Subgroups — C₁₃₉×#36033 #48030629

Order 35584.

2418 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2638×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2621×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2482×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2480×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2468×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2447×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2435×C₁₃₉	C₂	1	2	yes	maximal
13	#2396×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#556×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#126×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
26	#518×C₁₃₉	—	2	8	no	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	#399×C₁₃₉	C₂²	1	1	yes	characteristic
42	#399×C₁₃₉	C₂²	1	2	yes	complemented
43	#398×C₁₃₉	C₂²	1	2	yes	complemented
44	#398×C₁₃₉	C₂²	1	2	yes	complemented
45	#398×C₁₃₉	C₂²	1	2	yes	complemented
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	2	yes	complemented
49	#397×C₁₃₉	C₂²	1	2	yes	complemented
50	#397×C₁₃₉	C₂²	1	4	yes	complemented
51	#397×C₁₃₉	C₂²	1	4	yes	complemented
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#393×C₁₃₉	C₂²	1	1	yes	characteristic
57	#393×C₁₃₉	C₂²	1	2	yes	complemented
58	#391×C₁₃₉	C₂²	1	2	yes	complemented
59	#391×C₁₃₉	C₂²	1	2	yes	complemented
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#388×C₁₃₉	C₂²	1	4	yes	complemented
68	#387×C₁₃₉	C₂²	1	4	yes	complemented
69	#385×C₁₃₉	C₂²	1	4	yes	complemented
70	#385×C₁₃₉	C₂²	1	4	yes	complemented
71	#385×C₁₃₉	C₂²	1	4	yes	complemented
72	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
73	#381×C₁₃₉	C₂²	1	4	yes	complemented
74	#381×C₁₃₉	C₂²	1	2	yes	complemented
75	#380×C₁₃₉	C₂²	1	4	yes	complemented
76	#379×C₁₃₉	C₂²	1	4	yes	—
77	#379×C₁₃₉	C₂²	1	4	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	—	2	4	no	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
100	#126×C₁₃₉	—	2	16	no	—
101	#124×C₁₃₉	—	2	8	no	—
102	#124×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
105	C₄×Q₈×C₁₃₉	—	2	8	no	—
106	C₄×Q₈×C₁₃₉	—	2	4	no	—
107	C₄×D₄×C₁₃₉	—	2	4	no	—
108	C₄×D₄×C₁₃₉	—	2	8	no	—
109	C₄×D₄×C₁₃₉	—	2	4	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	4	no	—
112	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
113	#117×C₁₃₉	—	2	8	no	—
114	#117×C₁₃₉	—	2	4	no	—
115	#117×C₁₃₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
132	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	#95×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	4	yes	—
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	C₂⁴×C₁₃₉	—	2	4	no	—
173	C₂⁴×C₁₃₉	—	2	4	no	—
174	C₂⁴×C₁₃₉	—	2	4	no	—
175	C₂⁴×C₁₃₉	—	4	4	no	—
176	C₂⁴×C₁₃₉	—	4	4	no	—
177	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	2	4	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×Q₈×C₁₃₉	—	2	4	no	—
184	C₂×Q₈×C₁₃₉	—	4	2	no	—
185	C₂×D₄×C₁₃₉	—	2	32	no	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	—	2	2	no	—
192	C₂×D₄×C₁₃₉	—	2	2	no	—
193	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
194	C₂×D₄×C₁₃₉	#41	1	4	yes	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	4	4	no	—
201	C₂²×C₄×C₁₃₉	—	4	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	4	no	—
203	C₂²×C₄×C₁₃₉	—	4	4	no	—
204	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
205	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	2	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	8	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	8	no	—
230	C₄⋊C₄×C₁₃₉	—	4	2	no	—
231	C₄⋊C₄×C₁₃₉	—	4	4	no	—
232	C₄⋊C₄×C₁₃₉	—	4	2	no	—
233	C₄⋊C₄×C₁₃₉	—	4	2	no	—
234	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
235	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	8	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	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
247	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
252	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	2	2	no	—
255	C₄²×C₁₃₉	—	2	8	no	—
256	C₄²×C₁₃₉	—	2	4	no	—
257	C₄²×C₁₃₉	—	2	4	no	—
258	C₄²×C₁₃₉	—	4	4	no	—
259	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₂³×C₁₃₉	—	2	16	no	—
261	C₂³×C₁₃₉	—	2	1	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	4	no	—
268	C₂³×C₁₃₉	—	2	4	no	—
269	C₂³×C₁₃₉	—	2	4	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	8	4	no	—
274	C₂³×C₁₃₉	—	8	4	no	—
275	C₂³×C₁₃₉	—	8	8	no	—
276	C₂³×C₁₃₉	—	8	8	no	—
277	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
278	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
279	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
280	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
281	Q₈×C₁₃₉	—	4	4	no	—
282	Q₈×C₁₃₉	—	4	8	no	—
283	D₄×C₁₃₉	—	2	16	no	—
284	D₄×C₁₃₉	—	2	8	no	—
285	D₄×C₁₃₉	—	2	8	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	4	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	8	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	4	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	4	no	—
302	C₂×C₄×C₁₃₉	—	2	4	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	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	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	4	8	no	—
317	C₂×C₄×C₁₃₉	—	8	4	no	—
318	C₂×C₄×C₁₃₉	—	8	4	no	—
319	C₂×C₄×C₁₃₉	—	8	4	no	—
320	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
325	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
327	C₂²×C₁₃₉	—	2	2	no	—
328	C₂²×C₁₃₉	—	2	4	no	—
329	C₂²×C₁₃₉	—	2	4	no	—
330	C₂²×C₁₃₉	—	2	4	no	—
331	C₂²×C₁₃₉	—	2	4	no	—
332	C₂²×C₁₃₉	—	2	4	no	—
333	C₂²×C₁₃₉	—	2	8	no	—
334	C₂²×C₁₃₉	—	4	2	no	—
335	C₂²×C₁₃₉	—	4	1	no	—
336	C₂²×C₁₃₉	—	4	2	no	—
337	C₂²×C₁₃₉	—	4	1	no	—
338	C₂²×C₁₃₉	—	4	4	no	—
339	C₂²×C₁₃₉	—	4	4	no	—
340	C₂²×C₁₃₉	—	4	4	no	—
341	C₂²×C₁₃₉	—	4	2	no	—
342	C₂²×C₁₃₉	—	8	16	no	—
343	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
344	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₁₃₉	#585	1	2	yes	—
347	C₂²×C₁₃₉	#585	1	2	yes	—
348	C₄×C₁₃₉	—	2	2	no	—
349	C₄×C₁₃₉	—	2	2	no	—
350	C₄×C₁₃₉	—	2	4	no	—
351	C₄×C₁₃₉	—	2	2	no	—
352	C₄×C₁₃₉	—	4	4	no	—
353	C₄×C₁₃₉	—	4	1	no	—
354	C₄×C₁₃₉	—	4	2	no	—
355	C₄×C₁₃₉	—	4	2	no	—
356	C₄×C₁₃₉	—	4	2	no	—
357	C₄×C₁₃₉	—	4	1	no	—
358	C₄×C₁₃₉	—	4	4	no	—
359	C₄×C₁₃₉	—	4	2	no	—
360	C₄×C₁₃₉	—	4	2	no	—
361	C₄×C₁₃₉	#525	1	4	yes	—
362	C₂×C₁₃₉	—	4	4	no	—
363	C₂×C₁₃₉	—	4	4	no	—
364	C₂×C₁₃₉	—	4	2	no	—
365	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
366	C₂×C₁₃₉	#3485	1	1	yes	characteristic
367	C₂×C₁₃₉	#3500	1	1	yes	characteristic
368	C₂×C₁₃₉	#3510	1	2	yes	—
369	C₂×C₁₃₉	#3521	1	2	yes	—
370	#36033	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₁₃₉	#36033	1	1	yes	characteristic, direct product factor, Sylow
372	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic
374	#2638	C₂×C₁₃₉	1	2	yes	complemented
375	#2621	C₂×C₁₃₉	1	1	yes	characteristic, complemented
376	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	#2561	C₂×C₁₃₉	1	2	yes	complemented
378	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	#2482	C₂×C₁₃₉	1	2	yes	complemented
380	#2480	C₂×C₁₃₉	1	4	yes	complemented
381	#2468	C₂×C₁₃₉	1	4	yes	complemented
382	#2447	C₂×C₁₃₉	1	2	yes	complemented
383	#2435	C₂×C₁₃₉	1	2	yes	—
384	#2396	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	#2395	C₂×C₁₃₉	1	2	yes	complemented
386	#2367	C₂×C₁₃₉	1	2	yes	complemented
387	#2362	C₂×C₁₃₉	1	2	yes	complemented
388	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
389	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
390	#556	—	2	8	no	—
391	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
392	C₂×#126	C₂²×C₁₃₉	1	4	yes	complemented
393	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
394	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
397	#518	—	2	8	no	—
398	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
399	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
400	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
407	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
409	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
410	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
411	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
412	#399	C₂²×C₁₃₉	1	1	yes	characteristic
413	#399	C₂²×C₁₃₉	1	2	yes	complemented
414	#398	C₂²×C₁₃₉	1	2	yes	complemented
415	#398	C₂²×C₁₃₉	1	2	yes	complemented
416	#398	C₂²×C₁₃₉	1	2	yes	complemented
417	#397	C₂²×C₁₃₉	1	2	yes	—
418	#397	C₂²×C₁₃₉	1	2	yes	—
419	#397	C₂²×C₁₃₉	1	2	yes	complemented
420	#397	C₂²×C₁₃₉	1	4	yes	complemented
421	#397	C₂²×C₁₃₉	1	2	yes	complemented
422	#397	C₂²×C₁₃₉	1	4	yes	complemented
423	#396	C₂²×C₁₃₉	1	2	yes	—
424	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
425	#394	C₂²×C₁₃₉	1	4	yes	—
426	#394	C₂²×C₁₃₉	1	4	yes	—
427	#393	C₂²×C₁₃₉	1	1	yes	characteristic
428	#393	C₂²×C₁₃₉	1	2	yes	complemented
429	#391	C₂²×C₁₃₉	1	2	yes	complemented
430	#391	C₂²×C₁₃₉	1	2	yes	complemented
431	#390	C₂²×C₁₃₉	1	2	yes	—
432	#390	C₂²×C₁₃₉	1	2	yes	—
433	#389	C₂²×C₁₃₉	1	2	yes	complemented
434	#388	C₂²×C₁₃₉	1	4	yes	—
435	#388	C₂²×C₁₃₉	1	4	yes	—
436	#388	C₂²×C₁₃₉	1	4	yes	complemented
437	#388	C₂²×C₁₃₉	1	4	yes	complemented
438	#388	C₂²×C₁₃₉	1	4	yes	complemented
439	#387	C₂²×C₁₃₉	1	4	yes	complemented
440	#385	C₂²×C₁₃₉	1	4	yes	complemented
441	#385	C₂²×C₁₃₉	1	4	yes	complemented
442	#385	C₂²×C₁₃₉	1	4	yes	complemented
443	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
444	#381	C₂²×C₁₃₉	1	4	yes	complemented
445	#381	C₂²×C₁₃₉	1	2	yes	complemented
446	#380	C₂²×C₁₃₉	1	4	yes	complemented
447	#379	C₂²×C₁₃₉	1	4	yes	—
448	#379	C₂²×C₁₃₉	1	4	yes	—
449	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
450	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
451	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
452	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
453	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
455	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
456	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
457	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
458	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂²×D₄	—	2	4	no	—
460	C₂²×D₄	—	2	4	no	—
461	C₂²×D₄	—	2	4	no	—
462	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
468	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
470	C₄⋊Q₈	—	2	4	no	—
471	#126	—	2	16	no	—
472	#124	—	2	8	no	—
473	#124	—	2	8	no	—
474	C₂²⋊Q₈	—	2	8	no	—
475	C₂²⋊Q₈	—	2	8	no	—
476	C₄×Q₈	—	2	8	no	—
477	C₄×Q₈	—	2	4	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	—	2	8	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
484	#117	—	2	8	no	—
485	#117	—	2	4	no	—
486	#117	—	2	4	no	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	—	2	8	no	—
503	C₂×C₂²⋊C₄	—	2	8	no	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	2	yes	—
522	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
529	#95	C₂³×C₁₃₉	1	2	yes	—
530	#95	C₂³×C₁₃₉	1	2	yes	—
531	#95	C₂³×C₁₃₉	1	1	yes	characteristic
532	#95	C₂³×C₁₃₉	1	2	yes	—
533	#95	C₂³×C₁₃₉	1	2	yes	—
534	#95	C₂³×C₁₃₉	1	4	yes	—
535	#95	C₂³×C₁₃₉	1	4	yes	—
536	#95	C₂³×C₁₃₉	1	2	yes	—
537	#95	C₂³×C₁₃₉	1	1	yes	characteristic
538	#95	C₂³×C₁₃₉	1	4	yes	—
539	#95	C₂³×C₁₃₉	1	4	yes	—
540	#95	C₂³×C₁₃₉	1	4	yes	—
541	#95	C₂³×C₁₃₉	1	4	yes	—
542	#95	C₂³×C₁₃₉	1	2	yes	—
543	C₂⁴	—	2	4	no	—
544	C₂⁴	—	2	4	no	—
545	C₂⁴	—	2	4	no	—
546	C₂⁴	—	4	4	no	—
547	C₂⁴	—	4	4	no	—
548	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
549	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	4	2	no	—
556	C₂×D₄	—	2	32	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
565	C₂×D₄	#41×C₁₃₉	1	4	yes	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
576	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
584	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	8	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	4	4	no	—
630	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
631	C₂³	—	2	16	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	8	4	no	—
645	C₂³	—	8	4	no	—
646	C₂³	—	8	8	no	—
647	C₂³	—	8	8	no	—
648	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
649	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
650	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
651	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
652	Q₈	—	4	4	no	—
653	Q₈	—	4	8	no	—
654	D₄	—	2	16	no	—
655	D₄	—	2	8	no	—
656	D₄	—	2	8	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	8	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	8	4	no	—
689	C₂×C₄	—	8	4	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
692	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
694	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
695	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
696	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
697	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	8	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	8	16	no	—
714	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
715	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
716	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
717	C₂²	#585×C₁₃₉	1	2	yes	—
718	C₂²	#585×C₁₃₉	1	2	yes	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	4	no	—
722	C₄	—	2	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	4	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	#525×C₁₃₉	1	4	yes	—
733	C₂	—	4	2	no	—
734	C₂	—	4	4	no	—
735	C₂	—	4	4	no	—
736	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
737	C₂	#3485×C₁₃₉	1	1	yes	characteristic
738	C₂	#3500×C₁₃₉	1	1	yes	characteristic
739	C₂	#3510×C₁₃₉	1	2	yes	—
740	C₂	#3521×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#556×C₁₃₉	C₂	semidirect
3. #2638×C₁₃₉	C₂	semidirect
4. #2621×C₁₃₉	C₂	semidirect
5. #2580×C₁₃₉	C₂	semidirect
6. #2561×C₁₃₉	C₂	semidirect
7. #2547×C₁₃₉	C₂	semidirect
8. #2482×C₁₃₉	C₂	semidirect
9. #2480×C₁₃₉	C₂	semidirect
10. #2468×C₁₃₉	C₂	semidirect
11. #2447×C₁₃₉	C₂	semidirect
13. #2396×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. #2367×C₁₃₉	C₂	semidirect
16. #2362×C₁₃₉	C₂	semidirect
17. #2357×C₁₃₉	C₂	semidirect
20. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
21. C₂×#126×C₁₃₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
37. C₂×#117×C₁₃₉	C₂²	semidirect
40. #400×C₁₃₉	C₂²	semidirect
42. #399×C₁₃₉	C₂²	semidirect
43. #398×C₁₃₉	C₂²	semidirect
44. #398×C₁₃₉	C₂²	semidirect
45. #398×C₁₃₉	C₂²	semidirect
48. #397×C₁₃₉	C₂²	semidirect
49. #397×C₁₃₉	C₂²	semidirect
50. #397×C₁₃₉	C₂²	semidirect
51. #397×C₁₃₉	C₂²	semidirect
53. #395×C₁₃₉	C₂²	semidirect
57. #393×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #388×C₁₃₉	C₂²	semidirect
68. #387×C₁₃₉	C₂²	semidirect
69. #385×C₁₃₉	C₂²	semidirect
70. #385×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #382×C₁₃₉	C₂²	semidirect
73. #381×C₁₃₉	C₂²	semidirect
74. #381×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
78. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
370. #36033	C₁₃₉	direct (N × H)
371. C₁₃₉	#36033	direct (N × H)
372. C₂×#556	C₂×C₁₃₉	semidirect
374. #2638	C₂×C₁₃₉	semidirect
375. #2621	C₂×C₁₃₉	semidirect
376. #2580	C₂×C₁₃₉	semidirect
377. #2561	C₂×C₁₃₉	semidirect
378. #2547	C₂×C₁₃₉	semidirect
379. #2482	C₂×C₁₃₉	semidirect
380. #2480	C₂×C₁₃₉	semidirect
381. #2468	C₂×C₁₃₉	semidirect
382. #2447	C₂×C₁₃₉	semidirect
384. #2396	C₂×C₁₃₉	semidirect
385. #2395	C₂×C₁₃₉	semidirect
386. #2367	C₂×C₁₃₉	semidirect
387. #2362	C₂×C₁₃₉	semidirect
388. #2357	C₂×C₁₃₉	semidirect
391. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
392. C₂×#126	C₂²×C₁₃₉	semidirect
396. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
398. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
399. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
408. C₂×#117	C₂²×C₁₃₉	semidirect
411. #400	C₂²×C₁₃₉	semidirect
413. #399	C₂²×C₁₃₉	semidirect
414. #398	C₂²×C₁₃₉	semidirect
415. #398	C₂²×C₁₃₉	semidirect
416. #398	C₂²×C₁₃₉	semidirect
419. #397	C₂²×C₁₃₉	semidirect
420. #397	C₂²×C₁₃₉	semidirect
421. #397	C₂²×C₁₃₉	semidirect
422. #397	C₂²×C₁₃₉	semidirect
424. #395	C₂²×C₁₃₉	semidirect
428. #393	C₂²×C₁₃₉	semidirect
429. #391	C₂²×C₁₃₉	semidirect
430. #391	C₂²×C₁₃₉	semidirect
433. #389	C₂²×C₁₃₉	semidirect
436. #388	C₂²×C₁₃₉	semidirect
437. #388	C₂²×C₁₃₉	semidirect
438. #388	C₂²×C₁₃₉	semidirect
439. #387	C₂²×C₁₃₉	semidirect
440. #385	C₂²×C₁₃₉	semidirect
441. #385	C₂²×C₁₃₉	semidirect
442. #385	C₂²×C₁₃₉	semidirect
443. #382	C₂²×C₁₃₉	semidirect
444. #381	C₂²×C₁₃₉	semidirect
445. #381	C₂²×C₁₃₉	semidirect
446. #380	C₂²×C₁₃₉	semidirect
449. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
450. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
451. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
452. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
454. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
455. C₄×C₂²⋊C₄	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×#556×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2638×C₁₃₉	2
#2621×C₁₃₉	2
#2580×C₁₃₉	2
#2561×C₁₃₉	2
#2547×C₁₃₉	2
#2482×C₁₃₉	2
#2480×C₁₃₉	2
#2468×C₁₃₉	2
#2447×C₁₃₉	2
#2435×C₁₃₉	2
#2396×C₁₃₉	2
#2395×C₁₃₉	2
#2367×C₁₃₉	2
#2362×C₁₃₉	2
#2357×C₁₃₉	2
#36033	139

Subgroups — C139×#36033 #48030629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36033 #48030629