Subgroups — C₁₃₉×#36079 #48030675

Order 35584.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2637×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2632×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2614×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2604×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2599×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2592×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2498×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2482×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2458×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2458×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2438×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2411×C₁₃₉	C₂	1	2	yes	maximal
18	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2396×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#393×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2343×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2342×C₁₃₉	C₂	1	2	yes	maximal, complemented
24	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
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×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
36	#519×C₁₃₉	—	2	8	no	—
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
42	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
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	2	yes	—
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊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	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	#400×C₁₃₉	C₂²	1	2	yes	complemented
55	#399×C₁₃₉	C₂²	1	1	yes	characteristic
56	#399×C₁₃₉	C₂²	1	1	yes	characteristic
57	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#398×C₁₃₉	C₂²	1	2	yes	complemented
60	#398×C₁₃₉	C₂²	1	2	yes	complemented
61	#397×C₁₃₉	C₂²	1	1	yes	characteristic
62	#397×C₁₃₉	C₂²	1	1	yes	characteristic
63	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
64	#396×C₁₃₉	C₂²	1	2	yes	—
65	#396×C₁₃₉	C₂²	1	2	yes	—
66	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	#395×C₁₃₉	C₂²	1	2	yes	complemented
69	#395×C₁₃₉	C₂²	1	2	yes	complemented
70	#394×C₁₃₉	C₂²	1	2	yes	—
71	#394×C₁₃₉	C₂²	1	2	yes	—
72	#393×C₁₃₉	C₂²	1	1	yes	characteristic
73	#393×C₁₃₉	C₂²	1	1	yes	characteristic
74	#393×C₁₃₉	C₂²	1	1	yes	characteristic
75	#393×C₁₃₉	C₂²	1	1	yes	characteristic
76	#393×C₁₃₉	C₂²	1	2	yes	—
77	#393×C₁₃₉	C₂²	1	2	yes	—
78	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#393×C₁₃₉	C₂²	1	2	yes	complemented
81	#391×C₁₃₉	C₂²	1	2	yes	complemented
82	#390×C₁₃₉	C₂²	1	2	yes	—
83	#390×C₁₃₉	C₂²	1	2	yes	—
84	#389×C₁₃₉	C₂²	1	2	yes	complemented
85	#389×C₁₃₉	C₂²	1	2	yes	complemented
86	#388×C₁₃₉	C₂²	1	2	yes	—
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	complemented
95	#388×C₁₃₉	C₂²	1	2	yes	complemented
96	#388×C₁₃₉	C₂²	1	2	yes	complemented
97	#387×C₁₃₉	C₂²	1	2	yes	complemented
98	#387×C₁₃₉	C₂²	1	2	yes	complemented
99	#387×C₁₃₉	C₂²	1	2	yes	complemented
100	#387×C₁₃₉	C₂²	1	2	yes	complemented
101	#387×C₁₃₉	C₂²	1	2	yes	complemented
102	#387×C₁₃₉	C₂²	1	2	yes	complemented
103	#387×C₁₃₉	C₂²	1	2	yes	complemented
104	#386×C₁₃₉	C₂²	1	2	yes	—
105	#385×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#385×C₁₃₉	C₂²	1	2	yes	complemented
110	#383×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
111	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	#381×C₁₃₉	C₂²	1	2	yes	—
113	#381×C₁₃₉	C₂²	1	1	yes	characteristic
114	#380×C₁₃₉	C₂²	1	2	yes	—
115	#379×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
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	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	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	2	yes	—
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	—	2	4	no	—
127	C₂²×Q₈×C₁₃₉	—	2	8	no	—
128	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
131	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	#126×C₁₃₉	—	2	4	no	—
143	#126×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	#120×C₁₃₉	—	2	4	no	—
152	C₄×Q₈×C₁₃₉	—	2	8	no	—
153	C₄×Q₈×C₁₃₉	—	2	8	no	—
154	C₄×Q₈×C₁₃₉	—	2	4	no	—
155	C₄×Q₈×C₁₃₉	—	2	4	no	—
156	C₄×Q₈×C₁₃₉	—	2	4	no	—
157	C₄×Q₈×C₁₃₉	—	2	4	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	#117×C₁₃₉	—	2	4	no	—
161	#117×C₁₃₉	—	2	8	no	—
162	#117×C₁₃₉	—	2	8	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	#117×C₁₃₉	D₄	1	8	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
241	#95×C₁₃₉	C₂³	1	1	yes	characteristic
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	32	no	—
262	C₂×Q₈×C₁₃₉	—	2	4	no	—
263	C₂×Q₈×C₁₃₉	—	2	2	no	—
264	C₂×Q₈×C₁₃₉	—	2	2	no	—
265	C₂×Q₈×C₁₃₉	—	2	2	no	—
266	C₂×Q₈×C₁₃₉	—	2	4	no	—
267	C₂×Q₈×C₁₃₉	—	2	4	no	—
268	C₂×Q₈×C₁₃₉	—	2	4	no	—
269	C₂×Q₈×C₁₃₉	—	2	4	no	—
270	C₂×Q₈×C₁₃₉	—	4	2	no	—
271	C₂×D₄×C₁₃₉	—	2	2	no	—
272	C₂×D₄×C₁₃₉	—	2	4	no	—
273	C₂×D₄×C₁₃₉	—	2	2	no	—
274	C₂×D₄×C₁₃₉	—	2	2	no	—
275	C₂×D₄×C₁₃₉	—	2	2	no	—
276	C₂×D₄×C₁₃₉	—	4	1	no	—
277	C₂×D₄×C₁₃₉	—	4	2	no	—
278	C₂²×C₄×C₁₃₉	—	2	4	no	—
279	C₂²×C₄×C₁₃₉	—	2	4	no	—
280	C₂²×C₄×C₁₃₉	—	2	4	no	—
281	C₂²×C₄×C₁₃₉	—	2	2	no	—
282	C₂²×C₄×C₁₃₉	—	2	2	no	—
283	C₂²×C₄×C₁₃₉	—	2	4	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	2	no	—
287	C₂²×C₄×C₁₃₉	—	4	1	no	—
288	C₂²×C₄×C₁₃₉	—	4	2	no	—
289	C₂²×C₄×C₁₃₉	—	4	2	no	—
290	C₂²×C₄×C₁₃₉	—	4	2	no	—
291	C₂²×C₄×C₁₃₉	—	4	2	no	—
292	C₂²×C₄×C₁₃₉	—	4	2	no	—
293	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
294	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
295	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
310	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₁₃₉	—	2	4	no	—
315	C₄⋊C₄×C₁₃₉	—	2	4	no	—
316	C₄⋊C₄×C₁₃₉	—	2	4	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	2	no	—
321	C₄⋊C₄×C₁₃₉	—	2	2	no	—
322	C₄⋊C₄×C₁₃₉	—	2	2	no	—
323	C₄⋊C₄×C₁₃₉	—	2	2	no	—
324	C₄⋊C₄×C₁₃₉	—	2	2	no	—
325	C₄⋊C₄×C₁₃₉	—	2	2	no	—
326	C₄⋊C₄×C₁₃₉	—	2	4	no	—
327	C₄⋊C₄×C₁₃₉	—	2	4	no	—
328	C₄⋊C₄×C₁₃₉	—	4	2	no	—
329	C₄⋊C₄×C₁₃₉	—	4	2	no	—
330	C₄⋊C₄×C₁₃₉	—	4	2	no	—
331	C₄⋊C₄×C₁₃₉	—	4	2	no	—
332	C₄⋊C₄×C₁₃₉	—	4	2	no	—
333	C₄⋊C₄×C₁₃₉	—	4	2	no	—
334	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
335	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
336	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
337	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
338	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
339	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
340	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
341	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₃₉	—	2	2	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	4	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
358	C₂²⋊C₄×C₁₃₉	—	4	2	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	4	no	—
367	C₄²×C₁₃₉	—	2	4	no	—
368	C₄²×C₁₃₉	—	2	4	no	—
369	C₄²×C₁₃₉	—	2	4	no	—
370	C₄²×C₁₃₉	—	4	2	no	—
371	C₄²×C₁₃₉	—	4	2	no	—
372	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
373	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
374	C₂³×C₁₃₉	—	2	1	no	—
375	C₂³×C₁₃₉	—	2	1	no	—
376	C₂³×C₁₃₉	—	2	2	no	—
377	C₂³×C₁₃₉	—	2	1	no	—
378	C₂³×C₁₃₉	—	2	2	no	—
379	C₂³×C₁₃₉	—	2	2	no	—
380	C₂³×C₁₃₉	—	2	1	no	—
381	C₂³×C₁₃₉	—	2	1	no	—
382	C₂³×C₁₃₉	—	2	1	no	—
383	C₂³×C₁₃₉	—	2	2	no	—
384	C₂³×C₁₃₉	—	2	2	no	—
385	C₂³×C₁₃₉	—	2	1	no	—
386	C₂³×C₁₃₉	—	2	1	no	—
387	C₂³×C₁₃₉	—	2	1	no	—
388	C₂³×C₁₃₉	—	2	1	no	—
389	C₂³×C₁₃₉	—	2	2	no	—
390	C₂³×C₁₃₉	—	2	2	no	—
391	C₂³×C₁₃₉	—	4	4	no	—
392	C₂³×C₁₃₉	—	4	8	no	—
393	C₂³×C₁₃₉	—	4	4	no	—
394	C₂³×C₁₃₉	—	8	2	no	—
395	C₂³×C₁₃₉	—	8	4	no	—
396	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
397	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
398	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
399	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
400	Q₈×C₁₃₉	—	2	16	no	—
401	Q₈×C₁₃₉	—	2	8	no	—
402	Q₈×C₁₃₉	—	2	8	no	—
403	Q₈×C₁₃₉	—	8	2	no	—
404	D₄×C₁₃₉	—	4	4	no	—
405	D₄×C₁₃₉	—	4	4	no	—
406	D₄×C₁₃₉	—	8	2	no	—
407	C₂×C₄×C₁₃₉	—	2	8	no	—
408	C₂×C₄×C₁₃₉	—	2	16	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	2	no	—
415	C₂×C₄×C₁₃₉	—	2	1	no	—
416	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
421	C₂×C₄×C₁₃₉	—	2	2	no	—
422	C₂×C₄×C₁₃₉	—	2	2	no	—
423	C₂×C₄×C₁₃₉	—	2	1	no	—
424	C₂×C₄×C₁₃₉	—	2	1	no	—
425	C₂×C₄×C₁₃₉	—	2	1	no	—
426	C₂×C₄×C₁₃₉	—	2	1	no	—
427	C₂×C₄×C₁₃₉	—	2	1	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	2	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	2	no	—
443	C₂×C₄×C₁₃₉	—	2	2	no	—
444	C₂×C₄×C₁₃₉	—	2	2	no	—
445	C₂×C₄×C₁₃₉	—	2	1	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	2	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	2	no	—
450	C₂×C₄×C₁₃₉	—	4	4	no	—
451	C₂×C₄×C₁₃₉	—	8	2	no	—
452	C₂×C₄×C₁₃₉	—	8	2	no	—
453	C₂×C₄×C₁₃₉	—	8	2	no	—
454	C₂×C₄×C₁₃₉	—	8	4	no	—
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	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
462	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
463	C₂²×C₁₃₉	—	2	2	no	—
464	C₂²×C₁₃₉	—	2	4	no	—
465	C₂²×C₁₃₉	—	2	2	no	—
466	C₂²×C₁₃₉	—	2	4	no	—
467	C₂²×C₁₃₉	—	2	2	no	—
468	C₂²×C₁₃₉	—	2	4	no	—
469	C₂²×C₁₃₉	—	4	1	no	—
470	C₂²×C₁₃₉	—	4	1	no	—
471	C₂²×C₁₃₉	—	4	2	no	—
472	C₂²×C₁₃₉	—	4	1	no	—
473	C₂²×C₁₃₉	—	4	1	no	—
474	C₂²×C₁₃₉	—	4	1	no	—
475	C₂²×C₁₃₉	—	4	1	no	—
476	C₂²×C₁₃₉	—	4	2	no	—
477	C₂²×C₁₃₉	—	4	2	no	—
478	C₂²×C₁₃₉	—	4	1	no	—
479	C₂²×C₁₃₉	—	4	1	no	—
480	C₂²×C₁₃₉	—	4	2	no	—
481	C₂²×C₁₃₉	—	4	2	no	—
482	C₂²×C₁₃₉	—	8	8	no	—
483	C₂²×C₁₃₉	#525	1	4	yes	—
484	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
485	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
486	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
487	C₂²×C₁₃₉	#585	1	1	yes	characteristic
488	C₂²×C₁₃₉	#585	1	2	yes	—
489	C₄×C₁₃₉	—	2	2	no	—
490	C₄×C₁₃₉	—	2	2	no	—
491	C₄×C₁₃₉	—	2	4	no	—
492	C₄×C₁₃₉	—	2	4	no	—
493	C₄×C₁₃₉	—	2	2	no	—
494	C₄×C₁₃₉	—	2	2	no	—
495	C₄×C₁₃₉	—	2	2	no	—
496	C₄×C₁₃₉	—	2	2	no	—
497	C₄×C₁₃₉	—	4	1	no	—
498	C₄×C₁₃₉	—	4	2	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	1	no	—
505	C₄×C₁₃₉	—	4	2	no	—
506	C₄×C₁₃₉	—	4	2	no	—
507	C₄×C₁₃₉	—	4	2	no	—
508	C₂×C₁₃₉	—	2	4	no	—
509	C₂×C₁₃₉	—	4	2	no	—
510	C₂×C₁₃₉	—	8	1	no	—
511	C₂×C₁₃₉	—	8	1	no	—
512	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
513	C₂×C₁₃₉	#3489	1	1	yes	characteristic
514	C₂×C₁₃₉	#3495	1	2	yes	—
515	C₂×C₁₃₉	#3500	1	1	yes	characteristic
516	C₂×C₁₃₉	#3510	1	2	yes	—
517	#36079	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₁₃₉	#36079	1	1	yes	characteristic, direct product factor, Sylow
519	C₂×#551	C₂×C₁₃₉	1	1	yes	characteristic
520	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
521	#2637	C₂×C₁₃₉	1	1	yes	characteristic, complemented
522	#2632	C₂×C₁₃₉	1	1	yes	characteristic, complemented
523	#2614	C₂×C₁₃₉	1	1	yes	characteristic, complemented
524	#2604	C₂×C₁₃₉	1	1	yes	characteristic, complemented
525	#2599	C₂×C₁₃₉	1	1	yes	characteristic, complemented
526	#2592	C₂×C₁₃₉	1	1	yes	characteristic, complemented
527	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
528	#2498	C₂×C₁₃₉	1	1	yes	characteristic, complemented
529	#2482	C₂×C₁₃₉	1	1	yes	characteristic, complemented
530	#2469	C₂×C₁₃₉	1	2	yes	complemented
531	#2465	C₂×C₁₃₉	1	2	yes	complemented
532	#2458	C₂×C₁₃₉	1	2	yes	complemented
533	#2458	C₂×C₁₃₉	1	2	yes	complemented
534	#2438	C₂×C₁₃₉	1	2	yes	complemented
535	#2411	C₂×C₁₃₉	1	2	yes	—
536	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	#2396	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	C₂×#393	C₂×C₁₃₉	1	1	yes	characteristic, complemented
539	#2359	C₂×C₁₃₉	1	2	yes	complemented
540	#2343	C₂×C₁₃₉	1	1	yes	characteristic, complemented
541	#2342	C₂×C₁₃₉	1	2	yes	complemented
542	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
543	#551	—	2	8	no	—
544	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
545	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
546	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
547	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
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×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
552	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
553	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
554	#519	—	2	8	no	—
555	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
556	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
557	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
558	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
559	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
560	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
561	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
564	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
566	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₂×#117	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	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
571	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
572	#400	C₂²×C₁₃₉	1	2	yes	complemented
573	#399	C₂²×C₁₃₉	1	1	yes	characteristic
574	#399	C₂²×C₁₃₉	1	1	yes	characteristic
575	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
576	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
577	#398	C₂²×C₁₃₉	1	2	yes	complemented
578	#398	C₂²×C₁₃₉	1	2	yes	complemented
579	#397	C₂²×C₁₃₉	1	1	yes	characteristic
580	#397	C₂²×C₁₃₉	1	1	yes	characteristic
581	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
582	#396	C₂²×C₁₃₉	1	2	yes	—
583	#396	C₂²×C₁₃₉	1	2	yes	—
584	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
585	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
586	#395	C₂²×C₁₃₉	1	2	yes	complemented
587	#395	C₂²×C₁₃₉	1	2	yes	complemented
588	#394	C₂²×C₁₃₉	1	2	yes	—
589	#394	C₂²×C₁₃₉	1	2	yes	—
590	#393	C₂²×C₁₃₉	1	1	yes	characteristic
591	#393	C₂²×C₁₃₉	1	1	yes	characteristic
592	#393	C₂²×C₁₃₉	1	1	yes	characteristic
593	#393	C₂²×C₁₃₉	1	1	yes	characteristic
594	#393	C₂²×C₁₃₉	1	2	yes	—
595	#393	C₂²×C₁₃₉	1	2	yes	—
596	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
597	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
598	#393	C₂²×C₁₃₉	1	2	yes	complemented
599	#391	C₂²×C₁₃₉	1	2	yes	complemented
600	#390	C₂²×C₁₃₉	1	2	yes	—
601	#390	C₂²×C₁₃₉	1	2	yes	—
602	#389	C₂²×C₁₃₉	1	2	yes	complemented
603	#389	C₂²×C₁₃₉	1	2	yes	complemented
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	#388	C₂²×C₁₃₉	1	2	yes	—
612	#388	C₂²×C₁₃₉	1	2	yes	complemented
613	#388	C₂²×C₁₃₉	1	2	yes	complemented
614	#388	C₂²×C₁₃₉	1	2	yes	complemented
615	#387	C₂²×C₁₃₉	1	2	yes	complemented
616	#387	C₂²×C₁₃₉	1	2	yes	complemented
617	#387	C₂²×C₁₃₉	1	2	yes	complemented
618	#387	C₂²×C₁₃₉	1	2	yes	complemented
619	#387	C₂²×C₁₃₉	1	2	yes	complemented
620	#387	C₂²×C₁₃₉	1	2	yes	complemented
621	#387	C₂²×C₁₃₉	1	2	yes	complemented
622	#386	C₂²×C₁₃₉	1	2	yes	—
623	#385	C₂²×C₁₃₉	1	2	yes	—
624	#385	C₂²×C₁₃₉	1	2	yes	—
625	#385	C₂²×C₁₃₉	1	2	yes	—
626	#385	C₂²×C₁₃₉	1	2	yes	—
627	#385	C₂²×C₁₃₉	1	2	yes	complemented
628	#383	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
629	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
630	#381	C₂²×C₁₃₉	1	2	yes	—
631	#381	C₂²×C₁₃₉	1	1	yes	characteristic
632	#380	C₂²×C₁₃₉	1	2	yes	—
633	#379	C₂²×C₁₃₉	1	2	yes	—
634	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
635	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
636	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
637	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
638	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
639	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
640	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
641	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
642	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
643	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂²×Q₈	—	2	4	no	—
645	C₂²×Q₈	—	2	8	no	—
646	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
649	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
652	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
659	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
660	#126	—	2	4	no	—
661	#126	—	2	4	no	—
662	#124	—	2	4	no	—
663	#123	—	2	4	no	—
664	#123	—	2	8	no	—
665	#123	—	2	4	no	—
666	#123	—	2	4	no	—
667	C₂²⋊Q₈	—	2	4	no	—
668	C₂²⋊Q₈	—	2	4	no	—
669	#120	—	2	4	no	—
670	C₄×Q₈	—	2	8	no	—
671	C₄×Q₈	—	2	8	no	—
672	C₄×Q₈	—	2	4	no	—
673	C₄×Q₈	—	2	4	no	—
674	C₄×Q₈	—	2	4	no	—
675	C₄×Q₈	—	2	4	no	—
676	C₄×D₄	—	2	4	no	—
677	C₄×D₄	—	2	4	no	—
678	#117	—	2	4	no	—
679	#117	—	2	8	no	—
680	#117	—	2	8	no	—
681	#117	—	2	4	no	—
682	#117	D₄×C₁₃₉	1	8	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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂×C₂²⋊C₄	—	2	4	no	—
706	C₂×C₂²⋊C₄	—	2	8	no	—
707	C₂×C₂²⋊C₄	—	2	4	no	—
708	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	C₂×C₄²	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	1	yes	characteristic
749	#95	C₂³×C₁₃₉	1	2	yes	—
750	#95	C₂³×C₁₃₉	1	2	yes	—
751	#95	C₂³×C₁₃₉	1	2	yes	—
752	#95	C₂³×C₁₃₉	1	2	yes	—
753	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
769	#95	C₂³×C₁₃₉	1	2	yes	—
770	C₂⁴	—	2	2	no	—
771	C₂⁴	—	2	2	no	—
772	C₂⁴	—	2	4	no	—
773	C₂⁴	—	4	2	no	—
774	C₂⁴	—	4	1	no	—
775	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
776	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
777	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
778	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
779	C₂×Q₈	—	2	32	no	—
780	C₂×Q₈	—	2	4	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	2	2	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	4	no	—
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	4	no	—
787	C₂×Q₈	—	2	4	no	—
788	C₂×Q₈	—	4	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	4	1	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
812	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
813	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	4	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	4	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	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	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	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	4	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	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
881	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	4	no	—
884	C₄²	—	2	4	no	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	4	no	—
888	C₄²	—	4	2	no	—
889	C₄²	—	4	2	no	—
890	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
891	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	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	2	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	4	no	—
910	C₂³	—	4	8	no	—
911	C₂³	—	4	4	no	—
912	C₂³	—	8	2	no	—
913	C₂³	—	8	4	no	—
914	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
915	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
916	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
917	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
918	Q₈	—	2	16	no	—
919	Q₈	—	2	8	no	—
920	Q₈	—	2	8	no	—
921	Q₈	—	8	2	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	8	2	no	—
925	C₂×C₄	—	2	8	no	—
926	C₂×C₄	—	2	16	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	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	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	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	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	4	no	—
973	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
974	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
975	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
978	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
979	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
980	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	4	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	4	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	4	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	1	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	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	8	8	no	—
1001	C₂²	#525×C₁₃₉	1	4	yes	—
1002	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1003	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
1004	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1005	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1006	C₂²	#585×C₁₃₉	1	2	yes	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	4	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	1	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₂	—	2	4	no	—
1027	C₂	—	4	2	no	—
1028	C₂	—	8	1	no	—
1029	C₂	—	8	1	no	—
1030	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1031	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1032	C₂	#3495×C₁₃₉	1	2	yes	—
1033	C₂	#3500×C₁₃₉	1	1	yes	characteristic
1034	C₂	#3510×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
2. C₂×#519×C₁₃₉	C₂	semidirect
3. #2637×C₁₃₉	C₂	semidirect
4. #2632×C₁₃₉	C₂	semidirect
5. #2614×C₁₃₉	C₂	semidirect
6. #2604×C₁₃₉	C₂	semidirect
7. #2599×C₁₃₉	C₂	semidirect
8. #2592×C₁₃₉	C₂	semidirect
9. #2580×C₁₃₉	C₂	semidirect
10. #2498×C₁₃₉	C₂	semidirect
11. #2482×C₁₃₉	C₂	semidirect
12. #2469×C₁₃₉	C₂	semidirect
13. #2465×C₁₃₉	C₂	semidirect
14. #2458×C₁₃₉	C₂	semidirect
15. #2458×C₁₃₉	C₂	semidirect
16. #2438×C₁₃₉	C₂	semidirect
18. #2398×C₁₃₉	C₂	semidirect
19. #2396×C₁₃₉	C₂	semidirect
20. C₂×#393×C₁₃₉	C₂	semidirect
21. #2359×C₁₃₉	C₂	semidirect
22. #2343×C₁₃₉	C₂	semidirect
23. #2342×C₁₃₉	C₂	semidirect
37. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
38. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
39. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
40. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
41. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
42. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
53. #400×C₁₃₉	C₂²	semidirect
54. #400×C₁₃₉	C₂²	semidirect
57. #399×C₁₃₉	C₂²	semidirect
58. #398×C₁₃₉	C₂²	semidirect
59. #398×C₁₃₉	C₂²	semidirect
60. #398×C₁₃₉	C₂²	semidirect
63. #397×C₁₃₉	C₂²	semidirect
66. #395×C₁₃₉	C₂²	semidirect
67. #395×C₁₃₉	C₂²	semidirect
68. #395×C₁₃₉	C₂²	semidirect
69. #395×C₁₃₉	C₂²	semidirect
78. #393×C₁₃₉	C₂²	semidirect
79. #393×C₁₃₉	C₂²	semidirect
80. #393×C₁₃₉	C₂²	semidirect
81. #391×C₁₃₉	C₂²	semidirect
84. #389×C₁₃₉	C₂²	semidirect
85. #389×C₁₃₉	C₂²	semidirect
94. #388×C₁₃₉	C₂²	semidirect
95. #388×C₁₃₉	C₂²	semidirect
96. #388×C₁₃₉	C₂²	semidirect
97. #387×C₁₃₉	C₂²	semidirect
98. #387×C₁₃₉	C₂²	semidirect
99. #387×C₁₃₉	C₂²	semidirect
100. #387×C₁₃₉	C₂²	semidirect
101. #387×C₁₃₉	C₂²	semidirect
102. #387×C₁₃₉	C₂²	semidirect
103. #387×C₁₃₉	C₂²	semidirect
109. #385×C₁₃₉	C₂²	semidirect
110. #383×C₁₃₉	C₂²	semidirect
111. #382×C₁₃₉	C₂²	semidirect
116. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
117. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
122. #376×C₁₃₉	C₂²	semidirect
517. #36079	C₁₃₉	direct (N × H)
518. C₁₃₉	#36079	direct (N × H)
520. C₂×#519	C₂×C₁₃₉	semidirect
521. #2637	C₂×C₁₃₉	semidirect
522. #2632	C₂×C₁₃₉	semidirect
523. #2614	C₂×C₁₃₉	semidirect
524. #2604	C₂×C₁₃₉	semidirect
525. #2599	C₂×C₁₃₉	semidirect
526. #2592	C₂×C₁₃₉	semidirect
527. #2580	C₂×C₁₃₉	semidirect
528. #2498	C₂×C₁₃₉	semidirect
529. #2482	C₂×C₁₃₉	semidirect
530. #2469	C₂×C₁₃₉	semidirect
531. #2465	C₂×C₁₃₉	semidirect
532. #2458	C₂×C₁₃₉	semidirect
533. #2458	C₂×C₁₃₉	semidirect
534. #2438	C₂×C₁₃₉	semidirect
536. #2398	C₂×C₁₃₉	semidirect
537. #2396	C₂×C₁₃₉	semidirect
538. C₂×#393	C₂×C₁₃₉	semidirect
539. #2359	C₂×C₁₃₉	semidirect
540. #2343	C₂×C₁₃₉	semidirect
541. #2342	C₂×C₁₃₉	semidirect
555. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
556. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
557. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
558. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
559. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
560. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
571. #400	C₂²×C₁₃₉	semidirect
572. #400	C₂²×C₁₃₉	semidirect
575. #399	C₂²×C₁₃₉	semidirect
576. #398	C₂²×C₁₃₉	semidirect
577. #398	C₂²×C₁₃₉	semidirect
578. #398	C₂²×C₁₃₉	semidirect
581. #397	C₂²×C₁₃₉	semidirect
584. #395	C₂²×C₁₃₉	semidirect
585. #395	C₂²×C₁₃₉	semidirect
586. #395	C₂²×C₁₃₉	semidirect
587. #395	C₂²×C₁₃₉	semidirect
596. #393	C₂²×C₁₃₉	semidirect
597. #393	C₂²×C₁₃₉	semidirect
598. #393	C₂²×C₁₃₉	semidirect
599. #391	C₂²×C₁₃₉	semidirect
602. #389	C₂²×C₁₃₉	semidirect
603. #389	C₂²×C₁₃₉	semidirect
612. #388	C₂²×C₁₃₉	semidirect
613. #388	C₂²×C₁₃₉	semidirect
614. #388	C₂²×C₁₃₉	semidirect
615. #387	C₂²×C₁₃₉	semidirect
616. #387	C₂²×C₁₃₉	semidirect
617. #387	C₂²×C₁₃₉	semidirect
618. #387	C₂²×C₁₃₉	semidirect
619. #387	C₂²×C₁₃₉	semidirect
620. #387	C₂²×C₁₃₉	semidirect
621. #387	C₂²×C₁₃₉	semidirect
627. #385	C₂²×C₁₃₉	semidirect
628. #383	C₂²×C₁₃₉	semidirect
629. #382	C₂²×C₁₃₉	semidirect
634. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
635. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
639. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
640. #376	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×#551×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2637×C₁₃₉	2
#2632×C₁₃₉	2
#2614×C₁₃₉	2
#2604×C₁₃₉	2
#2599×C₁₃₉	2
#2592×C₁₃₉	2
#2580×C₁₃₉	2
#2498×C₁₃₉	2
#2482×C₁₃₉	2
#2469×C₁₃₉	2
#2465×C₁₃₉	2
#2458×C₁₃₉	2
#2438×C₁₃₉	2
#2411×C₁₃₉	2
#2398×C₁₃₉	2
#2396×C₁₃₉	2
C₂×#393×C₁₃₉	2
#2359×C₁₃₉	2
#2343×C₁₃₉	2
#2342×C₁₃₉	2
#36079	139

Subgroups — C139×#36079 #48030675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36079 #48030675