Group #18071277 — subgroups

Subgroups — #18071277

Order 4864.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14570667	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564866	C₂	1	2	yes	maximal
3	#14561461	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561459	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597390	—	2	1	no	—
7	C₂×#10597289	—	2	2	no	—
8	C₂×#10597289	—	2	2	no	—
9	#11926474	—	2	1	no	—
10	#11926465	—	2	2	no	—
11	#11926442	C₂²	1	2	yes	—
12	#11926429	—	2	2	no	—
13	#11926299	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₁₉	—	2	1	no	—
15	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#102	—	2	1	no	—
17	C₁₉×#391	C₂²	1	1	yes	characteristic
18	C₁₉×#336	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₂²×Dic₃₈	—	2	1	no	—
23	C₂×SD₁₆×C₁₉	—	4	2	no	—
24	C₂×SD₁₆×C₁₉	—	4	2	no	—
25	C₂×SD₁₆×C₁₉	—	4	2	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₁₉×#127	—	4	2	no	—
28	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	#10597390	—	4	2	no	—
31	#10597390	—	4	2	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
34	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
35	C₂×Dic₁₉⋊C₄	—	2	2	no	—
36	C₂×Dic₁₉⋊C₄	—	2	2	no	—
37	C₂×C₄×Dic₁₉	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₁₉×#102	—	4	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	#10597289	—	4	4	no	—
42	#10597289	—	4	4	no	—
43	C₁₉⋊#95	—	2	1	no	—
44	C₁₉⋊#95	—	2	2	no	—
45	C₁₉⋊#95	—	2	2	no	—
46	C₂⁴×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	2	1	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	D₈	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	4	no	—
53	C₂×D₄×C₁₉	—	4	1	no	—
54	C₂×D₄×C₁₉	—	4	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂×D₄×C₁₉	—	4	1	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂×D₄×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	4	1	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×Dic₁₉	—	2	2	no	—
68	C₂²×Dic₁₉	—	2	2	no	—
69	C₂×Dic₃₈	—	4	2	no	—
70	C₂×Dic₃₈	—	8	1	no	—
71	C₂×Dic₃₈	—	8	1	no	—
72	SD₁₆×C₁₉	—	4	8	no	—
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	4	1	no	—
75	C₂×C₈×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	—	4	1	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	4	2	no	—
80	C₄⋊Dic₁₉	—	8	1	no	—
81	C₄⋊Dic₁₉	SD₁₆	1	4	yes	complemented
82	Dic₁₉⋊C₄	—	4	4	no	—
83	Dic₁₉⋊C₄	—	4	2	no	—
84	Dic₁₉⋊C₄	—	4	2	no	—
85	C₄×Dic₁₉	—	4	2	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#7741	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	—	4	2	no	—
91	C₂³×C₁₉	—	8	1	no	—
92	C₂³×C₁₉	—	8	2	no	—
93	C₂³×C₁₉	—	8	1	no	—
94	C₂³×C₁₉	—	8	2	no	—
95	C₂³×C₁₉	#120	1	1	yes	characteristic
96	Q₈×C₁₉	—	4	2	no	—
97	Q₈×C₁₉	—	8	1	no	—
98	D₄×C₁₉	—	4	2	no	—
99	D₄×C₁₉	—	4	2	no	—
100	D₄×C₁₉	—	4	4	no	—
101	D₄×C₁₉	—	4	4	no	—
102	D₄×C₁₉	—	8	1	no	—
103	D₄×C₁₉	—	8	1	no	—
104	D₄×C₁₉	—	8	2	no	—
105	D₄×C₁₉	—	8	2	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	4	1	no	—
112	C₂×C₄×C₁₉	—	4	1	no	—
113	C₂×C₄×C₁₉	—	4	1	no	—
114	C₂×C₄×C₁₉	—	4	2	no	—
115	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
117	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#137	1	2	yes	—
119	C₂×Dic₁₉	—	2	4	no	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	4	2	no	—
123	C₂×Dic₁₉	—	4	2	no	—
124	C₂×Dic₁₉	—	4	2	no	—
125	Dic₃₈	—	8	4	no	—
126	C₈×C₁₉	—	4	2	no	—
127	C₁₉⋊C₈	—	8	2	no	—
128	#2734	—	19	1	no	—
129	#2041	—	19	2	no	—
130	#2014	D₁₉	1	1	yes	characteristic
131	#1272	—	19	1	no	—
132	#1271	—	19	2	no	—
133	C₂²×C₁₉	—	8	2	no	—
134	C₂²×C₁₉	—	8	4	no	—
135	C₂²×C₁₉	—	16	1	no	—
136	C₂²×C₁₉	—	16	2	no	—
137	C₂²×C₁₉	—	16	1	no	—
138	C₂²×C₁₉	#447	1	1	yes	characteristic
139	C₂²×C₁₉	#448	1	2	yes	—
140	C₂²×C₁₉	#453	1	1	yes	characteristic
141	C₂²×C₁₉	#454	1	2	yes	—
142	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	2	no	—
146	C₄×C₁₉	—	2	2	no	—
147	C₄×C₁₉	—	4	2	no	—
148	C₄×C₁₉	—	8	1	no	—
149	Dic₁₉	—	4	4	no	—
150	Dic₁₉	—	8	2	no	—
151	C₂²×SD₁₆	—	2	1	no	—
152	C₂×C₄⋊Q₈	—	38	1	no	—
153	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
154	C₂×#102	—	2	1	no	—
155	C₂×#102	—	38	2	no	—
156	C₂×#102	—	38	2	no	—
157	#398	—	38	1	no	—
158	#395	—	38	2	no	—
159	#391	C₂×D₁₉	1	1	yes	characteristic
160	#389	—	19	2	no	—
161	#387	—	38	2	no	—
162	#336	—	19	2	no	—
163	#336	C₂×D₁₉	1	1	yes	characteristic
164	C₂×C₁₉	—	16	2	no	—
165	C₂×C₁₉	#1595	1	1	yes	characteristic
166	C₂×C₁₉	#1599	1	2	yes	—
167	C₂×C₁₉	#1623	1	1	yes	characteristic
168	C₂×C₁₉	#1627	1	2	yes	—
169	C₂×C₁₉	#1657	1	1	yes	characteristic
170	C₂²×Q₈	—	38	1	no	—
171	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
172	C₂²×D₄	—	2	2	no	—
173	C₂²×D₄	—	2	1	no	—
174	C₂×SD₁₆	—	4	2	no	—
175	C₂×SD₁₆	—	4	2	no	—
176	C₂×SD₁₆	—	4	2	no	—
177	C₂²×C₈	—	2	1	no	—
178	C₂²×C₈	—	38	2	no	—
179	C₄⋊Q₈	—	76	2	no	—
180	C₄⋊Q₈	—	76	2	no	—
181	#127	—	4	2	no	—
182	C₂×C₄⋊C₄	—	19	2	no	—
183	C₂×C₄⋊C₄	—	19	2	no	—
184	C₂×C₄⋊C₄	—	38	2	no	—
185	C₂×C₄⋊C₄	—	38	2	no	—
186	C₂×C₄⋊C₄	—	38	1	no	—
187	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂×C₄²	—	38	1	no	—
189	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
190	#102	—	4	2	no	—
191	#102	—	76	4	no	—
192	#102	—	76	4	no	—
193	#95	—	2	2	no	—
194	#95	—	38	1	no	—
195	#95	—	38	2	no	—
196	#95	—	38	2	no	—
197	C₁₉	#7741	1	1	yes	characteristic, complemented, Sylow
198	C₂⁴	—	4	1	no	—
199	C₂×Q₈	—	2	1	no	—
200	C₂×Q₈	—	4	1	no	—
201	C₂×Q₈	—	4	1	no	—
202	C₂×Q₈	—	76	2	no	—
203	C₂×Q₈	—	152	1	no	—
204	C₂×Q₈	—	152	1	no	—
205	C₂×Q₈	#64525	1	2	yes	—
206	C₂×D₄	—	2	4	no	—
207	C₂×D₄	—	2	2	no	—
208	C₂×D₄	—	4	1	no	—
209	C₂×D₄	—	4	1	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	4	2	no	—
213	C₂×D₄	—	4	1	no	—
214	C₂×D₄	—	4	1	no	—
215	C₂×D₄	—	4	1	no	—
216	C₂×D₄	—	4	2	no	—
217	C₂×D₄	—	4	2	no	—
218	C₂²×C₄	—	2	1	no	—
219	C₂²×C₄	—	2	1	no	—
220	C₂²×C₄	—	38	2	no	—
221	C₂²×C₄	—	38	2	no	—
222	C₂²×C₄	D₄×D₁₉	1	2	yes	—
223	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
224	SD₁₆	—	4	8	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	4	1	no	—
227	C₂×C₈	—	4	1	no	—
228	C₂×C₈	—	76	2	no	—
229	C₂×C₈	—	76	2	no	—
230	C₂×C₈	—	76	2	no	—
231	C₄⋊C₄	—	4	1	no	—
232	C₄⋊C₄	—	19	4	no	—
233	C₄⋊C₄	—	38	2	no	—
234	C₄⋊C₄	—	76	2	no	—
235	C₄⋊C₄	—	76	4	no	—
236	C₄⋊C₄	—	76	2	no	—
237	C₄⋊C₄	—	76	2	no	—
238	C₄⋊C₄	—	152	1	no	—
239	C₄²	—	4	1	no	—
240	C₄²	—	76	2	no	—
241	C₂³	—	4	2	no	—
242	C₂³	—	8	1	no	—
243	C₂³	—	8	2	no	—
244	C₂³	—	8	1	no	—
245	C₂³	—	8	2	no	—
246	C₂³	#10597383	1	1	yes	characteristic
247	Q₈	—	4	2	no	—
248	Q₈	—	8	1	no	—
249	Q₈	—	152	4	no	—
250	D₄	—	4	2	no	—
251	D₄	—	4	4	no	—
252	D₄	—	4	4	no	—
253	D₄	—	4	2	no	—
254	D₄	—	8	2	no	—
255	D₄	—	8	2	no	—
256	D₄	—	8	1	no	—
257	D₄	—	8	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	4	1	no	—
264	C₂×C₄	—	4	1	no	—
265	C₂×C₄	—	4	1	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	38	4	no	—
268	C₂×C₄	—	76	2	no	—
269	C₂×C₄	—	76	2	no	—
270	C₂×C₄	—	76	2	no	—
271	C₂×C₄	—	76	2	no	—
272	C₂×C₄	—	76	2	no	—
273	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
274	C₂×C₄	#10597361	1	2	yes	—
275	C₂×C₄	C₂×#64525	1	1	yes	characteristic
276	C₂×C₄	#10597395	1	1	yes	characteristic
277	C₈	—	4	2	no	—
278	C₈	—	152	2	no	—
279	C₂²	—	8	4	no	—
280	C₂²	—	8	2	no	—
281	C₂²	—	16	1	no	—
282	C₂²	—	16	1	no	—
283	C₂²	—	16	2	no	—
284	C₂²	#11926677	1	1	yes	characteristic
285	C₂²	#11926681	1	2	yes	—
286	C₂²	#11926711	1	1	yes	characteristic
287	C₂²	#11926715	1	2	yes	—
288	C₂²	#11926730	1	1	yes	characteristic
289	C₄	—	2	2	no	—
290	C₄	—	2	2	no	—
291	C₄	—	2	1	no	—
292	C₄	—	2	1	no	—
293	C₄	—	4	2	no	—
294	C₄	—	8	1	no	—
295	C₄	—	76	4	no	—
296	C₄	—	152	2	no	—
297	C₂	—	16	2	no	—
298	C₂	#14562552	1	1	yes	characteristic
299	C₂	#14562573	1	2	yes	—
300	C₂	#14562711	1	1	yes	characteristic
301	C₂	#14562736	1	2	yes	—
302	C₂	#14562931	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14570667

C₂

yes

maximal, characteristic, complemented

#14564866

C₂

yes

maximal

#14561461

C₂

yes

maximal, characteristic, complemented

#14561459

C₂

yes

maximal, complemented

C₁₉×#2014

C₂

yes

maximal, characteristic

—

—

—

—

—

C₂²

yes

—

#11926429

—

#11926299

C₂²

yes

—

C₂²×SD₁₆×C₁₉

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#102

—

C₁₉×#391

C₂²

yes

characteristic

C₁₉×#336

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×Dic₃₈

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#127

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597390

—

#10597390

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#102

—

C₁₉×#95

—

#10597289

—

#10597289

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

—

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

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

SD₁₆

yes

complemented

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7741

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

D₄×C₁₉

—

105

D₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

—

113

C₂×C₄×C₁₉

—

114

C₂×C₄×C₁₉

—

115

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

116

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

117

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

118

C₂×C₄×C₁₉

#137

yes

—

119

C₂×Dic₁₉

—

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₂×Dic₁₉

—

124

C₂×Dic₁₉

—

125

Dic₃₈

—

126

C₈×C₁₉

—

127

C₁₉⋊C₈

—

128

#2734

—

129

#2041

—

130

#2014

D₁₉

yes

characteristic

131

#1272

—

132

#1271

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

#447

yes

characteristic

139

C₂²×C₁₉

#448

yes

—

140

C₂²×C₁₉

#453

yes

characteristic

141

C₂²×C₁₉

#454

yes

—

142

C₂²×C₁₉

B(4,𝔽₂)

yes

characteristic

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

Dic₁₉

—

150

Dic₁₉

—

151

C₂²×SD₁₆

—

152

C₂×C₄⋊Q₈

—

153

C₂×#127

C₂×D₁₉

yes

characteristic

154

C₂×#102

—

155

C₂×#102

—

156

C₂×#102

—

157

#398

—

158

#395

—

159

#391

C₂×D₁₉

yes

characteristic

160

#389

—

161

#387

—

162

#336

—

163

#336

C₂×D₁₉

yes

characteristic

164

C₂×C₁₉

—

165

C₂×C₁₉

#1595

yes

characteristic

166

C₂×C₁₉

#1599

yes

—

167

C₂×C₁₉

#1623

yes

characteristic

168

C₂×C₁₉

#1627

yes

—

169

C₂×C₁₉

#1657

yes

characteristic

170

C₂²×Q₈

—

171

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

172

C₂²×D₄

—

173

C₂²×D₄

—

174

C₂×SD₁₆

—

175

C₂×SD₁₆

—

176

C₂×SD₁₆

—

177

C₂²×C₈

—

178

C₂²×C₈

—

179

C₄⋊Q₈

—

180

C₄⋊Q₈

—

181

#127

—

182

C₂×C₄⋊C₄

—

183

C₂×C₄⋊C₄

—

184

C₂×C₄⋊C₄

—

185

C₂×C₄⋊C₄

—

186

C₂×C₄⋊C₄

—

187

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

188

C₂×C₄²

—

189

C₂×C₄²

C₂²×D₁₉

yes

characteristic

190

#102

—

191

#102

—

192

#102

—

193

#95

—

194

#95

—

195

#95

—

196

#95

—

197

C₁₉

#7741

yes

characteristic, complemented, Sylow

198

C₂⁴

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

—

152

—

204

C₂×Q₈

—

152

—

205

C₂×Q₈

#64525

yes

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

D₄×D₁₉

yes

—

223

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

224

SD₁₆

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

152

—

239

C₄²

—

240

C₄²

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

#10597383

yes

characteristic

247

Q₈

—

248

Q₈

—

249

Q₈

—

152

—

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

SD₁₆×D₁₉

yes

—

274

C₂×C₄

#10597361

yes

—

275

C₂×C₄

C₂×#64525

yes

characteristic

276

C₂×C₄

#10597395

yes

characteristic

277

C₈

—

278

C₈

—

152

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

#11926677

yes

characteristic

285

C₂²

#11926681

yes

—

286

C₂²

#11926711

yes

characteristic

287

C₂²

#11926715

yes

—

288

C₂²

#11926730

yes

characteristic

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

—

295

C₄

—

296

C₄

—

152

—

297

C₂

—

298

C₂

#14562552

yes

characteristic

299

C₂

#14562573

yes

—

300

C₂

#14562711

yes

characteristic

301

C₂

#14562736

yes

—

302

C₂

#14562931

yes

characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2014	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
hypercenter	#2014	D₁₉
hypocenter	C₁₉	#7741
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2014

subgroup

G/H

center

C₂³

#10597383

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2014

C₂

socle

C₂³×C₁₉

#120

prime radical

C₂×C₁₉×#127

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2014

N	H ≅ G/N	type
1. #14570667	C₂	semidirect
3. #14561461	C₂	semidirect
4. #14561459	C₂	semidirect
81. C₄⋊Dic₁₉	SD₁₆	semidirect
197. C₁₉	#7741	semidirect

H ≅ G/N

type

1. #14570667

C₂

semidirect

3. #14561461

C₂

semidirect

4. #14561459

C₂

semidirect

81. C₄⋊Dic₁₉

SD₁₆

semidirect

197. C₁₉

#7741

semidirect

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

subgroup	index
#14570667	2
#14564866	2
#14561461	2
#14561459	2
C₁₉×#2014	2
#7741	19

subgroup

index

C₁₉×#2014

Subgroups — #18071277

Conjugacy classes of subgroups

Complements

Maximal subgroups