Subgroups — C₁₃₉×#36001 #48030597

Order 35584.

2418 conjugacy classes of subgroups.

The subgroup lattice has 1034 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×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2637×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2633×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2623×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2603×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2599×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2536×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2479×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2475×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2430×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2425×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2406×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	#2343×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	#552×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
38	#520×C₁₃₉	—	2	8	no	—
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
51	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
56	#400×C₁₃₉	C₂²	1	2	yes	—
57	#399×C₁₃₉	C₂²	1	2	yes	—
58	#399×C₁₃₉	C₂²	1	2	yes	—
59	#398×C₁₃₉	C₂²	1	1	yes	characteristic
60	#398×C₁₃₉	C₂²	1	1	yes	characteristic
61	#398×C₁₃₉	C₂²	1	1	yes	characteristic
62	#398×C₁₃₉	C₂²	1	1	yes	characteristic
63	#398×C₁₃₉	C₂²	1	1	yes	characteristic
64	#398×C₁₃₉	C₂²	1	2	yes	—
65	#398×C₁₃₉	C₂²	1	1	yes	characteristic
66	#398×C₁₃₉	C₂²	1	2	yes	—
67	#398×C₁₃₉	C₂²	1	2	yes	—
68	#398×C₁₃₉	C₂²	1	2	yes	—
69	#397×C₁₃₉	C₂²	1	1	yes	characteristic
70	#397×C₁₃₉	C₂²	1	1	yes	characteristic
71	#397×C₁₃₉	C₂²	1	2	yes	—
72	#396×C₁₃₉	C₂²	1	2	yes	—
73	#396×C₁₃₉	C₂²	1	2	yes	—
74	#395×C₁₃₉	C₂²	1	1	yes	characteristic
75	#395×C₁₃₉	C₂²	1	1	yes	characteristic
76	#395×C₁₃₉	C₂²	1	1	yes	characteristic
77	#395×C₁₃₉	C₂²	1	2	yes	—
78	#394×C₁₃₉	C₂²	1	1	yes	characteristic
79	#394×C₁₃₉	C₂²	1	1	yes	characteristic
80	#394×C₁₃₉	C₂²	1	1	yes	characteristic
81	#394×C₁₃₉	C₂²	1	2	yes	—
82	#393×C₁₃₉	C₂²	1	1	yes	characteristic
83	#392×C₁₃₉	C₂²	1	1	yes	characteristic
84	#390×C₁₃₉	C₂²	1	2	yes	—
85	#389×C₁₃₉	C₂²	1	2	yes	—
86	#389×C₁₃₉	C₂²	1	2	yes	—
87	#389×C₁₃₉	C₂²	1	2	yes	—
88	#389×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	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	2	yes	—
97	#387×C₁₃₉	C₂²	1	2	yes	—
98	#387×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#386×C₁₃₉	C₂²	1	2	yes	—
102	#386×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#385×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	—
110	#385×C₁₃₉	C₂²	1	2	yes	—
111	#385×C₁₃₉	C₂²	1	2	yes	—
112	#385×C₁₃₉	C₂²	1	2	yes	—
113	#383×C₁₃₉	C₂²	1	1	yes	characteristic
114	#382×C₁₃₉	C₂²	1	1	yes	characteristic
115	#381×C₁₃₉	C₂²	1	1	yes	characteristic
116	#380×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
122	#376×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
125	C₂×#41×C₁₃₉	—	2	8	no	—
126	C₂×#41×C₁₃₉	—	2	4	no	—
127	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×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	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	#126×C₁₃₉	—	2	4	no	—
143	#126×C₁₃₉	—	2	4	no	—
144	#125×C₁₃₉	—	2	4	no	—
145	#125×C₁₃₉	—	2	4	no	—
146	#125×C₁₃₉	—	2	4	no	—
147	#123×C₁₃₉	—	2	8	no	—
148	#123×C₁₃₉	—	2	4	no	—
149	#123×C₁₃₉	—	2	4	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
153	#121×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×D₄×C₁₃₉	—	2	8	no	—
158	C₄×D₄×C₁₃₉	—	2	8	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	C₄×D₄×C₁₃₉	—	2	4	no	—
161	C₄×D₄×C₁₃₉	—	2	4	no	—
162	C₄×D₄×C₁₃₉	—	4	4	no	—
163	#117×C₁₃₉	—	2	8	no	—
164	#117×C₁₃₉	—	2	4	no	—
165	#117×C₁₃₉	—	2	4	no	—
166	#117×C₁₃₉	D₄	1	8	yes	complemented
167	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
169	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
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	2	yes	—
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	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×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	1	yes	characteristic
236	#95×C₁₃₉	C₂³	1	1	yes	characteristic
237	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	2	yes	—
255	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	#41×C₁₃₉	—	2	32	no	—
259	C₂×Q₈×C₁₃₉	—	2	2	no	—
260	C₂×Q₈×C₁₃₉	—	2	2	no	—
261	C₂×Q₈×C₁₃₉	—	2	4	no	—
262	C₂×Q₈×C₁₃₉	—	2	2	no	—
263	C₂×Q₈×C₁₃₉	—	4	1	no	—
264	C₂×D₄×C₁₃₉	—	2	4	no	—
265	C₂×D₄×C₁₃₉	—	2	4	no	—
266	C₂×D₄×C₁₃₉	—	2	4	no	—
267	C₂×D₄×C₁₃₉	—	2	2	no	—
268	C₂×D₄×C₁₃₉	—	2	4	no	—
269	C₂×D₄×C₁₃₉	—	2	4	no	—
270	C₂×D₄×C₁₃₉	—	2	2	no	—
271	C₂×D₄×C₁₃₉	—	2	4	no	—
272	C₂×D₄×C₁₃₉	—	4	2	no	—
273	C₂×D₄×C₁₃₉	#41	1	8	yes	—
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	4	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	—	2	4	no	—
282	C₂²×C₄×C₁₃₉	—	2	4	no	—
283	C₂²×C₄×C₁₃₉	—	2	2	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	4	no	—
287	C₂²×C₄×C₁₃₉	—	2	4	no	—
288	C₂²×C₄×C₁₃₉	—	2	4	no	—
289	C₂²×C₄×C₁₃₉	—	4	2	no	—
290	C₂²×C₄×C₁₃₉	—	4	1	no	—
291	C₂²×C₄×C₁₃₉	—	4	1	no	—
292	C₂²×C₄×C₁₃₉	—	4	2	no	—
293	C₂²×C₄×C₁₃₉	—	4	2	no	—
294	C₂²×C₄×C₁₃₉	—	4	2	no	—
295	C₂²×C₄×C₁₃₉	—	4	2	no	—
296	C₂²×C₄×C₁₃₉	—	4	2	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
299	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₁₃₉	—	2	4	no	—
320	C₄⋊C₄×C₁₃₉	—	2	2	no	—
321	C₄⋊C₄×C₁₃₉	—	2	4	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	2	no	—
326	C₄⋊C₄×C₁₃₉	—	2	2	no	—
327	C₄⋊C₄×C₁₃₉	—	2	2	no	—
328	C₄⋊C₄×C₁₃₉	—	2	2	no	—
329	C₄⋊C₄×C₁₃₉	—	2	2	no	—
330	C₄⋊C₄×C₁₃₉	—	2	2	no	—
331	C₄⋊C₄×C₁₃₉	—	2	2	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	no	—
333	C₄⋊C₄×C₁₃₉	—	2	2	no	—
334	C₄⋊C₄×C₁₃₉	—	2	2	no	—
335	C₄⋊C₄×C₁₃₉	—	2	2	no	—
336	C₄⋊C₄×C₁₃₉	—	2	2	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	4	no	—
339	C₄⋊C₄×C₁₃₉	—	2	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	4	no	—
342	C₄⋊C₄×C₁₃₉	—	2	4	no	—
343	C₄⋊C₄×C₁₃₉	—	2	4	no	—
344	C₄⋊C₄×C₁₃₉	—	4	2	no	—
345	C₄⋊C₄×C₁₃₉	—	4	2	no	—
346	C₄⋊C₄×C₁₃₉	—	4	2	no	—
347	C₄⋊C₄×C₁₃₉	—	4	2	no	—
348	C₄⋊C₄×C₁₃₉	—	4	2	no	—
349	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
350	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
351	C₂²⋊C₄×C₁₃₉	—	2	2	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	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
370	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
371	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
372	C₄²×C₁₃₉	—	2	2	no	—
373	C₄²×C₁₃₉	—	2	4	no	—
374	C₄²×C₁₃₉	—	2	4	no	—
375	C₄²×C₁₃₉	—	2	2	no	—
376	C₄²×C₁₃₉	—	2	2	no	—
377	C₄²×C₁₃₉	—	2	4	no	—
378	C₄²×C₁₃₉	—	4	2	no	—
379	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
380	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
381	C₂³×C₁₃₉	—	2	1	no	—
382	C₂³×C₁₃₉	—	2	2	no	—
383	C₂³×C₁₃₉	—	2	1	no	—
384	C₂³×C₁₃₉	—	2	2	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	2	no	—
387	C₂³×C₁₃₉	—	2	2	no	—
388	C₂³×C₁₃₉	—	2	2	no	—
389	C₂³×C₁₃₉	—	2	2	no	—
390	C₂³×C₁₃₉	—	2	1	no	—
391	C₂³×C₁₃₉	—	2	2	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	—	2	2	no	—
394	C₂³×C₁₃₉	—	2	1	no	—
395	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
396	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
397	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
398	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
399	Q₈×C₁₃₉	—	2	8	no	—
400	Q₈×C₁₃₉	—	4	4	no	—
401	D₄×C₁₃₉	—	2	8	no	—
402	D₄×C₁₃₉	—	2	16	no	—
403	D₄×C₁₃₉	—	4	8	no	—
404	D₄×C₁₃₉	—	4	4	no	—
405	C₂×C₄×C₁₃₉	—	2	16	no	—
406	C₂×C₄×C₁₃₉	—	2	8	no	—
407	C₂×C₄×C₁₃₉	—	2	2	no	—
408	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
414	C₂×C₄×C₁₃₉	—	2	2	no	—
415	C₂×C₄×C₁₃₉	—	2	1	no	—
416	C₂×C₄×C₁₃₉	—	2	2	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
424	C₂×C₄×C₁₃₉	—	2	2	no	—
425	C₂×C₄×C₁₃₉	—	2	2	no	—
426	C₂×C₄×C₁₃₉	—	2	1	no	—
427	C₂×C₄×C₁₃₉	—	2	1	no	—
428	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
436	C₂×C₄×C₁₃₉	—	2	1	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	1	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	2	no	—
446	C₂×C₄×C₁₃₉	—	2	1	no	—
447	C₂×C₄×C₁₃₉	—	2	2	no	—
448	C₂×C₄×C₁₃₉	—	2	1	no	—
449	C₂×C₄×C₁₃₉	—	2	2	no	—
450	C₂×C₄×C₁₃₉	—	4	4	no	—
451	C₂×C₄×C₁₃₉	—	4	4	no	—
452	C₂×C₄×C₁₃₉	—	4	8	no	—
453	C₂×C₄×C₁₃₉	—	4	4	no	—
454	C₂×C₄×C₁₃₉	—	8	4	no	—
455	C₂×C₄×C₁₃₉	—	8	4	no	—
456	C₂×C₄×C₁₃₉	—	8	4	no	—
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	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
464	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
465	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
466	C₂²×C₁₃₉	—	2	2	no	—
467	C₂²×C₁₃₉	—	2	2	no	—
468	C₂²×C₁₃₉	—	2	4	no	—
469	C₂²×C₁₃₉	—	2	4	no	—
470	C₂²×C₁₃₉	—	2	4	no	—
471	C₂²×C₁₃₉	—	2	4	no	—
472	C₂²×C₁₃₉	—	2	4	no	—
473	C₂²×C₁₃₉	—	4	2	no	—
474	C₂²×C₁₃₉	—	4	2	no	—
475	C₂²×C₁₃₉	—	4	2	no	—
476	C₂²×C₁₃₉	—	4	2	no	—
477	C₂²×C₁₃₉	—	4	1	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	#525	1	4	yes	—
483	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
484	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
485	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
487	C₂²×C₁₃₉	#585	1	1	yes	characteristic
488	C₄×C₁₃₉	—	2	2	no	—
489	C₄×C₁₃₉	—	2	2	no	—
490	C₄×C₁₃₉	—	2	4	no	—
491	C₄×C₁₃₉	—	2	2	no	—
492	C₄×C₁₃₉	—	2	2	no	—
493	C₄×C₁₃₉	—	2	2	no	—
494	C₄×C₁₃₉	—	2	2	no	—
495	C₄×C₁₃₉	—	2	2	no	—
496	C₄×C₁₃₉	—	2	4	no	—
497	C₄×C₁₃₉	—	4	1	no	—
498	C₄×C₁₃₉	—	4	1	no	—
499	C₄×C₁₃₉	—	4	1	no	—
500	C₄×C₁₃₉	—	4	1	no	—
501	C₄×C₁₃₉	—	4	2	no	—
502	C₄×C₁₃₉	—	4	2	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	4	no	—
510	C₂×C₁₃₉	—	8	1	no	—
511	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
512	C₂×C₁₃₉	#3488	1	1	yes	characteristic
513	C₂×C₁₃₉	#3499	1	1	yes	characteristic
514	C₂×C₁₃₉	#3515	1	2	yes	—
515	C₂×C₁₃₉	#3520	1	2	yes	—
516	#36001	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
517	C₁₃₉	#36001	1	1	yes	characteristic, direct product factor, Sylow
518	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
519	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
520	#2637	C₂×C₁₃₉	1	1	yes	characteristic, complemented
521	#2633	C₂×C₁₃₉	1	1	yes	characteristic, complemented
522	#2623	C₂×C₁₃₉	1	1	yes	characteristic, complemented
523	#2603	C₂×C₁₃₉	1	1	yes	characteristic, complemented
524	#2599	C₂×C₁₃₉	1	1	yes	characteristic, complemented
525	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
526	#2536	C₂×C₁₃₉	1	1	yes	characteristic, complemented
527	#2479	C₂×C₁₃₉	1	2	yes	complemented
528	#2475	C₂×C₁₃₉	1	2	yes	complemented
529	#2473	C₂×C₁₃₉	1	2	yes	complemented
530	#2449	C₂×C₁₃₉	1	2	yes	complemented
531	#2449	C₂×C₁₃₉	1	2	yes	complemented
532	#2430	C₂×C₁₃₉	1	1	yes	characteristic
533	#2425	C₂×C₁₃₉	1	2	yes	complemented
534	#2406	C₂×C₁₃₉	1	1	yes	characteristic, complemented
535	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
536	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	C₂×#398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	#2361	C₂×C₁₃₉	1	2	yes	complemented
539	#2359	C₂×C₁₃₉	1	2	yes	complemented
540	#2343	C₂×C₁₃₉	1	1	yes	characteristic, complemented
541	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
542	#552	—	2	8	no	—
543	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
544	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
545	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
546	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
547	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
548	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
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×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
554	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
555	#520	—	2	8	no	—
556	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
558	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
561	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
564	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
565	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
566	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
568	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
571	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
572	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
573	#400	C₂²×C₁₃₉	1	2	yes	—
574	#399	C₂²×C₁₃₉	1	2	yes	—
575	#399	C₂²×C₁₃₉	1	2	yes	—
576	#398	C₂²×C₁₃₉	1	1	yes	characteristic
577	#398	C₂²×C₁₃₉	1	1	yes	characteristic
578	#398	C₂²×C₁₃₉	1	1	yes	characteristic
579	#398	C₂²×C₁₃₉	1	1	yes	characteristic
580	#398	C₂²×C₁₃₉	1	1	yes	characteristic
581	#398	C₂²×C₁₃₉	1	2	yes	—
582	#398	C₂²×C₁₃₉	1	1	yes	characteristic
583	#398	C₂²×C₁₃₉	1	2	yes	—
584	#398	C₂²×C₁₃₉	1	2	yes	—
585	#398	C₂²×C₁₃₉	1	2	yes	—
586	#397	C₂²×C₁₃₉	1	1	yes	characteristic
587	#397	C₂²×C₁₃₉	1	1	yes	characteristic
588	#397	C₂²×C₁₃₉	1	2	yes	—
589	#396	C₂²×C₁₃₉	1	2	yes	—
590	#396	C₂²×C₁₃₉	1	2	yes	—
591	#395	C₂²×C₁₃₉	1	1	yes	characteristic
592	#395	C₂²×C₁₃₉	1	1	yes	characteristic
593	#395	C₂²×C₁₃₉	1	1	yes	characteristic
594	#395	C₂²×C₁₃₉	1	2	yes	—
595	#394	C₂²×C₁₃₉	1	1	yes	characteristic
596	#394	C₂²×C₁₃₉	1	1	yes	characteristic
597	#394	C₂²×C₁₃₉	1	1	yes	characteristic
598	#394	C₂²×C₁₃₉	1	2	yes	—
599	#393	C₂²×C₁₃₉	1	1	yes	characteristic
600	#392	C₂²×C₁₃₉	1	1	yes	characteristic
601	#390	C₂²×C₁₃₉	1	2	yes	—
602	#389	C₂²×C₁₃₉	1	2	yes	—
603	#389	C₂²×C₁₃₉	1	2	yes	—
604	#389	C₂²×C₁₃₉	1	2	yes	—
605	#389	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	—
612	#387	C₂²×C₁₃₉	1	2	yes	—
613	#387	C₂²×C₁₃₉	1	2	yes	—
614	#387	C₂²×C₁₃₉	1	2	yes	—
615	#387	C₂²×C₁₃₉	1	2	yes	—
616	#386	C₂²×C₁₃₉	1	2	yes	—
617	#386	C₂²×C₁₃₉	1	2	yes	—
618	#386	C₂²×C₁₃₉	1	2	yes	—
619	#386	C₂²×C₁₃₉	1	2	yes	—
620	#386	C₂²×C₁₃₉	1	2	yes	—
621	#385	C₂²×C₁₃₉	1	2	yes	—
622	#385	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	—
628	#385	C₂²×C₁₃₉	1	2	yes	—
629	#385	C₂²×C₁₃₉	1	2	yes	—
630	#383	C₂²×C₁₃₉	1	1	yes	characteristic
631	#382	C₂²×C₁₃₉	1	1	yes	characteristic
632	#381	C₂²×C₁₃₉	1	1	yes	characteristic
633	#380	C₂²×C₁₃₉	1	2	yes	—
634	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
636	C₄×C₄⋊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	#376	C₂²×C₁₃₉	1	1	yes	characteristic
640	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
641	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
642	C₂×#41	—	2	8	no	—
643	C₂×#41	—	2	4	no	—
644	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
649	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
654	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
659	#126	—	2	4	no	—
660	#126	—	2	4	no	—
661	#125	—	2	4	no	—
662	#125	—	2	4	no	—
663	#125	—	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	C₂²⋊Q₈	—	4	4	no	—
670	#121	—	2	8	no	—
671	C₄×Q₈	—	2	4	no	—
672	C₄×Q₈	—	2	4	no	—
673	C₄×Q₈	—	2	4	no	—
674	C₄×D₄	—	2	8	no	—
675	C₄×D₄	—	2	8	no	—
676	C₄×D₄	—	2	4	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	—	2	4	no	—
679	C₄×D₄	—	4	4	no	—
680	#117	—	2	8	no	—
681	#117	—	2	4	no	—
682	#117	—	2	4	no	—
683	#117	D₄×C₁₃₉	1	8	yes	complemented
684	C₂×C₄⋊C₄	—	2	4	no	—
685	C₂×C₄⋊C₄	—	2	4	no	—
686	C₂×C₄⋊C₄	—	2	8	no	—
687	C₂×C₄⋊C₄	—	4	4	no	—
688	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
712	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
747	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
748	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
750	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
771	#95	C₂³×C₁₃₉	1	2	yes	—
772	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
774	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
775	#41	—	2	32	no	—
776	C₂×Q₈	—	2	2	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	4	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	4	1	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	4	no	—
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	#41×C₁₃₉	1	8	yes	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	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	2	yes	—
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	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	4	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	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	4	2	no	—
862	C₄⋊C₄	—	4	2	no	—
863	C₄⋊C₄	—	4	2	no	—
864	C₄⋊C₄	—	4	2	no	—
865	C₄⋊C₄	—	4	2	no	—
866	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
867	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
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	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	2	4	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	4	2	no	—
884	C₂²⋊C₄	—	4	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
888	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	4	no	—
891	C₄²	—	2	4	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	4	no	—
895	C₄²	—	4	2	no	—
896	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
897	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
913	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
914	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
915	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
916	Q₈	—	2	8	no	—
917	Q₈	—	4	4	no	—
918	D₄	—	2	8	no	—
919	D₄	—	2	16	no	—
920	D₄	—	4	8	no	—
921	D₄	—	4	4	no	—
922	C₂×C₄	—	2	16	no	—
923	C₂×C₄	—	2	8	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	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	1	no	—
933	C₂×C₄	—	2	2	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	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	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	1	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	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	8	4	no	—
972	C₂×C₄	—	8	4	no	—
973	C₂×C₄	—	8	4	no	—
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	C₂²×D₄×C₁₃₉	1	2	yes	—
980	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
981	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
982	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	4	no	—
986	C₂²	—	2	4	no	—
987	C₂²	—	2	4	no	—
988	C₂²	—	2	4	no	—
989	C₂²	—	2	4	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	#525×C₁₃₉	1	4	yes	—
1000	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1001	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
1002	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1003	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1004	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	2	4	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	4	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	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	C₂	—	2	4	no	—
1026	C₂	—	4	4	no	—
1027	C₂	—	8	1	no	—
1028	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1029	C₂	#3488×C₁₃₉	1	1	yes	characteristic
1030	C₂	#3499×C₁₃₉	1	1	yes	characteristic
1031	C₂	#3515×C₁₃₉	1	2	yes	—
1032	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2430×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#552×C₁₃₉	C₂	semidirect
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2637×C₁₃₉	C₂	semidirect
4. #2633×C₁₃₉	C₂	semidirect
5. #2623×C₁₃₉	C₂	semidirect
6. #2603×C₁₃₉	C₂	semidirect
7. #2599×C₁₃₉	C₂	semidirect
8. #2584×C₁₃₉	C₂	semidirect
9. #2536×C₁₃₉	C₂	semidirect
10. #2479×C₁₃₉	C₂	semidirect
11. #2475×C₁₃₉	C₂	semidirect
12. #2473×C₁₃₉	C₂	semidirect
13. #2449×C₁₃₉	C₂	semidirect
14. #2449×C₁₃₉	C₂	semidirect
16. #2425×C₁₃₉	C₂	semidirect
17. #2406×C₁₃₉	C₂	semidirect
18. #2399×C₁₃₉	C₂	semidirect
19. #2392×C₁₃₉	C₂	semidirect
20. C₂×#398×C₁₃₉	C₂	semidirect
21. #2361×C₁₃₉	C₂	semidirect
22. #2359×C₁₃₉	C₂	semidirect
23. #2343×C₁₃₉	C₂	semidirect
166. #117×C₁₃₉	D₄	semidirect
516. #36001	C₁₃₉	direct (N × H)
517. C₁₃₉	#36001	direct (N × H)
518. C₂×#552	C₂×C₁₃₉	semidirect
519. C₂×#520	C₂×C₁₃₉	semidirect
520. #2637	C₂×C₁₃₉	semidirect
521. #2633	C₂×C₁₃₉	semidirect
522. #2623	C₂×C₁₃₉	semidirect
523. #2603	C₂×C₁₃₉	semidirect
524. #2599	C₂×C₁₃₉	semidirect
525. #2584	C₂×C₁₃₉	semidirect
526. #2536	C₂×C₁₃₉	semidirect
527. #2479	C₂×C₁₃₉	semidirect
528. #2475	C₂×C₁₃₉	semidirect
529. #2473	C₂×C₁₃₉	semidirect
530. #2449	C₂×C₁₃₉	semidirect
531. #2449	C₂×C₁₃₉	semidirect
533. #2425	C₂×C₁₃₉	semidirect
534. #2406	C₂×C₁₃₉	semidirect
535. #2399	C₂×C₁₃₉	semidirect
536. #2392	C₂×C₁₃₉	semidirect
537. C₂×#398	C₂×C₁₃₉	semidirect
538. #2361	C₂×C₁₃₉	semidirect
539. #2359	C₂×C₁₃₉	semidirect
540. #2343	C₂×C₁₃₉	semidirect
683. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2637×C₁₃₉	2
#2633×C₁₃₉	2
#2623×C₁₃₉	2
#2603×C₁₃₉	2
#2599×C₁₃₉	2
#2584×C₁₃₉	2
#2536×C₁₃₉	2
#2479×C₁₃₉	2
#2475×C₁₃₉	2
#2473×C₁₃₉	2
#2449×C₁₃₉	2
#2430×C₁₃₉	2
#2425×C₁₃₉	2
#2406×C₁₃₉	2
#2399×C₁₃₉	2
#2392×C₁₃₉	2
C₂×#398×C₁₃₉	2
#2361×C₁₃₉	2
#2359×C₁₃₉	2
#2343×C₁₃₉	2
#36001	139

Subgroups — C139×#36001 #48030597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36001 #48030597