Subgroups — C₁₃₉×#29265 #48023861

Order 35584.

790 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2330×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2328×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2094×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2093×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2025×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2025×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1982×C₁₃₉	C₂	1	2	yes	maximal
8	#1949×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1864×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1862×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#1832×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
23	#390×C₁₃₉	C₂²	1	1	yes	characteristic
24	#390×C₁₃₉	C₂²	1	1	yes	characteristic
25	#389×C₁₃₉	—	2	2	no	—
26	#389×C₁₃₉	C₂²	1	2	yes	—
27	#387×C₁₃₉	—	2	2	no	—
28	#386×C₁₃₉	—	2	2	no	—
29	#386×C₁₃₉	—	2	2	no	—
30	#384×C₁₃₉	C₂²	1	1	yes	characteristic
31	#382×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	#376×C₁₃₉	C₂²	1	1	yes	characteristic
34	#340×C₁₃₉	C₂²	1	2	yes	—
35	#340×C₁₃₉	C₂²	1	2	yes	—
36	#336×C₁₃₉	C₂²	1	1	yes	characteristic
37	#336×C₁₃₉	C₂²	1	1	yes	characteristic
38	#336×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₃₉	—	2	2	no	—
40	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₉	—	2	1	no	—
43	C₂³×C₄×C₁₃₉	—	2	1	no	—
44	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
46	#127×C₁₃₉	—	2	2	no	—
47	#127×C₁₃₉	Q₈	1	4	yes	—
48	#125×C₁₃₉	—	2	4	no	—
49	C₄×D₄×C₁₃₉	—	4	2	no	—
50	C₄×D₄×C₁₃₉	—	4	2	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₄²×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
66	#107×C₁₃₉	—	4	2	no	—
67	#106×C₁₃₉	—	4	2	no	—
68	C₄⋊C₈×C₁₃₉	—	2	4	no	—
69	#102×C₁₃₉	—	2	4	no	—
70	#102×C₁₃₉	—	2	4	no	—
71	#102×C₁₃₉	—	4	2	no	—
72	#102×C₁₃₉	—	4	2	no	—
73	#95×C₁₃₉	—	2	2	no	—
74	#95×C₁₃₉	—	2	2	no	—
75	#95×C₁₃₉	—	2	2	no	—
76	#95×C₁₃₉	D₄	1	2	yes	—
77	#95×C₁₃₉	D₄	1	2	yes	—
78	C₂⁴×C₁₃₉	—	2	1	no	—
79	C₂⁴×C₁₃₉	—	2	1	no	—
80	C₂×D₄×C₁₃₉	—	2	8	no	—
81	C₂×D₄×C₁₃₉	—	2	2	no	—
82	C₂×D₄×C₁₃₉	—	2	2	no	—
83	C₂×D₄×C₁₃₉	—	2	1	no	—
84	C₂×D₄×C₁₃₉	—	2	1	no	—
85	C₂×D₄×C₁₃₉	—	2	2	no	—
86	C₂×D₄×C₁₃₉	—	2	2	no	—
87	C₂×D₄×C₁₃₉	—	8	2	no	—
88	C₂×D₄×C₁₃₉	—	8	2	no	—
89	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
90	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	2	2	no	—
93	C₂²×C₄×C₁₃₉	—	2	1	no	—
94	C₂²×C₄×C₁₃₉	—	2	1	no	—
95	C₂²×C₄×C₁₃₉	—	4	2	no	—
96	C₂²×C₄×C₁₃₉	—	4	2	no	—
97	C₂²×C₄×C₁₃₉	—	8	2	no	—
98	C₂²×C₄×C₁₃₉	—	8	2	no	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₁₃₉	—	2	2	no	—
105	C₂×C₈×C₁₃₉	—	2	2	no	—
106	C₂×C₈×C₁₃₉	—	2	2	no	—
107	C₂×C₈×C₁₃₉	—	2	2	no	—
108	C₂×C₈×C₁₃₉	—	2	2	no	—
109	C₂×C₈×C₁₃₉	—	2	2	no	—
110	C₄⋊C₄×C₁₃₉	—	2	8	no	—
111	C₄⋊C₄×C₁₃₉	—	2	2	no	—
112	C₄⋊C₄×C₁₃₉	—	2	2	no	—
113	C₄⋊C₄×C₁₃₉	—	2	2	no	—
114	C₄⋊C₄×C₁₃₉	—	2	2	no	—
115	C₄⋊C₄×C₁₃₉	—	2	2	no	—
116	C₄⋊C₄×C₁₃₉	—	8	2	no	—
117	C₄⋊C₄×C₁₃₉	—	8	2	no	—
118	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
119	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
121	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
122	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
123	C₄²×C₁₃₉	—	2	2	no	—
124	C₄²×C₁₃₉	—	2	2	no	—
125	C₄²×C₁₃₉	—	8	2	no	—
126	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
127	C₄²×C₁₃₉	#41	1	2	yes	—
128	C₂³×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	—	2	2	no	—
130	C₂³×C₁₃₉	—	4	1	no	—
131	C₂³×C₁₃₉	—	4	1	no	—
132	C₂³×C₁₃₉	—	4	1	no	—
133	C₂³×C₁₃₉	—	4	1	no	—
134	C₂³×C₁₃₉	—	4	2	no	—
135	C₂³×C₁₃₉	—	4	2	no	—
136	C₂³×C₁₃₉	—	4	2	no	—
137	C₂³×C₁₃₉	—	4	2	no	—
138	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
139	D₄×C₁₃₉	—	2	4	no	—
140	D₄×C₁₃₉	—	2	4	no	—
141	D₄×C₁₃₉	—	4	2	no	—
142	D₄×C₁₃₉	—	4	2	no	—
143	D₄×C₁₃₉	—	8	8	no	—
144	C₂×C₄×C₁₃₉	—	2	2	no	—
145	C₂×C₄×C₁₃₉	—	2	2	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	4	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	2	2	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	1	no	—
157	C₂×C₄×C₁₃₉	—	4	1	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	—	4	2	no	—
161	C₂×C₄×C₁₃₉	—	4	2	no	—
162	C₂×C₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	—	8	4	no	—
164	C₂×C₄×C₁₃₉	—	8	4	no	—
165	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
168	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
170	C₈×C₁₃₉	—	4	2	no	—
171	C₈×C₁₃₉	—	4	2	no	—
172	C₂²×C₁₃₉	—	4	4	no	—
173	C₂²×C₁₃₉	—	4	4	no	—
174	C₂²×C₁₃₉	—	4	2	no	—
175	C₂²×C₁₃₉	—	4	2	no	—
176	C₂²×C₁₃₉	—	8	2	no	—
177	C₂²×C₁₃₉	—	8	2	no	—
178	C₂²×C₁₃₉	—	8	1	no	—
179	C₂²×C₁₃₉	—	8	1	no	—
180	C₂²×C₁₃₉	—	8	1	no	—
181	C₂²×C₁₃₉	—	8	1	no	—
182	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₁₃₉	#525	1	1	yes	characteristic
184	C₂²×C₁₃₉	#535	1	1	yes	characteristic
185	C₂²×C₁₃₉	#576	1	2	yes	—
186	C₂²×C₁₃₉	#577	1	2	yes	—
187	C₄×C₁₃₉	—	2	4	no	—
188	C₄×C₁₃₉	—	4	2	no	—
189	C₄×C₁₃₉	—	4	4	no	—
190	C₄×C₁₃₉	—	4	1	no	—
191	C₄×C₁₃₉	—	4	1	no	—
192	C₄×C₁₃₉	—	8	2	no	—
193	C₄×C₁₃₉	—	8	1	no	—
194	C₄×C₁₃₉	—	8	1	no	—
195	C₄×C₁₃₉	#554	1	2	yes	—
196	C₄×C₁₃₉	#559	1	2	yes	—
197	C₂×C₁₃₉	—	8	2	no	—
198	C₂×C₁₃₉	—	8	2	no	—
199	C₂×C₁₃₉	#2580	1	1	yes	characteristic
200	C₂×C₁₃₉	#3081	1	2	yes	—
201	C₂×C₁₃₉	#3119	1	2	yes	—
202	C₂×C₁₃₉	#3220	1	1	yes	characteristic
203	C₂×C₁₃₉	#3222	1	1	yes	characteristic
204	#29265	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#29265	1	1	yes	characteristic, direct product factor, Sylow
206	#2330	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	#2328	C₂×C₁₃₉	1	1	yes	characteristic
208	#2094	C₂×C₁₃₉	1	1	yes	characteristic, complemented
209	#2093	C₂×C₁₃₉	1	1	yes	characteristic, complemented
210	#2025	C₂×C₁₃₉	1	1	yes	characteristic, complemented
211	#2025	C₂×C₁₃₉	1	1	yes	characteristic, complemented
212	#1982	C₂×C₁₃₉	1	2	yes	—
213	#1949	C₂×C₁₃₉	1	2	yes	complemented
214	#1864	C₂×C₁₃₉	1	2	yes	complemented
215	#1862	C₂×C₁₃₉	1	2	yes	complemented
216	#1832	C₂×C₁₃₉	1	1	yes	characteristic, complemented
217	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
218	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
221	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
222	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
224	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
225	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
226	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
227	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
228	#390	C₂²×C₁₃₉	1	1	yes	characteristic
229	#390	C₂²×C₁₃₉	1	1	yes	characteristic
230	#389	—	2	2	no	—
231	#389	C₂²×C₁₃₉	1	2	yes	—
232	#387	—	2	2	no	—
233	#386	—	2	2	no	—
234	#386	—	2	2	no	—
235	#384	C₂²×C₁₃₉	1	1	yes	characteristic
236	#382	C₂²×C₁₃₉	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
238	#376	C₂²×C₁₃₉	1	1	yes	characteristic
239	#340	C₂²×C₁₃₉	1	2	yes	—
240	#340	C₂²×C₁₃₉	1	2	yes	—
241	#336	C₂²×C₁₃₉	1	1	yes	characteristic
242	#336	C₂²×C₁₃₉	1	1	yes	characteristic
243	#336	C₂²×C₁₃₉	1	2	yes	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
246	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	—	2	1	no	—
249	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
251	#127	—	2	2	no	—
252	#127	Q₈×C₁₃₉	1	4	yes	—
253	#125	—	2	4	no	—
254	C₄×D₄	—	4	2	no	—
255	C₄×D₄	—	4	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
271	#107	—	4	2	no	—
272	#106	—	4	2	no	—
273	C₄⋊C₈	—	2	4	no	—
274	#102	—	2	4	no	—
275	#102	—	2	4	no	—
276	#102	—	4	2	no	—
277	#102	—	4	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	D₄×C₁₃₉	1	2	yes	—
282	#95	D₄×C₁₃₉	1	2	yes	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	—	2	1	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	8	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
295	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	8	2	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	8	2	no	—
331	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
332	C₄²	#41×C₁₃₉	1	2	yes	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
344	D₄	—	2	4	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	8	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
371	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
373	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
388	C₂²	#525×C₁₃₉	1	1	yes	characteristic
389	C₂²	#535×C₁₃₉	1	1	yes	characteristic
390	C₂²	#576×C₁₃₉	1	2	yes	—
391	C₂²	#577×C₁₃₉	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	1	no	—
400	C₄	#554×C₁₃₉	1	2	yes	—
401	C₄	#559×C₁₃₉	1	2	yes	—
402	C₂	—	8	2	no	—
403	C₂	—	8	2	no	—
404	C₂	#2580×C₁₃₉	1	1	yes	characteristic
405	C₂	#3081×C₁₃₉	1	2	yes	—
406	C₂	#3119×C₁₃₉	1	2	yes	—
407	C₂	#3220×C₁₃₉	1	1	yes	characteristic
408	C₂	#3222×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ #376×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2330×C₁₃₉	C₂	semidirect
3. #2094×C₁₃₉	C₂	semidirect
4. #2093×C₁₃₉	C₂	semidirect
5. #2025×C₁₃₉	C₂	semidirect
6. #2025×C₁₃₉	C₂	semidirect
8. #1949×C₁₃₉	C₂	semidirect
9. #1864×C₁₃₉	C₂	semidirect
10. #1862×C₁₃₉	C₂	semidirect
11. #1832×C₁₃₉	C₂	semidirect
204. #29265	C₁₃₉	direct (N × H)
205. C₁₃₉	#29265	direct (N × H)
206. #2330	C₂×C₁₃₉	semidirect
208. #2094	C₂×C₁₃₉	semidirect
209. #2093	C₂×C₁₃₉	semidirect
210. #2025	C₂×C₁₃₉	semidirect
211. #2025	C₂×C₁₃₉	semidirect
213. #1949	C₂×C₁₃₉	semidirect
214. #1864	C₂×C₁₃₉	semidirect
215. #1862	C₂×C₁₃₉	semidirect
216. #1832	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2330×C₁₃₉	2
#2328×C₁₃₉	2
#2094×C₁₃₉	2
#2093×C₁₃₉	2
#2025×C₁₃₉	2
#1982×C₁₃₉	2
#1949×C₁₃₉	2
#1864×C₁₃₉	2
#1862×C₁₃₉	2
#1832×C₁₃₉	2
#29265	139

Subgroups — C139×#29265 #48023861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29265 #48023861