Group #18083380 — subgroups

Subgroups — #18083380

Order 4864.

734 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 105 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	#14573635	C₂	1	2	yes	maximal, complemented
2	#14564467	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562060	C₂	1	2	yes	maximal, complemented
4	#14561464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2397	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	1	yes	characteristic
7	#11926857	—	2	2	no	—
8	#11926824	—	2	2	no	—
9	#11926739	—	2	2	no	—
10	#11926678	—	2	2	no	—
11	C₄×#64525	—	2	4	no	—
12	#11926597	C₂²	1	2	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×#10597262	—	2	2	no	—
15	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
16	C₂×C₄×D₄×C₁₉	—	2	2	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#399	—	2	2	no	—
19	C₁₉×#392	—	2	2	no	—
20	C₁₉×#376	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	D₄	1	2	yes	—
23	C₂³×C₄×C₁₉	—	2	2	no	—
24	C₂×#64541	—	2	1	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	4	4	no	—
30	C₄×D₄×C₁₉	—	4	4	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64525	—	2	4	no	—
38	#10597376	—	2	2	no	—
39	C₂×#64520	—	2	1	no	—
40	#10597321	—	2	1	no	—
41	#10597320	D₄	1	1	yes	characteristic, complemented
42	C₄×D₇₆	—	2	2	no	—
43	#10597315	D₄	1	1	yes	characteristic, complemented
44	C₁₉×#95	—	2	2	no	—
45	#10597289	—	2	4	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
47	#10597266	—	2	4	no	—
48	#10597264	—	2	4	no	—
49	#10597262	—	4	4	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₄×C₁₉⋊C₈	D₄	1	4	yes	complemented
53	C₂⁴×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	—	4	4	no	—
57	C₂×D₄×C₁₉	—	4	4	no	—
58	C₂×D₄×C₁₉	—	4	8	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	4	4	no	—
64	C₂²×C₄×C₁₉	—	4	4	no	—
65	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₉	—	4	1	no	—
68	#64541	—	4	2	no	—
69	#64541	—	4	2	no	—
70	C₂×D₇₆	—	2	2	no	—
71	C₂×D₇₆	—	2	1	no	—
72	C₂×C₄×D₁₉	—	4	1	no	—
73	C₂×Dic₃₈	—	2	1	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	4	4	no	—
77	C₂²⋊C₄×C₁₉	—	4	8	no	—
78	C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₂²⋊C₄×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	D₈	1	4	yes	complemented
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	2	yes	—
84	C₄²×C₁₉	#41	1	1	yes	characteristic
85	#64525	—	4	8	no	—
86	(C₂×D₁₉)⋊C₄	—	4	2	no	—
87	C₄⋊Dic₁₉	—	2	2	no	—
88	#64520	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	2	4	no	—
90	C₂×C₁₉⋊C₈	—	4	1	no	—
91	#10012	—	19	1	no	maximal, Sylow
92	C₂³×C₁₉	—	2	4	no	—
93	C₂³×C₁₉	—	4	4	no	—
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	4	no	—
97	C₂³×C₁₉	#120	1	1	yes	characteristic
98	C₂²×D₁₉	—	4	1	no	—
99	D₄×C₁₉	—	2	4	no	—
100	D₄×C₁₉	—	2	4	no	—
101	D₄×C₁₉	—	4	2	no	—
102	D₄×C₁₉	—	4	2	no	—
103	D₄×C₁₉	—	4	16	no	—
104	C₂×C₄×C₁₉	—	2	4	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	4	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	8	4	no	—
110	C₂×C₄×C₁₉	—	8	2	no	—
111	C₂×C₄×C₁₉	—	8	2	no	—
112	C₂×C₄×C₁₉	#120	1	2	yes	—
113	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#121	1	2	yes	—
115	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
117	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
118	C₂²⋊D₁₉	—	8	2	no	—
119	C₂×Dic₁₉	—	4	1	no	—
120	D₇₆	—	4	4	no	—
121	D₇₆	—	4	2	no	—
122	C₄×D₁₉	—	8	1	no	—
123	C₄×D₁₉	—	8	1	no	—
124	Dic₃₈	—	4	2	no	—
125	C₁₉⋊C₈	—	4	4	no	—
126	C₁₉⋊C₈	—	8	1	no	—
127	#3100	—	19	2	no	—
128	#2397	D₁₉	1	1	yes	characteristic, complemented
129	#1963	—	19	1	no	—
130	#1486	—	19	2	no	—
131	#1274	—	19	1	no	—
132	C₂²×C₁₉	—	2	2	no	—
133	C₂²×C₁₉	—	4	8	no	—
134	C₂²×C₁₉	—	4	4	no	—
135	C₂²×C₁₉	—	8	4	no	—
136	C₂²×C₁₉	—	8	2	no	—
137	C₂²×C₁₉	—	8	2	no	—
138	C₂²×C₁₉	#392	1	1	yes	characteristic
139	C₂²×C₁₉	#447	1	2	yes	—
140	C₂×D₁₉	—	8	2	no	—
141	C₂×D₁₉	—	8	1	no	—
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	—	2	2	no	—
144	C₄×C₁₉	—	4	4	no	—
145	C₄×C₁₉	—	8	2	no	—
146	C₄×C₁₉	#459	1	2	yes	—
147	C₄×C₁₉	#493	1	1	yes	characteristic
148	C₄×C₁₉	#496	1	1	yes	characteristic
149	Dic₁₉	—	8	1	no	—
150	#532	—	19	1	no	—
151	C₂×C₄×D₄	—	2	2	no	—
152	C₂×C₄×D₄	C₂×D₁₉	1	2	yes	—
153	#480	—	38	2	no	—
154	#474	—	38	2	no	—
155	#459	—	38	2	no	—
156	#447	—	38	2	no	—
157	C₄×D₈	—	38	4	no	—
158	#431	—	19	2	no	—
159	#423	—	19	1	no	—
160	C₂×#104	—	38	2	no	—
161	#399	—	2	2	no	—
162	#392	—	2	2	no	—
163	#376	C₂×D₁₉	1	1	yes	characteristic
164	D₄⋊C₈	—	38	4	no	—
165	C₂×C₁₉	—	2	2	no	—
166	C₂×C₁₉	—	8	4	no	—
167	C₂×C₁₉	#2010	1	2	yes	—
168	C₂×C₁₉	#2011	1	1	yes	characteristic
169	D₁₉	—	16	1	no	—
170	C₂×#41	—	38	1	no	—
171	C₂²×D₄	—	2	2	no	—
172	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
173	C₂³×C₄	—	2	2	no	—
174	C₂×D₈	—	38	4	no	—
175	C₂×M₁₆	—	38	1	no	—
176	C₄⋊Q₈	—	19	1	no	—
177	#127	—	19	1	no	—
178	#124	—	38	1	no	—
179	#121	—	38	2	no	—
180	C₄×D₄	—	2	2	no	—
181	C₄×D₄	—	2	2	no	—
182	C₄×D₄	—	2	2	no	—
183	C₄×D₄	—	2	2	no	—
184	C₄×D₄	—	4	4	no	—
185	C₄×D₄	—	4	4	no	—
186	C₄×D₄	—	38	2	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
189	C₂×C₂²⋊C₄	—	2	4	no	—
190	C₂×C₂²⋊C₄	—	2	2	no	—
191	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
192	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
193	#107	—	38	4	no	—
194	C₄⋊C₈	—	38	2	no	—
195	C₄⋊C₈	—	38	2	no	—
196	#104	—	76	4	no	—
197	#102	—	38	4	no	—
198	#102	—	38	4	no	—
199	C₂²⋊C₈	—	38	2	no	—
200	C₄×C₈	—	19	4	no	—
201	#95	—	2	2	no	—
202	C₁₉	#10012	1	1	yes	characteristic, complemented, Sylow
203	C₂⁴	—	2	2	no	—
204	#41	—	76	2	no	—
205	#41	—	76	2	no	—
206	C₂×Q₈	—	38	1	no	—
207	C₂×D₄	—	2	2	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	4	4	no	—
210	C₂×D₄	—	4	4	no	—
211	C₂×D₄	—	4	8	no	—
212	C₂×D₄	—	38	2	no	—
213	C₂×D₄	—	38	1	no	—
214	C₂×D₄	—	76	1	no	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	4	4	no	—
218	C₂²×C₄	—	4	4	no	—
219	C₂²×C₄	—	4	2	no	—
220	C₂²×C₄	—	4	2	no	—
221	C₂²×C₄	—	76	1	no	—
222	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
223	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
224	D₈	—	76	8	no	—
225	M₁₆	—	76	2	no	—
226	C₂×C₈	—	38	4	no	—
227	C₂×C₈	—	76	1	no	—
228	C₄⋊C₄	—	2	2	no	—
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	4	4	no	—
231	C₄⋊C₄	—	38	2	no	—
232	C₂²⋊C₄	—	4	8	no	—
233	C₂²⋊C₄	—	4	2	no	—
234	C₂²⋊C₄	—	4	2	no	—
235	C₂²⋊C₄	—	76	2	no	—
236	C₄²	—	2	2	no	—
237	C₄²	#64525	1	4	yes	complemented
238	C₄²	D₄×D₁₉	1	1	yes	characteristic
239	C₄²	D₄×D₁₉	1	2	yes	—
240	C₄²	#64543	1	1	yes	characteristic
241	C₂³	—	2	4	no	—
242	C₂³	—	4	4	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	4	4	no	—
245	C₂³	—	4	2	no	—
246	C₂³	—	76	1	no	—
247	C₂³	#10597399	1	1	yes	characteristic
248	Q₈	—	76	2	no	—
249	D₄	—	2	4	no	—
250	D₄	—	2	4	no	—
251	D₄	—	4	2	no	—
252	D₄	—	4	2	no	—
253	D₄	—	4	16	no	—
254	D₄	—	76	4	no	—
255	D₄	—	76	2	no	—
256	D₄	—	152	2	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	4	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	8	2	no	—
263	C₂×C₄	—	8	2	no	—
264	C₂×C₄	—	8	4	no	—
265	C₂×C₄	—	76	1	no	—
266	C₂×C₄	—	152	1	no	—
267	C₂×C₄	—	152	1	no	—
268	C₂×C₄	C₂×#64525	1	2	yes	—
269	C₂×C₄	#10597378	1	2	yes	—
270	C₂×C₄	#10597383	1	2	yes	—
271	C₂×C₄	#10597384	1	1	yes	characteristic
272	C₂×C₄	#10597385	1	2	yes	—
273	C₂×C₄	#10597386	1	1	yes	characteristic
274	C₈	—	76	4	no	—
275	C₈	—	152	1	no	—
276	C₂²	—	2	2	no	—
277	C₂²	—	4	8	no	—
278	C₂²	—	4	4	no	—
279	C₂²	—	8	4	no	—
280	C₂²	—	8	2	no	—
281	C₂²	—	8	2	no	—
282	C₂²	—	152	2	no	—
283	C₂²	—	152	1	no	—
284	C₂²	#11926452	1	1	yes	characteristic
285	C₂²	#11926678	1	2	yes	—
286	C₄	—	2	2	no	—
287	C₄	—	2	2	no	—
288	C₄	—	4	4	no	—
289	C₄	—	8	2	no	—
290	C₄	—	152	1	no	—
291	C₄	#11926736	1	2	yes	—
292	C₄	#11926920	1	1	yes	characteristic
293	C₄	#11926931	1	1	yes	characteristic
294	C₂	—	2	2	no	—
295	C₂	—	8	4	no	—
296	C₂	—	304	1	no	—
297	C₂	#14564700	1	2	yes	—
298	C₂	#14564706	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573635

C₂

yes

maximal, complemented

#14564467

C₂

yes

maximal, characteristic, complemented

#14562060

C₂

yes

maximal, complemented

#14561464

C₂

yes

maximal, characteristic, complemented

C₁₉×#2397

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

—

—

—

—

C₂²

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597262

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₄×D₄×C₁₉

—

C₂×C₄×D₄×C₁₉

C₂²

yes

—

C₁₉×#399

—

C₁₉×#392

—

C₁₉×#376

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

—

C₂×#64541

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

D₄

yes

characteristic, complemented

C₄×D₇₆

—

#10597315

D₄

yes

characteristic, complemented

C₁₉×#95

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

#10597266

—

#10597264

—

#10597262

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

complemented

C₂⁴×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

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

#64525

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10012

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

C₂²×D₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×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

#120

yes

—

113

C₂×C₄×C₁₉

#121

yes

characteristic

114

C₂×C₄×C₁₉

#121

yes

—

115

C₂×C₄×C₁₉

#127

yes

characteristic

116

C₂×C₄×C₁₉

C₂×D₈

yes

—

117

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

118

C₂²⋊D₁₉

—

119

C₂×Dic₁₉

—

120

D₇₆

—

121

D₇₆

—

122

C₄×D₁₉

—

123

C₄×D₁₉

—

124

Dic₃₈

—

125

C₁₉⋊C₈

—

126

C₁₉⋊C₈

—

127

#3100

—

128

#2397

D₁₉

yes

characteristic, complemented

129

#1963

—

130

#1486

—

131

#1274

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

#392

yes

characteristic

139

C₂²×C₁₉

#447

yes

—

140

C₂×D₁₉

—

141

C₂×D₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

#459

yes

—

147

C₄×C₁₉

#493

yes

characteristic

148

C₄×C₁₉

#496

yes

characteristic

149

Dic₁₉

—

150

#532

—

151

C₂×C₄×D₄

—

152

C₂×C₄×D₄

C₂×D₁₉

yes

—

153

#480

—

154

#474

—

155

#459

—

156

#447

—

157

C₄×D₈

—

158

#431

—

159

#423

—

160

C₂×#104

—

161

#399

—

162

#392

—

163

#376

C₂×D₁₉

yes

characteristic

164

D₄⋊C₈

—

165

C₂×C₁₉

—

166

C₂×C₁₉

—

167

C₂×C₁₉

#2010

yes

—

168

C₂×C₁₉

#2011

yes

characteristic

169

D₁₉

—

170

C₂×#41

—

171

C₂²×D₄

—

172

C₂²×D₄

C₂²⋊D₁₉

yes

—

173

C₂³×C₄

—

174

C₂×D₈

—

175

C₂×M₁₆

—

176

C₄⋊Q₈

—

177

#127

—

178

#124

—

179

#121

—

180

C₄×D₄

—

181

C₄×D₄

—

182

C₄×D₄

—

183

C₄×D₄

—

184

C₄×D₄

—

185

C₄×D₄

—

186

C₄×D₄

—

187

C₂×C₄⋊C₄

—

188

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

189

C₂×C₂²⋊C₄

—

190

C₂×C₂²⋊C₄

—

191

C₂×C₄²

C₂²⋊D₁₉

yes

—

192

C₂×C₄²

C₂²×D₁₉

yes

characteristic

193

#107

—

194

C₄⋊C₈

—

195

C₄⋊C₈

—

196

#104

—

197

#102

—

198

#102

—

199

C₂²⋊C₈

—

200

C₄×C₈

—

201

#95

—

202

C₁₉

#10012

yes

characteristic, complemented, Sylow

203

C₂⁴

—

204

#41

—

205

#41

—

206

C₂×Q₈

—

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

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

223

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

224

D₈

—

225

M₁₆

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₂²⋊C₄

—

233

C₂²⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₄²

—

237

C₄²

#64525

yes

complemented

238

C₄²

D₄×D₁₉

yes

characteristic

239

C₄²

D₄×D₁₉

yes

—

240

C₄²

#64543

yes

characteristic

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

#10597399

yes

characteristic

248

Q₈

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

254

D₄

—

255

D₄

—

256

D₄

—

152

—

257

C₂×C₄

—

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

—

152

—

267

C₂×C₄

—

152

—

268

C₂×C₄

C₂×#64525

yes

—

269

C₂×C₄

#10597378

yes

—

270

C₂×C₄

#10597383

yes

—

271

C₂×C₄

#10597384

yes

characteristic

272

C₂×C₄

#10597385

yes

—

273

C₂×C₄

#10597386

yes

characteristic

274

C₈

—

275

C₈

—

152

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

152

—

283

C₂²

—

152

—

284

C₂²

#11926452

yes

characteristic

285

C₂²

#11926678

yes

—

286

C₄

—

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

152

—

291

C₄

#11926736

yes

—

292

C₄

#11926920

yes

characteristic

293

C₄

#11926931

yes

characteristic

294

C₂

—

295

C₂

—

296

C₂

—

304

—

297

C₂

#14564700

yes

—

298

C₂

#14564706

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2397	C₂
socle	C₂²×C₁₉	#392
hypercenter	#2397	D₁₉
hypocenter	C₁₉	#10012
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2397

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2397

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2397

N	H ≅ G/N	type
1. #14573635	C₂	semidirect
2. #14564467	C₂	semidirect
3. #14562060	C₂	semidirect
4. #14561464	C₂	semidirect
5. C₁₉×#2397	C₂	semidirect
41. #10597320	D₄	semidirect
43. #10597315	D₄	semidirect
52. C₄×C₁₉⋊C₈	D₄	semidirect
81. C₄²×C₁₉	D₈	semidirect
128. #2397	D₁₉	semidirect
202. C₁₉	#10012	semidirect
237. C₄²	#64525	semidirect

H ≅ G/N

type

1. #14573635

C₂

semidirect

2. #14564467

C₂

semidirect

3. #14562060

C₂

semidirect

4. #14561464

C₂

semidirect

5. C₁₉×#2397

C₂

semidirect

41. #10597320

D₄

semidirect

43. #10597315

D₄

semidirect

52. C₄×C₁₉⋊C₈

D₄

semidirect

81. C₄²×C₁₉

D₈

semidirect

128. #2397

D₁₉

semidirect

202. C₁₉

#10012

semidirect

237. C₄²

#64525

semidirect

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

subgroup	index
#14573635	2
#14564467	2
#14562060	2
#14561464	2
C₁₉×#2397	2
#10012	19

subgroup

index

C₁₉×#2397

Subgroups — #18083380

Conjugacy classes of subgroups

Complements

Maximal subgroups