Subgroups — C₁₃₉×#14467 #48009063

Order 35584.

1398 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#391×C₁₃₉	C₂	1	2	yes	maximal
2	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#1444×C₁₃₉	C₂	1	4	yes	maximal
4	#1441×C₁₃₉	C₂	1	2	yes	maximal
5	#1436×C₁₃₉	C₂	1	4	yes	maximal
6	C₄⋊#95×C₁₃₉	C₂	1	2	yes	maximal
7	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
15	#391×C₁₃₉	—	2	8	no	—
16	#391×C₁₃₉	C₄	1	8	yes	complemented
17	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₃₉	—	4	1	no	—
24	C₂²×Q₈×C₁₃₉	—	4	1	no	—
25	C₂²×Q₈×C₁₃₉	—	4	1	no	—
26	C₂²×Q₈×C₁₃₉	—	4	1	no	—
27	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₁₃₉	D₄	1	4	yes	—
29	C₂²×Q₈×C₁₃₉	Q₈	1	4	yes	—
30	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
31	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
39	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	8	yes	complemented
50	C₂×C₄²×C₁₃₉	—	2	4	no	—
51	C₂×C₄²×C₁₃₉	—	4	1	no	—
52	C₂×C₄²×C₁₃₉	—	4	1	no	—
53	C₂×C₄²×C₁₃₉	—	4	2	no	—
54	C₂×C₄²×C₁₃₉	—	4	2	no	—
55	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
56	#95×C₁₃₉	—	2	8	no	—
57	#95×C₁₃₉	—	2	8	no	—
58	#95×C₁₃₉	—	2	8	no	—
59	#95×C₁₃₉	—	4	2	no	—
60	#95×C₁₃₉	—	4	4	no	—
61	#95×C₁₃₉	C₂×C₄	1	16	yes	—
62	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
63	C₂×Q₈×C₁₃₉	—	4	4	no	—
64	C₂×Q₈×C₁₃₉	—	4	4	no	—
65	C₂×Q₈×C₁₃₉	—	4	4	no	—
66	C₂×Q₈×C₁₃₉	—	4	4	no	—
67	C₂×Q₈×C₁₃₉	—	4	4	no	—
68	C₂×Q₈×C₁₃₉	—	4	4	no	—
69	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	16	yes	complemented
70	C₂²×C₄×C₁₃₉	—	2	2	no	—
71	C₂²×C₄×C₁₃₉	—	2	2	no	—
72	C₂²×C₄×C₁₃₉	—	2	1	no	—
73	C₂²×C₄×C₁₃₉	—	2	1	no	—
74	C₂²×C₄×C₁₃₉	—	2	2	no	—
75	C₂²×C₄×C₁₃₉	—	2	2	no	—
76	C₂²×C₄×C₁₃₉	—	2	2	no	—
77	C₂²×C₄×C₁₃₉	—	2	1	no	—
78	C₂²×C₄×C₁₃₉	—	2	1	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	4	no	—
83	C₂²×C₄×C₁₃₉	—	2	4	no	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	2	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	4	no	—
91	C₂²×C₄×C₁₃₉	—	2	4	no	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	4	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	4	no	—
96	C₂²×C₄×C₁₃₉	—	2	4	no	—
97	C₂²×C₄×C₁₃₉	—	2	4	no	—
98	C₂²×C₄×C₁₃₉	—	2	4	no	—
99	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
106	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
110	C₄⋊C₄×C₁₃₉	—	4	4	no	—
111	C₄⋊C₄×C₁₃₉	—	4	8	no	—
112	C₄⋊C₄×C₁₃₉	—	4	8	no	—
113	C₄⋊C₄×C₁₃₉	—	4	8	no	—
114	C₄⋊C₄×C₁₃₉	—	4	8	no	—
115	C₄²×C₁₃₉	—	4	4	no	—
116	C₄²×C₁₃₉	—	4	8	no	—
117	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
118	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
119	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
120	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
121	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
122	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
123	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
124	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
125	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
126	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
127	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
128	Q₈×C₁₃₉	—	4	16	no	—
129	C₂×C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄×C₁₃₉	—	2	2	no	—
131	C₂×C₄×C₁₃₉	—	2	2	no	—
132	C₂×C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	4	no	—
140	C₂×C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄×C₁₃₉	—	2	2	no	—
143	C₂×C₄×C₁₃₉	—	2	4	no	—
144	C₂×C₄×C₁₃₉	—	2	2	no	—
145	C₂×C₄×C₁₃₉	—	2	4	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	4	no	—
148	C₂×C₄×C₁₃₉	—	2	8	no	—
149	C₂×C₄×C₁₃₉	—	2	8	no	—
150	C₂×C₄×C₁₃₉	—	2	8	no	—
151	C₂×C₄×C₁₃₉	—	2	8	no	—
152	C₂×C₄×C₁₃₉	—	4	4	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	4	4	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	4	no	—
157	C₂×C₄×C₁₃₉	—	4	4	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	4	no	—
160	C₂×C₄×C₁₃₉	—	4	4	no	—
161	C₂×C₄×C₁₃₉	—	4	4	no	—
162	C₂×C₄×C₁₃₉	—	4	4	no	—
163	C₂×C₄×C₁₃₉	—	4	4	no	—
164	C₂×C₄×C₁₃₉	—	4	4	no	—
165	C₂×C₄×C₁₃₉	—	4	4	no	—
166	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	8	yes	—
167	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
168	C₂×C₄×C₁₃₉	C₄×Q₈	1	8	yes	—
169	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₁₃₉	C₂×C₄×Q₈	1	2	yes	—
171	C₂²×C₁₃₉	#518	1	1	yes	characteristic
172	C₂²×C₁₃₉	#518	1	1	yes	characteristic
173	C₂²×C₁₃₉	#520	1	2	yes	—
174	C₂²×C₁₃₉	#534	1	1	yes	characteristic
175	C₂²×C₁₃₉	#534	1	1	yes	characteristic
176	C₂²×C₁₃₉	#538	1	2	yes	—
177	C₂²×C₁₃₉	#539	1	2	yes	—
178	C₂²×C₁₃₉	#543	1	1	yes	characteristic
179	C₂²×C₁₃₉	#543	1	1	yes	characteristic
180	C₂²×C₁₃₉	#543	1	2	yes	—
181	C₂²×C₁₃₉	#544	1	2	yes	—
182	C₂²×C₁₃₉	D₄×Q₈	1	2	yes	—
183	C₂²×C₁₃₉	#550	1	2	yes	—
184	C₂²×C₁₃₉	#554	1	2	yes	—
185	C₂²×C₁₃₉	#555	1	1	yes	characteristic
186	C₂²×C₁₃₉	#557	1	2	yes	—
187	C₂²×C₁₃₉	Q₈²	1	2	yes	—
188	C₂²×C₁₃₉	Q₈²	1	1	yes	characteristic
189	C₂²×C₁₃₉	H(3,𝔽₄)	1	1	yes	characteristic
190	C₂²×C₁₃₉	#562	1	2	yes	—
191	C₂²×C₁₃₉	#563	1	1	yes	characteristic
192	C₄×C₁₃₉	—	2	4	no	—
193	C₄×C₁₃₉	—	2	8	no	—
194	C₄×C₁₃₉	—	2	8	no	—
195	C₄×C₁₃₉	—	4	4	no	—
196	C₄×C₁₃₉	—	4	8	no	—
197	C₄×C₁₃₉	—	8	4	no	—
198	C₂×C₁₃₉	#2315	1	1	yes	characteristic
199	C₂×C₁₃₉	#2329	1	2	yes	—
200	C₂×C₁₃₉	Q₈×C₄⋊C₄	1	2	yes	—
201	C₂×C₁₃₉	#2369	1	1	yes	characteristic
202	C₂×C₁₃₉	#2379	1	1	yes	characteristic
203	C₂×C₁₃₉	#2732	1	2	yes	—
204	C₂×C₁₃₉	#2733	1	1	yes	characteristic
205	C₂×C₁₃₉	#2734	1	1	yes	characteristic
206	C₂×C₁₃₉	#2806	1	2	yes	—
207	C₂×C₁₃₉	#2809	1	1	yes	characteristic
208	C₂×C₁₃₉	#2811	1	1	yes	characteristic
209	#14467	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₁₃₉	#14467	1	1	yes	characteristic, direct product factor, Sylow
211	C₂×#391	C₂×C₁₃₉	1	2	yes	—
212	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic
213	#1444	C₂×C₁₃₉	1	4	yes	—
214	#1441	C₂×C₁₃₉	1	2	yes	—
215	#1436	C₂×C₁₃₉	1	4	yes	—
216	C₄⋊#95	C₂×C₁₃₉	1	2	yes	—
217	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
219	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
224	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
225	#391	—	2	8	no	—
226	#391	C₄×C₁₃₉	1	8	yes	complemented
227	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
228	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
229	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
230	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
231	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
232	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
233	C₂²×Q₈	—	4	1	no	—
234	C₂²×Q₈	—	4	1	no	—
235	C₂²×Q₈	—	4	1	no	—
236	C₂²×Q₈	—	4	1	no	—
237	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
238	C₂²×Q₈	D₄×C₁₃₉	1	4	yes	—
239	C₂²×Q₈	Q₈×C₁₃₉	1	4	yes	—
240	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
241	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
243	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	4	1	no	—
249	C₂×C₄⋊C₄	—	4	1	no	—
250	C₂×C₄⋊C₄	—	4	2	no	—
251	C₂×C₄⋊C₄	—	4	2	no	—
252	C₂×C₄⋊C₄	—	4	2	no	—
253	C₂×C₄⋊C₄	—	4	2	no	—
254	C₂×C₄⋊C₄	—	4	2	no	—
255	C₂×C₄⋊C₄	—	4	2	no	—
256	C₂×C₄⋊C₄	—	4	4	no	—
257	C₂×C₄⋊C₄	—	4	2	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
259	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	8	yes	complemented
260	C₂×C₄²	—	2	4	no	—
261	C₂×C₄²	—	4	1	no	—
262	C₂×C₄²	—	4	1	no	—
263	C₂×C₄²	—	4	2	no	—
264	C₂×C₄²	—	4	2	no	—
265	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
266	#95	—	2	8	no	—
267	#95	—	2	8	no	—
268	#95	—	2	8	no	—
269	#95	—	4	2	no	—
270	#95	—	4	4	no	—
271	#95	C₂×C₄×C₁₃₉	1	16	yes	—
272	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
273	C₂×Q₈	—	4	4	no	—
274	C₂×Q₈	—	4	4	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×Q₈	—	4	4	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	16	yes	complemented
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
315	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
316	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
317	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
318	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
319	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	8	no	—
322	C₄⋊C₄	—	4	8	no	—
323	C₄⋊C₄	—	4	8	no	—
324	C₄⋊C₄	—	4	8	no	—
325	C₄²	—	4	4	no	—
326	C₄²	—	4	8	no	—
327	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
328	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
329	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
330	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
331	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
332	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
333	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
334	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
335	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
336	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
337	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
338	Q₈	—	4	16	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	8	yes	—
377	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
378	C₂×C₄	C₄×Q₈×C₁₃₉	1	8	yes	—
379	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
380	C₂²	C₂×C₄×Q₈×C₁₃₉	1	2	yes	—
381	C₂²	#518×C₁₃₉	1	1	yes	characteristic
382	C₂²	#518×C₁₃₉	1	1	yes	characteristic
383	C₂²	#520×C₁₃₉	1	2	yes	—
384	C₂²	#534×C₁₃₉	1	1	yes	characteristic
385	C₂²	#534×C₁₃₉	1	1	yes	characteristic
386	C₂²	#538×C₁₃₉	1	2	yes	—
387	C₂²	#539×C₁₃₉	1	2	yes	—
388	C₂²	#543×C₁₃₉	1	1	yes	characteristic
389	C₂²	#543×C₁₃₉	1	1	yes	characteristic
390	C₂²	#543×C₁₃₉	1	2	yes	—
391	C₂²	#544×C₁₃₉	1	2	yes	—
392	C₂²	D₄×Q₈×C₁₃₉	1	2	yes	—
393	C₂²	#550×C₁₃₉	1	2	yes	—
394	C₂²	#554×C₁₃₉	1	2	yes	—
395	C₂²	#555×C₁₃₉	1	1	yes	characteristic
396	C₂²	#557×C₁₃₉	1	2	yes	—
397	C₂²	Q₈²×C₁₃₉	1	2	yes	—
398	C₂²	Q₈²×C₁₃₉	1	1	yes	characteristic
399	C₂²	H(3,𝔽₄)×C₁₃₉	1	1	yes	characteristic
400	C₂²	#562×C₁₃₉	1	2	yes	—
401	C₂²	#563×C₁₃₉	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	2	8	no	—
404	C₄	—	2	8	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	8	no	—
407	C₄	—	8	4	no	—
408	C₂	#2315×C₁₃₉	1	1	yes	characteristic
409	C₂	#2329×C₁₃₉	1	2	yes	—
410	C₂	Q₈×C₄⋊C₄×C₁₃₉	1	2	yes	—
411	C₂	#2369×C₁₃₉	1	1	yes	characteristic
412	C₂	#2379×C₁₃₉	1	1	yes	characteristic
413	C₂	#2732×C₁₃₉	1	2	yes	—
414	C₂	#2733×C₁₃₉	1	1	yes	characteristic
415	C₂	#2734×C₁₃₉	1	1	yes	characteristic
416	C₂	#2806×C₁₃₉	1	2	yes	—
417	C₂	#2809×C₁₃₉	1	1	yes	characteristic
418	C₂	#2811×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. #391×C₁₃₉	C₄	semidirect
49. C₂×C₄⋊C₄×C₁₃₉	Q₈	semidirect
69. C₂×Q₈×C₁₃₉	C₄⋊C₄	semidirect
209. #14467	C₁₃₉	direct (N × H)
210. C₁₃₉	#14467	direct (N × H)
226. #391	C₄×C₁₃₉	semidirect
259. C₂×C₄⋊C₄	Q₈×C₁₃₉	semidirect
279. C₂×Q₈	C₄⋊C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#391×C₁₃₉	2
#1444×C₁₃₉	2
#1441×C₁₃₉	2
#1436×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#14467	139

Subgroups — C139×#14467 #48009063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#14467 #48009063