Subgroups — C₁₃₉×#36061 #48030657

Order 35584.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#551×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2664×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2663×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2659×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2611×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2604×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2564×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2561×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2556×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2553×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2534×C₁₃₉	C₂	1	2	yes	maximal
13	#2521×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2498×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2486×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2396×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2344×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2342×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#552×C₁₃₉	—	2	8	no	—
25	#551×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
54	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#399×C₁₃₉	C₂²	1	2	yes	—
59	#399×C₁₃₉	C₂²	1	2	yes	—
60	#399×C₁₃₉	C₂²	1	1	yes	characteristic
61	#399×C₁₃₉	C₂²	1	1	yes	characteristic
62	#399×C₁₃₉	C₂²	1	1	yes	characteristic
63	#399×C₁₃₉	C₂²	1	1	yes	characteristic
64	#398×C₁₃₉	C₂²	1	2	yes	complemented
65	#398×C₁₃₉	C₂²	1	2	yes	complemented
66	#398×C₁₃₉	C₂²	1	2	yes	complemented
67	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
69	#397×C₁₃₉	C₂²	1	1	yes	characteristic
70	#397×C₁₃₉	C₂²	1	1	yes	characteristic
71	#397×C₁₃₉	C₂²	1	2	yes	complemented
72	#397×C₁₃₉	C₂²	1	2	yes	complemented
73	#396×C₁₃₉	C₂²	1	2	yes	—
74	#396×C₁₃₉	C₂²	1	2	yes	—
75	#395×C₁₃₉	C₂²	1	2	yes	complemented
76	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
78	#394×C₁₃₉	C₂²	1	2	yes	—
79	#394×C₁₃₉	C₂²	1	2	yes	—
80	#393×C₁₃₉	C₂²	1	1	yes	characteristic
81	#393×C₁₃₉	C₂²	1	1	yes	characteristic
82	#391×C₁₃₉	C₂²	1	2	yes	complemented
83	#389×C₁₃₉	C₂²	1	2	yes	complemented
84	#389×C₁₃₉	C₂²	1	2	yes	complemented
85	#389×C₁₃₉	C₂²	1	2	yes	complemented
86	#389×C₁₃₉	C₂²	1	2	yes	complemented
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#388×C₁₃₉	C₂²	1	2	yes	—
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#388×C₁₃₉	C₂²	1	2	yes	—
94	#388×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	complemented
96	#387×C₁₃₉	C₂²	1	2	yes	complemented
97	#387×C₁₃₉	C₂²	1	2	yes	complemented
98	#387×C₁₃₉	C₂²	1	2	yes	complemented
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#385×C₁₃₉	C₂²	1	2	yes	—
102	#385×C₁₃₉	C₂²	1	2	yes	—
103	#382×C₁₃₉	C₂²	1	2	yes	complemented
104	#381×C₁₃₉	C₂²	1	2	yes	—
105	#381×C₁₃₉	C₂²	1	2	yes	—
106	#381×C₁₃₉	C₂²	1	2	yes	—
107	#380×C₁₃₉	C₂²	1	2	yes	—
108	#380×C₁₃₉	C₂²	1	2	yes	—
109	#380×C₁₃₉	C₂²	1	2	yes	complemented
110	#380×C₁₃₉	C₂²	1	2	yes	complemented
111	#379×C₁₃₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
122	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
123	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
139	#126×C₁₃₉	—	2	4	no	—
140	#126×C₁₃₉	—	2	8	no	—
141	#126×C₁₃₉	—	2	4	no	—
142	#125×C₁₃₉	—	2	8	no	—
143	#125×C₁₃₉	—	2	4	no	—
144	#124×C₁₃₉	—	2	4	no	—
145	#123×C₁₃₉	—	2	4	no	—
146	#123×C₁₃₉	—	2	8	no	—
147	#123×C₁₃₉	—	2	4	no	—
148	#123×C₁₃₉	—	2	4	no	—
149	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
153	#120×C₁₃₉	—	2	4	no	—
154	C₄×Q₈×C₁₃₉	—	2	4	no	—
155	C₄×D₄×C₁₃₉	—	2	4	no	—
156	C₄×D₄×C₁₃₉	—	2	8	no	—
157	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
158	#117×C₁₃₉	—	2	4	no	—
159	#117×C₁₃₉	—	2	4	no	—
160	#117×C₁₃₉	—	2	8	no	—
161	#117×C₁₃₉	—	2	4	no	—
162	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
192	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
224	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	1	yes	characteristic
232	#95×C₁₃₉	C₂³	1	1	yes	characteristic
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	#95×C₁₃₉	C₂³	1	2	yes	—
235	#95×C₁₃₉	C₂³	1	2	yes	—
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	1	yes	characteristic
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	C₂⁴×C₁₃₉	—	2	2	no	—
253	C₂⁴×C₁₃₉	—	2	2	no	—
254	C₂⁴×C₁₃₉	—	2	4	no	—
255	C₂⁴×C₁₃₉	—	4	2	no	—
256	C₂⁴×C₁₃₉	—	4	1	no	—
257	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂×Q₈×C₁₃₉	—	2	2	no	—
262	C₂×Q₈×C₁₃₉	—	2	2	no	—
263	C₂×Q₈×C₁₃₉	—	4	2	no	—
264	C₂×Q₈×C₁₃₉	—	4	2	no	—
265	C₂×D₄×C₁₃₉	—	2	4	no	—
266	C₂×D₄×C₁₃₉	—	2	2	no	—
267	C₂×D₄×C₁₃₉	—	2	2	no	—
268	C₂×D₄×C₁₃₉	—	2	2	no	—
269	C₂×D₄×C₁₃₉	—	4	1	no	—
270	C₂×D₄×C₁₃₉	—	4	2	no	—
271	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
272	C₂²×C₄×C₁₃₉	—	2	2	no	—
273	C₂²×C₄×C₁₃₉	—	2	4	no	—
274	C₂²×C₄×C₁₃₉	—	2	4	no	—
275	C₂²×C₄×C₁₃₉	—	2	4	no	—
276	C₂²×C₄×C₁₃₉	—	2	4	no	—
277	C₂²×C₄×C₁₃₉	—	2	2	no	—
278	C₂²×C₄×C₁₃₉	—	2	2	no	—
279	C₂²×C₄×C₁₃₉	—	2	2	no	—
280	C₂²×C₄×C₁₃₉	—	2	4	no	—
281	C₂²×C₄×C₁₃₉	—	4	1	no	—
282	C₂²×C₄×C₁₃₉	—	4	2	no	—
283	C₂²×C₄×C₁₃₉	—	4	2	no	—
284	C₂²×C₄×C₁₃₉	—	4	2	no	—
285	C₂²×C₄×C₁₃₉	—	4	2	no	—
286	C₂²×C₄×C₁₃₉	—	4	2	no	—
287	C₂²×C₄×C₁₃₉	—	4	2	no	—
288	C₂²×C₄×C₁₃₉	—	4	2	no	—
289	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
290	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
291	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
292	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₁₃₉	—	2	2	no	—
312	C₄⋊C₄×C₁₃₉	—	2	2	no	—
313	C₄⋊C₄×C₁₃₉	—	2	4	no	—
314	C₄⋊C₄×C₁₃₉	—	2	2	no	—
315	C₄⋊C₄×C₁₃₉	—	2	2	no	—
316	C₄⋊C₄×C₁₃₉	—	2	2	no	—
317	C₄⋊C₄×C₁₃₉	—	2	4	no	—
318	C₄⋊C₄×C₁₃₉	—	2	2	no	—
319	C₄⋊C₄×C₁₃₉	—	2	2	no	—
320	C₄⋊C₄×C₁₃₉	—	2	4	no	—
321	C₄⋊C₄×C₁₃₉	—	2	2	no	—
322	C₄⋊C₄×C₁₃₉	—	2	4	no	—
323	C₄⋊C₄×C₁₃₉	—	2	2	no	—
324	C₄⋊C₄×C₁₃₉	—	2	2	no	—
325	C₄⋊C₄×C₁₃₉	—	2	4	no	—
326	C₄⋊C₄×C₁₃₉	—	2	4	no	—
327	C₄⋊C₄×C₁₃₉	—	2	4	no	—
328	C₄⋊C₄×C₁₃₉	—	2	4	no	—
329	C₄⋊C₄×C₁₃₉	—	2	4	no	—
330	C₄⋊C₄×C₁₃₉	—	2	4	no	—
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	4	2	no	—
333	C₄⋊C₄×C₁₃₉	—	4	2	no	—
334	C₄⋊C₄×C₁₃₉	—	4	2	no	—
335	C₄⋊C₄×C₁₃₉	—	4	2	no	—
336	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
337	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
338	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
339	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
340	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
341	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
343	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
345	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
346	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
350	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
362	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
363	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
364	C₄²×C₁₃₉	—	2	2	no	—
365	C₄²×C₁₃₉	—	2	4	no	—
366	C₄²×C₁₃₉	—	2	2	no	—
367	C₄²×C₁₃₉	—	2	4	no	—
368	C₄²×C₁₃₉	—	2	4	no	—
369	C₄²×C₁₃₉	—	4	2	no	—
370	C₄²×C₁₃₉	—	4	2	no	—
371	C₄²×C₁₃₉	—	4	2	no	—
372	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
373	C₂³×C₁₃₉	—	2	1	no	—
374	C₂³×C₁₃₉	—	2	2	no	—
375	C₂³×C₁₃₉	—	2	1	no	—
376	C₂³×C₁₃₉	—	2	1	no	—
377	C₂³×C₁₃₉	—	2	2	no	—
378	C₂³×C₁₃₉	—	2	2	no	—
379	C₂³×C₁₃₉	—	2	1	no	—
380	C₂³×C₁₃₉	—	2	2	no	—
381	C₂³×C₁₃₉	—	2	2	no	—
382	C₂³×C₁₃₉	—	2	1	no	—
383	C₂³×C₁₃₉	—	2	1	no	—
384	C₂³×C₁₃₉	—	2	1	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	1	no	—
387	C₂³×C₁₃₉	—	2	1	no	—
388	C₂³×C₁₃₉	—	2	2	no	—
389	C₂³×C₁₃₉	—	4	4	no	—
390	C₂³×C₁₃₉	—	4	8	no	—
391	C₂³×C₁₃₉	—	4	4	no	—
392	C₂³×C₁₃₉	—	8	2	no	—
393	C₂³×C₁₃₉	—	8	4	no	—
394	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
395	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
396	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
397	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
398	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
399	Q₈×C₁₃₉	—	4	4	no	—
400	Q₈×C₁₃₉	—	8	2	no	—
401	D₄×C₁₃₉	—	2	8	no	—
402	D₄×C₁₃₉	—	4	4	no	—
403	D₄×C₁₃₉	—	8	2	no	—
404	C₂×C₄×C₁₃₉	—	2	2	no	—
405	C₂×C₄×C₁₃₉	—	2	1	no	—
406	C₂×C₄×C₁₃₉	—	2	1	no	—
407	C₂×C₄×C₁₃₉	—	2	2	no	—
408	C₂×C₄×C₁₃₉	—	2	2	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	2	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	2	2	no	—
414	C₂×C₄×C₁₃₉	—	2	1	no	—
415	C₂×C₄×C₁₃₉	—	2	2	no	—
416	C₂×C₄×C₁₃₉	—	2	2	no	—
417	C₂×C₄×C₁₃₉	—	2	1	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	2	1	no	—
420	C₂×C₄×C₁₃₉	—	2	1	no	—
421	C₂×C₄×C₁₃₉	—	2	1	no	—
422	C₂×C₄×C₁₃₉	—	2	1	no	—
423	C₂×C₄×C₁₃₉	—	2	2	no	—
424	C₂×C₄×C₁₃₉	—	2	2	no	—
425	C₂×C₄×C₁₃₉	—	2	2	no	—
426	C₂×C₄×C₁₃₉	—	2	2	no	—
427	C₂×C₄×C₁₃₉	—	2	2	no	—
428	C₂×C₄×C₁₃₉	—	2	2	no	—
429	C₂×C₄×C₁₃₉	—	2	2	no	—
430	C₂×C₄×C₁₃₉	—	2	2	no	—
431	C₂×C₄×C₁₃₉	—	2	2	no	—
432	C₂×C₄×C₁₃₉	—	2	2	no	—
433	C₂×C₄×C₁₃₉	—	2	2	no	—
434	C₂×C₄×C₁₃₉	—	2	1	no	—
435	C₂×C₄×C₁₃₉	—	2	1	no	—
436	C₂×C₄×C₁₃₉	—	2	2	no	—
437	C₂×C₄×C₁₃₉	—	2	2	no	—
438	C₂×C₄×C₁₃₉	—	2	2	no	—
439	C₂×C₄×C₁₃₉	—	2	2	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	2	no	—
442	C₂×C₄×C₁₃₉	—	2	1	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	2	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	4	4	no	—
447	C₂×C₄×C₁₃₉	—	4	4	no	—
448	C₂×C₄×C₁₃₉	—	4	8	no	—
449	C₂×C₄×C₁₃₉	—	4	4	no	—
450	C₂×C₄×C₁₃₉	—	4	4	no	—
451	C₂×C₄×C₁₃₉	—	4	8	no	—
452	C₂×C₄×C₁₃₉	—	8	2	no	—
453	C₂×C₄×C₁₃₉	—	8	4	no	—
454	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
460	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
461	C₂²×C₁₃₉	—	2	2	no	—
462	C₂²×C₁₃₉	—	2	2	no	—
463	C₂²×C₁₃₉	—	2	4	no	—
464	C₂²×C₁₃₉	—	2	4	no	—
465	C₂²×C₁₃₉	—	2	2	no	—
466	C₂²×C₁₃₉	—	2	2	no	—
467	C₂²×C₁₃₉	—	2	2	no	—
468	C₂²×C₁₃₉	—	2	2	no	—
469	C₂²×C₁₃₉	—	2	4	no	—
470	C₂²×C₁₃₉	—	4	1	no	—
471	C₂²×C₁₃₉	—	4	1	no	—
472	C₂²×C₁₃₉	—	4	2	no	—
473	C₂²×C₁₃₉	—	4	2	no	—
474	C₂²×C₁₃₉	—	4	2	no	—
475	C₂²×C₁₃₉	—	4	1	no	—
476	C₂²×C₁₃₉	—	4	1	no	—
477	C₂²×C₁₃₉	—	4	1	no	—
478	C₂²×C₁₃₉	—	4	2	no	—
479	C₂²×C₁₃₉	—	4	2	no	—
480	C₂²×C₁₃₉	—	8	8	no	—
481	C₂²×C₁₃₉	#532	1	4	yes	—
482	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
483	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
484	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂²×C₁₃₉	#585	1	2	yes	—
486	C₂²×C₁₃₉	#585	1	1	yes	characteristic
487	C₄×C₁₃₉	—	2	2	no	—
488	C₄×C₁₃₉	—	2	2	no	—
489	C₄×C₁₃₉	—	2	2	no	—
490	C₄×C₁₃₉	—	2	2	no	—
491	C₄×C₁₃₉	—	2	2	no	—
492	C₄×C₁₃₉	—	2	4	no	—
493	C₄×C₁₃₉	—	2	4	no	—
494	C₄×C₁₃₉	—	4	1	no	—
495	C₄×C₁₃₉	—	4	2	no	—
496	C₄×C₁₃₉	—	4	1	no	—
497	C₄×C₁₃₉	—	4	2	no	—
498	C₄×C₁₃₉	—	4	1	no	—
499	C₄×C₁₃₉	—	4	1	no	—
500	C₄×C₁₃₉	—	4	2	no	—
501	C₄×C₁₃₉	—	4	2	no	—
502	C₄×C₁₃₉	—	4	1	no	—
503	C₄×C₁₃₉	—	4	1	no	—
504	C₄×C₁₃₉	—	4	2	no	—
505	C₄×C₁₃₉	—	4	2	no	—
506	C₂×C₁₃₉	—	2	4	no	—
507	C₂×C₁₃₉	—	4	2	no	—
508	C₂×C₁₃₉	—	4	2	no	—
509	C₂×C₁₃₉	—	8	1	no	—
510	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
511	C₂×C₁₃₉	#3485	1	1	yes	characteristic
512	C₂×C₁₃₉	#3489	1	1	yes	characteristic
513	C₂×C₁₃₉	#3491	1	2	yes	—
514	C₂×C₁₃₉	#3495	1	2	yes	—
515	#36061	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₁₃₉	#36061	1	1	yes	characteristic, direct product factor, Sylow
517	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
518	C₂×#551	C₂×C₁₃₉	1	1	yes	characteristic
519	#2664	C₂×C₁₃₉	1	1	yes	characteristic, complemented
520	#2663	C₂×C₁₃₉	1	1	yes	characteristic, complemented
521	#2659	C₂×C₁₃₉	1	1	yes	characteristic, complemented
522	#2611	C₂×C₁₃₉	1	1	yes	characteristic, complemented
523	#2604	C₂×C₁₃₉	1	1	yes	characteristic, complemented
524	#2564	C₂×C₁₃₉	1	1	yes	characteristic, complemented
525	#2561	C₂×C₁₃₉	1	1	yes	characteristic, complemented
526	#2556	C₂×C₁₃₉	1	2	yes	complemented
527	#2553	C₂×C₁₃₉	1	2	yes	complemented
528	#2534	C₂×C₁₃₉	1	2	yes	—
529	#2521	C₂×C₁₃₉	1	2	yes	complemented
530	#2519	C₂×C₁₃₉	1	2	yes	complemented
531	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
532	#2498	C₂×C₁₃₉	1	1	yes	characteristic, complemented
533	#2486	C₂×C₁₃₉	1	2	yes	complemented
534	#2396	C₂×C₁₃₉	1	1	yes	characteristic, complemented
535	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
536	C₂×#399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	#2344	C₂×C₁₃₉	1	2	yes	complemented
538	#2342	C₂×C₁₃₉	1	2	yes	complemented
539	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
540	#552	—	2	8	no	—
541	#551	—	2	8	no	—
542	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
543	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
544	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
545	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
546	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
547	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
548	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
549	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
550	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
551	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
552	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
553	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
554	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
555	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
556	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
558	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
560	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
561	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
562	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
564	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
565	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
566	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
568	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
570	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
571	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
572	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
573	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
574	#399	C₂²×C₁₃₉	1	1	yes	characteristic
575	#399	C₂²×C₁₃₉	1	1	yes	characteristic
576	#399	C₂²×C₁₃₉	1	1	yes	characteristic
577	#399	C₂²×C₁₃₉	1	1	yes	characteristic
578	#399	C₂²×C₁₃₉	1	2	yes	—
579	#399	C₂²×C₁₃₉	1	2	yes	—
580	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
581	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
582	#398	C₂²×C₁₃₉	1	2	yes	complemented
583	#398	C₂²×C₁₃₉	1	2	yes	complemented
584	#398	C₂²×C₁₃₉	1	2	yes	complemented
585	#397	C₂²×C₁₃₉	1	1	yes	characteristic
586	#397	C₂²×C₁₃₉	1	1	yes	characteristic
587	#397	C₂²×C₁₃₉	1	2	yes	complemented
588	#397	C₂²×C₁₃₉	1	2	yes	complemented
589	#396	C₂²×C₁₃₉	1	2	yes	—
590	#396	C₂²×C₁₃₉	1	2	yes	—
591	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
592	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
593	#395	C₂²×C₁₃₉	1	2	yes	complemented
594	#394	C₂²×C₁₃₉	1	2	yes	—
595	#394	C₂²×C₁₃₉	1	2	yes	—
596	#393	C₂²×C₁₃₉	1	1	yes	characteristic
597	#393	C₂²×C₁₃₉	1	1	yes	characteristic
598	#391	C₂²×C₁₃₉	1	2	yes	complemented
599	#389	C₂²×C₁₃₉	1	2	yes	complemented
600	#389	C₂²×C₁₃₉	1	2	yes	complemented
601	#389	C₂²×C₁₃₉	1	2	yes	complemented
602	#389	C₂²×C₁₃₉	1	2	yes	complemented
603	#388	C₂²×C₁₃₉	1	2	yes	—
604	#388	C₂²×C₁₃₉	1	2	yes	—
605	#388	C₂²×C₁₃₉	1	2	yes	—
606	#388	C₂²×C₁₃₉	1	2	yes	—
607	#388	C₂²×C₁₃₉	1	2	yes	—
608	#388	C₂²×C₁₃₉	1	2	yes	—
609	#388	C₂²×C₁₃₉	1	2	yes	—
610	#388	C₂²×C₁₃₉	1	2	yes	—
611	#387	C₂²×C₁₃₉	1	2	yes	complemented
612	#387	C₂²×C₁₃₉	1	2	yes	complemented
613	#387	C₂²×C₁₃₉	1	2	yes	complemented
614	#387	C₂²×C₁₃₉	1	2	yes	complemented
615	#386	C₂²×C₁₃₉	1	2	yes	—
616	#386	C₂²×C₁₃₉	1	2	yes	—
617	#385	C₂²×C₁₃₉	1	2	yes	—
618	#385	C₂²×C₁₃₉	1	2	yes	—
619	#382	C₂²×C₁₃₉	1	2	yes	complemented
620	#381	C₂²×C₁₃₉	1	2	yes	—
621	#381	C₂²×C₁₃₉	1	2	yes	—
622	#381	C₂²×C₁₃₉	1	2	yes	—
623	#380	C₂²×C₁₃₉	1	2	yes	—
624	#380	C₂²×C₁₃₉	1	2	yes	—
625	#380	C₂²×C₁₃₉	1	2	yes	complemented
626	#380	C₂²×C₁₃₉	1	2	yes	complemented
627	#379	C₂²×C₁₃₉	1	2	yes	—
628	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
629	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
630	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
631	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
632	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
633	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
634	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
636	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
637	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
638	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
639	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
640	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
641	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
649	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
655	#126	—	2	4	no	—
656	#126	—	2	8	no	—
657	#126	—	2	4	no	—
658	#125	—	2	8	no	—
659	#125	—	2	4	no	—
660	#124	—	2	4	no	—
661	#123	—	2	4	no	—
662	#123	—	2	8	no	—
663	#123	—	2	4	no	—
664	#123	—	2	4	no	—
665	C₂²⋊Q₈	—	2	4	no	—
666	C₂²⋊Q₈	—	2	4	no	—
667	C₂²⋊Q₈	—	2	4	no	—
668	C₂²⋊Q₈	—	2	4	no	—
669	#120	—	2	4	no	—
670	C₄×Q₈	—	2	4	no	—
671	C₄×D₄	—	2	4	no	—
672	C₄×D₄	—	2	8	no	—
673	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
674	#117	—	2	4	no	—
675	#117	—	2	4	no	—
676	#117	—	2	8	no	—
677	#117	—	2	4	no	—
678	C₂×C₄⋊C₄	—	2	4	no	—
679	C₂×C₄⋊C₄	—	2	8	no	—
680	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	—	2	4	no	—
707	C₂×C₂²⋊C₄	—	2	8	no	—
708	C₂×C₂²⋊C₄	—	2	4	no	—
709	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
738	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
742	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
744	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
745	#95	C₂³×C₁₃₉	1	1	yes	characteristic
746	#95	C₂³×C₁₃₉	1	1	yes	characteristic
747	#95	C₂³×C₁₃₉	1	2	yes	—
748	#95	C₂³×C₁₃₉	1	2	yes	—
749	#95	C₂³×C₁₃₉	1	1	yes	characteristic
750	#95	C₂³×C₁₃₉	1	2	yes	—
751	#95	C₂³×C₁₃₉	1	1	yes	characteristic
752	#95	C₂³×C₁₃₉	1	2	yes	—
753	#95	C₂³×C₁₃₉	1	2	yes	—
754	#95	C₂³×C₁₃₉	1	2	yes	—
755	#95	C₂³×C₁₃₉	1	2	yes	—
756	#95	C₂³×C₁₃₉	1	2	yes	—
757	#95	C₂³×C₁₃₉	1	2	yes	—
758	#95	C₂³×C₁₃₉	1	2	yes	—
759	#95	C₂³×C₁₃₉	1	2	yes	—
760	#95	C₂³×C₁₃₉	1	2	yes	—
761	#95	C₂³×C₁₃₉	1	2	yes	—
762	#95	C₂³×C₁₃₉	1	2	yes	—
763	#95	C₂³×C₁₃₉	1	2	yes	—
764	#95	C₂³×C₁₃₉	1	2	yes	—
765	#95	C₂³×C₁₃₉	1	2	yes	—
766	#95	C₂³×C₁₃₉	1	2	yes	—
767	#95	C₂³×C₁₃₉	1	2	yes	—
768	C₂⁴	—	2	2	no	—
769	C₂⁴	—	2	2	no	—
770	C₂⁴	—	2	4	no	—
771	C₂⁴	—	4	2	no	—
772	C₂⁴	—	4	1	no	—
773	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
774	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
775	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
776	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	4	2	no	—
780	C₂×Q₈	—	4	2	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	4	1	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
806	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
807	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
808	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	4	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	4	no	—
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
879	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	4	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	4	no	—
884	C₄²	—	2	4	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	—	4	2	no	—
888	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	4	4	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	4	no	—
908	C₂³	—	8	2	no	—
909	C₂³	—	8	4	no	—
910	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
911	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
912	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
913	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
914	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
915	Q₈	—	4	4	no	—
916	Q₈	—	8	2	no	—
917	D₄	—	2	8	no	—
918	D₄	—	4	4	no	—
919	D₄	—	8	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	4	no	—
964	C₂×C₄	—	4	8	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	4	no	—
970	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
971	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
972	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
973	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
974	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
975	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
976	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	4	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	4	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	8	8	no	—
997	C₂²	#532×C₁₃₉	1	4	yes	—
998	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
999	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
1000	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1001	C₂²	#585×C₁₃₉	1	2	yes	—
1002	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	4	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₂	—	2	4	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	1	no	—
1026	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
1027	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1028	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1029	C₂	#3491×C₁₃₉	1	2	yes	—
1030	C₂	#3495×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#120×C₁₃₉	C₂²
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×#552×C₁₃₉	C₂	semidirect
3. #2664×C₁₃₉	C₂	semidirect
4. #2663×C₁₃₉	C₂	semidirect
5. #2659×C₁₃₉	C₂	semidirect
6. #2611×C₁₃₉	C₂	semidirect
7. #2604×C₁₃₉	C₂	semidirect
8. #2564×C₁₃₉	C₂	semidirect
9. #2561×C₁₃₉	C₂	semidirect
10. #2556×C₁₃₉	C₂	semidirect
11. #2553×C₁₃₉	C₂	semidirect
13. #2521×C₁₃₉	C₂	semidirect
14. #2519×C₁₃₉	C₂	semidirect
15. #2503×C₁₃₉	C₂	semidirect
16. #2498×C₁₃₉	C₂	semidirect
17. #2486×C₁₃₉	C₂	semidirect
18. #2396×C₁₃₉	C₂	semidirect
19. #2395×C₁₃₉	C₂	semidirect
20. C₂×#399×C₁₃₉	C₂	semidirect
21. #2344×C₁₃₉	C₂	semidirect
22. #2342×C₁₃₉	C₂	semidirect
23. #2275×C₁₃₉	C₂	semidirect
28. C₂×#126×C₁₃₉	C₂²	semidirect
29. C₂×#125×C₁₃₉	C₂²	semidirect
30. C₂×#125×C₁₃₉	C₂²	semidirect
39. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
41. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
48. C₂×#117×C₁₃₉	C₂²	semidirect
54. #400×C₁₃₉	C₂²	semidirect
55. #400×C₁₃₉	C₂²	semidirect
56. #400×C₁₃₉	C₂²	semidirect
57. #400×C₁₃₉	C₂²	semidirect
64. #398×C₁₃₉	C₂²	semidirect
65. #398×C₁₃₉	C₂²	semidirect
66. #398×C₁₃₉	C₂²	semidirect
67. #398×C₁₃₉	C₂²	semidirect
68. #398×C₁₃₉	C₂²	semidirect
71. #397×C₁₃₉	C₂²	semidirect
72. #397×C₁₃₉	C₂²	semidirect
75. #395×C₁₃₉	C₂²	semidirect
76. #395×C₁₃₉	C₂²	semidirect
77. #395×C₁₃₉	C₂²	semidirect
82. #391×C₁₃₉	C₂²	semidirect
83. #389×C₁₃₉	C₂²	semidirect
84. #389×C₁₃₉	C₂²	semidirect
85. #389×C₁₃₉	C₂²	semidirect
86. #389×C₁₃₉	C₂²	semidirect
95. #387×C₁₃₉	C₂²	semidirect
96. #387×C₁₃₉	C₂²	semidirect
97. #387×C₁₃₉	C₂²	semidirect
98. #387×C₁₃₉	C₂²	semidirect
103. #382×C₁₃₉	C₂²	semidirect
109. #380×C₁₃₉	C₂²	semidirect
110. #380×C₁₃₉	C₂²	semidirect
112. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
113. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
114. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
115. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
122. #376×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
515. #36061	C₁₃₉	direct (N × H)
516. C₁₃₉	#36061	direct (N × H)
517. C₂×#552	C₂×C₁₃₉	semidirect
519. #2664	C₂×C₁₃₉	semidirect
520. #2663	C₂×C₁₃₉	semidirect
521. #2659	C₂×C₁₃₉	semidirect
522. #2611	C₂×C₁₃₉	semidirect
523. #2604	C₂×C₁₃₉	semidirect
524. #2564	C₂×C₁₃₉	semidirect
525. #2561	C₂×C₁₃₉	semidirect
526. #2556	C₂×C₁₃₉	semidirect
527. #2553	C₂×C₁₃₉	semidirect
529. #2521	C₂×C₁₃₉	semidirect
530. #2519	C₂×C₁₃₉	semidirect
531. #2503	C₂×C₁₃₉	semidirect
532. #2498	C₂×C₁₃₉	semidirect
533. #2486	C₂×C₁₃₉	semidirect
534. #2396	C₂×C₁₃₉	semidirect
535. #2395	C₂×C₁₃₉	semidirect
536. C₂×#399	C₂×C₁₃₉	semidirect
537. #2344	C₂×C₁₃₉	semidirect
538. #2342	C₂×C₁₃₉	semidirect
539. #2275	C₂×C₁₃₉	semidirect
544. C₂×#126	C₂²×C₁₃₉	semidirect
545. C₂×#125	C₂²×C₁₃₉	semidirect
546. C₂×#125	C₂²×C₁₃₉	semidirect
555. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
557. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
564. C₂×#117	C₂²×C₁₃₉	semidirect
570. #400	C₂²×C₁₃₉	semidirect
571. #400	C₂²×C₁₃₉	semidirect
572. #400	C₂²×C₁₃₉	semidirect
573. #400	C₂²×C₁₃₉	semidirect
580. #398	C₂²×C₁₃₉	semidirect
581. #398	C₂²×C₁₃₉	semidirect
582. #398	C₂²×C₁₃₉	semidirect
583. #398	C₂²×C₁₃₉	semidirect
584. #398	C₂²×C₁₃₉	semidirect
587. #397	C₂²×C₁₃₉	semidirect
588. #397	C₂²×C₁₃₉	semidirect
591. #395	C₂²×C₁₃₉	semidirect
592. #395	C₂²×C₁₃₉	semidirect
593. #395	C₂²×C₁₃₉	semidirect
598. #391	C₂²×C₁₃₉	semidirect
599. #389	C₂²×C₁₃₉	semidirect
600. #389	C₂²×C₁₃₉	semidirect
601. #389	C₂²×C₁₃₉	semidirect
602. #389	C₂²×C₁₃₉	semidirect
611. #387	C₂²×C₁₃₉	semidirect
612. #387	C₂²×C₁₃₉	semidirect
613. #387	C₂²×C₁₃₉	semidirect
614. #387	C₂²×C₁₃₉	semidirect
619. #382	C₂²×C₁₃₉	semidirect
625. #380	C₂²×C₁₃₉	semidirect
626. #380	C₂²×C₁₃₉	semidirect
628. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
629. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
630. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
631. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
636. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
637. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
638. #376	C₂²×C₁₃₉	semidirect
640. C₂×#95	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂×#551×C₁₃₉	2
#2664×C₁₃₉	2
#2663×C₁₃₉	2
#2659×C₁₃₉	2
#2611×C₁₃₉	2
#2604×C₁₃₉	2
#2564×C₁₃₉	2
#2561×C₁₃₉	2
#2556×C₁₃₉	2
#2553×C₁₃₉	2
#2534×C₁₃₉	2
#2521×C₁₃₉	2
#2519×C₁₃₉	2
#2503×C₁₃₉	2
#2498×C₁₃₉	2
#2486×C₁₃₉	2
#2396×C₁₃₉	2
#2395×C₁₃₉	2
C₂×#399×C₁₃₉	2
#2344×C₁₃₉	2
#2342×C₁₃₉	2
#2275×C₁₃₉	2
#36061	139

Subgroups — C139×#36061 #48030657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36061 #48030657