Group #18074773 — subgroups

Subgroups — #18074773

Order 4864.

834 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564476	C₂	1	2	yes	maximal, complemented
2	#14562373	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562230	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562074	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3508	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×#10597290	—	2	4	no	—
8	C₄×#64520	C₂²	1	2	yes	—
9	#11926290	—	2	2	no	—
10	#11926286	—	2	2	no	—
11	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
12	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
13	C₁₉×#559	—	2	2	no	—
14	C₁₉×#550	—	2	2	no	—
15	C₁₉×#546	—	2	4	no	—
16	C₁₉×#540	—	2	2	no	—
17	C₁₉×#535	C₄	1	2	yes	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#532	—	2	2	no	—
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₁₉×#518	C₄	1	2	yes	—
22	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×#41×C₁₉	—	2	4	no	—
24	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×D₄×C₁₉	D₄	1	4	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×#127	—	2	2	no	—
29	C₁₉×#127	—	2	1	no	—
30	C₁₉×#127	—	2	1	no	—
31	C₁₉×#127	—	2	2	no	—
32	C₁₉×#125	D₄	1	2	yes	—
33	C₁₉×#124	—	2	4	no	—
34	C₁₉×#124	—	2	2	no	—
35	C₁₉×#123	—	2	8	no	—
36	C₁₉×C₂²⋊Q₈	—	2	2	no	—
37	C₁₉×#121	—	2	4	no	—
38	C₁₉×#121	—	2	8	no	—
39	C₁₉×#121	—	2	4	no	—
40	C₁₉×#120	—	2	4	no	—
41	C₄×Q₈×C₁₉	—	2	2	no	—
42	C₄×Q₈×C₁₉	D₄	1	2	yes	—
43	C₄×D₄×C₁₉	—	2	4	no	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₄×D₄×C₁₉	—	2	4	no	—
46	C₄×D₄×C₁₉	—	2	4	no	—
47	C₄×D₄×C₁₉	D₄	1	2	yes	—
48	C₁₉×#117	—	2	1	no	—
49	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
50	C₁₉×#117	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×#64520	—	2	2	no	—
55	C₂×#64520	—	2	2	no	—
56	#10597290	—	4	8	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	#10597260	—	2	2	no	—
60	C₄×C₁₉⋊C₈	—	2	2	no	—
61	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
62	#41×C₁₉	—	4	2	no	—
63	#41×C₁₉	—	8	4	no	—
64	#41×C₁₉	—	8	4	no	—
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	8	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	2	4	no	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	4	4	no	—
74	C₂×D₄×C₁₉	—	4	4	no	—
75	C₂×D₄×C₁₉	—	4	4	no	—
76	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	—	2	8	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
82	C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
86	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
87	C₂²⋊C₄×C₁₉	—	2	8	no	—
88	C₂²⋊C₄×C₁₉	—	2	8	no	—
89	C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₄²×C₁₉	—	2	1	no	—
93	C₄²×C₁₉	—	2	2	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂×D₄	1	2	yes	—
98	#64520	—	2	4	no	—
99	#64520	—	4	2	no	—
100	#64520	—	4	4	no	—
101	C₂×C₁₉⋊C₈	—	4	2	no	—
102	C₂×C₁₉⋊C₈	—	4	2	no	—
103	#8472	—	19	1	no	maximal, Sylow
104	C₂³×C₁₉	—	2	4	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	—	4	8	no	—
107	C₂³×C₁₉	—	4	4	no	—
108	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	Q₈×C₁₉	—	2	2	no	—
110	Q₈×C₁₉	—	4	2	no	—
111	Q₈×C₁₉	—	4	2	no	—
112	D₄×C₁₉	—	2	2	no	—
113	D₄×C₁₉	—	4	4	no	—
114	D₄×C₁₉	—	4	2	no	—
115	D₄×C₁₉	—	4	4	no	—
116	D₄×C₁₉	—	4	4	no	—
117	D₄×C₁₉	—	4	4	no	—
118	D₄×C₁₉	—	8	4	no	—
119	D₄×C₁₉	—	8	8	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	4	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	8	8	no	—
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#120	1	2	yes	—
133	C₂×C₄×C₁₉	#120	1	2	yes	—
134	C₁₉⋊C₈	—	4	4	no	—
135	C₁₉⋊C₈	—	8	2	no	—
136	#3508	D₁₉	1	1	yes	characteristic
137	#1965	—	19	2	no	—
138	#1561	—	19	1	no	—
139	#1526	—	19	1	no	—
140	#1489	—	19	2	no	—
141	C₂²×C₁₉	—	2	2	no	—
142	C₂²×C₁₉	—	2	1	no	—
143	C₂²×C₁₉	—	4	2	no	—
144	C₂²×C₁₉	—	4	8	no	—
145	C₂²×C₁₉	—	4	1	no	—
146	C₂²×C₁₉	—	4	4	no	—
147	C₂²×C₁₉	—	16	4	no	—
148	C₂²×C₁₉	#379	1	1	yes	characteristic
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	4	2	no	—
152	C₄×C₁₉	—	4	4	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	#413	1	2	yes	—
155	C₄×C₁₉	#453	1	2	yes	—
156	C₄×C₁₉	#455	1	2	yes	—
157	#559	—	2	2	no	—
158	#550	—	2	2	no	—
159	#546	—	2	4	no	—
160	#540	—	2	2	no	—
161	#535	Dic₁₉	1	2	yes	—
162	#533	C₂×D₁₉	1	1	yes	characteristic
163	#532	—	2	2	no	—
164	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
165	#518	Dic₁₉	1	2	yes	—
166	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
167	#423	—	19	2	no	—
168	C₂×#100	—	38	4	no	—
169	C₄×M₁₆	—	19	2	no	—
170	#332	—	38	2	no	—
171	#330	—	38	2	no	—
172	Q₈⋊C₈	—	38	2	no	—
173	D₄⋊C₈	—	38	2	no	—
174	C₂×C₁₉	—	4	1	no	—
175	C₂×C₁₉	—	8	1	no	—
176	C₂×C₁₉	—	8	4	no	—
177	C₂×C₁₉	#1785	1	1	yes	characteristic
178	C₂×C₁₉	#1792	1	2	yes	—
179	C₂×#41	—	2	4	no	—
180	C₂×#41	C₂×Dic₁₉	1	1	yes	characteristic
181	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
182	C₂²×D₄	C₂²⋊D₁₉	1	4	yes	—
183	C₂×M₁₆	—	38	2	no	—
184	C₂×M₁₆	—	38	2	no	—
185	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
186	#127	—	2	2	no	—
187	#127	—	2	1	no	—
188	#127	—	2	1	no	—
189	#127	—	2	2	no	—
190	#125	C₂²⋊D₁₉	1	2	yes	—
191	#124	—	2	4	no	—
192	#124	—	2	2	no	—
193	#123	—	2	8	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	#121	—	2	4	no	—
196	#121	—	2	8	no	—
197	#121	—	2	4	no	—
198	#120	—	2	4	no	—
199	C₄×Q₈	—	2	2	no	—
200	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
201	C₄×D₄	—	2	4	no	—
202	C₄×D₄	—	2	2	no	—
203	C₄×D₄	—	2	4	no	—
204	C₄×D₄	—	2	4	no	—
205	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
206	#117	—	2	1	no	—
207	#117	C₂×Dic₁₉	1	1	yes	characteristic
208	#117	C₂×Dic₁₉	1	2	yes	—
209	C₂×C₂²⋊C₄	—	2	4	no	—
210	C₂×C₄²	—	2	1	no	—
211	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
212	C₄⋊C₈	—	38	2	no	—
213	C₄⋊C₈	—	38	2	no	—
214	#100	—	76	8	no	—
215	#97	—	38	2	no	—
216	C₄×C₈	—	38	2	no	—
217	C₁₉	#8472	1	1	yes	characteristic, complemented, Sylow
218	C₂⁴	C₂²⋊Dic₁₉	1	4	yes	—
219	#41	—	4	2	no	—
220	#41	—	8	4	no	—
221	#41	—	8	4	no	—
222	C₂×Q₈	—	2	2	no	—
223	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
224	C₂×D₄	—	2	1	no	—
225	C₂×D₄	—	2	8	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	—	4	4	no	—
231	C₂×D₄	—	4	4	no	—
232	C₂×D₄	—	4	4	no	—
233	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
238	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
239	M₁₆	—	38	4	no	—
240	M₁₆	—	76	2	no	—
241	M₁₆	—	76	4	no	—
242	C₂×C₈	—	76	2	no	—
243	C₂×C₈	—	76	2	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
248	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
249	C₂²⋊C₄	—	2	8	no	—
250	C₂²⋊C₄	—	2	8	no	—
251	C₂²⋊C₄	—	2	1	no	—
252	C₂²⋊C₄	—	2	2	no	—
253	C₂²⋊C₄	—	2	2	no	—
254	C₄²	—	2	1	no	—
255	C₄²	—	2	2	no	—
256	C₄²	—	2	2	no	—
257	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
258	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
259	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂³	—	2	4	no	—
261	C₂³	—	2	1	no	—
262	C₂³	—	4	8	no	—
263	C₂³	—	4	4	no	—
264	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
265	Q₈	—	2	2	no	—
266	Q₈	—	4	2	no	—
267	Q₈	—	4	2	no	—
268	D₄	—	2	2	no	—
269	D₄	—	4	4	no	—
270	D₄	—	4	2	no	—
271	D₄	—	4	4	no	—
272	D₄	—	4	4	no	—
273	D₄	—	4	4	no	—
274	D₄	—	8	4	no	—
275	D₄	—	8	8	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	8	8	no	—
286	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
287	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
288	C₂×C₄	#10597399	1	2	yes	—
289	C₂×C₄	#10597399	1	2	yes	—
290	C₈	—	76	4	no	—
291	C₈	—	152	2	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	4	2	no	—
295	C₂²	—	4	8	no	—
296	C₂²	—	4	1	no	—
297	C₂²	—	4	4	no	—
298	C₂²	—	16	4	no	—
299	C₂²	#11926400	1	1	yes	characteristic
300	C₄	—	2	2	no	—
301	C₄	—	2	1	no	—
302	C₄	—	4	2	no	—
303	C₄	—	4	4	no	—
304	C₄	—	4	1	no	—
305	C₄	#11926528	1	2	yes	—
306	C₄	#11926712	1	2	yes	—
307	C₄	#11926722	1	2	yes	—
308	C₂	—	4	1	no	—
309	C₂	—	8	4	no	—
310	C₂	—	8	1	no	—
311	C₂	#14563563	1	1	yes	characteristic
312	C₂	#14563589	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564476

C₂

yes

maximal, complemented

#14562373

C₂

yes

maximal, characteristic, complemented

#14562230

C₂

yes

maximal, characteristic, complemented

#14562074

C₂

yes

maximal, complemented

C₁₉×#3508

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×#10597290

—

C₄×#64520

C₂²

yes

—

#11926290

—

#11926286

—

Q₈⋊(C₁₉⋊C₈)

—

D₄⋊(C₁₉⋊C₈)

—

C₁₉×#559

—

C₁₉×#550

—

C₁₉×#546

—

C₁₉×#540

—

C₁₉×#535

C₄

yes

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#532

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₁₉×#518

C₄

yes

—

C₄×#41×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂×#41×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂²×D₄×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#125

D₄

yes

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#120

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

C₂×C₄

yes

characteristic

C₁₉×#117

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

100

#64520

—

101

C₂×C₁₉⋊C₈

—

102

C₂×C₁₉⋊C₈

—

103

#8472

—

maximal, Sylow

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

—

108

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

109

Q₈×C₁₉

—

110

Q₈×C₁₉

—

111

Q₈×C₁₉

—

112

D₄×C₁₉

—

113

D₄×C₁₉

—

114

D₄×C₁₉

—

115

D₄×C₁₉

—

116

D₄×C₁₉

—

117

D₄×C₁₉

—

118

D₄×C₁₉

—

119

D₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

—

130

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

131

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

132

C₂×C₄×C₁₉

#120

yes

—

133

C₂×C₄×C₁₉

#120

yes

—

134

C₁₉⋊C₈

—

135

C₁₉⋊C₈

—

136

#3508

D₁₉

yes

characteristic

137

#1965

—

138

#1561

—

139

#1526

—

140

#1489

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

#379

yes

characteristic

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

C₄×C₁₉

—

154

C₄×C₁₉

#413

yes

—

155

C₄×C₁₉

#453

yes

—

156

C₄×C₁₉

#455

yes

—

157

#559

—

158

#550

—

159

#546

—

160

#540

—

161

#535

Dic₁₉

yes

—

162

#533

C₂×D₁₉

yes

characteristic

163

#532

—

164

C₂×#127

C₂×D₁₉

yes

characteristic

165

#518

Dic₁₉

yes

—

166

C₄×#41

C₂×D₁₉

yes

characteristic

167

#423

—

168

C₂×#100

—

169

C₄×M₁₆

—

170

#332

—

171

#330

—

172

Q₈⋊C₈

—

173

D₄⋊C₈

—

174

C₂×C₁₉

—

175

C₂×C₁₉

—

176

C₂×C₁₉

—

177

C₂×C₁₉

#1785

yes

characteristic

178

C₂×C₁₉

#1792

yes

—

179

C₂×#41

—

180

C₂×#41

C₂×Dic₁₉

yes

characteristic

181

C₂²×D₄

C₂×Dic₁₉

yes

—

182

C₂²×D₄

C₂²⋊D₁₉

yes

—

183

C₂×M₁₆

—

184

C₂×M₁₆

—

185

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

186

#127

—

187

#127

—

188

#127

—

189

#127

—

190

#125

C₂²⋊D₁₉

yes

—

191

#124

—

192

#124

—

193

#123

—

194

C₂²⋊Q₈

—

195

#121

—

196

#121

—

197

#121

—

198

#120

—

199

C₄×Q₈

—

200

C₄×Q₈

C₂²⋊D₁₉

yes

—

201

C₄×D₄

—

202

C₄×D₄

—

203

C₄×D₄

—

204

C₄×D₄

—

205

C₄×D₄

C₂²⋊D₁₉

yes

—

206

#117

—

207

#117

C₂×Dic₁₉

yes

characteristic

208

#117

C₂×Dic₁₉

yes

—

209

C₂×C₂²⋊C₄

—

210

C₂×C₄²

—

211

C₂×C₄²

C₂²×D₁₉

yes

characteristic

212

C₄⋊C₈

—

213

C₄⋊C₈

—

214

#100

—

215

#97

—

216

C₄×C₈

—

217

C₁₉

#8472

yes

characteristic, complemented, Sylow

218

C₂⁴

C₂²⋊Dic₁₉

yes

—

219

#41

—

220

#41

—

221

#41

—

222

C₂×Q₈

—

223

C₂×Q₈

C₂²⋊Dic₁₉

yes

characteristic

224

C₂×D₄

—

225

C₂×D₄

—

226

C₂×D₄

—

227

C₂×D₄

—

228

C₂×D₄

—

229

C₂×D₄

—

230

C₂×D₄

—

231

C₂×D₄

—

232

C₂×D₄

—

233

C₂×D₄

C₂²⋊Dic₁₉

yes

characteristic

234

C₂²×C₄

—

235

C₂²×C₄

—

236

C₂²×C₄

—

237

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

238

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

239

M₁₆

—

240

M₁₆

—

241

M₁₆

—

242

C₂×C₈

—

243

C₂×C₈

—

244

C₄⋊C₄

—

245

C₄⋊C₄

—

246

C₄⋊C₄

—

247

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

248

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

249

C₂²⋊C₄

—

250

C₂²⋊C₄

—

251

C₂²⋊C₄

—

252

C₂²⋊C₄

—

253

C₂²⋊C₄

—

254

C₄²

—

255

C₄²

—

256

C₄²

—

257

C₄²

C₂×C₂²⋊D₁₉

yes

—

258

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

259

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

260

C₂³

—

261

C₂³

—

262

C₂³

—

263

C₂³

—

264

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

265

Q₈

—

266

Q₈

—

267

Q₈

—

268

D₄

—

269

D₄

—

270

D₄

—

271

D₄

—

272

D₄

—

273

D₄

—

274

D₄

—

275

D₄

—

276

C₂×C₄

—

277

C₂×C₄

—

278

C₂×C₄

—

279

C₂×C₄

—

280

C₂×C₄

—

281

C₂×C₄

—

282

C₂×C₄

—

283

C₂×C₄

—

284

C₂×C₄

—

285

C₂×C₄

—

286

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

287

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

288

C₂×C₄

#10597399

yes

—

289

C₂×C₄

#10597399

yes

—

290

C₈

—

291

C₈

—

152

—

292

C₂²

—

293

C₂²

—

294

C₂²

—

295

C₂²

—

296

C₂²

—

297

C₂²

—

298

C₂²

—

299

C₂²

#11926400

yes

characteristic

300

C₄

—

301

C₄

—

302

C₄

—

303

C₄

—

304

C₄

—

305

C₄

#11926528

yes

—

306

C₄

#11926712

yes

—

307

C₄

#11926722

yes

—

308

C₂

—

309

C₂

—

310

C₂

—

311

C₂

#14563563

yes

characteristic

312

C₂

#14563589

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3508	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3508	D₁₉
hypocenter	C₁₉	#8472
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3508

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#3508

C₂

socle

C₂²×C₁₉

#379

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3508

N	H ≅ G/N	type
1. #14564476	C₂	semidirect
2. #14562373	C₂	semidirect
3. #14562230	C₂	semidirect
4. #14562074	C₂	semidirect
217. C₁₉	#8472	semidirect

H ≅ G/N

type

1. #14564476

C₂

semidirect

2. #14562373

C₂

semidirect

3. #14562230

C₂

semidirect

4. #14562074

C₂

semidirect

217. C₁₉

#8472

semidirect

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

subgroup	index
#14564476	2
#14562373	2
#14562230	2
#14562074	2
C₁₉×#3508	2
#8472	19

subgroup

index

C₁₉×#3508

Subgroups — #18074773

Conjugacy classes of subgroups

Complements

Maximal subgroups