Group #18073541 — subgroups

Subgroups — #18073541

Order 4864.

452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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	#14572346	C₂	1	1	yes	maximal, characteristic
2	#14562295	C₂	1	1	yes	maximal, characteristic
3	#14562226	C₂	1	1	yes	maximal, characteristic
4	#14561916	C₂	1	1	yes	maximal, characteristic, complemented
5	M₁₆×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561524	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1299	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597353	C₄	1	2	yes	—
9	#11927094	C₂²	1	1	yes	characteristic
10	#11926621	—	2	1	no	—
11	#11926621	—	2	1	no	—
12	#11926609	—	2	1	no	—
13	#11926609	—	2	1	no	—
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926512	C₄	1	2	yes	—
16	C₄×#64520	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	#11926292	C₄	1	2	yes	—
19	#11926287	C₄	1	2	yes	—
20	#11926283	C₄	1	4	yes	—
21	#11926266	—	2	1	no	—
22	#11926265	—	2	1	no	—
23	C₈×C₁₉⋊C₈	—	2	1	no	—
24	C₈×C₁₉⋊C₈	—	2	1	no	—
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×#423	C₂²	1	1	yes	characteristic
27	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×#64541	C₂×C₄	1	2	yes	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	#10597376	—	2	1	no	—
33	#10597376	—	2	1	no	—
34	C₂×#64520	—	2	1	no	—
35	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	#10597353	—	4	4	no	—
38	C₂×#64515	—	2	2	no	—
39	C₂×C₈×D₁₉	—	2	2	no	—
40	#10597321	C₂×C₄	1	2	yes	—
41	#10597320	C₂×C₄	1	1	yes	characteristic
42	C₄×D₇₆	—	2	1	no	—
43	C₄×D₇₆	—	2	1	no	—
44	#10597315	C₂×C₄	1	1	yes	characteristic
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
48	C₁₉×C₂²⋊C₈	—	2	1	no	—
49	C₁₉×#97	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
53	(C₂×D₁₉)⋊C₈	—	2	2	no	—
54	(C₂×D₁₉)⋊C₈	—	2	2	no	—
55	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
56	#10597260	C₂×C₄	1	2	yes	—
57	C₄×C₁₉⋊C₈	—	2	1	no	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
61	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
62	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₉	—	2	2	no	—
67	#64541	—	4	2	no	—
68	#64541	—	4	2	no	—
69	C₂×D₇₆	—	2	1	no	—
70	C₂×D₇₆	—	2	1	no	—
71	C₂×D₇₆	C₄²	1	2	yes	—
72	C₂×C₄×D₁₉	—	2	2	no	—
73	C₂×Dic₃₈	C₄²	1	2	yes	—
74	M₁₆×C₁₉	—	2	4	no	—
75	M₁₆×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	(C₂×D₁₉)⋊C₄	—	2	2	no	—
84	(C₂×D₁₉)⋊C₄	—	2	2	no	—
85	C₄⋊Dic₁₉	—	2	1	no	—
86	C₄⋊Dic₁₉	—	2	1	no	—
87	#64520	—	2	4	no	—
88	C₂×C₁₉⋊C₈	—	2	2	no	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	4	1	no	—
92	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
96	#64515	—	4	4	no	—
97	C₈×D₁₉	—	4	4	no	—
98	#8241	—	19	1	no	maximal, Sylow
99	C₂³×C₁₉	#117	1	1	yes	characteristic
100	C₂²×D₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
111	C₂²⋊D₁₉	—	4	4	no	—
112	C₂×Dic₁₉	—	2	2	no	—
113	D₇₆	—	4	2	no	—
114	D₇₆	—	4	2	no	—
115	D₇₆	—	4	2	no	—
116	C₄×D₁₉	—	4	2	no	—
117	C₄×D₁₉	—	4	2	no	—
118	Dic₃₈	—	4	2	no	—
119	C₈×C₁₉	—	2	4	no	—
120	C₈×C₁₉	—	4	2	no	—
121	C₈×C₁₉	—	4	2	no	—
122	C₁₉⋊C₈	—	2	4	no	—
123	C₁₉⋊C₈	—	2	1	no	—
124	C₁₉⋊C₈	—	2	1	no	—
125	C₁₉⋊C₈	—	2	1	no	—
126	C₁₉⋊C₈	—	4	2	no	—
127	C₁₉⋊C₈	#100	1	2	yes	—
128	#2931	—	19	1	no	—
129	#1543	—	19	1	no	—
130	#1525	—	19	1	no	—
131	C₈×M₁₆	—	19	1	no	—
132	C₈×M₁₆	—	19	1	no	—
133	#1299	—	19	1	no	—
134	#1299	D₁₉	1	1	yes	characteristic, complemented
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×D₁₉	—	4	2	no	—
140	C₂×D₁₉	—	4	2	no	—
141	C₂×D₁₉	—	4	2	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
146	C₄×C₁₉	#413	1	1	yes	characteristic
147	C₄×C₁₉	#443	1	2	yes	—
148	C₄×C₁₉	#443	1	2	yes	—
149	Dic₁₉	—	4	2	no	—
150	C₂×#131	—	19	2	no	—
151	#532	—	19	1	no	—
152	#436	—	38	1	no	—
153	#436	—	38	1	no	—
154	C₈×D₄	—	38	1	no	—
155	C₈×D₄	—	38	1	no	—
156	#431	—	19	1	no	—
157	#431	C₂×D₁₉	1	1	yes	characteristic
158	#423	C₂×D₁₉	1	1	yes	characteristic
159	#408	—	19	2	no	—
160	C₄×M₁₆	—	19	1	no	—
161	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
162	C₂×C₄×C₈	—	19	1	no	—
163	#333	—	19	2	no	—
164	#331	—	19	2	no	—
165	#329	—	19	4	no	—
166	#322	—	38	1	no	—
167	#322	—	38	1	no	—
168	C₈²	—	38	1	no	—
169	C₈²	—	38	1	no	—
170	C₂×C₁₉	—	4	1	no	—
171	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
172	C₂×C₁₉	#1764	1	1	yes	characteristic
173	C₂×C₁₉	#1764	1	1	yes	characteristic
174	D₁₉	—	8	2	no	—
175	C₂×#41	—	19	2	no	—
176	#131	—	76	4	no	—
177	C₂×M₁₆	—	2	1	no	—
178	C₂×M₁₆	—	38	2	no	—
179	C₂×M₁₆	—	38	1	no	—
180	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
181	C₂²×C₈	—	19	1	no	—
182	C₂²×C₈	—	19	1	no	—
183	C₂²×C₈	—	38	2	no	—
184	C₄⋊Q₈	—	19	1	no	—
185	#127	—	19	1	no	—
186	#124	—	19	2	no	—
187	#121	—	38	1	no	—
188	#121	—	38	1	no	—
189	C₄×D₄	—	38	1	no	—
190	C₄×D₄	—	38	1	no	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	C₄⋊C₈	—	2	1	no	—
193	C₄⋊C₈	—	2	1	no	—
194	C₄⋊C₈	—	19	2	no	—
195	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
196	C₂²⋊C₈	—	2	1	no	—
197	C₂²⋊C₈	—	38	2	no	—
198	C₂²⋊C₈	—	38	2	no	—
199	C₂²⋊C₈	—	38	1	no	—
200	#97	—	19	2	no	—
201	#97	C₄×D₁₉	1	2	yes	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	19	1	no	—
205	C₄×C₈	—	19	1	no	—
206	C₄×C₈	—	19	1	no	—
207	C₄×C₈	—	19	1	no	—
208	C₄×C₈	—	38	1	no	—
209	C₄×C₈	—	38	1	no	—
210	C₁₉	#8241	1	1	yes	characteristic, complemented, Sylow
211	#41	—	76	2	no	—
212	#41	—	76	2	no	—
213	C₂×Q₈	—	19	2	no	—
214	C₂×D₄	—	19	2	no	—
215	C₂×D₄	—	38	2	no	—
216	C₂×D₄	—	38	1	no	—
217	C₂×D₄	—	38	1	no	—
218	C₂²×C₄	—	38	2	no	—
219	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
220	C₂²×C₄	#64543	1	1	yes	characteristic
221	C₂²×C₄	#64545	1	1	yes	characteristic
222	M₁₆	—	2	4	no	—
223	M₁₆	—	4	2	no	—
224	M₁₆	—	38	4	no	—
225	M₁₆	—	76	4	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	—	19	1	no	—
230	C₂×C₈	—	19	1	no	—
231	C₂×C₈	—	19	1	no	—
232	C₂×C₈	—	19	1	no	—
233	C₂×C₈	—	38	2	no	—
234	C₂×C₈	—	38	2	no	—
235	C₂×C₈	—	38	2	no	—
236	C₂×C₈	—	76	4	no	—
237	C₂×C₈	—	76	1	no	—
238	C₄⋊C₄	—	38	1	no	—
239	C₄⋊C₄	—	38	1	no	—
240	C₂²⋊C₄	—	38	2	no	—
241	C₂²⋊C₄	—	38	2	no	—
242	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
243	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
244	C₄²	D₄×D₁₉	1	1	yes	characteristic
245	C₄²	D₄×D₁₉	1	1	yes	characteristic
246	C₂³	—	38	2	no	—
247	C₂³	#10597338	1	1	yes	characteristic
248	Q₈	—	76	2	no	—
249	D₄	—	76	2	no	—
250	D₄	—	76	4	no	—
251	D₄	—	76	2	no	—
252	D₄	—	76	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	38	2	no	—
258	C₂×C₄	—	76	2	no	—
259	C₂×C₄	—	76	2	no	—
260	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
261	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
262	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
263	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
264	C₂×C₄	#10597339	1	1	yes	characteristic
265	C₂×C₄	#10597339	1	1	yes	characteristic
266	C₈	—	2	4	no	—
267	C₈	—	4	2	no	—
268	C₈	—	4	2	no	—
269	C₈	—	19	2	no	—
270	C₈	—	38	4	no	—
271	C₈	—	38	1	no	—
272	C₈	—	38	1	no	—
273	C₈	—	38	1	no	—
274	C₈	—	76	2	no	—
275	C₂²	—	2	1	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	76	2	no	—
279	C₂²	—	76	2	no	—
280	C₂²	—	76	2	no	—
281	C₂²	#11926391	1	1	yes	characteristic
282	C₄	—	2	1	no	—
283	C₄	—	2	1	no	—
284	C₄	—	2	1	no	—
285	C₄	—	76	2	no	—
286	C₄	#100×D₁₉	1	1	yes	characteristic
287	C₄	#11926527	1	1	yes	characteristic
288	C₄	#11926658	1	2	yes	—
289	C₄	#11926660	1	2	yes	—
290	C₂	—	4	1	no	—
291	C₂	—	152	2	no	—
292	C₂	#14563426	1	1	yes	characteristic
293	C₂	#14563469	1	1	yes	characteristic
294	C₂	#14563471	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572346

C₂

yes

maximal, characteristic

#14562295

C₂

yes

maximal, characteristic

#14562226

C₂

yes

maximal, characteristic

#14561916

C₂

yes

maximal, characteristic, complemented

M₁₆×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#14561524

C₂

yes

maximal, characteristic, complemented

C₁₉×#1299

C₂

yes

maximal, characteristic, complemented

C₂×#10597353

C₄

yes

—

#11927094

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#11926512

C₄

yes

—

C₄×#64520

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926292

C₄

yes

—

#11926287

C₄

yes

—

#11926283

C₄

yes

—

#11926266

—

#11926265

—

C₈×C₁₉⋊C₈

—

C₈×C₁₉⋊C₈

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×#64541

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#10597353

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

C₂×C₄

yes

—

#10597320

C₂×C₄

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄²

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄²

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

100

C₂²×D₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

106

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

107

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

108

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

109

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

110

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

111

C₂²⋊D₁₉

—

112

C₂×Dic₁₉

—

113

D₇₆

—

114

D₇₆

—

115

D₇₆

—

116

C₄×D₁₉

—

117

C₄×D₁₉

—

118

Dic₃₈

—

119

C₈×C₁₉

—

120

C₈×C₁₉

—

121

C₈×C₁₉

—

122

C₁₉⋊C₈

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

C₁₉⋊C₈

—

126

C₁₉⋊C₈

—

127

C₁₉⋊C₈

#100

yes

—

128

#2931

—

129

#1543

—

130

#1525

—

131

C₈×M₁₆

—

132

C₈×M₁₆

—

133

#1299

—

134

#1299

D₁₉

yes

characteristic, complemented

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

139

C₂×D₁₉

—

140

C₂×D₁₉

—

141

C₂×D₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

C₂×#100

yes

characteristic

146

C₄×C₁₉

#413

yes

characteristic

147

C₄×C₁₉

#443

yes

—

148

C₄×C₁₉

#443

yes

—

149

Dic₁₉

—

150

C₂×#131

—

151

#532

—

152

#436

—

153

#436

—

154

C₈×D₄

—

155

C₈×D₄

—

156

#431

—

157

#431

C₂×D₁₉

yes

characteristic

158

#423

C₂×D₁₉

yes

characteristic

159

#408

—

160

C₄×M₁₆

—

161

C₄×M₁₆

C₂×D₁₉

yes

characteristic

162

C₂×C₄×C₈

—

163

#333

—

164

#331

—

165

#329

—

166

#322

—

167

#322

—

168

C₈²

—

169

C₈²

—

170

C₂×C₁₉

—

171

C₂×C₁₉

C₄×#100

yes

characteristic

172

C₂×C₁₉

#1764

yes

characteristic

173

C₂×C₁₉

#1764

yes

characteristic

174

D₁₉

—

175

C₂×#41

—

176

#131

—

177

C₂×M₁₆

—

178

C₂×M₁₆

—

179

C₂×M₁₆

—

180

C₂×M₁₆

C₄×D₁₉

yes

—

181

C₂²×C₈

—

182

C₂²×C₈

—

183

C₂²×C₈

—

184

C₄⋊Q₈

—

185

#127

—

186

#124

—

187

#121

—

188

#121

—

189

C₄×D₄

—

190

C₄×D₄

—

191

C₂×C₄²

C₂²×D₁₉

yes

characteristic

192

C₄⋊C₈

—

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

C₄⋊C₈

C₄×D₁₉

yes

—

196

C₂²⋊C₈

—

197

C₂²⋊C₈

—

198

C₂²⋊C₈

—

199

C₂²⋊C₈

—

200

#97

—

201

#97

C₄×D₁₉

yes

—

202

C₄×C₈

—

203

C₄×C₈

—

204

C₄×C₈

—

205

C₄×C₈

—

206

C₄×C₈

—

207

C₄×C₈

—

208

C₄×C₈

—

209

C₄×C₈

—

210

C₁₉

#8241

yes

characteristic, complemented, Sylow

211

#41

—

212

#41

—

213

C₂×Q₈

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂²×C₄

—

219

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

220

C₂²×C₄

#64543

yes

characteristic

221

C₂²×C₄

#64545

yes

characteristic

222

M₁₆

—

223

M₁₆

—

224

M₁₆

—

225

M₁₆

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₂×C₈

—

238

C₄⋊C₄

—

239

C₄⋊C₄

—

240

C₂²⋊C₄

—

241

C₂²⋊C₄

—

242

C₄²

C₂×C₄×D₁₉

yes

characteristic

243

C₄²

C₂×C₄×D₁₉

yes

characteristic

244

C₄²

D₄×D₁₉

yes

characteristic

245

C₄²

D₄×D₁₉

yes

characteristic

246

C₂³

—

247

C₂³

#10597338

yes

characteristic

248

Q₈

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

C₄²×D₁₉

yes

characteristic

261

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

262

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

263

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

264

C₂×C₄

#10597339

yes

characteristic

265

C₂×C₄

#10597339

yes

characteristic

266

C₈

—

267

C₈

—

268

C₈

—

269

C₈

—

270

C₈

—

271

C₈

—

272

C₈

—

273

C₈

—

274

C₈

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

#11926391

yes

characteristic

282

C₄

—

283

C₄

—

284

C₄

—

285

C₄

—

286

C₄

#100×D₁₉

yes

characteristic

287

C₄

#11926527

yes

characteristic

288

C₄

#11926658

yes

—

289

C₄

#11926660

yes

—

290

C₂

—

291

C₂

—

152

—

292

C₂

#14563426

yes

characteristic

293

C₂

#14563469

yes

characteristic

294

C₂

#14563471

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1299	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1299	D₁₉
hypocenter	C₁₉	#8241
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1299

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1299

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

prime radical

#11927094

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1299

N	H ≅ G/N	type
4. #14561916	C₂	semidirect
5. M₁₆×C₁₉⋊C₈	C₂	semidirect
6. #14561524	C₂	semidirect
7. C₁₉×#1299	C₂	semidirect
134. #1299	D₁₉	semidirect
210. C₁₉	#8241	semidirect

H ≅ G/N

type

4. #14561916

C₂

semidirect

5. M₁₆×C₁₉⋊C₈

C₂

semidirect

6. #14561524

C₂

semidirect

7. C₁₉×#1299

C₂

semidirect

134. #1299

D₁₉

semidirect

210. C₁₉

#8241

semidirect

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

subgroup	index
#14572346	2
#14562295	2
#14562226	2
#14561916	2
M₁₆×C₁₉⋊C₈	2
#14561524	2
C₁₉×#1299	2
#8241	19

subgroup

index

M₁₆×C₁₉⋊C₈

C₁₉×#1299

Subgroups — #18073541

Conjugacy classes of subgroups

Complements

Maximal subgroups