Subgroups — C₁₃₉×#36260 #48030856

Order 35584.

4154 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	C₂×D₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2540×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2539×C₁₃₉	C₂	1	8	yes	maximal, complemented
10	#2501×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2433×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₄×#127×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	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
18	#547×C₁₃₉	—	2	8	no	—
19	#546×C₁₃₉	—	2	32	no	—
20	D₄²×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×#123×C₁₃₉	C₂²	1	8	yes	complemented
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	8	yes	complemented
33	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
34	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
35	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
36	C₂×#120×C₁₃₉	C₂²	1	8	yes	complemented
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
43	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	complemented
44	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
45	#399×C₁₃₉	C₂²	1	4	yes	complemented
46	#399×C₁₃₉	C₂²	1	8	yes	complemented
47	#392×C₁₃₉	C₂²	1	4	yes	complemented
48	#392×C₁₃₉	C₂²	1	8	yes	complemented
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	1	yes	characteristic
51	#390×C₁₃₉	C₂²	1	4	yes	complemented
52	#390×C₁₃₉	C₂²	1	4	yes	complemented
53	#390×C₁₃₉	C₂²	1	8	yes	complemented
54	#390×C₁₃₉	C₂²	1	8	yes	complemented
55	#390×C₁₃₉	C₂²	1	2	yes	complemented
56	#390×C₁₃₉	C₂²	1	2	yes	complemented
57	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#390×C₁₃₉	C₂²	1	2	yes	complemented
59	#384×C₁₃₉	C₂²	1	2	yes	complemented
60	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
62	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
65	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
67	C₂×#41×C₁₃₉	—	2	16	no	—
68	C₂×#41×C₁₃₉	—	2	8	no	—
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	—	2	8	no	—
71	C₂²×D₄×C₁₃₉	—	2	16	no	—
72	C₂²×D₄×C₁₃₉	—	2	8	no	—
73	C₂²×D₄×C₁₃₉	—	2	8	no	—
74	C₂²×D₄×C₁₃₉	—	4	4	no	—
75	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
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	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
92	#127×C₁₃₉	—	2	4	no	—
93	#127×C₁₃₉	—	2	4	no	—
94	#127×C₁₃₉	—	4	4	no	—
95	#124×C₁₃₉	—	2	16	no	—
96	#123×C₁₃₉	—	2	16	no	—
97	#123×C₁₃₉	—	2	32	no	—
98	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
99	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
100	#121×C₁₃₉	—	2	8	no	—
101	#121×C₁₃₉	—	2	8	no	—
102	#121×C₁₃₉	—	2	32	no	—
103	#121×C₁₃₉	—	2	8	no	—
104	#121×C₁₃₉	—	2	16	no	—
105	#120×C₁₃₉	—	2	16	no	—
106	#120×C₁₃₉	—	2	32	no	—
107	C₄×D₄×C₁₃₉	—	2	4	no	—
108	C₄×D₄×C₁₃₉	—	2	4	no	—
109	C₄×D₄×C₁₃₉	—	2	16	no	—
110	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
111	C₄×D₄×C₁₃₉	D₄	1	16	yes	complemented
112	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	—	2	32	no	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₉	—	4	4	no	—
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
143	#95×C₁₃₉	C₂³	1	2	yes	—
144	#95×C₁₃₉	C₂³	1	4	yes	—
145	C₂⁴×C₁₃₉	—	2	8	no	—
146	C₂⁴×C₁₃₉	—	2	16	no	—
147	C₂⁴×C₁₃₉	—	2	8	no	—
148	C₂⁴×C₁₃₉	—	4	4	no	—
149	C₂⁴×C₁₃₉	—	4	8	no	—
150	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
151	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
154	#41×C₁₃₉	—	4	32	no	—
155	C₂×Q₈×C₁₃₉	—	2	8	no	—
156	C₂×Q₈×C₁₃₉	—	2	4	no	—
157	C₂×D₄×C₁₃₉	—	2	8	no	—
158	C₂×D₄×C₁₃₉	—	2	16	no	—
159	C₂×D₄×C₁₃₉	—	2	16	no	—
160	C₂×D₄×C₁₃₉	—	2	8	no	—
161	C₂×D₄×C₁₃₉	—	2	8	no	—
162	C₂×D₄×C₁₃₉	—	2	8	no	—
163	C₂×D₄×C₁₃₉	—	2	2	no	—
164	C₂×D₄×C₁₃₉	—	2	8	no	—
165	C₂×D₄×C₁₃₉	—	2	2	no	—
166	C₂×D₄×C₁₃₉	—	2	8	no	—
167	C₂×D₄×C₁₃₉	—	2	8	no	—
168	C₂×D₄×C₁₃₉	—	2	4	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	2	4	no	—
171	C₂×D₄×C₁₃₉	—	2	16	no	—
172	C₂×D₄×C₁₃₉	—	2	2	no	—
173	C₂×D₄×C₁₃₉	—	2	4	no	—
174	C₂×D₄×C₁₃₉	—	2	2	no	—
175	C₂×D₄×C₁₃₉	—	2	2	no	—
176	C₂×D₄×C₁₃₉	—	2	4	no	—
177	C₂×D₄×C₁₃₉	—	4	32	no	—
178	C₂×D₄×C₁₃₉	—	4	4	no	—
179	C₂×D₄×C₁₃₉	—	4	4	no	—
180	C₂×D₄×C₁₃₉	—	4	8	no	—
181	C₂×D₄×C₁₃₉	—	4	4	no	—
182	C₂×D₄×C₁₃₉	—	4	8	no	—
183	C₂×D₄×C₁₃₉	—	4	32	no	—
184	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
185	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
186	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
187	C₂²×C₄×C₁₃₉	—	2	4	no	—
188	C₂²×C₄×C₁₃₉	—	2	4	no	—
189	C₂²×C₄×C₁₃₉	—	2	16	no	—
190	C₂²×C₄×C₁₃₉	—	2	8	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	8	no	—
193	C₂²×C₄×C₁₃₉	—	2	8	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	4	4	no	—
196	C₂²×C₄×C₁₃₉	—	4	4	no	—
197	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
198	C₂²×C₄×C₁₃₉	C₂×D₄	1	16	yes	complemented
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₄⋊C₄×C₁₃₉	—	2	2	no	—
210	C₄⋊C₄×C₁₃₉	—	2	4	no	—
211	C₄⋊C₄×C₁₃₉	—	2	8	no	—
212	C₄⋊C₄×C₁₃₉	—	2	2	no	—
213	C₄⋊C₄×C₁₃₉	—	2	8	no	—
214	C₄⋊C₄×C₁₃₉	—	2	16	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
217	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
218	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
219	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
220	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
221	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
222	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
224	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
226	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
229	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	complemented
230	C₄²×C₁₃₉	—	2	2	no	—
231	C₄²×C₁₃₉	—	2	2	no	—
232	C₄²×C₁₃₉	—	2	4	no	—
233	C₄²×C₁₃₉	—	4	4	no	—
234	C₄²×C₁₃₉	—	4	2	no	—
235	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
236	C₄²×C₁₃₉	C₂×D₄	1	8	yes	complemented
237	C₂³×C₁₃₉	—	2	2	no	—
238	C₂³×C₁₃₉	—	2	2	no	—
239	C₂³×C₁₃₉	—	2	4	no	—
240	C₂³×C₁₃₉	—	2	4	no	—
241	C₂³×C₁₃₉	—	2	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	4	no	—
244	C₂³×C₁₃₉	—	2	2	no	—
245	C₂³×C₁₃₉	—	2	8	no	—
246	C₂³×C₁₃₉	—	2	4	no	—
247	C₂³×C₁₃₉	—	2	4	no	—
248	C₂³×C₁₃₉	—	2	2	no	—
249	C₂³×C₁₃₉	—	2	4	no	—
250	C₂³×C₁₃₉	—	2	2	no	—
251	C₂³×C₁₃₉	—	2	4	no	—
252	C₂³×C₁₃₉	—	2	4	no	—
253	C₂³×C₁₃₉	—	2	8	no	—
254	C₂³×C₁₃₉	—	4	16	no	—
255	C₂³×C₁₃₉	—	4	32	no	—
256	C₂³×C₁₃₉	—	4	16	no	—
257	C₂³×C₁₃₉	—	8	16	no	—
258	C₂³×C₁₃₉	—	8	8	no	—
259	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
260	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
261	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
262	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
263	Q₈×C₁₃₉	—	4	8	no	—
264	D₄×C₁₃₉	—	2	8	no	—
265	D₄×C₁₃₉	—	4	16	no	—
266	D₄×C₁₃₉	—	4	16	no	—
267	D₄×C₁₃₉	—	4	16	no	—
268	D₄×C₁₃₉	—	4	16	no	—
269	D₄×C₁₃₉	—	4	8	no	—
270	D₄×C₁₃₉	—	4	4	no	—
271	D₄×C₁₃₉	—	4	8	no	—
272	D₄×C₁₃₉	—	8	16	no	—
273	D₄×C₁₃₉	—	8	4	no	—
274	D₄×C₁₃₉	#127	1	16	yes	complemented
275	C₂×C₄×C₁₃₉	—	2	2	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	4	no	—
284	C₂×C₄×C₁₃₉	—	2	16	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	8	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	4	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	4	16	no	—
292	C₂×C₄×C₁₃₉	—	4	16	no	—
293	C₂×C₄×C₁₃₉	—	4	8	no	—
294	C₂×C₄×C₁₃₉	—	4	8	no	—
295	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
300	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
304	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
305	C₂²×C₁₃₉	—	2	4	no	—
306	C₂²×C₁₃₉	—	2	8	no	—
307	C₂²×C₁₃₉	—	2	8	no	—
308	C₂²×C₁₃₉	—	2	4	no	—
309	C₂²×C₁₃₉	—	2	4	no	—
310	C₂²×C₁₃₉	—	2	8	no	—
311	C₂²×C₁₃₉	—	4	2	no	—
312	C₂²×C₁₃₉	—	4	4	no	—
313	C₂²×C₁₃₉	—	4	2	no	—
314	C₂²×C₁₃₉	—	4	2	no	—
315	C₂²×C₁₃₉	—	4	4	no	—
316	C₂²×C₁₃₉	—	4	4	no	—
317	C₂²×C₁₃₉	—	4	2	no	—
318	C₂²×C₁₃₉	—	4	4	no	—
319	C₂²×C₁₃₉	—	4	8	no	—
320	C₂²×C₁₃₉	—	4	4	no	—
321	C₂²×C₁₃₉	—	4	8	no	—
322	C₂²×C₁₃₉	—	4	4	no	—
323	C₂²×C₁₃₉	—	4	2	no	—
324	C₂²×C₁₃₉	—	8	32	no	—
325	C₂²×C₁₃₉	C₂×#127	1	8	yes	—
326	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
327	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
328	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
329	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂²×C₁₃₉	#585	1	2	yes	—
331	C₄×C₁₃₉	—	2	4	no	—
332	C₄×C₁₃₉	—	2	4	no	—
333	C₄×C₁₃₉	—	2	4	no	—
334	C₄×C₁₃₉	—	2	8	no	—
335	C₄×C₁₃₉	—	2	2	no	—
336	C₄×C₁₃₉	—	4	2	no	—
337	C₄×C₁₃₉	—	4	2	no	—
338	C₄×C₁₃₉	—	4	4	no	—
339	C₄×C₁₃₉	C₂×#127	1	4	yes	—
340	C₄×C₁₃₉	#546	1	4	yes	complemented
341	C₂×C₁₃₉	—	2	8	no	—
342	C₂×C₁₃₉	—	4	4	no	—
343	C₂×C₁₃₉	—	8	2	no	—
344	C₂×C₁₃₉	—	8	4	no	—
345	C₂×C₁₃₉	C₂²×#127	1	1	yes	characteristic
346	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
347	C₂×C₁₃₉	D₄×#41	1	2	yes	—
348	C₂×C₁₃₉	#3496	1	2	yes	—
349	C₂×C₁₃₉	#3500	1	1	yes	characteristic
350	#36260	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
351	C₁₃₉	#36260	1	1	yes	characteristic, direct product factor, Sylow
352	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
353	C₂×#546	C₂×C₁₃₉	1	4	yes	complemented
354	C₂×D₄²	C₂×C₁₃₉	1	1	yes	characteristic, complemented
355	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	#2856	C₂×C₁₃₉	1	2	yes	complemented
357	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
358	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
359	#2540	C₂×C₁₃₉	1	4	yes	complemented
360	#2539	C₂×C₁₃₉	1	8	yes	complemented
361	#2501	C₂×C₁₃₉	1	2	yes	complemented
362	#2433	C₂×C₁₃₉	1	2	yes	complemented
363	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
364	C₂×#390	C₂×C₁₃₉	1	2	yes	complemented
365	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
366	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
367	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
368	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
369	#547	—	2	8	no	—
370	#546	—	2	32	no	—
371	D₄²	—	2	8	no	—
372	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
373	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
374	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂×#127	C₂²×C₁₃₉	1	2	yes	complemented
376	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
377	C₂×#123	C₂²×C₁₃₉	1	8	yes	complemented
378	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
379	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
380	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
381	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
382	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
383	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
384	C₂×#121	C₂²×C₁₃₉	1	8	yes	complemented
385	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
386	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
387	C₂×#120	C₂²×C₁₃₉	1	8	yes	complemented
388	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
392	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
393	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
394	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	complemented
395	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
396	#399	C₂²×C₁₃₉	1	8	yes	complemented
397	#399	C₂²×C₁₃₉	1	4	yes	complemented
398	#392	C₂²×C₁₃₉	1	8	yes	complemented
399	#392	C₂²×C₁₃₉	1	4	yes	complemented
400	#390	C₂²×C₁₃₉	1	1	yes	characteristic
401	#390	C₂²×C₁₃₉	1	2	yes	—
402	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
403	#390	C₂²×C₁₃₉	1	4	yes	complemented
404	#390	C₂²×C₁₃₉	1	2	yes	complemented
405	#390	C₂²×C₁₃₉	1	8	yes	complemented
406	#390	C₂²×C₁₃₉	1	2	yes	complemented
407	#390	C₂²×C₁₃₉	1	4	yes	complemented
408	#390	C₂²×C₁₃₉	1	2	yes	complemented
409	#390	C₂²×C₁₃₉	1	8	yes	complemented
410	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
411	#384	C₂²×C₁₃₉	1	2	yes	complemented
412	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
413	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
414	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
415	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
416	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
417	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
418	C₂×#41	—	2	16	no	—
419	C₂×#41	—	2	8	no	—
420	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
421	C₂²×D₄	—	2	8	no	—
422	C₂²×D₄	—	2	16	no	—
423	C₂²×D₄	—	2	8	no	—
424	C₂²×D₄	—	2	8	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
428	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
429	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
431	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
432	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
433	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
434	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
435	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
436	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
438	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
439	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
440	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
441	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
442	C₄⋊Q₈	—	2	4	no	—
443	#127	—	2	4	no	—
444	#127	—	2	4	no	—
445	#127	—	4	4	no	—
446	#124	—	2	16	no	—
447	#123	—	2	16	no	—
448	#123	—	2	32	no	—
449	C₂²⋊Q₈	—	2	8	no	—
450	C₂²⋊Q₈	—	2	16	no	—
451	#121	—	2	8	no	—
452	#121	—	2	8	no	—
453	#121	—	2	32	no	—
454	#121	—	2	8	no	—
455	#121	—	2	16	no	—
456	#120	—	2	16	no	—
457	#120	—	2	32	no	—
458	C₄×D₄	—	2	4	no	—
459	C₄×D₄	—	2	4	no	—
460	C₄×D₄	—	2	16	no	—
461	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
462	C₄×D₄	D₄×C₁₃₉	1	16	yes	complemented
463	C₂×C₄⋊C₄	—	2	8	no	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₂²⋊C₄	—	2	32	no	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	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	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₄²	—	4	4	no	—
487	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
492	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
494	#95	C₂³×C₁₃₉	1	4	yes	—
495	#95	C₂³×C₁₃₉	1	2	yes	—
496	C₂⁴	—	2	8	no	—
497	C₂⁴	—	2	16	no	—
498	C₂⁴	—	2	8	no	—
499	C₂⁴	—	4	4	no	—
500	C₂⁴	—	4	8	no	—
501	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
502	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
503	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
504	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
505	#41	—	4	32	no	—
506	C₂×Q₈	—	2	8	no	—
507	C₂×Q₈	—	2	4	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	16	no	—
510	C₂×D₄	—	2	16	no	—
511	C₂×D₄	—	2	8	no	—
512	C₂×D₄	—	2	8	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	8	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	16	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	4	32	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	8	no	—
532	C₂×D₄	—	4	4	no	—
533	C₂×D₄	—	4	8	no	—
534	C₂×D₄	—	4	32	no	—
535	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
536	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
537	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	16	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
549	C₂²×C₄	C₂×D₄×C₁₃₉	1	16	yes	complemented
550	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	16	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
568	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	16	no	—
571	C₂²⋊C₄	—	2	16	no	—
572	C₂²⋊C₄	—	2	16	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	8	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	16	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
580	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	complemented
581	C₄²	—	2	2	no	—
582	C₄²	—	2	2	no	—
583	C₄²	—	2	4	no	—
584	C₄²	—	4	4	no	—
585	C₄²	—	4	2	no	—
586	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
587	C₄²	C₂×D₄×C₁₃₉	1	8	yes	complemented
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	8	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	4	16	no	—
606	C₂³	—	4	32	no	—
607	C₂³	—	4	16	no	—
608	C₂³	—	8	16	no	—
609	C₂³	—	8	8	no	—
610	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
611	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
612	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
613	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
614	Q₈	—	4	8	no	—
615	D₄	—	2	8	no	—
616	D₄	—	4	16	no	—
617	D₄	—	4	16	no	—
618	D₄	—	4	16	no	—
619	D₄	—	4	16	no	—
620	D₄	—	4	8	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	4	no	—
623	D₄	—	8	16	no	—
624	D₄	—	8	4	no	—
625	D₄	#127×C₁₃₉	1	16	yes	complemented
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	16	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	8	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	4	16	no	—
643	C₂×C₄	—	4	16	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	8	no	—
646	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
651	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
653	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
654	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
655	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	8	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	8	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	8	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	8	32	no	—
676	C₂²	C₂×#127×C₁₃₉	1	8	yes	—
677	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
678	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
679	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
680	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
681	C₂²	#585×C₁₃₉	1	2	yes	—
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	8	no	—
686	C₄	—	2	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	4	no	—
690	C₄	C₂×#127×C₁₃₉	1	4	yes	—
691	C₄	#546×C₁₃₉	1	4	yes	complemented
692	C₂	—	2	8	no	—
693	C₂	—	4	4	no	—
694	C₂	—	8	4	no	—
695	C₂	—	8	2	no	—
696	C₂	C₂²×#127×C₁₃₉	1	1	yes	characteristic
697	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
698	C₂	D₄×#41×C₁₃₉	1	2	yes	—
699	C₂	#3496×C₁₃₉	1	2	yes	—
700	C₂	#3500×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#547×C₁₃₉	C₂	semidirect
2. C₂×#546×C₁₃₉	C₂	semidirect
3. C₂×D₄²×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2856×C₁₃₉	C₂	semidirect
6. #2542×C₁₃₉	C₂	semidirect
7. #2541×C₁₃₉	C₂	semidirect
8. #2540×C₁₃₉	C₂	semidirect
9. #2539×C₁₃₉	C₂	semidirect
10. #2501×C₁₃₉	C₂	semidirect
11. #2433×C₁₃₉	C₂	semidirect
12. C₄×#127×C₁₃₉	C₂	semidirect
13. C₂×#390×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×#127×C₁₃₉	C₂²	semidirect
25. C₂×#124×C₁₃₉	C₂²	semidirect
26. C₂×#123×C₁₃₉	C₂²	semidirect
27. C₂×#123×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×#121×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×#121×C₁₃₉	C₂²	semidirect
36. C₂×#120×C₁₃₉	C₂²	semidirect
40. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
42. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
44. C₂²×C₄²×C₁₃₉	C₂²	semidirect
45. #399×C₁₃₉	C₂²	semidirect
46. #399×C₁₃₉	C₂²	semidirect
47. #392×C₁₃₉	C₂²	semidirect
48. #392×C₁₃₉	C₂²	semidirect
51. #390×C₁₃₉	C₂²	semidirect
52. #390×C₁₃₉	C₂²	semidirect
53. #390×C₁₃₉	C₂²	semidirect
54. #390×C₁₃₉	C₂²	semidirect
55. #390×C₁₃₉	C₂²	semidirect
56. #390×C₁₃₉	C₂²	semidirect
57. #390×C₁₃₉	C₂²	semidirect
58. #390×C₁₃₉	C₂²	semidirect
59. #384×C₁₃₉	C₂²	semidirect
60. #384×C₁₃₉	C₂²	semidirect
61. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
62. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
65. C₄³×C₁₃₉	C₂²	semidirect
110. C₄×D₄×C₁₃₉	D₄	semidirect
111. C₄×D₄×C₁₃₉	D₄	semidirect
186. C₂×D₄×C₁₃₉	#41	semidirect
198. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
217. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
229. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
236. C₄²×C₁₃₉	C₂×D₄	semidirect
274. D₄×C₁₃₉	#127	semidirect
340. C₄×C₁₃₉	#546	semidirect
350. #36260	C₁₃₉	direct (N × H)
351. C₁₃₉	#36260	direct (N × H)
352. C₂×#547	C₂×C₁₃₉	semidirect
353. C₂×#546	C₂×C₁₃₉	semidirect
354. C₂×D₄²	C₂×C₁₃₉	semidirect
355. #2858	C₂×C₁₃₉	semidirect
356. #2856	C₂×C₁₃₉	semidirect
357. #2542	C₂×C₁₃₉	semidirect
358. #2541	C₂×C₁₃₉	semidirect
359. #2540	C₂×C₁₃₉	semidirect
360. #2539	C₂×C₁₃₉	semidirect
361. #2501	C₂×C₁₃₉	semidirect
362. #2433	C₂×C₁₃₉	semidirect
363. C₄×#127	C₂×C₁₃₉	semidirect
364. C₂×#390	C₂×C₁₃₉	semidirect
365. C₄²×D₄	C₂×C₁₃₉	semidirect
372. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
375. C₂×#127	C₂²×C₁₃₉	semidirect
376. C₂×#124	C₂²×C₁₃₉	semidirect
377. C₂×#123	C₂²×C₁₃₉	semidirect
378. C₂×#123	C₂²×C₁₃₉	semidirect
379. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
380. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
383. C₂×#121	C₂²×C₁₃₉	semidirect
384. C₂×#121	C₂²×C₁₃₉	semidirect
385. C₂×#121	C₂²×C₁₃₉	semidirect
387. C₂×#120	C₂²×C₁₃₉	semidirect
391. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
392. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
393. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
394. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
395. C₂²×C₄²	C₂²×C₁₃₉	semidirect
396. #399	C₂²×C₁₃₉	semidirect
397. #399	C₂²×C₁₃₉	semidirect
398. #392	C₂²×C₁₃₉	semidirect
399. #392	C₂²×C₁₃₉	semidirect
402. #390	C₂²×C₁₃₉	semidirect
403. #390	C₂²×C₁₃₉	semidirect
404. #390	C₂²×C₁₃₉	semidirect
405. #390	C₂²×C₁₃₉	semidirect
406. #390	C₂²×C₁₃₉	semidirect
407. #390	C₂²×C₁₃₉	semidirect
408. #390	C₂²×C₁₃₉	semidirect
409. #390	C₂²×C₁₃₉	semidirect
410. #384	C₂²×C₁₃₉	semidirect
411. #384	C₂²×C₁₃₉	semidirect
412. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
413. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
415. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
416. C₄³	C₂²×C₁₃₉	semidirect
461. C₄×D₄	D₄×C₁₃₉	semidirect
462. C₄×D₄	D₄×C₁₃₉	semidirect
537. C₂×D₄	#41×C₁₃₉	semidirect
549. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
568. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
580. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
587. C₄²	C₂×D₄×C₁₃₉	semidirect
625. D₄	#127×C₁₃₉	semidirect
691. C₄	#546×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂×#546×C₁₃₉	2
C₂×D₄²×C₁₃₉	2
#2858×C₁₃₉	2
#2856×C₁₃₉	2
#2542×C₁₃₉	2
#2541×C₁₃₉	2
#2540×C₁₃₉	2
#2539×C₁₃₉	2
#2501×C₁₃₉	2
#2433×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36260	139

Subgroups — C139×#36260 #48030856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36260 #48030856