Subgroups — C₁₃₉×#36476 #48031072

Order 35584.

1806 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	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2855×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2607×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2589×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2580×C₁₃₉	C₂	1	2	yes	maximal
6	#2570×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2492×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2423×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2357×C₁₃₉	C₂	1	2	yes	maximal
14	#2355×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	4	yes	—
30	#399×C₁₃₉	C₂²	1	4	yes	—
31	#399×C₁₃₉	C₂²	1	4	yes	—
32	#398×C₁₃₉	C₂²	1	4	yes	—
33	#393×C₁₃₉	C₂²	1	4	yes	—
34	#393×C₁₃₉	C₂²	1	4	yes	—
35	#391×C₁₃₉	C₂²	1	2	yes	—
36	#391×C₁₃₉	C₂²	1	2	yes	—
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#391×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	2	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#391×C₁₃₉	C₂²	1	4	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	1	yes	characteristic
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#389×C₁₃₉	C₂²	1	1	yes	characteristic
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#387×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#385×C₁₃₉	C₂²	1	4	yes	—
60	#384×C₁₃₉	C₂²	1	2	yes	—
61	#384×C₁₃₉	C₂²	1	1	yes	characteristic
62	#382×C₁₃₉	C₂²	1	2	yes	—
63	#382×C₁₃₉	C₂²	1	2	yes	—
64	#382×C₁₃₉	C₂²	1	2	yes	—
65	#381×C₁₃₉	C₂²	1	4	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
82	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
91	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
92	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
93	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
94	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
95	C₄×Q₈×C₁₃₉	—	2	8	no	—
96	C₄×Q₈×C₁₃₉	—	4	4	no	—
97	C₄×D₄×C₁₃₉	—	2	4	no	—
98	C₄×D₄×C₁₃₉	—	2	4	no	—
99	C₄×D₄×C₁₃₉	Q₈	1	8	yes	complemented
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	—	4	4	no	—
128	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
142	#95×C₁₃₉	C₂³	1	2	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	4	yes	—
145	#95×C₁₃₉	C₂³	1	2	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	4	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	2	yes	—
151	#95×C₁₃₉	C₂³	1	2	yes	—
152	#95×C₁₃₉	C₂³	1	2	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	C₂⁴	1	2	yes	—
160	C₂×Q₈×C₁₃₉	—	2	4	no	—
161	C₂×Q₈×C₁₃₉	—	2	4	no	—
162	C₂×Q₈×C₁₃₉	—	2	4	no	—
163	C₂×Q₈×C₁₃₉	—	2	4	no	—
164	C₂×Q₈×C₁₃₉	—	2	4	no	—
165	C₂×Q₈×C₁₃₉	—	2	4	no	—
166	C₂×Q₈×C₁₃₉	—	4	2	no	—
167	C₂×Q₈×C₁₃₉	—	4	2	no	—
168	C₂×Q₈×C₁₃₉	—	4	2	no	—
169	C₂×D₄×C₁₃₉	—	2	2	no	—
170	C₂×D₄×C₁₃₉	—	2	2	no	—
171	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
172	C₂²×C₄×C₁₃₉	—	2	4	no	—
173	C₂²×C₄×C₁₃₉	—	2	4	no	—
174	C₂²×C₄×C₁₃₉	—	2	4	no	—
175	C₂²×C₄×C₁₃₉	—	2	4	no	—
176	C₂²×C₄×C₁₃₉	—	4	2	no	—
177	C₂²×C₄×C₁₃₉	—	4	2	no	—
178	C₂²×C₄×C₁₃₉	—	4	2	no	—
179	C₂²×C₄×C₁₃₉	—	4	2	no	—
180	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
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	2	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₁₃₉	—	2	2	no	—
198	C₄⋊C₄×C₁₃₉	—	2	2	no	—
199	C₄⋊C₄×C₁₃₉	—	2	4	no	—
200	C₄⋊C₄×C₁₃₉	—	2	4	no	—
201	C₄⋊C₄×C₁₃₉	—	2	4	no	—
202	C₄⋊C₄×C₁₃₉	—	2	8	no	—
203	C₄⋊C₄×C₁₃₉	—	2	4	no	—
204	C₄⋊C₄×C₁₃₉	—	2	4	no	—
205	C₄⋊C₄×C₁₃₉	—	2	4	no	—
206	C₄⋊C₄×C₁₃₉	—	2	4	no	—
207	C₄⋊C₄×C₁₃₉	—	2	2	no	—
208	C₄⋊C₄×C₁₃₉	—	2	4	no	—
209	C₄⋊C₄×C₁₃₉	—	2	2	no	—
210	C₄⋊C₄×C₁₃₉	—	2	2	no	—
211	C₄⋊C₄×C₁₃₉	—	4	2	no	—
212	C₄⋊C₄×C₁₃₉	—	4	4	no	—
213	C₄⋊C₄×C₁₃₉	—	4	4	no	—
214	C₄⋊C₄×C₁₃₉	—	4	4	no	—
215	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
216	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
217	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
220	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
221	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
222	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
223	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
224	C₄²×C₁₃₉	—	2	4	no	—
225	C₄²×C₁₃₉	—	2	4	no	—
226	C₄²×C₁₃₉	—	2	2	no	—
227	C₄²×C₁₃₉	—	2	2	no	—
228	C₄²×C₁₃₉	—	2	4	no	—
229	C₄²×C₁₃₉	—	4	2	no	—
230	C₄²×C₁₃₉	—	4	2	no	—
231	C₄²×C₁₃₉	—	4	4	no	—
232	C₄²×C₁₃₉	—	4	1	no	—
233	C₄²×C₁₃₉	—	4	1	no	—
234	C₄²×C₁₃₉	—	4	4	no	—
235	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
236	C₄²×C₁₃₉	#41	1	4	yes	—
237	C₄²×C₁₃₉	#41	1	4	yes	—
238	C₂³×C₁₃₉	—	2	2	no	—
239	C₂³×C₁₃₉	—	2	2	no	—
240	C₂³×C₁₃₉	—	2	2	no	—
241	C₂³×C₁₃₉	—	2	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	2	no	—
244	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
245	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
246	Q₈×C₁₃₉	—	4	8	no	—
247	Q₈×C₁₃₉	—	4	8	no	—
248	Q₈×C₁₃₉	—	8	4	no	—
249	D₄×C₁₃₉	—	2	8	no	—
250	C₂×C₄×C₁₃₉	—	2	1	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	1	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	1	no	—
255	C₂×C₄×C₁₃₉	—	2	1	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	1	no	—
259	C₂×C₄×C₁₃₉	—	2	1	no	—
260	C₂×C₄×C₁₃₉	—	2	1	no	—
261	C₂×C₄×C₁₃₉	—	2	1	no	—
262	C₂×C₄×C₁₃₉	—	2	1	no	—
263	C₂×C₄×C₁₃₉	—	2	1	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	4	no	—
273	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	4	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	4	8	no	—
286	C₂×C₄×C₁₃₉	—	4	8	no	—
287	C₂×C₄×C₁₃₉	—	4	8	no	—
288	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
289	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
290	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
291	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
292	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
293	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
294	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
295	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
296	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
297	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
298	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
299	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
300	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
301	C₂²×C₁₃₉	—	2	4	no	—
302	C₂²×C₁₃₉	—	2	4	no	—
303	C₂²×C₁₃₉	—	2	4	no	—
304	C₂²×C₁₃₉	—	4	2	no	—
305	C₂²×C₁₃₉	—	4	2	no	—
306	C₂²×C₁₃₉	—	4	2	no	—
307	C₂²×C₁₃₉	—	4	2	no	—
308	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
309	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
310	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
311	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
312	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂²×C₁₃₉	#585	1	1	yes	characteristic
314	C₂²×C₁₃₉	#585	1	1	yes	characteristic
315	C₄×C₁₃₉	—	2	4	no	—
316	C₄×C₁₃₉	—	2	2	no	—
317	C₄×C₁₃₉	—	2	2	no	—
318	C₄×C₁₃₉	—	2	2	no	—
319	C₄×C₁₃₉	—	2	4	no	—
320	C₄×C₁₃₉	—	2	2	no	—
321	C₄×C₁₃₉	—	2	2	no	—
322	C₄×C₁₃₉	—	4	2	no	—
323	C₄×C₁₃₉	—	4	2	no	—
324	C₄×C₁₃₉	—	4	4	no	—
325	C₄×C₁₃₉	—	4	2	no	—
326	C₄×C₁₃₉	—	4	2	no	—
327	C₄×C₁₃₉	—	4	2	no	—
328	C₄×C₁₃₉	—	4	4	no	—
329	C₄×C₁₃₉	#533	1	4	yes	—
330	C₄×C₁₃₉	#559	1	4	yes	—
331	C₂×C₁₃₉	—	4	4	no	—
332	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
333	C₂×C₁₃₉	#3475	1	1	yes	characteristic
334	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
335	C₂×C₁₃₉	C₂×#559	1	1	yes	characteristic
336	C₂×C₁₃₉	#3501	1	1	yes	characteristic
337	C₂×C₁₃₉	#3506	1	1	yes	characteristic
338	C₂×C₁₃₉	#3510	1	1	yes	characteristic
339	#36476	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₁₃₉	#36476	1	1	yes	characteristic, direct product factor, Sylow
341	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
342	#2855	C₂×C₁₃₉	1	2	yes	complemented
343	#2607	C₂×C₁₃₉	1	4	yes	complemented
344	#2589	C₂×C₁₃₉	1	4	yes	complemented
345	#2580	C₂×C₁₃₉	1	2	yes	—
346	#2570	C₂×C₁₃₉	1	2	yes	complemented
347	#2563	C₂×C₁₃₉	1	1	yes	characteristic
348	#2542	C₂×C₁₃₉	1	1	yes	characteristic
349	#2492	C₂×C₁₃₉	1	2	yes	complemented
350	#2423	C₂×C₁₃₉	1	2	yes	complemented
351	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
352	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
353	#2357	C₂×C₁₃₉	1	2	yes	—
354	#2355	C₂×C₁₃₉	1	2	yes	complemented
355	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
357	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
358	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
359	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
360	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
361	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
363	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
364	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
369	#400	C₂²×C₁₃₉	1	4	yes	—
370	#399	C₂²×C₁₃₉	1	4	yes	—
371	#399	C₂²×C₁₃₉	1	4	yes	—
372	#398	C₂²×C₁₃₉	1	4	yes	—
373	#393	C₂²×C₁₃₉	1	4	yes	—
374	#393	C₂²×C₁₃₉	1	4	yes	—
375	#391	C₂²×C₁₃₉	1	2	yes	—
376	#391	C₂²×C₁₃₉	1	2	yes	—
377	#391	C₂²×C₁₃₉	1	4	yes	—
378	#391	C₂²×C₁₃₉	1	2	yes	—
379	#391	C₂²×C₁₃₉	1	2	yes	—
380	#391	C₂²×C₁₃₉	1	2	yes	—
381	#391	C₂²×C₁₃₉	1	2	yes	—
382	#391	C₂²×C₁₃₉	1	4	yes	—
383	#390	C₂²×C₁₃₉	1	2	yes	—
384	#390	C₂²×C₁₃₉	1	2	yes	—
385	#389	C₂²×C₁₃₉	1	2	yes	—
386	#389	C₂²×C₁₃₉	1	1	yes	characteristic
387	#389	C₂²×C₁₃₉	1	1	yes	characteristic
388	#389	C₂²×C₁₃₉	1	2	yes	—
389	#389	C₂²×C₁₃₉	1	2	yes	—
390	#389	C₂²×C₁₃₉	1	2	yes	—
391	#388	C₂²×C₁₃₉	1	4	yes	—
392	#388	C₂²×C₁₃₉	1	4	yes	—
393	#387	C₂²×C₁₃₉	1	4	yes	—
394	#387	C₂²×C₁₃₉	1	4	yes	—
395	#387	C₂²×C₁₃₉	1	4	yes	—
396	#387	C₂²×C₁₃₉	1	4	yes	—
397	#387	C₂²×C₁₃₉	1	4	yes	—
398	#385	C₂²×C₁₃₉	1	4	yes	—
399	#385	C₂²×C₁₃₉	1	4	yes	—
400	#384	C₂²×C₁₃₉	1	1	yes	characteristic
401	#384	C₂²×C₁₃₉	1	2	yes	—
402	#382	C₂²×C₁₃₉	1	2	yes	—
403	#382	C₂²×C₁₃₉	1	2	yes	—
404	#382	C₂²×C₁₃₉	1	2	yes	—
405	#381	C₂²×C₁₃₉	1	4	yes	—
406	#380	C₂²×C₁₃₉	1	2	yes	—
407	#380	C₂²×C₁₃₉	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
413	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
422	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
424	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
425	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
426	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
428	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
429	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₄⋊Q₈	—	2	4	no	—
431	C₄⋊Q₈	—	2	4	no	—
432	C₄⋊Q₈	—	2	4	no	—
433	C₂²⋊Q₈	—	2	8	no	—
434	C₂²⋊Q₈	—	4	4	no	—
435	C₄×Q₈	—	2	8	no	—
436	C₄×Q₈	—	4	4	no	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	Q₈×C₁₃₉	1	8	yes	complemented
440	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₄²	—	4	4	no	—
468	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
470	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
474	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
478	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
482	#95	C₂³×C₁₃₉	1	2	yes	—
483	#95	C₂³×C₁₃₉	1	2	yes	—
484	#95	C₂³×C₁₃₉	1	2	yes	—
485	#95	C₂³×C₁₃₉	1	2	yes	—
486	#95	C₂³×C₁₃₉	1	4	yes	—
487	#95	C₂³×C₁₃₉	1	4	yes	—
488	#95	C₂³×C₁₃₉	1	2	yes	—
489	#95	C₂³×C₁₃₉	1	4	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	2	yes	—
494	#95	C₂³×C₁₃₉	1	2	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	C₂⁴×C₁₃₉	1	2	yes	—
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	4	no	—
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×Q₈	—	4	2	no	—
508	C₂×Q₈	—	4	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
521	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	8	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	—	4	4	no	—
554	C₄⋊C₄	—	4	4	no	—
555	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
556	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	4	no	—
572	C₄²	—	4	1	no	—
573	C₄²	—	4	1	no	—
574	C₄²	—	4	4	no	—
575	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
576	C₄²	#41×C₁₃₉	1	4	yes	—
577	C₄²	#41×C₁₃₉	1	4	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
585	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
586	Q₈	—	4	8	no	—
587	Q₈	—	4	8	no	—
588	Q₈	—	8	4	no	—
589	D₄	—	2	8	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	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	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	4	8	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	8	no	—
628	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
629	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
630	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
631	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
632	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
633	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
634	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
635	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
636	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
637	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
638	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
639	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
640	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	4	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
649	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
650	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
651	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
652	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
653	C₂²	#585×C₁₃₉	1	1	yes	characteristic
654	C₂²	#585×C₁₃₉	1	1	yes	characteristic
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	4	no	—
669	C₄	#533×C₁₃₉	1	4	yes	—
670	C₄	#559×C₁₃₉	1	4	yes	—
671	C₂	—	4	4	no	—
672	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
673	C₂	#3475×C₁₃₉	1	1	yes	characteristic
674	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
675	C₂	C₂×#559×C₁₃₉	1	1	yes	characteristic
676	C₂	#3501×C₁₃₉	1	1	yes	characteristic
677	C₂	#3506×C₁₃₉	1	1	yes	characteristic
678	C₂	#3510×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2862×C₁₃₉	C₂	semidirect
2. #2855×C₁₃₉	C₂	semidirect
3. #2607×C₁₃₉	C₂	semidirect
4. #2589×C₁₃₉	C₂	semidirect
6. #2570×C₁₃₉	C₂	semidirect
9. #2492×C₁₃₉	C₂	semidirect
10. #2423×C₁₃₉	C₂	semidirect
11. #2369×C₁₃₉	C₂	semidirect
12. #2365×C₁₃₉	C₂	semidirect
14. #2355×C₁₃₉	C₂	semidirect
15. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
99. C₄×D₄×C₁₃₉	Q₈	semidirect
339. #36476	C₁₃₉	direct (N × H)
340. C₁₃₉	#36476	direct (N × H)
341. #2862	C₂×C₁₃₉	semidirect
342. #2855	C₂×C₁₃₉	semidirect
343. #2607	C₂×C₁₃₉	semidirect
344. #2589	C₂×C₁₃₉	semidirect
346. #2570	C₂×C₁₃₉	semidirect
349. #2492	C₂×C₁₃₉	semidirect
350. #2423	C₂×C₁₃₉	semidirect
351. #2369	C₂×C₁₃₉	semidirect
352. #2365	C₂×C₁₃₉	semidirect
354. #2355	C₂×C₁₃₉	semidirect
355. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
356. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
439. C₄×D₄	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2862×C₁₃₉	2
#2855×C₁₃₉	2
#2607×C₁₃₉	2
#2589×C₁₃₉	2
#2580×C₁₃₉	2
#2570×C₁₃₉	2
#2563×C₁₃₉	2
#2542×C₁₃₉	2
#2492×C₁₃₉	2
#2423×C₁₃₉	2
#2369×C₁₃₉	2
#2365×C₁₃₉	2
#2357×C₁₃₉	2
#2355×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36476	139

Subgroups — C139×#36476 #48031072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36476 #48031072