Subgroups — C₁₃₉×#36115 #48030711

Order 35584.

2470 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2471×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2467×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2366×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2366×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2354×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
21	#529×C₁₃₉	—	2	16	no	—
22	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
39	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
40	#399×C₁₃₉	C₂²	1	4	yes	—
41	#397×C₁₃₉	C₂²	1	4	yes	—
42	#396×C₁₃₉	C₂²	1	4	yes	—
43	#394×C₁₃₉	C₂²	1	4	yes	—
44	#394×C₁₃₉	C₂²	1	4	yes	—
45	#392×C₁₃₉	C₂²	1	4	yes	—
46	#391×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	2	yes	—
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	2	yes	—
51	#390×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	2	yes	—
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	4	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	1	yes	characteristic
58	#389×C₁₃₉	C₂²	1	1	yes	characteristic
59	#388×C₁₃₉	C₂²	1	4	yes	—
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#387×C₁₃₉	C₂²	1	2	yes	—
63	#387×C₁₃₉	C₂²	1	2	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#386×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#384×C₁₃₉	C₂²	1	2	yes	—
70	#382×C₁₃₉	C₂²	1	1	yes	characteristic
71	#380×C₁₃₉	C₂²	1	4	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
96	#127×C₁₃₉	—	2	8	no	—
97	#127×C₁₃₉	—	2	4	no	—
98	#126×C₁₃₉	—	2	16	no	—
99	#125×C₁₃₉	D₄	1	8	yes	complemented
100	#124×C₁₃₉	—	2	8	no	—
101	#124×C₁₃₉	—	4	4	no	—
102	#123×C₁₃₉	—	2	16	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
105	#121×C₁₃₉	—	2	8	no	—
106	#121×C₁₃₉	—	4	4	no	—
107	C₄×Q₈×C₁₃₉	—	2	8	no	—
108	C₄×D₄×C₁₃₉	—	2	4	no	—
109	C₄×D₄×C₁₃₉	—	2	8	no	—
110	C₄×D₄×C₁₃₉	—	2	16	no	—
111	C₄×D₄×C₁₃₉	—	2	4	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	2	4	no	—
114	#117×C₁₃₉	—	2	16	no	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₁₃₉	—	2	8	no	—
146	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
171	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂×Q₈×C₁₃₉	—	2	4	no	—
173	C₂×Q₈×C₁₃₉	—	2	4	no	—
174	C₂×Q₈×C₁₃₉	—	2	4	no	—
175	C₂×D₄×C₁₃₉	—	2	8	no	—
176	C₂×D₄×C₁₃₉	—	2	8	no	—
177	C₂×D₄×C₁₃₉	—	2	8	no	—
178	C₂×D₄×C₁₃₉	—	2	4	no	—
179	C₂×D₄×C₁₃₉	—	2	2	no	—
180	C₂×D₄×C₁₃₉	—	2	2	no	—
181	C₂×D₄×C₁₃₉	—	2	4	no	—
182	C₂×D₄×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	4	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	4	4	no	—
188	C₂×D₄×C₁₃₉	—	4	4	no	—
189	C₂×D₄×C₁₃₉	—	4	2	no	—
190	C₂×D₄×C₁₃₉	—	4	2	no	—
191	C₂×D₄×C₁₃₉	—	4	4	no	—
192	C₂×D₄×C₁₃₉	#41	1	4	yes	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	8	no	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	8	no	—
200	C₂²×C₄×C₁₃₉	—	2	4	no	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	2	no	—
203	C₂²×C₄×C₁₃₉	—	4	2	no	—
204	C₂²×C₄×C₁₃₉	—	4	4	no	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₃₉	—	2	8	no	—
221	C₄⋊C₄×C₁₃₉	—	2	8	no	—
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	2	2	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	2	no	—
228	C₄⋊C₄×C₁₃₉	—	4	2	no	—
229	C₄⋊C₄×C₁₃₉	—	4	2	no	—
230	C₄⋊C₄×C₁₃₉	—	4	4	no	—
231	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
232	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
234	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
235	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
236	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
246	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
247	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
250	C₄²×C₁₃₉	—	2	4	no	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₄²×C₁₃₉	—	2	4	no	—
253	C₄²×C₁₃₉	—	2	8	no	—
254	C₄²×C₁₃₉	—	2	2	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	—	2	4	no	—
257	C₄²×C₁₃₉	—	2	4	no	—
258	C₄²×C₁₃₉	—	2	2	no	—
259	C₄²×C₁₃₉	—	4	1	no	—
260	C₄²×C₁₃₉	—	4	1	no	—
261	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
262	C₄²×C₁₃₉	#41	1	4	yes	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	2	no	—
269	C₂³×C₁₃₉	—	2	4	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	4	no	—
272	C₂³×C₁₃₉	—	2	4	no	—
273	C₂³×C₁₃₉	—	2	4	no	—
274	C₂³×C₁₃₉	—	2	4	no	—
275	C₂³×C₁₃₉	—	2	4	no	—
276	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
277	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
278	Q₈×C₁₃₉	—	4	8	no	—
279	D₄×C₁₃₉	—	2	8	no	—
280	D₄×C₁₃₉	—	4	16	no	—
281	D₄×C₁₃₉	—	4	8	no	—
282	D₄×C₁₃₉	—	4	8	no	—
283	D₄×C₁₃₉	—	8	4	no	—
284	D₄×C₁₃₉	—	8	8	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	4	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	4	8	no	—
319	C₂×C₄×C₁₃₉	—	4	16	no	—
320	C₂×C₄×C₁₃₉	—	4	8	no	—
321	C₂×C₄×C₁₃₉	—	4	8	no	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
328	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
329	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
331	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
332	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
333	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
334	C₂²×C₁₃₉	—	2	4	no	—
335	C₂²×C₁₃₉	—	2	4	no	—
336	C₂²×C₁₃₉	—	2	4	no	—
337	C₂²×C₁₃₉	—	4	2	no	—
338	C₂²×C₁₃₉	—	4	2	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	—	4	2	no	—
341	C₂²×C₁₃₉	—	4	4	no	—
342	C₂²×C₁₃₉	—	4	4	no	—
343	C₂²×C₁₃₉	—	4	4	no	—
344	C₂²×C₁₃₉	—	4	4	no	—
345	C₂²×C₁₃₉	—	4	4	no	—
346	C₂²×C₁₃₉	—	4	4	no	—
347	C₂²×C₁₃₉	—	4	4	no	—
348	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
349	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
350	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
352	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₁₃₉	#585	1	1	yes	characteristic
354	C₂²×C₁₃₉	#585	1	1	yes	characteristic
355	C₄×C₁₃₉	—	2	4	no	—
356	C₄×C₁₃₉	—	2	2	no	—
357	C₄×C₁₃₉	—	2	4	no	—
358	C₄×C₁₃₉	—	2	2	no	—
359	C₄×C₁₃₉	—	2	4	no	—
360	C₄×C₁₃₉	—	2	2	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	4	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	—	4	1	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	1	no	—
367	C₄×C₁₃₉	—	4	2	no	—
368	C₄×C₁₃₉	#529	1	4	yes	complemented
369	C₄×C₁₃₉	#550	1	4	yes	—
370	C₂×C₁₃₉	—	4	4	no	—
371	C₂×C₁₃₉	—	8	4	no	—
372	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
373	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
374	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
375	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
376	C₂×C₁₃₉	#3510	1	1	yes	characteristic
377	C₂×C₁₃₉	#3514	1	1	yes	characteristic
378	C₂×C₁₃₉	#3517	1	1	yes	characteristic
379	#36115	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₁₃₉	#36115	1	1	yes	characteristic, direct product factor, Sylow
381	C₂×#529	C₂×C₁₃₉	1	2	yes	complemented
382	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
383	#2850	C₂×C₁₃₉	1	2	yes	complemented
384	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	#2541	C₂×C₁₃₉	1	1	yes	characteristic
386	#2512	C₂×C₁₃₉	1	2	yes	complemented
387	#2471	C₂×C₁₃₉	1	4	yes	complemented
388	#2467	C₂×C₁₃₉	1	4	yes	complemented
389	#2445	C₂×C₁₃₉	1	2	yes	complemented
390	#2427	C₂×C₁₃₉	1	2	yes	complemented
391	#2426	C₂×C₁₃₉	1	2	yes	complemented
392	#2366	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2366	C₂×C₁₃₉	1	2	yes	complemented
394	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2354	C₂×C₁₃₉	1	2	yes	complemented
396	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
399	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
401	#529	—	2	16	no	—
402	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
403	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
405	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
406	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
408	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
409	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
410	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
411	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
415	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
416	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
419	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
420	#399	C₂²×C₁₃₉	1	4	yes	—
421	#397	C₂²×C₁₃₉	1	4	yes	—
422	#396	C₂²×C₁₃₉	1	4	yes	—
423	#394	C₂²×C₁₃₉	1	4	yes	—
424	#394	C₂²×C₁₃₉	1	4	yes	—
425	#392	C₂²×C₁₃₉	1	4	yes	—
426	#391	C₂²×C₁₃₉	1	2	yes	—
427	#390	C₂²×C₁₃₉	1	2	yes	—
428	#390	C₂²×C₁₃₉	1	2	yes	—
429	#390	C₂²×C₁₃₉	1	2	yes	—
430	#390	C₂²×C₁₃₉	1	2	yes	—
431	#390	C₂²×C₁₃₉	1	2	yes	—
432	#390	C₂²×C₁₃₉	1	2	yes	—
433	#390	C₂²×C₁₃₉	1	4	yes	—
434	#390	C₂²×C₁₃₉	1	2	yes	—
435	#390	C₂²×C₁₃₉	1	2	yes	—
436	#389	C₂²×C₁₃₉	1	1	yes	characteristic
437	#389	C₂²×C₁₃₉	1	1	yes	characteristic
438	#389	C₂²×C₁₃₉	1	2	yes	—
439	#388	C₂²×C₁₃₉	1	4	yes	—
440	#388	C₂²×C₁₃₉	1	4	yes	—
441	#388	C₂²×C₁₃₉	1	4	yes	—
442	#387	C₂²×C₁₃₉	1	2	yes	—
443	#387	C₂²×C₁₃₉	1	2	yes	—
444	#387	C₂²×C₁₃₉	1	4	yes	—
445	#386	C₂²×C₁₃₉	1	4	yes	—
446	#386	C₂²×C₁₃₉	1	4	yes	—
447	#386	C₂²×C₁₃₉	1	4	yes	—
448	#386	C₂²×C₁₃₉	1	4	yes	—
449	#384	C₂²×C₁₃₉	1	2	yes	—
450	#382	C₂²×C₁₃₉	1	1	yes	characteristic
451	#380	C₂²×C₁₃₉	1	4	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
463	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
465	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
468	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
470	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
471	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
473	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₄⋊Q₈	—	2	4	no	—
476	#127	—	2	8	no	—
477	#127	—	2	4	no	—
478	#126	—	2	16	no	—
479	#125	D₄×C₁₃₉	1	8	yes	complemented
480	#124	—	2	8	no	—
481	#124	—	4	4	no	—
482	#123	—	2	16	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	—	4	4	no	—
485	#121	—	2	8	no	—
486	#121	—	4	4	no	—
487	C₄×Q₈	—	2	8	no	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	16	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	8	no	—
493	C₄×D₄	—	2	4	no	—
494	#117	—	2	16	no	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄²	—	2	8	no	—
526	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
539	#95	C₂³×C₁₃₉	1	2	yes	—
540	#95	C₂³×C₁₃₉	1	2	yes	—
541	#95	C₂³×C₁₃₉	1	2	yes	—
542	#95	C₂³×C₁₃₉	1	4	yes	—
543	#95	C₂³×C₁₃₉	1	2	yes	—
544	#95	C₂³×C₁₃₉	1	2	yes	—
545	#95	C₂³×C₁₃₉	1	2	yes	—
546	#95	C₂³×C₁₃₉	1	2	yes	—
547	#95	C₂³×C₁₃₉	1	2	yes	—
548	#95	C₂³×C₁₃₉	1	2	yes	—
549	#95	C₂³×C₁₃₉	1	4	yes	—
550	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
551	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×D₄	—	2	8	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	#41×C₁₃₉	1	4	yes	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
612	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
613	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
614	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
615	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	8	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	4	1	no	—
640	C₄²	—	4	1	no	—
641	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
642	C₄²	#41×C₁₃₉	1	4	yes	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
657	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
658	Q₈	—	4	8	no	—
659	D₄	—	2	8	no	—
660	D₄	—	4	16	no	—
661	D₄	—	4	8	no	—
662	D₄	—	4	8	no	—
663	D₄	—	8	4	no	—
664	D₄	—	8	8	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	16	no	—
700	C₂×C₄	—	4	8	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
705	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
706	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
707	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
708	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
709	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
711	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
712	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
713	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
729	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
730	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
731	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
732	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
733	C₂²	#585×C₁₃₉	1	1	yes	characteristic
734	C₂²	#585×C₁₃₉	1	1	yes	characteristic
735	C₄	—	2	4	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	#529×C₁₃₉	1	4	yes	complemented
749	C₄	#550×C₁₃₉	1	4	yes	—
750	C₂	—	4	4	no	—
751	C₂	—	8	4	no	—
752	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
753	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
754	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
755	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
756	C₂	#3510×C₁₃₉	1	1	yes	characteristic
757	C₂	#3514×C₁₃₉	1	1	yes	characteristic
758	C₂	#3517×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2541×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×#529×C₁₃₉	C₂	semidirect
2. #2858×C₁₃₉	C₂	semidirect
3. #2850×C₁₃₉	C₂	semidirect
4. #2542×C₁₃₉	C₂	semidirect
6. #2512×C₁₃₉	C₂	semidirect
7. #2471×C₁₃₉	C₂	semidirect
8. #2467×C₁₃₉	C₂	semidirect
9. #2445×C₁₃₉	C₂	semidirect
10. #2427×C₁₃₉	C₂	semidirect
11. #2426×C₁₃₉	C₂	semidirect
12. #2366×C₁₃₉	C₂	semidirect
13. #2366×C₁₃₉	C₂	semidirect
14. #2365×C₁₃₉	C₂	semidirect
15. #2354×C₁₃₉	C₂	semidirect
16. C₄×#125×C₁₃₉	C₂	semidirect
17. C₄²×D₄×C₁₃₉	C₂	semidirect
99. #125×C₁₃₉	D₄	semidirect
368. C₄×C₁₃₉	#529	semidirect
379. #36115	C₁₃₉	direct (N × H)
380. C₁₃₉	#36115	direct (N × H)
381. C₂×#529	C₂×C₁₃₉	semidirect
382. #2858	C₂×C₁₃₉	semidirect
383. #2850	C₂×C₁₃₉	semidirect
384. #2542	C₂×C₁₃₉	semidirect
386. #2512	C₂×C₁₃₉	semidirect
387. #2471	C₂×C₁₃₉	semidirect
388. #2467	C₂×C₁₃₉	semidirect
389. #2445	C₂×C₁₃₉	semidirect
390. #2427	C₂×C₁₃₉	semidirect
391. #2426	C₂×C₁₃₉	semidirect
392. #2366	C₂×C₁₃₉	semidirect
393. #2366	C₂×C₁₃₉	semidirect
394. #2365	C₂×C₁₃₉	semidirect
395. #2354	C₂×C₁₃₉	semidirect
396. C₄×#125	C₂×C₁₃₉	semidirect
397. C₄²×D₄	C₂×C₁₃₉	semidirect
479. #125	D₄×C₁₃₉	semidirect
748. C₄	#529×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₉	2
#2858×C₁₃₉	2
#2850×C₁₃₉	2
#2542×C₁₃₉	2
#2541×C₁₃₉	2
#2512×C₁₃₉	2
#2471×C₁₃₉	2
#2467×C₁₃₉	2
#2445×C₁₃₉	2
#2427×C₁₃₉	2
#2426×C₁₃₉	2
#2366×C₁₃₉	2
#2365×C₁₃₉	2
#2354×C₁₃₉	2
C₄×#125×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36115	139

Subgroups — C139×#36115 #48030711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36115 #48030711