33	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
34	#10597385	C₂²	1	4	yes	—
35	#10597384	C₂²	1	2	yes	—
36	#10597382	C₂²	1	2	yes	—
37	#10597381	C₂²	1	4	yes	—
38	D₄×Dic₁₉	C₂²	1	2	yes	—
39	#10597376	C₂²	1	1	yes	characteristic
40	#10597376	C₂²	1	2	yes	complemented
41	#10597375	C₂²	1	2	yes	—
42	#10597375	C₂²	1	4	yes	complemented
43	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	—
44	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
45	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
46	#10597372	C₂²	1	2	yes	—
47	#10597372	C₂²	1	2	yes	complemented
48	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
49	#10597370	C₂²	1	1	yes	characteristic
50	#10597370	C₂²	1	2	yes	—
51	#10597370	C₂²	1	4	yes	—
52	#10597370	C₂²	1	2	yes	—
53	#10597370	C₂²	1	4	yes	complemented
54	#10597370	C₂²	1	2	yes	complemented
55	#10597370	C₂²	1	2	yes	complemented
56	#10597370	C₂²	1	2	yes	complemented
57	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	complemented
58	#10597343	C₂²	1	2	yes	complemented
59	#10597342	C₂²	1	4	yes	complemented
60	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
61	#10597335	C₂²	1	4	yes	complemented
62	#10597334	C₂²	1	2	yes	complemented
63	#10597333	C₂²	1	2	yes	complemented
64	#10597332	C₂²	1	4	yes	complemented
65	#10597331	C₂²	1	4	yes	complemented
66	#10597329	C₂²	1	4	yes	complemented
67	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
68	#10597325	C₂²	1	4	yes	complemented
69	#10597325	C₂²	1	4	yes	complemented
70	#10597324	C₂²	1	4	yes	complemented
71	#10597323	C₂²	1	4	yes	complemented
72	#10597322	C₂²	1	2	yes	complemented
73	#10597321	C₂²	1	1	yes	characteristic, complemented
74	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
75	#10597318	C₂²	1	2	yes	complemented
76	#10597316	C₂²	1	1	yes	characteristic, complemented
77	#10597316	C₂²	1	2	yes	complemented
78	#10597315	C₂²	1	1	yes	characteristic, complemented
79	#10597315	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₃₈	C₂²	1	2	yes	complemented
82	C₄×Dic₃₈	C₂²	1	2	yes	complemented
83	C₂⁴×C₁₉	C₂³	1	2	yes	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	C₂³	1	2	yes	—
86	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	—	4	4	no	—
89	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
100	C₂²×Dic₁₉	C₂³	1	4	yes	—
101	C₂²×Dic₁₉	C₂³	1	4	yes	—
102	#64543	—	2	8	no	—
103	#64541	—	4	4	no	—
104	C₂×D₇₆	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₉	C₂³	1	2	yes	—
106	C₂×C₄×D₁₉	C₂³	1	4	yes	—
107	C₂×Dic₃₈	—	4	4	no	—
108	C₂×Dic₃₈	C₂³	1	2	yes	—
109	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
110	C₂×Dic₃₈	C₂³	1	2	yes	—
111	C₂×Dic₃₈	C₂³	1	4	yes	—
112	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
124	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
126	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
127	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
128	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
134	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₁₉	C₂³	1	2	yes	—
136	C₄⋊Dic₁₉	C₂³	1	2	yes	—
137	C₄⋊Dic₁₉	C₂³	1	2	yes	—
138	C₄⋊Dic₁₉	C₂³	1	2	yes	—
139	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₉	C₂³	1	4	yes	—
141	Dic₁₉⋊C₄	C₂³	1	2	yes	—
142	Dic₁₉⋊C₄	C₂³	1	4	yes	—
143	Dic₁₉⋊C₄	C₂³	1	4	yes	—
144	Dic₁₉⋊C₄	C₂³	1	2	yes	—
145	Dic₁₉⋊C₄	C₂³	1	2	yes	—
146	Dic₁₉⋊C₄	C₂³	1	2	yes	—
147	Dic₁₉⋊C₄	C₂³	1	4	yes	—
148	Dic₁₉⋊C₄	C₂³	1	4	yes	—
149	Dic₁₉⋊C₄	C₂³	1	4	yes	—
150	C₄×Dic₁₉	C₂³	1	2	yes	—
151	C₄×Dic₁₉	C₂³	1	4	yes	—
152	C₄×Dic₁₉	C₂³	1	4	yes	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	C₂⁴	1	2	yes	—
157	C₂³×C₁₉	C₂⁴	1	2	yes	—
158	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂²×D₁₉	C₂⁴	1	2	yes	—
160	D₄×C₁₉	—	2	4	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	#41	1	4	yes	complemented
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
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	2	yes	—
177	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂²⋊D₁₉	—	2	8	no	—
180	C₂²⋊D₁₉	—	2	4	no	—
181	C₂²⋊D₁₉	—	4	4	no	—
182	C₂×Dic₁₉	—	2	8	no	—
183	C₂×Dic₁₉	—	4	4	no	—
184	C₂×Dic₁₉	C₂⁴	1	2	yes	—
185	C₂×Dic₁₉	C₂⁴	1	4	yes	—
186	C₂×Dic₁₉	C₂⁴	1	4	yes	—
187	C₂×Dic₁₉	C₂⁴	1	2	yes	—
188	C₂×Dic₁₉	C₂⁴	1	2	yes	—
189	D₇₆	—	2	2	no	—
190	C₄×D₁₉	—	2	4	no	—
191	C₄×D₁₉	—	4	4	no	—
192	Dic₃₈	—	2	4	no	—
193	Dic₃₈	—	2	2	no	—
194	Dic₃₈	—	2	4	no	—
195	Dic₃₈	—	4	4	no	—
196	#3520	—	19	1	no	maximal, Sylow
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	4	8	no	—
205	C₂²×C₁₉	C₂×#41	1	4	yes	—
206	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
207	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
208	C₂×D₁₉	—	2	2	no	—
209	C₂×D₁₉	—	2	2	no	—
210	C₂×D₁₉	—	2	2	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	C₂×#41	1	2	yes	—
218	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
219	Dic₁₉	—	2	4	no	—
220	Dic₁₉	—	2	2	no	—
221	Dic₁₉	—	2	2	no	—
222	Dic₁₉	—	2	4	no	—
223	Dic₁₉	—	2	2	no	—
224	#556	—	19	1	no	—
225	#554	—	19	2	no	—
226	#552	—	19	2	no	—
227	#551	—	19	4	no	—
228	D₄×Q₈	—	19	1	no	—
229	#548	—	19	2	no	—
230	#547	—	19	1	no	—
231	#547	—	19	1	no	—
232	#546	—	19	2	no	—
233	#542	—	19	2	no	—
234	#539	—	19	4	no	—
235	#533	—	19	1	no	—
236	#529	—	19	1	no	—
237	#525	—	19	2	no	—
238	C₂×C₂²⋊Q₈	—	19	2	no	—
239	#520	—	19	2	no	—
240	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
241	C₂×C₁₉	—	2	2	no	—
242	C₂×C₁₉	—	2	4	no	—
243	C₂×C₁₉	—	4	2	no	—
244	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
245	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
247	D₁₉	—	4	2	no	—
248	C₂×#41	—	19	2	no	—
249	C₂×#41	—	19	2	no	—
250	C₂²×Q₈	—	19	2	no	—
251	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
252	C₂³×C₄	C₂×D₁₉	1	2	yes	—
253	C₄⋊Q₈	—	19	2	no	—
254	C₄⋊Q₈	—	19	1	no	—
255	C₄⋊Q₈	—	19	1	no	—
256	#126	—	19	4	no	—
257	#126	—	19	4	no	—
258	#126	—	19	2	no	—
259	#125	—	19	4	no	—
260	#125	—	19	1	no	—
261	#125	—	19	2	no	—
262	#124	—	19	2	no	—
263	#124	—	19	4	no	—
264	#124	—	19	1	no	—
265	#123	—	19	4	no	—
266	#123	—	19	4	no	—
267	#123	—	19	2	no	—
268	#123	—	19	4	no	—
269	#123	—	19	4	no	—
270	C₂²⋊Q₈	—	19	1	no	—
271	C₂²⋊Q₈	—	19	2	no	—
272	C₂²⋊Q₈	—	19	4	no	—
273	C₂²⋊Q₈	—	19	2	no	—
274	C₂²⋊Q₈	—	19	2	no	—
275	C₂²⋊Q₈	—	19	4	no	—
276	C₂²⋊Q₈	—	19	2	no	—
277	C₂²⋊Q₈	—	19	2	no	—
278	C₂²⋊Q₈	—	19	4	no	—
279	C₂²⋊Q₈	—	19	2	no	—
280	C₂²⋊Q₈	—	19	4	no	—
281	#121	—	19	2	no	—
282	#121	—	19	4	no	—
283	#121	—	19	1	no	—
284	#121	—	19	2	no	—
285	#120	—	19	4	no	—
286	C₄×Q₈	—	19	2	no	—
287	C₄×Q₈	—	19	2	no	—
288	C₄×Q₈	—	19	1	no	—
289	C₄×Q₈	—	19	2	no	—
290	C₄×D₄	—	19	2	no	—
291	C₄×D₄	—	19	4	no	—
292	C₄×D₄	—	19	4	no	—
293	C₄×D₄	—	19	2	no	—
294	C₄×D₄	—	19	4	no	—
295	C₄×D₄	—	19	1	no	—
296	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
297	C₄×D₄	C₂×D₁₉	1	2	yes	—
298	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
299	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
300	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
301	C₄×D₄	C₂×D₁₉	1	2	yes	—
302	#117	—	19	2	no	—
303	#117	—	19	2	no	—
304	#117	—	19	4	no	—
305	#117	—	19	2	no	—
306	C₂×C₄⋊C₄	—	19	4	no	—
307	C₂×C₄⋊C₄	—	19	2	no	—
308	C₂×C₄⋊C₄	—	19	2	no	—
309	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	19	4	no	—
311	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
312	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
313	C₁₉	#3520	1	1	yes	characteristic, complemented, Sylow
314	C₂⁴	C₂²×D₁₉	1	2	yes	—
315	#41	—	38	8	no	—
316	#41	—	76	4	no	—
317	C₂×Q₈	—	19	2	no	—
318	C₂×Q₈	—	19	1	no	—
319	C₂×Q₈	—	19	2	no	—
320	C₂×Q₈	—	19	4	no	—
321	C₂×Q₈	—	76	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	19	2	no	—
324	C₂×D₄	—	19	4	no	—
325	C₂×D₄	—	19	4	no	—
326	C₂×D₄	—	19	1	no	—
327	C₂×D₄	C₂²×D₁₉	1	2	yes	—
328	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
329	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	19	4	no	—
332	C₂²×C₄	—	19	4	no	—
333	C₂²×C₄	—	19	2	no	—
334	C₂²×C₄	—	19	4	no	—
335	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
340	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
341	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
342	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
343	C₄⋊C₄	—	19	2	no	—
344	C₄⋊C₄	—	19	4	no	—
345	C₄⋊C₄	—	19	4	no	—
346	C₄⋊C₄	—	19	4	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	19	4	no	—
349	C₄⋊C₄	—	19	2	no	—
350	C₄⋊C₄	—	19	4	no	—
351	C₄⋊C₄	—	19	2	no	—
352	C₄⋊C₄	—	19	1	no	—
353	C₄⋊C₄	—	19	2	no	—
354	C₄⋊C₄	—	19	2	no	—
355	C₄⋊C₄	—	19	4	no	—
356	C₄⋊C₄	—	19	1	no	—
357	C₄⋊C₄	—	19	2	no	—
358	C₄⋊C₄	—	19	2	no	—
359	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
362	C₂²⋊C₄	—	19	2	no	—
363	C₂²⋊C₄	—	19	4	no	—
364	C₂²⋊C₄	—	19	4	no	—
365	C₂²⋊C₄	—	19	4	no	—
366	C₂²⋊C₄	—	19	4	no	—
367	C₂²⋊C₄	—	19	4	no	—
368	C₂²⋊C₄	—	19	2	no	—
369	C₂²⋊C₄	—	19	2	no	—
370	C₂²⋊C₄	—	19	2	no	—
371	C₂²⋊C₄	—	19	4	no	—
372	C₂²⋊C₄	—	19	2	no	—
373	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
377	C₄²	—	19	4	no	—
378	C₄²	—	19	4	no	—
379	C₄²	—	19	2	no	—
380	C₄²	C₂²×D₁₉	1	1	yes	characteristic
381	C₄²	C₂²×D₁₉	1	1	yes	characteristic
382	C₄²	C₂²×D₁₉	1	1	yes	characteristic
383	C₄²	C₂²×D₁₉	1	1	yes	characteristic
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	19	2	no	—
388	C₂³	C₂³×D₁₉	1	2	yes	—
389	C₂³	C₂³×D₁₉	1	2	yes	—
390	C₂³	C₂³×D₁₉	1	1	yes	characteristic
391	Q₈	—	38	4	no	—
392	Q₈	—	38	2	no	—
393	Q₈	—	38	4	no	—
394	Q₈	—	76	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	38	8	no	—
398	D₄	—	38	4	no	—
399	D₄	—	38	2	no	—
400	D₄	—	76	4	no	—
401	D₄	#64541	1	4	yes	complemented
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	19	2	no	—
411	C₂×C₄	—	19	4	no	—
412	C₂×C₄	—	19	2	no	—
413	C₂×C₄	—	19	4	no	—
414	C₂×C₄	—	19	2	no	—
415	C₂×C₄	—	38	8	no	—
416	C₂×C₄	—	38	4	no	—
417	C₂×C₄	—	76	4	no	—
418	C₂×C₄	—	76	4	no	—
419	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₁₉	1	2	yes	—
421	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₉	1	2	yes	—
425	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	38	2	no	—
436	C₂²	—	38	2	no	—
437	C₂²	—	38	2	no	—
438	C₂²	C₂×#64541	1	4	yes	—
439	C₂²	#10597436	1	2	yes	—
440	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	38	2	no	—
448	C₄	—	38	4	no	—
449	C₄	—	38	4	no	—
450	C₄	—	38	2	no	—
451	C₄	—	38	2	no	—
452	C₄	C₂×#64541	1	2	yes	—
453	C₄	#10597430	1	2	yes	—
454	C₂	—	2	2	no	—
455	C₂	—	2	4	no	—
456	C₂	—	4	2	no	—
457	C₂	—	76	2	no	—
458	C₂	C₂²×#64541	1	1	yes	characteristic
459	C₂	C₂×#10597430	1	1	yes	characteristic
460	C₂	C₂×#10597436	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₄×D₄×C₁₉	C₂
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#3520
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #11927264	C₂	semidirect
2. #11927249	C₂	semidirect
3. #11927234	C₂	semidirect
4. #11927220	C₂	semidirect
5. D₄×Dic₃₈	C₂	semidirect
6. #11927203	C₂	semidirect
7. #11927199	C₂	semidirect
8. #11927198	C₂	semidirect
9. #11927188	C₂	semidirect
10. #11927159	C₂	semidirect
11. #11927136	C₂	semidirect
12. #11927101	C₂	semidirect
13. #11927078	C₂	semidirect
14. #11927055	C₂	semidirect
15. C₂×#10597370	C₂	semidirect
16. #11927023	C₂	semidirect
17. C₂×C₄×D₄×C₁₉	C₂	semidirect
21. C₂×#64541	C₂²	semidirect
22. C₂²×Dic₃₈	C₂²	semidirect
40. #10597376	C₂²	semidirect
42. #10597375	C₂²	semidirect
45. C₄×C₂²⋊D₁₉	C₂²	semidirect
47. #10597372	C₂²	semidirect
48. C₂×C₄⋊Dic₁₉	C₂²	semidirect
53. #10597370	C₂²	semidirect
54. #10597370	C₂²	semidirect
55. #10597370	C₂²	semidirect
56. #10597370	C₂²	semidirect
57. C₂×Dic₁₉⋊C₄	C₂²	semidirect
58. #10597343	C₂²	semidirect
59. #10597342	C₂²	semidirect
60. C₄⋊C₄×D₁₉	C₂²	semidirect
61. #10597335	C₂²	semidirect
62. #10597334	C₂²	semidirect
63. #10597333	C₂²	semidirect
64. #10597332	C₂²	semidirect
65. #10597331	C₂²	semidirect
66. #10597329	C₂²	semidirect
67. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
68. #10597325	C₂²	semidirect
69. #10597325	C₂²	semidirect
70. #10597324	C₂²	semidirect
71. #10597323	C₂²	semidirect
72. #10597322	C₂²	semidirect
73. #10597321	C₂²	semidirect
74. C₄×D₇₆	C₂²	semidirect
75. #10597318	C₂²	semidirect
76. #10597316	C₂²	semidirect
77. #10597316	C₂²	semidirect
78. #10597315	C₂²	semidirect
79. #10597315	C₂²	semidirect
80. C₄×Dic₃₈	C₂²	semidirect
81. C₄×Dic₃₈	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
162. D₄×C₁₉	#41	semidirect
240. C₂×C₄×D₄	D₁₉	semidirect
313. C₁₉	#3520	semidirect
401. D₄	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927264	2
#11927249	2
#11927234	2
#11927220	2
D₄×Dic₃₈	2
#11927203	2
#11927199	2
#11927198	2
#11927188	2
#11927159	2
#11927136	2
#11927101	2
#11927078	2
#11927055	2
C₂×#10597370	2
#11927023	2
C₂×C₄×D₄×C₁₉	2
#3520	19