Subgroups — C₁₃₉×#29339 #48023935

Order 35584.

796 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2101×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2042×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1936×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1935×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1875×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#1875×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#1873×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#1873×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1749×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
25	#391×C₁₃₉	C₂²	1	1	yes	characteristic
26	#390×C₁₃₉	C₂²	1	1	yes	characteristic
27	#389×C₁₃₉	C₂²	1	2	yes	—
28	#389×C₁₃₉	C₂²	1	2	yes	—
29	#388×C₁₃₉	—	2	2	no	—
30	#386×C₁₃₉	—	2	2	no	—
31	#385×C₁₃₉	—	2	2	no	—
32	#382×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₃₉	—	2	2	no	—
34	#340×C₁₃₉	C₂²	1	2	yes	—
35	#340×C₁₃₉	C₂²	1	2	yes	—
36	#340×C₁₃₉	C₂²	1	2	yes	—
37	#340×C₁₃₉	C₂²	1	2	yes	—
38	#336×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃₉	—	2	1	no	—
41	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
46	#124×C₁₃₉	—	4	2	no	—
47	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
48	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
49	#121×C₁₃₉	—	2	2	no	—
50	#121×C₁₃₉	—	2	2	no	—
51	#117×C₁₃₉	—	2	4	no	—
52	#117×C₁₃₉	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
66	C₂×C₄²×C₁₃₉	—	2	1	no	—
67	C₂×C₄²×C₁₃₉	—	2	1	no	—
68	C₂×C₄²×C₁₃₉	—	4	2	no	—
69	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
72	#103×C₁₃₉	—	2	4	no	—
73	#103×C₁₃₉	—	4	2	no	—
74	#102×C₁₃₉	—	2	4	no	—
75	#102×C₁₃₉	—	4	2	no	—
76	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
77	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
78	#97×C₁₃₉	—	4	2	no	—
79	#95×C₁₃₉	—	2	2	no	—
80	#95×C₁₃₉	—	2	2	no	—
81	#95×C₁₃₉	—	2	2	no	—
82	#95×C₁₃₉	—	2	2	no	—
83	C₂⁴×C₁₃₉	—	2	1	no	—
84	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₃₉	—	2	2	no	—
86	C₂×Q₈×C₁₃₉	—	2	1	no	—
87	C₂×Q₈×C₁₃₉	—	2	1	no	—
88	C₂×Q₈×C₁₃₉	—	2	2	no	—
89	C₂×D₄×C₁₃₉	—	2	2	no	—
90	C₂×D₄×C₁₃₉	—	2	1	no	—
91	C₂×D₄×C₁₃₉	—	2	1	no	—
92	C₂×D₄×C₁₃₉	—	2	2	no	—
93	C₂×D₄×C₁₃₉	—	4	4	no	—
94	C₂×D₄×C₁₃₉	—	4	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	1	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	1	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	4	2	no	—
103	C₂²×C₄×C₁₃₉	—	4	2	no	—
104	C₂²×C₄×C₁₃₉	—	4	2	no	—
105	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
109	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₁₃₉	—	2	2	no	—
112	C₂×C₈×C₁₃₉	—	2	2	no	—
113	C₂×C₈×C₁₃₉	—	2	2	no	—
114	C₂×C₈×C₁₃₉	—	2	2	no	—
115	C₂×C₈×C₁₃₉	—	2	2	no	—
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	2	1	no	—
119	C₄⋊C₄×C₁₃₉	—	2	1	no	—
120	C₄⋊C₄×C₁₃₉	—	2	1	no	—
121	C₄⋊C₄×C₁₃₉	—	2	1	no	—
122	C₄⋊C₄×C₁₃₉	—	2	2	no	—
123	C₄⋊C₄×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	4	4	no	—
125	C₄⋊C₄×C₁₃₉	—	4	4	no	—
126	C₄⋊C₄×C₁₃₉	—	4	2	no	—
127	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
128	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
130	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
131	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
134	C₄²×C₁₃₉	—	2	4	no	—
135	C₄²×C₁₃₉	—	2	2	no	—
136	C₄²×C₁₃₉	—	2	2	no	—
137	C₄²×C₁₃₉	—	4	2	no	—
138	C₄²×C₁₃₉	—	4	2	no	—
139	C₂³×C₁₃₉	—	2	1	no	—
140	C₂³×C₁₃₉	—	2	1	no	—
141	C₂³×C₁₃₉	—	2	2	no	—
142	C₂³×C₁₃₉	—	2	2	no	—
143	C₂³×C₁₃₉	—	4	1	no	—
144	C₂³×C₁₃₉	—	4	1	no	—
145	C₂³×C₁₃₉	—	4	1	no	—
146	C₂³×C₁₃₉	—	4	2	no	—
147	C₂³×C₁₃₉	—	4	2	no	—
148	C₂³×C₁₃₉	#124	1	2	yes	—
149	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₃₉	—	4	2	no	—
151	Q₈×C₁₃₉	—	4	2	no	—
152	D₄×C₁₃₉	—	4	2	no	—
153	D₄×C₁₃₉	—	4	2	no	—
154	D₄×C₁₃₉	—	8	4	no	—
155	C₂×C₄×C₁₃₉	—	2	1	no	—
156	C₂×C₄×C₁₃₉	—	2	1	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	2	no	—
161	C₂×C₄×C₁₃₉	—	2	2	no	—
162	C₂×C₄×C₁₃₉	—	2	2	no	—
163	C₂×C₄×C₁₃₉	—	2	2	no	—
164	C₂×C₄×C₁₃₉	—	2	2	no	—
165	C₂×C₄×C₁₃₉	—	2	2	no	—
166	C₂×C₄×C₁₃₉	—	4	8	no	—
167	C₂×C₄×C₁₃₉	—	4	2	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	—	4	1	no	—
170	C₂×C₄×C₁₃₉	—	4	1	no	—
171	C₂×C₄×C₁₃₉	—	4	1	no	—
172	C₂×C₄×C₁₃₉	—	4	1	no	—
173	C₂×C₄×C₁₃₉	—	4	2	no	—
174	C₂×C₄×C₁₃₉	—	4	1	no	—
175	C₂×C₄×C₁₃₉	—	4	2	no	—
176	C₂×C₄×C₁₃₉	—	4	2	no	—
177	C₂×C₄×C₁₃₉	—	4	2	no	—
178	C₂×C₄×C₁₃₉	—	4	2	no	—
179	C₂×C₄×C₁₃₉	#124	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₁₃₉	—	4	2	no	—
185	C₈×C₁₃₉	—	4	2	no	—
186	C₂²×C₁₃₉	—	2	2	no	—
187	C₂²×C₁₃₉	—	2	2	no	—
188	C₂²×C₁₃₉	—	2	2	no	—
189	C₂²×C₁₃₉	—	4	2	no	—
190	C₂²×C₁₃₉	—	4	2	no	—
191	C₂²×C₁₃₉	—	8	1	no	—
192	C₂²×C₁₃₉	—	8	2	no	—
193	C₂²×C₁₃₉	—	8	1	no	—
194	C₂²×C₁₃₉	—	8	1	no	—
195	C₂²×C₁₃₉	—	8	2	no	—
196	C₂²×C₁₃₉	#525	1	1	yes	characteristic
197	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
198	C₂²×C₁₃₉	#534	1	1	yes	characteristic
199	C₂²×C₁₃₉	#575	1	2	yes	—
200	C₂²×C₁₃₉	#575	1	2	yes	—
201	C₄×C₁₃₉	—	2	2	no	—
202	C₄×C₁₃₉	—	4	4	no	—
203	C₄×C₁₃₉	—	4	2	no	—
204	C₄×C₁₃₉	—	4	2	no	—
205	C₄×C₁₃₉	—	8	1	no	—
206	C₄×C₁₃₉	—	8	1	no	—
207	C₄×C₁₃₉	—	8	1	no	—
208	C₄×C₁₃₉	—	8	2	no	—
209	C₄×C₁₃₉	#553	1	2	yes	—
210	C₄×C₁₃₉	#553	1	2	yes	—
211	C₂×C₁₃₉	—	4	2	no	—
212	C₂×C₁₃₉	—	16	1	no	—
213	C₂×C₁₃₉	#2591	1	1	yes	characteristic
214	C₂×C₁₃₉	#3111	1	2	yes	—
215	C₂×C₁₃₉	#3135	1	1	yes	characteristic
216	C₂×C₁₃₉	#3140	1	1	yes	characteristic
217	C₂×C₁₃₉	#3197	1	2	yes	—
218	#29339	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₁₃₉	#29339	1	1	yes	characteristic, direct product factor, Sylow
220	#2850	C₂×C₁₃₉	1	1	yes	characteristic
221	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
222	#2101	C₂×C₁₃₉	1	2	yes	complemented
223	#2042	C₂×C₁₃₉	1	2	yes	complemented
224	#1936	C₂×C₁₃₉	1	2	yes	complemented
225	#1935	C₂×C₁₃₉	1	2	yes	complemented
226	#1875	C₂×C₁₃₉	1	1	yes	characteristic
227	#1875	C₂×C₁₃₉	1	1	yes	characteristic
228	#1873	C₂×C₁₃₉	1	1	yes	characteristic, complemented
229	#1873	C₂×C₁₃₉	1	1	yes	characteristic, complemented
230	#1749	C₂×C₁₃₉	1	1	yes	characteristic, complemented
231	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
233	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
234	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
235	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
236	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
237	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
238	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
239	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
240	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
243	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
244	#391	C₂²×C₁₃₉	1	1	yes	characteristic
245	#390	C₂²×C₁₃₉	1	1	yes	characteristic
246	#389	C₂²×C₁₃₉	1	2	yes	—
247	#389	C₂²×C₁₃₉	1	2	yes	—
248	#388	—	2	2	no	—
249	#386	—	2	2	no	—
250	#385	—	2	2	no	—
251	#382	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₄×C₄⋊C₄	—	2	2	no	—
253	#340	C₂²×C₁₃₉	1	2	yes	—
254	#340	C₂²×C₁₃₉	1	2	yes	—
255	#340	C₂²×C₁₃₉	1	2	yes	—
256	#340	C₂²×C₁₃₉	1	2	yes	—
257	#336	C₂²×C₁₃₉	1	2	yes	—
258	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
262	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
264	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
265	#124	—	4	2	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	#121	—	2	2	no	—
269	#121	—	2	2	no	—
270	#117	—	2	4	no	—
271	#117	—	4	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	4	2	no	—
288	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
291	#103	—	2	4	no	—
292	#103	—	4	2	no	—
293	#102	—	2	4	no	—
294	#102	—	4	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	#97	—	4	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
327	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
328	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	4	2	no	—
357	C₄²	—	4	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	#124×C₁₃₉	1	2	yes	—
368	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	4	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	#124×C₁₃₉	1	2	yes	—
399	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
400	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	#525×C₁₃₉	1	1	yes	characteristic
416	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
417	C₂²	#534×C₁₃₉	1	1	yes	characteristic
418	C₂²	#575×C₁₃₉	1	2	yes	—
419	C₂²	#575×C₁₃₉	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	#553×C₁₃₉	1	2	yes	—
429	C₄	#553×C₁₃₉	1	2	yes	—
430	C₂	—	4	2	no	—
431	C₂	—	16	1	no	—
432	C₂	#2591×C₁₃₉	1	1	yes	characteristic
433	C₂	#3111×C₁₃₉	1	2	yes	—
434	C₂	#3135×C₁₃₉	1	1	yes	characteristic
435	C₂	#3140×C₁₃₉	1	1	yes	characteristic
436	C₂	#3197×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#121×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2296×C₁₃₉	C₂	semidirect
3. #2101×C₁₃₉	C₂	semidirect
4. #2042×C₁₃₉	C₂	semidirect
5. #1936×C₁₃₉	C₂	semidirect
6. #1935×C₁₃₉	C₂	semidirect
9. #1873×C₁₃₉	C₂	semidirect
10. #1873×C₁₃₉	C₂	semidirect
11. #1749×C₁₃₉	C₂	semidirect
218. #29339	C₁₃₉	direct (N × H)
219. C₁₃₉	#29339	direct (N × H)
221. #2296	C₂×C₁₃₉	semidirect
222. #2101	C₂×C₁₃₉	semidirect
223. #2042	C₂×C₁₃₉	semidirect
224. #1936	C₂×C₁₃₉	semidirect
225. #1935	C₂×C₁₃₉	semidirect
228. #1873	C₂×C₁₃₉	semidirect
229. #1873	C₂×C₁₃₉	semidirect
230. #1749	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2850×C₁₃₉	2
#2296×C₁₃₉	2
#2101×C₁₃₉	2
#2042×C₁₃₉	2
#1936×C₁₃₉	2
#1935×C₁₃₉	2
#1875×C₁₃₉	2
#1873×C₁₃₉	2
#1749×C₁₃₉	2
#29339	139

Subgroups — C139×#29339 #48023935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29339 #48023935