Subgroups — C₁₃₉×#37118 #48031714

Order 35584.

2406 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2723×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2720×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2696×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2692×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2614×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2561×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2539×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2534×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2486×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2313×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	#539×C₁₃₉	—	2	8	no	—
19	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
20	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	#400×C₁₃₉	C₂²	1	4	yes	complemented
40	#399×C₁₃₉	C₂²	1	2	yes	—
41	#399×C₁₃₉	C₂²	1	4	yes	complemented
42	#398×C₁₃₉	C₂²	1	4	yes	complemented
43	#397×C₁₃₉	C₂²	1	2	yes	—
44	#397×C₁₃₉	C₂²	1	4	yes	complemented
45	#396×C₁₃₉	C₂²	1	4	yes	—
46	#395×C₁₃₉	C₂²	1	4	yes	complemented
47	#395×C₁₃₉	C₂²	1	4	yes	complemented
48	#394×C₁₃₉	C₂²	1	4	yes	—
49	#393×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	4	yes	complemented
51	#393×C₁₃₉	C₂²	1	4	yes	complemented
52	#392×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	complemented
54	#390×C₁₃₉	C₂²	1	4	yes	—
55	#390×C₁₃₉	C₂²	1	2	yes	complemented
56	#389×C₁₃₉	C₂²	1	4	yes	complemented
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	complemented
60	#387×C₁₃₉	C₂²	1	4	yes	complemented
61	#386×C₁₃₉	C₂²	1	4	yes	—
62	#386×C₁₃₉	C₂²	1	4	yes	—
63	#386×C₁₃₉	C₂²	1	4	yes	—
64	#385×C₁₃₉	C₂²	1	4	yes	—
65	#385×C₁₃₉	C₂²	1	4	yes	—
66	#384×C₁₃₉	C₂²	1	2	yes	complemented
67	#382×C₁₃₉	C₂²	1	2	yes	complemented
68	#381×C₁₃₉	C₂²	1	2	yes	—
69	#381×C₁₃₉	C₂²	1	2	yes	—
70	#381×C₁₃₉	C₂²	1	2	yes	—
71	#381×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	4	yes	complemented
74	#379×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃₉	—	2	4	no	—
79	C₂²×Q₈×C₁₃₉	—	4	4	no	—
80	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₉	—	2	4	no	—
86	C₂³×C₄×C₁₃₉	—	4	4	no	—
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	#126×C₁₃₉	—	2	8	no	—
96	#125×C₁₃₉	—	2	8	no	—
97	#123×C₁₃₉	—	2	8	no	—
98	#123×C₁₃₉	—	2	8	no	—
99	#123×C₁₃₉	—	4	4	no	—
100	#123×C₁₃₉	—	4	4	no	—
101	#123×C₁₃₉	—	4	4	no	—
102	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	#121×C₁₃₉	—	2	4	no	—
107	#120×C₁₃₉	—	4	4	no	—
108	C₄×D₄×C₁₃₉	—	2	8	no	—
109	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
110	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
111	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	4	yes	—
154	#95×C₁₃₉	C₂³	1	2	yes	—
155	#95×C₁₃₉	C₂³	1	4	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	C₂⁴×C₁₃₉	—	2	2	no	—
160	C₂⁴×C₁₃₉	—	2	4	no	—
161	C₂⁴×C₁₃₉	—	2	4	no	—
162	C₂⁴×C₁₃₉	—	4	2	no	—
163	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
165	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
166	C₂×Q₈×C₁₃₉	—	2	8	no	—
167	C₂×Q₈×C₁₃₉	—	2	2	no	—
168	C₂×Q₈×C₁₃₉	—	4	8	no	—
169	C₂×Q₈×C₁₃₉	—	4	2	no	—
170	C₂×Q₈×C₁₃₉	—	4	16	no	—
171	C₂×D₄×C₁₃₉	—	2	4	no	—
172	C₂×D₄×C₁₃₉	—	2	4	no	—
173	C₂×D₄×C₁₃₉	—	2	4	no	—
174	C₂×D₄×C₁₃₉	—	2	8	no	—
175	C₂×D₄×C₁₃₉	—	2	2	no	—
176	C₂×D₄×C₁₃₉	—	4	4	no	—
177	C₂×D₄×C₁₃₉	—	4	2	no	—
178	C₂×D₄×C₁₃₉	—	4	4	no	—
179	C₂²×C₄×C₁₃₉	—	2	4	no	—
180	C₂²×C₄×C₁₃₉	—	2	2	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	2	2	no	—
183	C₂²×C₄×C₁₃₉	—	2	4	no	—
184	C₂²×C₄×C₁₃₉	—	2	4	no	—
185	C₂²×C₄×C₁₃₉	—	2	4	no	—
186	C₂²×C₄×C₁₃₉	—	2	8	no	—
187	C₂²×C₄×C₁₃₉	—	2	4	no	—
188	C₂²×C₄×C₁₃₉	—	4	8	no	—
189	C₂²×C₄×C₁₃₉	—	4	2	no	—
190	C₂²×C₄×C₁₃₉	—	4	2	no	—
191	C₂²×C₄×C₁₃₉	—	4	4	no	—
192	C₂²×C₄×C₁₃₉	—	4	16	no	—
193	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₄⋊C₄×C₁₃₉	—	2	8	no	—
209	C₄⋊C₄×C₁₃₉	—	2	4	no	—
210	C₄⋊C₄×C₁₃₉	—	2	4	no	—
211	C₄⋊C₄×C₁₃₉	—	2	4	no	—
212	C₄⋊C₄×C₁₃₉	—	2	2	no	—
213	C₄⋊C₄×C₁₃₉	—	2	4	no	—
214	C₄⋊C₄×C₁₃₉	—	2	4	no	—
215	C₄⋊C₄×C₁₃₉	—	2	2	no	—
216	C₄⋊C₄×C₁₃₉	—	2	4	no	—
217	C₄⋊C₄×C₁₃₉	—	4	4	no	—
218	C₄⋊C₄×C₁₃₉	—	4	4	no	—
219	C₄⋊C₄×C₁₃₉	—	4	4	no	—
220	C₄⋊C₄×C₁₃₉	—	4	4	no	—
221	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
222	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
223	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
229	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
231	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
239	C₄²×C₁₃₉	—	2	4	no	—
240	C₄²×C₁₃₉	—	4	2	no	—
241	C₄²×C₁₃₉	—	4	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	2	no	—
244	C₂³×C₁₃₉	—	2	8	no	—
245	C₂³×C₁₃₉	—	2	2	no	—
246	C₂³×C₁₃₉	—	2	4	no	—
247	C₂³×C₁₃₉	—	2	2	no	—
248	C₂³×C₁₃₉	—	2	4	no	—
249	C₂³×C₁₃₉	—	2	2	no	—
250	C₂³×C₁₃₉	—	2	2	no	—
251	C₂³×C₁₃₉	—	2	2	no	—
252	C₂³×C₁₃₉	—	2	4	no	—
253	C₂³×C₁₃₉	—	2	4	no	—
254	C₂³×C₁₃₉	—	4	16	no	—
255	C₂³×C₁₃₉	—	4	4	no	—
256	C₂³×C₁₃₉	—	4	4	no	—
257	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
258	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
259	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
260	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
261	Q₈×C₁₃₉	—	4	16	no	—
262	Q₈×C₁₃₉	—	8	2	no	—
263	D₄×C₁₃₉	—	4	8	no	—
264	D₄×C₁₃₉	—	8	2	no	—
265	D₄×C₁₃₉	—	8	8	no	—
266	C₂×C₄×C₁₃₉	—	2	8	no	—
267	C₂×C₄×C₁₃₉	—	2	4	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	2	no	—
270	C₂×C₄×C₁₃₉	—	2	4	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	2	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	4	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	4	no	—
281	C₂×C₄×C₁₃₉	—	2	4	no	—
282	C₂×C₄×C₁₃₉	—	2	4	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	4	no	—
287	C₂×C₄×C₁₃₉	—	2	4	no	—
288	C₂×C₄×C₁₃₉	—	2	4	no	—
289	C₂×C₄×C₁₃₉	—	2	4	no	—
290	C₂×C₄×C₁₃₉	—	4	4	no	—
291	C₂×C₄×C₁₃₉	—	4	4	no	—
292	C₂×C₄×C₁₃₉	—	4	16	no	—
293	C₂×C₄×C₁₃₉	—	4	4	no	—
294	C₂×C₄×C₁₃₉	—	4	4	no	—
295	C₂×C₄×C₁₃₉	—	4	4	no	—
296	C₂×C₄×C₁₃₉	—	8	4	no	—
297	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
301	C₂²×C₁₃₉	—	2	2	no	—
302	C₂²×C₁₃₉	—	2	2	no	—
303	C₂²×C₁₃₉	—	2	8	no	—
304	C₂²×C₁₃₉	—	2	4	no	—
305	C₂²×C₁₃₉	—	2	8	no	—
306	C₂²×C₁₃₉	—	4	16	no	—
307	C₂²×C₁₃₉	—	4	2	no	—
308	C₂²×C₁₃₉	—	4	2	no	—
309	C₂²×C₁₃₉	—	4	4	no	—
310	C₂²×C₁₃₉	—	4	2	no	—
311	C₂²×C₁₃₉	—	4	2	no	—
312	C₂²×C₁₃₉	—	4	2	no	—
313	C₂²×C₁₃₉	—	4	4	no	—
314	C₂²×C₁₃₉	—	4	4	no	—
315	C₂²×C₁₃₉	#535	1	4	yes	—
316	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
317	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
319	C₂²×C₁₃₉	#585	1	2	yes	—
320	C₄×C₁₃₉	—	2	4	no	—
321	C₄×C₁₃₉	—	2	4	no	—
322	C₄×C₁₃₉	—	2	2	no	—
323	C₄×C₁₃₉	—	2	2	no	—
324	C₄×C₁₃₉	—	4	2	no	—
325	C₄×C₁₃₉	—	4	2	no	—
326	C₄×C₁₃₉	—	4	2	no	—
327	C₄×C₁₃₉	—	4	2	no	—
328	C₄×C₁₃₉	—	4	2	no	—
329	C₄×C₁₃₉	—	4	2	no	—
330	C₄×C₁₃₉	—	4	4	no	—
331	C₄×C₁₃₉	—	4	4	no	—
332	C₂×C₁₃₉	—	2	4	no	—
333	C₂×C₁₃₉	—	4	4	no	—
334	C₂×C₁₃₉	—	8	2	no	—
335	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
336	C₂×C₁₃₉	#3485	1	1	yes	characteristic
337	C₂×C₁₃₉	#3486	1	1	yes	characteristic
338	C₂×C₁₃₉	#3535	1	4	yes	—
339	#37118	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₁₃₉	#37118	1	1	yes	characteristic, direct product factor, Sylow
341	C₂×#539	C₂×C₁₃₉	1	1	yes	characteristic, complemented
342	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
343	#2849	C₂×C₁₃₉	1	2	yes	complemented
344	#2723	C₂×C₁₃₉	1	4	yes	complemented
345	#2720	C₂×C₁₃₉	1	4	yes	complemented
346	#2696	C₂×C₁₃₉	1	4	yes	complemented
347	#2692	C₂×C₁₃₉	1	4	yes	complemented
348	#2614	C₂×C₁₃₉	1	2	yes	complemented
349	#2561	C₂×C₁₃₉	1	1	yes	characteristic, complemented
350	#2539	C₂×C₁₃₉	1	1	yes	characteristic
351	#2534	C₂×C₁₃₉	1	2	yes	complemented
352	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
353	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
354	#2486	C₂×C₁₃₉	1	2	yes	complemented
355	#2313	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
358	#539	—	2	8	no	—
359	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
360	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
361	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
362	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
363	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
364	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
365	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
366	C₂×C₂²⋊Q₈	—	2	8	no	—
367	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
369	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
370	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
371	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
372	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
374	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
379	#400	C₂²×C₁₃₉	1	4	yes	complemented
380	#399	C₂²×C₁₃₉	1	2	yes	—
381	#399	C₂²×C₁₃₉	1	4	yes	complemented
382	#398	C₂²×C₁₃₉	1	4	yes	complemented
383	#397	C₂²×C₁₃₉	1	2	yes	—
384	#397	C₂²×C₁₃₉	1	4	yes	complemented
385	#396	C₂²×C₁₃₉	1	4	yes	—
386	#395	C₂²×C₁₃₉	1	4	yes	complemented
387	#395	C₂²×C₁₃₉	1	4	yes	complemented
388	#394	C₂²×C₁₃₉	1	4	yes	—
389	#393	C₂²×C₁₃₉	1	2	yes	—
390	#393	C₂²×C₁₃₉	1	4	yes	complemented
391	#393	C₂²×C₁₃₉	1	4	yes	complemented
392	#392	C₂²×C₁₃₉	1	2	yes	—
393	#391	C₂²×C₁₃₉	1	2	yes	complemented
394	#390	C₂²×C₁₃₉	1	4	yes	—
395	#390	C₂²×C₁₃₉	1	2	yes	complemented
396	#389	C₂²×C₁₃₉	1	4	yes	complemented
397	#388	C₂²×C₁₃₉	1	4	yes	—
398	#388	C₂²×C₁₃₉	1	4	yes	—
399	#387	C₂²×C₁₃₉	1	4	yes	complemented
400	#387	C₂²×C₁₃₉	1	4	yes	complemented
401	#386	C₂²×C₁₃₉	1	4	yes	—
402	#386	C₂²×C₁₃₉	1	4	yes	—
403	#386	C₂²×C₁₃₉	1	4	yes	—
404	#385	C₂²×C₁₃₉	1	4	yes	—
405	#385	C₂²×C₁₃₉	1	4	yes	—
406	#384	C₂²×C₁₃₉	1	2	yes	complemented
407	#382	C₂²×C₁₃₉	1	2	yes	complemented
408	#381	C₂²×C₁₃₉	1	2	yes	—
409	#381	C₂²×C₁₃₉	1	2	yes	—
410	#381	C₂²×C₁₃₉	1	2	yes	—
411	#381	C₂²×C₁₃₉	1	2	yes	—
412	#380	C₂²×C₁₃₉	1	2	yes	—
413	#380	C₂²×C₁₃₉	1	4	yes	complemented
414	#379	C₂²×C₁₃₉	1	2	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
418	C₂²×Q₈	—	2	4	no	—
419	C₂²×Q₈	—	4	4	no	—
420	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
421	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
422	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
424	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
425	C₂³×C₄	—	2	4	no	—
426	C₂³×C₄	—	4	4	no	—
427	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
432	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
433	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
435	#126	—	2	8	no	—
436	#125	—	2	8	no	—
437	#123	—	2	8	no	—
438	#123	—	2	8	no	—
439	#123	—	4	4	no	—
440	#123	—	4	4	no	—
441	#123	—	4	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	—	2	16	no	—
444	C₂²⋊Q₈	—	2	16	no	—
445	C₂²⋊Q₈	—	2	8	no	—
446	#121	—	2	4	no	—
447	#120	—	4	4	no	—
448	C₄×D₄	—	2	8	no	—
449	C₂×C₄⋊C₄	—	2	4	no	—
450	C₂×C₄⋊C₄	—	2	4	no	—
451	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
452	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
485	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
488	#95	C₂³×C₁₃₉	1	2	yes	—
489	#95	C₂³×C₁₃₉	1	2	yes	—
490	#95	C₂³×C₁₃₉	1	4	yes	—
491	#95	C₂³×C₁₃₉	1	4	yes	—
492	#95	C₂³×C₁₃₉	1	4	yes	—
493	#95	C₂³×C₁₃₉	1	4	yes	—
494	#95	C₂³×C₁₃₉	1	4	yes	—
495	#95	C₂³×C₁₃₉	1	4	yes	—
496	#95	C₂³×C₁₃₉	1	4	yes	—
497	#95	C₂³×C₁₃₉	1	4	yes	—
498	#95	C₂³×C₁₃₉	1	4	yes	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	2	4	no	—
501	C₂⁴	—	2	4	no	—
502	C₂⁴	—	4	2	no	—
503	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
504	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
505	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
506	C₂×Q₈	—	2	8	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	4	8	no	—
509	C₂×Q₈	—	4	2	no	—
510	C₂×Q₈	—	4	16	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	4	4	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	8	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	4	8	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	16	no	—
533	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
534	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
535	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
536	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
548	C₄⋊C₄	—	2	8	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₄⋊C₄	—	4	4	no	—
561	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
562	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	4	4	no	—
575	C₂²⋊C₄	—	4	4	no	—
576	C₂²⋊C₄	—	4	4	no	—
577	C₂²⋊C₄	—	4	4	no	—
578	C₂²⋊C₄	—	4	4	no	—
579	C₄²	—	2	4	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	8	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	4	16	no	—
595	C₂³	—	4	4	no	—
596	C₂³	—	4	4	no	—
597	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
598	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
599	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
600	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
601	Q₈	—	4	16	no	—
602	Q₈	—	8	2	no	—
603	D₄	—	4	8	no	—
604	D₄	—	8	2	no	—
605	D₄	—	8	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	4	no	—
632	C₂×C₄	—	4	16	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	4	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
638	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	16	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	#535×C₁₃₉	1	4	yes	—
656	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
657	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
658	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
659	C₂²	#585×C₁₃₉	1	2	yes	—
660	C₄	—	2	4	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₂	—	2	4	no	—
673	C₂	—	4	4	no	—
674	C₂	—	8	2	no	—
675	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
676	C₂	#3485×C₁₃₉	1	1	yes	characteristic
677	C₂	#3486×C₁₃₉	1	1	yes	characteristic
678	C₂	#3535×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2539×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×#539×C₁₃₉	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
3. #2849×C₁₃₉	C₂	semidirect
4. #2723×C₁₃₉	C₂	semidirect
5. #2720×C₁₃₉	C₂	semidirect
6. #2696×C₁₃₉	C₂	semidirect
7. #2692×C₁₃₉	C₂	semidirect
8. #2614×C₁₃₉	C₂	semidirect
9. #2561×C₁₃₉	C₂	semidirect
11. #2534×C₁₃₉	C₂	semidirect
12. #2503×C₁₃₉	C₂	semidirect
13. #2501×C₁₃₉	C₂	semidirect
14. #2486×C₁₃₉	C₂	semidirect
15. #2313×C₁₃₉	C₂	semidirect
19. C₂×#126×C₁₃₉	C₂²	semidirect
20. C₂×#125×C₁₃₉	C₂²	semidirect
25. C₂×#123×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
39. #400×C₁₃₉	C₂²	semidirect
41. #399×C₁₃₉	C₂²	semidirect
42. #398×C₁₃₉	C₂²	semidirect
44. #397×C₁₃₉	C₂²	semidirect
46. #395×C₁₃₉	C₂²	semidirect
47. #395×C₁₃₉	C₂²	semidirect
50. #393×C₁₃₉	C₂²	semidirect
51. #393×C₁₃₉	C₂²	semidirect
53. #391×C₁₃₉	C₂²	semidirect
55. #390×C₁₃₉	C₂²	semidirect
56. #389×C₁₃₉	C₂²	semidirect
59. #387×C₁₃₉	C₂²	semidirect
60. #387×C₁₃₉	C₂²	semidirect
66. #384×C₁₃₉	C₂²	semidirect
67. #382×C₁₃₉	C₂²	semidirect
73. #380×C₁₃₉	C₂²	semidirect
111. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
339. #37118	C₁₃₉	direct (N × H)
340. C₁₃₉	#37118	direct (N × H)
341. C₂×#539	C₂×C₁₃₉	semidirect
342. C₂²×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
343. #2849	C₂×C₁₃₉	semidirect
344. #2723	C₂×C₁₃₉	semidirect
345. #2720	C₂×C₁₃₉	semidirect
346. #2696	C₂×C₁₃₉	semidirect
347. #2692	C₂×C₁₃₉	semidirect
348. #2614	C₂×C₁₃₉	semidirect
349. #2561	C₂×C₁₃₉	semidirect
351. #2534	C₂×C₁₃₉	semidirect
352. #2503	C₂×C₁₃₉	semidirect
353. #2501	C₂×C₁₃₉	semidirect
354. #2486	C₂×C₁₃₉	semidirect
355. #2313	C₂×C₁₃₉	semidirect
359. C₂×#126	C₂²×C₁₃₉	semidirect
360. C₂×#125	C₂²×C₁₃₉	semidirect
365. C₂×#123	C₂²×C₁₃₉	semidirect
370. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
379. #400	C₂²×C₁₃₉	semidirect
381. #399	C₂²×C₁₃₉	semidirect
382. #398	C₂²×C₁₃₉	semidirect
384. #397	C₂²×C₁₃₉	semidirect
386. #395	C₂²×C₁₃₉	semidirect
387. #395	C₂²×C₁₃₉	semidirect
390. #393	C₂²×C₁₃₉	semidirect
391. #393	C₂²×C₁₃₉	semidirect
393. #391	C₂²×C₁₃₉	semidirect
395. #390	C₂²×C₁₃₉	semidirect
396. #389	C₂²×C₁₃₉	semidirect
399. #387	C₂²×C₁₃₉	semidirect
400. #387	C₂²×C₁₃₉	semidirect
406. #384	C₂²×C₁₃₉	semidirect
407. #382	C₂²×C₁₃₉	semidirect
413. #380	C₂²×C₁₃₉	semidirect
451. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₁₃₉	2
C₂²×C₂²⋊Q₈×C₁₃₉	2
#2849×C₁₃₉	2
#2723×C₁₃₉	2
#2720×C₁₃₉	2
#2696×C₁₃₉	2
#2692×C₁₃₉	2
#2614×C₁₃₉	2
#2561×C₁₃₉	2
#2539×C₁₃₉	2
#2534×C₁₃₉	2
#2503×C₁₃₉	2
#2501×C₁₃₉	2
#2486×C₁₃₉	2
#2313×C₁₃₉	2
#37118	139

Subgroups — C139×#37118 #48031714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37118 #48031714