Subgroups — C₁₃₉×#36289 #48030885

Order 35584.

3146 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2504×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2490×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2472×C₁₃₉	C₂	1	8	yes	maximal, complemented
10	#2435×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#390×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
17	#554×C₁₃₉	—	2	8	no	—
18	D₄²×C₁₃₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	complemented
37	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
38	#397×C₁₃₉	C₂²	1	8	yes	complemented
39	#394×C₁₃₉	C₂²	1	4	yes	complemented
40	#394×C₁₃₉	C₂²	1	8	yes	complemented
41	#393×C₁₃₉	C₂²	1	4	yes	complemented
42	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
43	#390×C₁₃₉	C₂²	1	1	yes	characteristic
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	complemented
46	#390×C₁₃₉	C₂²	1	2	yes	complemented
47	#390×C₁₃₉	C₂²	1	8	yes	complemented
48	#390×C₁₃₉	C₂²	1	4	yes	complemented
49	#390×C₁₃₉	C₂²	1	4	yes	complemented
50	#390×C₁₃₉	C₂²	1	2	yes	complemented
51	#388×C₁₃₉	C₂²	1	4	yes	complemented
52	#388×C₁₃₉	C₂²	1	8	yes	complemented
53	#386×C₁₃₉	C₂²	1	8	yes	complemented
54	#386×C₁₃₉	C₂²	1	8	yes	complemented
55	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#382×C₁₃₉	C₂²	1	2	yes	complemented
57	#380×C₁₃₉	C₂²	1	4	yes	complemented
58	#379×C₁₃₉	C₂²	1	8	yes	complemented
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
66	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃₉	—	2	8	no	—
69	C₂²×D₄×C₁₃₉	—	2	8	no	—
70	C₂²×D₄×C₁₃₉	—	2	16	no	—
71	C₂²×D₄×C₁₃₉	—	2	8	no	—
72	C₂²×D₄×C₁₃₉	—	4	4	no	—
73	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
85	#127×C₁₃₉	—	2	4	no	—
86	#125×C₁₃₉	—	2	8	no	—
87	#124×C₁₃₉	—	2	4	no	—
88	#124×C₁₃₉	—	4	8	no	—
89	#124×C₁₃₉	—	4	4	no	—
90	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
91	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
92	#121×C₁₃₉	—	2	8	no	—
93	#121×C₁₃₉	—	2	8	no	—
94	#120×C₁₃₉	—	2	16	no	—
95	C₄×Q₈×C₁₃₉	—	2	4	no	—
96	C₄×D₄×C₁₃₉	—	2	8	no	—
97	C₄×D₄×C₁₃₉	—	2	8	no	—
98	C₄×D₄×C₁₃₉	—	2	4	no	—
99	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₃₉	—	4	16	no	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	—	4	4	no	—
124	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	8	yes	—
135	#95×C₁₃₉	C₂³	1	2	yes	—
136	#95×C₁₃₉	C₂³	1	4	yes	—
137	C₂⁴×C₁₃₉	—	2	8	no	—
138	C₂⁴×C₁₃₉	—	2	8	no	—
139	C₂⁴×C₁₃₉	—	2	16	no	—
140	C₂⁴×C₁₃₉	—	4	8	no	—
141	C₂⁴×C₁₃₉	—	4	4	no	—
142	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
143	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂×Q₈×C₁₃₉	—	2	2	no	—
146	C₂×Q₈×C₁₃₉	—	2	4	no	—
147	C₂×Q₈×C₁₃₉	—	2	2	no	—
148	C₂×Q₈×C₁₃₉	—	2	2	no	—
149	C₂×Q₈×C₁₃₉	—	4	4	no	—
150	C₂×D₄×C₁₃₉	—	2	8	no	—
151	C₂×D₄×C₁₃₉	—	2	8	no	—
152	C₂×D₄×C₁₃₉	—	2	16	no	—
153	C₂×D₄×C₁₃₉	—	2	2	no	—
154	C₂×D₄×C₁₃₉	—	2	8	no	—
155	C₂×D₄×C₁₃₉	—	2	4	no	—
156	C₂×D₄×C₁₃₉	—	2	4	no	—
157	C₂×D₄×C₁₃₉	—	2	4	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	4	no	—
160	C₂×D₄×C₁₃₉	—	2	2	no	—
161	C₂×D₄×C₁₃₉	—	2	4	no	—
162	C₂×D₄×C₁₃₉	—	4	32	no	—
163	C₂×D₄×C₁₃₉	—	4	4	no	—
164	C₂×D₄×C₁₃₉	—	4	4	no	—
165	C₂×D₄×C₁₃₉	—	4	32	no	—
166	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
167	C₂×D₄×C₁₃₉	#41	1	4	yes	—
168	C₂×D₄×C₁₃₉	#41	1	8	yes	—
169	C₂²×C₄×C₁₃₉	—	2	4	no	—
170	C₂²×C₄×C₁₃₉	—	2	4	no	—
171	C₂²×C₄×C₁₃₉	—	2	8	no	—
172	C₂²×C₄×C₁₃₉	—	2	8	no	—
173	C₂²×C₄×C₁₃₉	—	2	4	no	—
174	C₂²×C₄×C₁₃₉	—	2	8	no	—
175	C₂²×C₄×C₁₃₉	—	2	8	no	—
176	C₂²×C₄×C₁₃₉	—	4	4	no	—
177	C₂²×C₄×C₁₃₉	—	4	8	no	—
178	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₄⋊C₄×C₁₃₉	—	2	2	no	—
191	C₄⋊C₄×C₁₃₉	—	2	8	no	—
192	C₄⋊C₄×C₁₃₉	—	2	4	no	—
193	C₄⋊C₄×C₁₃₉	—	2	2	no	—
194	C₄⋊C₄×C₁₃₉	—	2	4	no	—
195	C₄⋊C₄×C₁₃₉	—	2	4	no	—
196	C₄⋊C₄×C₁₃₉	—	2	8	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
199	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
200	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
201	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
202	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
203	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
204	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
205	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
206	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
207	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
208	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
209	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
210	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
211	C₄²×C₁₃₉	—	2	4	no	—
212	C₄²×C₁₃₉	—	2	4	no	—
213	C₄²×C₁₃₉	—	2	2	no	—
214	C₄²×C₁₃₉	—	2	2	no	—
215	C₄²×C₁₃₉	—	2	4	no	—
216	C₄²×C₁₃₉	—	2	4	no	—
217	C₄²×C₁₃₉	—	4	4	no	—
218	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
219	C₂³×C₁₃₉	—	2	2	no	—
220	C₂³×C₁₃₉	—	2	2	no	—
221	C₂³×C₁₃₉	—	2	4	no	—
222	C₂³×C₁₃₉	—	2	2	no	—
223	C₂³×C₁₃₉	—	2	4	no	—
224	C₂³×C₁₃₉	—	2	4	no	—
225	C₂³×C₁₃₉	—	2	2	no	—
226	C₂³×C₁₃₉	—	2	4	no	—
227	C₂³×C₁₃₉	—	2	8	no	—
228	C₂³×C₁₃₉	—	2	4	no	—
229	C₂³×C₁₃₉	—	2	8	no	—
230	C₂³×C₁₃₉	—	2	4	no	—
231	C₂³×C₁₃₉	—	4	16	no	—
232	C₂³×C₁₃₉	—	4	32	no	—
233	C₂³×C₁₃₉	—	4	16	no	—
234	C₂³×C₁₃₉	—	8	8	no	—
235	C₂³×C₁₃₉	—	8	16	no	—
236	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
237	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
238	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
239	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
240	Q₈×C₁₃₉	—	4	4	no	—
241	Q₈×C₁₃₉	—	8	4	no	—
242	D₄×C₁₃₉	—	2	8	no	—
243	D₄×C₁₃₉	—	4	16	no	—
244	D₄×C₁₃₉	—	4	16	no	—
245	D₄×C₁₃₉	—	4	8	no	—
246	D₄×C₁₃₉	—	4	8	no	—
247	D₄×C₁₃₉	—	8	4	no	—
248	D₄×C₁₃₉	#124	1	16	yes	complemented
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	16	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	4	no	—
263	C₂×C₄×C₁₃₉	—	2	4	no	—
264	C₂×C₄×C₁₃₉	—	2	4	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	4	no	—
267	C₂×C₄×C₁₃₉	—	2	8	no	—
268	C₂×C₄×C₁₃₉	—	2	4	no	—
269	C₂×C₄×C₁₃₉	—	2	2	no	—
270	C₂×C₄×C₁₃₉	—	4	16	no	—
271	C₂×C₄×C₁₃₉	—	4	8	no	—
272	C₂×C₄×C₁₃₉	—	8	8	no	—
273	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
278	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
279	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
280	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
281	C₂²×C₁₃₉	—	2	4	no	—
282	C₂²×C₁₃₉	—	2	8	no	—
283	C₂²×C₁₃₉	—	2	4	no	—
284	C₂²×C₁₃₉	—	2	8	no	—
285	C₂²×C₁₃₉	—	2	4	no	—
286	C₂²×C₁₃₉	—	2	8	no	—
287	C₂²×C₁₃₉	—	4	2	no	—
288	C₂²×C₁₃₉	—	4	2	no	—
289	C₂²×C₁₃₉	—	4	4	no	—
290	C₂²×C₁₃₉	—	4	4	no	—
291	C₂²×C₁₃₉	—	4	4	no	—
292	C₂²×C₁₃₉	—	4	8	no	—
293	C₂²×C₁₃₉	—	4	4	no	—
294	C₂²×C₁₃₉	—	4	8	no	—
295	C₂²×C₁₃₉	—	8	32	no	—
296	C₂²×C₁₃₉	C₂×#124	1	8	yes	—
297	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
298	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
299	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
302	C₄×C₁₃₉	—	2	4	no	—
303	C₄×C₁₃₉	—	2	2	no	—
304	C₄×C₁₃₉	—	2	4	no	—
305	C₄×C₁₃₉	—	4	2	no	—
306	C₄×C₁₃₉	—	4	2	no	—
307	C₄×C₁₃₉	—	4	2	no	—
308	C₄×C₁₃₉	—	4	2	no	—
309	C₄×C₁₃₉	—	4	4	no	—
310	C₄×C₁₃₉	—	4	4	no	—
311	C₄×C₁₃₉	C₂×#124	1	4	yes	—
312	C₄×C₁₃₉	#546	1	4	yes	—
313	C₂×C₁₃₉	—	2	8	no	—
314	C₂×C₁₃₉	—	4	4	no	—
315	C₂×C₁₃₉	—	8	4	no	—
316	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
317	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
318	C₂×C₁₃₉	#3481	1	2	yes	—
319	C₂×C₁₃₉	#3498	1	1	yes	characteristic
320	C₂×C₁₃₉	#3519	1	2	yes	—
321	#36289	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₁₃₉	#36289	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
324	C₂×D₄²	C₂×C₁₃₉	1	1	yes	characteristic
325	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
326	#2850	C₂×C₁₃₉	1	2	yes	complemented
327	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
328	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
329	#2504	C₂×C₁₃₉	1	2	yes	complemented
330	#2490	C₂×C₁₃₉	1	4	yes	complemented
331	#2472	C₂×C₁₃₉	1	8	yes	complemented
332	#2435	C₂×C₁₃₉	1	2	yes	complemented
333	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
334	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
335	C₂×#390	C₂×C₁₃₉	1	2	yes	complemented
336	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
337	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
338	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
339	#554	—	2	8	no	—
340	D₄²	—	2	8	no	—
341	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
342	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
343	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
344	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
345	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
346	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
347	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
348	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
349	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
350	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
351	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
352	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
353	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
355	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
356	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
358	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	complemented
359	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
360	#397	C₂²×C₁₃₉	1	8	yes	complemented
361	#394	C₂²×C₁₃₉	1	8	yes	complemented
362	#394	C₂²×C₁₃₉	1	4	yes	complemented
363	#393	C₂²×C₁₃₉	1	4	yes	complemented
364	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
365	#390	C₂²×C₁₃₉	1	2	yes	—
366	#390	C₂²×C₁₃₉	1	1	yes	characteristic
367	#390	C₂²×C₁₃₉	1	4	yes	complemented
368	#390	C₂²×C₁₃₉	1	4	yes	complemented
369	#390	C₂²×C₁₃₉	1	2	yes	complemented
370	#390	C₂²×C₁₃₉	1	2	yes	complemented
371	#390	C₂²×C₁₃₉	1	8	yes	complemented
372	#390	C₂²×C₁₃₉	1	2	yes	complemented
373	#388	C₂²×C₁₃₉	1	8	yes	complemented
374	#388	C₂²×C₁₃₉	1	4	yes	complemented
375	#386	C₂²×C₁₃₉	1	8	yes	complemented
376	#386	C₂²×C₁₃₉	1	8	yes	complemented
377	#382	C₂²×C₁₃₉	1	2	yes	complemented
378	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
379	#380	C₂²×C₁₃₉	1	4	yes	complemented
380	#379	C₂²×C₁₃₉	1	8	yes	complemented
381	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
382	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
383	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
384	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
385	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
386	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
387	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
388	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
389	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
390	C₂²×D₄	—	2	8	no	—
391	C₂²×D₄	—	2	8	no	—
392	C₂²×D₄	—	2	16	no	—
393	C₂²×D₄	—	2	8	no	—
394	C₂²×D₄	—	4	4	no	—
395	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
396	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
397	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
398	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
401	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
403	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
404	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
405	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
406	C₄⋊Q₈	—	2	4	no	—
407	#127	—	2	4	no	—
408	#125	—	2	8	no	—
409	#124	—	2	4	no	—
410	#124	—	4	8	no	—
411	#124	—	4	4	no	—
412	C₂²⋊Q₈	—	2	8	no	—
413	C₂²⋊Q₈	—	2	16	no	—
414	#121	—	2	8	no	—
415	#121	—	2	8	no	—
416	#120	—	2	16	no	—
417	C₄×Q₈	—	2	4	no	—
418	C₄×D₄	—	2	8	no	—
419	C₄×D₄	—	2	8	no	—
420	C₄×D₄	—	2	4	no	—
421	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
422	C₂×C₄⋊C₄	—	2	8	no	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	4	16	no	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
445	C₂×C₄²	—	4	4	no	—
446	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
447	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
448	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
451	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
453	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
454	#95	C₂³×C₁₃₉	1	2	yes	—
455	#95	C₂³×C₁₃₉	1	4	yes	—
456	#95	C₂³×C₁₃₉	1	4	yes	—
457	#95	C₂³×C₁₃₉	1	4	yes	—
458	#95	C₂³×C₁₃₉	1	8	yes	—
459	C₂⁴	—	2	8	no	—
460	C₂⁴	—	2	8	no	—
461	C₂⁴	—	2	16	no	—
462	C₂⁴	—	4	8	no	—
463	C₂⁴	—	4	4	no	—
464	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
465	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
466	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	4	4	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	2	8	no	—
474	C₂×D₄	—	2	16	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	8	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	8	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	4	32	no	—
485	C₂×D₄	—	4	4	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	—	4	32	no	—
488	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
489	C₂×D₄	#41×C₁₃₉	1	4	yes	—
490	C₂×D₄	#41×C₁₃₉	1	8	yes	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	8	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	8	no	—
500	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
501	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	2	4	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	8	no	—
526	C₂²⋊C₄	—	2	8	no	—
527	C₂²⋊C₄	—	2	16	no	—
528	C₂²⋊C₄	—	4	8	no	—
529	C₂²⋊C₄	—	4	8	no	—
530	C₂²⋊C₄	—	4	8	no	—
531	C₂²⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
533	C₄²	—	2	4	no	—
534	C₄²	—	2	4	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	4	4	no	—
540	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	8	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	8	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	4	16	no	—
554	C₂³	—	4	32	no	—
555	C₂³	—	4	16	no	—
556	C₂³	—	8	8	no	—
557	C₂³	—	8	16	no	—
558	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
559	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
560	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
561	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
562	Q₈	—	4	4	no	—
563	Q₈	—	8	4	no	—
564	D₄	—	2	8	no	—
565	D₄	—	4	16	no	—
566	D₄	—	4	16	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	8	no	—
569	D₄	—	8	4	no	—
570	D₄	#124×C₁₃₉	1	16	yes	complemented
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	16	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	4	16	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	8	8	no	—
595	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
599	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
600	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
601	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
602	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	8	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	8	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	8	no	—
617	C₂²	—	8	32	no	—
618	C₂²	C₂×#124×C₁₃₉	1	8	yes	—
619	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
620	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
621	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
622	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
623	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	4	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	4	no	—
633	C₄	C₂×#124×C₁₃₉	1	4	yes	—
634	C₄	#546×C₁₃₉	1	4	yes	—
635	C₂	—	2	8	no	—
636	C₂	—	4	4	no	—
637	C₂	—	8	4	no	—
638	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
639	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
640	C₂	#3481×C₁₃₉	1	2	yes	—
641	C₂	#3498×C₁₃₉	1	1	yes	characteristic
642	C₂	#3519×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×D₄²×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2563×C₁₃₉	C₂	semidirect
6. #2548×C₁₃₉	C₂	semidirect
7. #2504×C₁₃₉	C₂	semidirect
8. #2490×C₁₃₉	C₂	semidirect
9. #2472×C₁₃₉	C₂	semidirect
10. #2435×C₁₃₉	C₂	semidirect
11. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
12. C₄×#124×C₁₃₉	C₂	semidirect
13. C₂×#390×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
19. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
21. C₂×#125×C₁₃₉	C₂²	semidirect
23. C₂×#124×C₁₃₉	C₂²	semidirect
24. C₂×#124×C₁₃₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
37. C₂²×C₄²×C₁₃₉	C₂²	semidirect
38. #397×C₁₃₉	C₂²	semidirect
39. #394×C₁₃₉	C₂²	semidirect
40. #394×C₁₃₉	C₂²	semidirect
41. #393×C₁₃₉	C₂²	semidirect
42. #391×C₁₃₉	C₂²	semidirect
45. #390×C₁₃₉	C₂²	semidirect
46. #390×C₁₃₉	C₂²	semidirect
47. #390×C₁₃₉	C₂²	semidirect
48. #390×C₁₃₉	C₂²	semidirect
49. #390×C₁₃₉	C₂²	semidirect
50. #390×C₁₃₉	C₂²	semidirect
51. #388×C₁₃₉	C₂²	semidirect
52. #388×C₁₃₉	C₂²	semidirect
53. #386×C₁₃₉	C₂²	semidirect
54. #386×C₁₃₉	C₂²	semidirect
55. #382×C₁₃₉	C₂²	semidirect
56. #382×C₁₃₉	C₂²	semidirect
57. #380×C₁₃₉	C₂²	semidirect
58. #379×C₁₃₉	C₂²	semidirect
59. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
60. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
64. C₄³×C₁₃₉	C₂²	semidirect
248. D₄×C₁₃₉	#124	semidirect
321. #36289	C₁₃₉	direct (N × H)
322. C₁₃₉	#36289	direct (N × H)
323. C₂×#554	C₂×C₁₃₉	semidirect
325. #2858	C₂×C₁₃₉	semidirect
326. #2850	C₂×C₁₃₉	semidirect
327. #2563	C₂×C₁₃₉	semidirect
328. #2548	C₂×C₁₃₉	semidirect
329. #2504	C₂×C₁₃₉	semidirect
330. #2490	C₂×C₁₃₉	semidirect
331. #2472	C₂×C₁₃₉	semidirect
332. #2435	C₂×C₁₃₉	semidirect
333. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
334. C₄×#124	C₂×C₁₃₉	semidirect
335. C₂×#390	C₂×C₁₃₉	semidirect
336. C₄²×D₄	C₂×C₁₃₉	semidirect
341. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
343. C₂×#125	C₂²×C₁₃₉	semidirect
345. C₂×#124	C₂²×C₁₃₉	semidirect
346. C₂×#124	C₂²×C₁₃₉	semidirect
347. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
348. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
352. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
357. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
358. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
359. C₂²×C₄²	C₂²×C₁₃₉	semidirect
360. #397	C₂²×C₁₃₉	semidirect
361. #394	C₂²×C₁₃₉	semidirect
362. #394	C₂²×C₁₃₉	semidirect
363. #393	C₂²×C₁₃₉	semidirect
364. #391	C₂²×C₁₃₉	semidirect
367. #390	C₂²×C₁₃₉	semidirect
368. #390	C₂²×C₁₃₉	semidirect
369. #390	C₂²×C₁₃₉	semidirect
370. #390	C₂²×C₁₃₉	semidirect
371. #390	C₂²×C₁₃₉	semidirect
372. #390	C₂²×C₁₃₉	semidirect
373. #388	C₂²×C₁₃₉	semidirect
374. #388	C₂²×C₁₃₉	semidirect
375. #386	C₂²×C₁₃₉	semidirect
376. #386	C₂²×C₁₃₉	semidirect
377. #382	C₂²×C₁₃₉	semidirect
378. #382	C₂²×C₁₃₉	semidirect
379. #380	C₂²×C₁₃₉	semidirect
380. #379	C₂²×C₁₃₉	semidirect
381. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
382. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
383. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
384. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
385. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
386. C₄³	C₂²×C₁₃₉	semidirect
570. D₄	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂×D₄²×C₁₃₉	2
#2858×C₁₃₉	2
#2850×C₁₃₉	2
#2563×C₁₃₉	2
#2548×C₁₃₉	2
#2504×C₁₃₉	2
#2490×C₁₃₉	2
#2472×C₁₃₉	2
#2435×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36289	139

Subgroups — C139×#36289 #48030885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36289 #48030885