Subgroups — C₁₃₉×#37304 #48031900

Order 35584.

2158 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#540×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2694×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2681×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2674×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2672×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2641×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₁₃₉	—	2	8	no	—
21	#540×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	#399×C₁₃₉	C₂²	1	4	yes	—
47	#399×C₁₃₉	C₂²	1	4	yes	—
48	#398×C₁₃₉	C₂²	1	4	yes	—
49	#397×C₁₃₉	C₂²	1	4	yes	—
50	#396×C₁₃₉	C₂²	1	4	yes	—
51	#396×C₁₃₉	C₂²	1	4	yes	—
52	#395×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#394×C₁₃₉	C₂²	1	4	yes	—
57	#393×C₁₃₉	C₂²	1	4	yes	—
58	#390×C₁₃₉	C₂²	1	1	yes	characteristic
59	#390×C₁₃₉	C₂²	1	1	yes	characteristic
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	4	yes	—
67	#389×C₁₃₉	C₂²	1	4	yes	—
68	#389×C₁₃₉	C₂²	1	4	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#388×C₁₃₉	C₂²	1	4	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#386×C₁₃₉	C₂²	1	4	yes	—
76	#385×C₁₃₉	C₂²	1	4	yes	—
77	#385×C₁₃₉	C₂²	1	4	yes	—
78	#384×C₁₃₉	C₂²	1	1	yes	characteristic
79	#384×C₁₃₉	C₂²	1	1	yes	characteristic
80	#384×C₁₃₉	C₂²	1	1	yes	characteristic
81	#384×C₁₃₉	C₂²	1	1	yes	characteristic
82	#382×C₁₃₉	C₂²	1	1	yes	characteristic
83	#382×C₁₃₉	C₂²	1	1	yes	characteristic
84	#382×C₁₃₉	C₂²	1	1	yes	characteristic
85	#382×C₁₃₉	C₂²	1	1	yes	characteristic
86	#380×C₁₃₉	C₂²	1	4	yes	—
87	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
91	#376×C₁₃₉	C₂²	1	1	yes	characteristic
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
107	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
108	#127×C₁₃₉	—	2	4	no	—
109	#125×C₁₃₉	—	2	8	no	—
110	#125×C₁₃₉	—	2	4	no	—
111	#125×C₁₃₉	—	2	4	no	—
112	#125×C₁₃₉	—	2	4	no	—
113	#124×C₁₃₉	—	4	8	no	—
114	#123×C₁₃₉	—	2	8	no	—
115	#123×C₁₃₉	—	2	8	no	—
116	#123×C₁₃₉	—	4	8	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
118	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
119	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
120	#121×C₁₃₉	—	2	4	no	—
121	#121×C₁₃₉	—	2	4	no	—
122	#121×C₁₃₉	—	2	8	no	—
123	#121×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	—	2	4	no	—
126	#117×C₁₃₉	—	2	4	no	—
127	#117×C₁₃₉	D₄	1	8	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	4	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂×Q₈×C₁₃₉	—	2	4	no	—
192	C₂×Q₈×C₁₃₉	—	2	4	no	—
193	C₂×Q₈×C₁₃₉	—	4	4	no	—
194	C₂×Q₈×C₁₃₉	—	4	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	2	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	2	no	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	2	2	no	—
205	C₂×D₄×C₁₃₉	—	4	4	no	—
206	C₂×D₄×C₁₃₉	—	4	4	no	—
207	C₂×D₄×C₁₃₉	—	4	4	no	—
208	C₂×D₄×C₁₃₉	—	4	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	4	4	no	—
215	C₂²×C₄×C₁₃₉	—	4	4	no	—
216	C₂²×C₄×C₁₃₉	—	4	4	no	—
217	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	2	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	2	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	8	no	—
251	C₄⋊C₄×C₁₃₉	—	4	4	no	—
252	C₄⋊C₄×C₁₃₉	—	4	2	no	—
253	C₄⋊C₄×C₁₃₉	—	4	4	no	—
254	C₄⋊C₄×C₁₃₉	—	4	4	no	—
255	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃₉	—	2	4	no	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	2	no	—
277	C₄²×C₁₃₉	—	2	2	no	—
278	C₄²×C₁₃₉	—	2	2	no	—
279	C₄²×C₁₃₉	—	2	2	no	—
280	C₄²×C₁₃₉	—	4	2	no	—
281	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
282	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	4	no	—
290	C₂³×C₁₃₉	—	2	4	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	4	no	—
296	C₂³×C₁₃₉	—	2	4	no	—
297	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
298	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
299	Q₈×C₁₃₉	—	8	4	no	—
300	Q₈×C₁₃₉	—	8	4	no	—
301	D₄×C₁₃₉	—	4	4	no	—
302	D₄×C₁₃₉	—	4	4	no	—
303	D₄×C₁₃₉	—	8	4	no	—
304	D₄×C₁₃₉	—	8	4	no	—
305	D₄×C₁₃₉	—	8	4	no	—
306	D₄×C₁₃₉	—	8	4	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	8	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	4	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	4	no	—
328	C₂×C₄×C₁₃₉	—	2	4	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	4	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	4	no	—
337	C₂×C₄×C₁₃₉	—	8	4	no	—
338	C₂×C₄×C₁₃₉	—	8	4	no	—
339	C₂×C₄×C₁₃₉	—	8	4	no	—
340	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
347	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
348	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
349	C₂²×C₁₃₉	—	2	2	no	—
350	C₂²×C₁₃₉	—	2	2	no	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	—	4	4	no	—
361	C₂²×C₁₃₉	—	4	4	no	—
362	C₂²×C₁₃₉	—	4	4	no	—
363	C₂²×C₁₃₉	—	4	4	no	—
364	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
366	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂²×C₁₃₉	#585	1	2	yes	—
369	C₄×C₁₃₉	—	2	2	no	—
370	C₄×C₁₃₉	—	2	2	no	—
371	C₄×C₁₃₉	—	2	2	no	—
372	C₄×C₁₃₉	—	2	2	no	—
373	C₄×C₁₃₉	—	2	2	no	—
374	C₄×C₁₃₉	—	2	4	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	#536	1	4	yes	—
385	C₂×C₁₃₉	—	4	2	no	—
386	C₂×C₁₃₉	—	8	2	no	—
387	C₂×C₁₃₉	—	8	2	no	—
388	C₂×C₁₃₉	C₂×#536	1	1	yes	characteristic
389	C₂×C₁₃₉	#3498	1	1	yes	characteristic
390	C₂×C₁₃₉	#3500	1	1	yes	characteristic
391	C₂×C₁₃₉	#3547	1	2	yes	—
392	C₂×C₁₃₉	#3559	1	2	yes	—
393	#37304	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₁₃₉	#37304	1	1	yes	characteristic, direct product factor, Sylow
395	C₂×#544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	C₂×#540	C₂×C₁₃₉	1	1	yes	characteristic
397	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2694	C₂×C₁₃₉	1	4	yes	complemented
400	#2681	C₂×C₁₃₉	1	4	yes	complemented
401	#2674	C₂×C₁₃₉	1	4	yes	complemented
402	#2672	C₂×C₁₃₉	1	4	yes	complemented
403	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	#2641	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	#2504	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
414	#544	—	2	8	no	—
415	#540	—	2	8	no	—
416	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
425	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
426	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
427	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
428	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
429	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
430	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
431	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
432	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	#399	C₂²×C₁₃₉	1	4	yes	—
441	#399	C₂²×C₁₃₉	1	4	yes	—
442	#398	C₂²×C₁₃₉	1	4	yes	—
443	#397	C₂²×C₁₃₉	1	4	yes	—
444	#396	C₂²×C₁₃₉	1	4	yes	—
445	#396	C₂²×C₁₃₉	1	4	yes	—
446	#395	C₂²×C₁₃₉	1	4	yes	—
447	#394	C₂²×C₁₃₉	1	4	yes	—
448	#394	C₂²×C₁₃₉	1	4	yes	—
449	#394	C₂²×C₁₃₉	1	4	yes	—
450	#394	C₂²×C₁₃₉	1	4	yes	—
451	#393	C₂²×C₁₃₉	1	4	yes	—
452	#390	C₂²×C₁₃₉	1	1	yes	characteristic
453	#390	C₂²×C₁₃₉	1	1	yes	characteristic
454	#390	C₂²×C₁₃₉	1	1	yes	characteristic
455	#390	C₂²×C₁₃₉	1	1	yes	characteristic
456	#390	C₂²×C₁₃₉	1	1	yes	characteristic
457	#390	C₂²×C₁₃₉	1	1	yes	characteristic
458	#390	C₂²×C₁₃₉	1	4	yes	—
459	#390	C₂²×C₁₃₉	1	1	yes	characteristic
460	#390	C₂²×C₁₃₉	1	1	yes	characteristic
461	#389	C₂²×C₁₃₉	1	4	yes	—
462	#389	C₂²×C₁₃₉	1	4	yes	—
463	#388	C₂²×C₁₃₉	1	2	yes	—
464	#388	C₂²×C₁₃₉	1	4	yes	—
465	#388	C₂²×C₁₃₉	1	4	yes	—
466	#388	C₂²×C₁₃₉	1	2	yes	—
467	#387	C₂²×C₁₃₉	1	2	yes	—
468	#387	C₂²×C₁₃₉	1	2	yes	—
469	#386	C₂²×C₁₃₉	1	4	yes	—
470	#385	C₂²×C₁₃₉	1	4	yes	—
471	#385	C₂²×C₁₃₉	1	4	yes	—
472	#384	C₂²×C₁₃₉	1	1	yes	characteristic
473	#384	C₂²×C₁₃₉	1	1	yes	characteristic
474	#384	C₂²×C₁₃₉	1	1	yes	characteristic
475	#384	C₂²×C₁₃₉	1	1	yes	characteristic
476	#382	C₂²×C₁₃₉	1	1	yes	characteristic
477	#382	C₂²×C₁₃₉	1	1	yes	characteristic
478	#382	C₂²×C₁₃₉	1	1	yes	characteristic
479	#382	C₂²×C₁₃₉	1	1	yes	characteristic
480	#380	C₂²×C₁₃₉	1	4	yes	—
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
485	#376	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
488	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₄⋊Q₈	—	2	8	no	—
500	C₄⋊Q₈	—	2	4	no	—
501	C₄⋊Q₈	—	2	4	no	—
502	#127	—	2	4	no	—
503	#125	—	2	8	no	—
504	#125	—	2	4	no	—
505	#125	—	2	4	no	—
506	#125	—	2	4	no	—
507	#124	—	4	8	no	—
508	#123	—	2	8	no	—
509	#123	—	2	8	no	—
510	#123	—	4	8	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₂²⋊Q₈	—	2	8	no	—
513	C₂²⋊Q₈	—	4	8	no	—
514	#121	—	2	4	no	—
515	#121	—	2	4	no	—
516	#121	—	2	8	no	—
517	#121	—	2	8	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	D₄×C₁₃₉	1	8	yes	—
522	C₂×C₄⋊C₄	—	2	4	no	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	4	yes	—
579	#95	C₂³×C₁₃₉	1	4	yes	—
580	#95	C₂³×C₁₃₉	1	4	yes	—
581	#95	C₂³×C₁₃₉	1	4	yes	—
582	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
583	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
584	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
585	C₂×Q₈	—	2	4	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	4	4	no	—
611	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	8	no	—
645	C₄⋊C₄	—	4	4	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	—	4	4	no	—
649	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	8	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	4	no	—
661	C₂²⋊C₄	—	4	4	no	—
662	C₂²⋊C₄	—	4	4	no	—
663	C₂²⋊C₄	—	4	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
667	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	4	2	no	—
675	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
676	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	4	no	—
691	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
692	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
693	Q₈	—	8	4	no	—
694	Q₈	—	8	4	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	4	no	—
697	D₄	—	8	4	no	—
698	D₄	—	8	4	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
737	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
740	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
741	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
742	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
759	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
760	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
761	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
762	C₂²	#585×C₁₃₉	1	2	yes	—
763	C₄	—	2	4	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	#536×C₁₃₉	1	4	yes	—
779	C₂	—	4	2	no	—
780	C₂	—	8	2	no	—
781	C₂	—	8	2	no	—
782	C₂	C₂×#536×C₁₃₉	1	1	yes	characteristic
783	C₂	#3498×C₁₃₉	1	1	yes	characteristic
784	C₂	#3500×C₁₃₉	1	1	yes	characteristic
785	C₂	#3547×C₁₃₉	1	2	yes	—
786	C₂	#3559×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#540×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×#544×C₁₃₉	C₂	semidirect
3. #2859×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2694×C₁₃₉	C₂	semidirect
6. #2681×C₁₃₉	C₂	semidirect
7. #2674×C₁₃₉	C₂	semidirect
8. #2672×C₁₃₉	C₂	semidirect
9. #2660×C₁₃₉	C₂	semidirect
10. #2641×C₁₃₉	C₂	semidirect
11. #2566×C₁₃₉	C₂	semidirect
12. #2566×C₁₃₉	C₂	semidirect
13. #2563×C₁₃₉	C₂	semidirect
14. #2542×C₁₃₉	C₂	semidirect
15. #2504×C₁₃₉	C₂	semidirect
16. #2501×C₁₃₉	C₂	semidirect
17. #2500×C₁₃₉	C₂	semidirect
18. #2500×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
393. #37304	C₁₃₉	direct (N × H)
394. C₁₃₉	#37304	direct (N × H)
395. C₂×#544	C₂×C₁₃₉	semidirect
397. #2859	C₂×C₁₃₉	semidirect
398. #2858	C₂×C₁₃₉	semidirect
399. #2694	C₂×C₁₃₉	semidirect
400. #2681	C₂×C₁₃₉	semidirect
401. #2674	C₂×C₁₃₉	semidirect
402. #2672	C₂×C₁₃₉	semidirect
403. #2660	C₂×C₁₃₉	semidirect
404. #2641	C₂×C₁₃₉	semidirect
405. #2566	C₂×C₁₃₉	semidirect
406. #2566	C₂×C₁₃₉	semidirect
407. #2563	C₂×C₁₃₉	semidirect
408. #2542	C₂×C₁₃₉	semidirect
409. #2504	C₂×C₁₃₉	semidirect
410. #2501	C₂×C₁₃₉	semidirect
411. #2500	C₂×C₁₃₉	semidirect
412. #2500	C₂×C₁₃₉	semidirect
413. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₁₃₉	2
C₂×#540×C₁₃₉	2
#2859×C₁₃₉	2
#2858×C₁₃₉	2
#2694×C₁₃₉	2
#2681×C₁₃₉	2
#2674×C₁₃₉	2
#2672×C₁₃₉	2
#2660×C₁₃₉	2
#2641×C₁₃₉	2
#2566×C₁₃₉	2
#2563×C₁₃₉	2
#2542×C₁₃₉	2
#2504×C₁₃₉	2
#2501×C₁₃₉	2
#2500×C₁₃₉	2
#2298×C₁₃₉	2
#37304	139

Subgroups — C139×#37304 #48031900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37304 #48031900