Subgroups — C₁₃₉×#35950 #48030546

Order 35584.

2240 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2659×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2583×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2552×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2550×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2549×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2502×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2440×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#398×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2349×C₁₃₉	C₂	1	2	yes	maximal
16	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#554×C₁₃₉	—	2	8	no	—
19	#554×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	4	yes	—
45	#398×C₁₃₉	C₂²	1	4	yes	—
46	#398×C₁₃₉	C₂²	1	4	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	2	yes	—
49	#398×C₁₃₉	C₂²	1	1	yes	characteristic
50	#398×C₁₃₉	C₂²	1	2	yes	—
51	#398×C₁₃₉	C₂²	1	1	yes	characteristic
52	#395×C₁₃₉	C₂²	1	4	yes	—
53	#395×C₁₃₉	C₂²	1	4	yes	—
54	#395×C₁₃₉	C₂²	1	1	yes	characteristic
55	#395×C₁₃₉	C₂²	1	2	yes	—
56	#395×C₁₃₉	C₂²	1	1	yes	characteristic
57	#395×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	4	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	4	yes	—
63	#389×C₁₃₉	C₂²	1	4	yes	—
64	#389×C₁₃₉	C₂²	1	4	yes	—
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	4	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#384×C₁₃₉	C₂²	1	2	yes	—
72	#384×C₁₃₉	C₂²	1	4	yes	—
73	#382×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	#380×C₁₃₉	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	4	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	#376×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
85	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₉	C₂³	1	4	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	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
97	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
98	#125×C₁₃₉	—	2	4	no	—
99	#125×C₁₃₉	—	2	8	no	—
100	#125×C₁₃₉	—	2	4	no	—
101	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
102	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₄×Q₈×C₁₃₉	—	2	4	no	—
107	C₄×Q₈×C₁₃₉	—	2	4	no	—
108	C₄×D₄×C₁₃₉	—	2	8	no	—
109	C₄×D₄×C₁₃₉	—	2	4	no	—
110	C₄×D₄×C₁₃₉	—	2	4	no	—
111	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
112	C₄×D₄×C₁₃₉	Q₈	1	16	yes	complemented
113	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
114	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
115	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	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	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊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	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	1	yes	characteristic
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	4	yes	—
163	#95×C₁₃₉	C₂³	1	1	yes	characteristic
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂×Q₈×C₁₃₉	—	2	2	no	—
173	C₂×Q₈×C₁₃₉	—	2	2	no	—
174	C₂×Q₈×C₁₃₉	—	2	4	no	—
175	C₂×Q₈×C₁₃₉	—	2	4	no	—
176	C₂×Q₈×C₁₃₉	—	2	2	no	—
177	C₂×Q₈×C₁₃₉	—	4	1	no	—
178	C₂×Q₈×C₁₃₉	—	4	2	no	—
179	C₂×Q₈×C₁₃₉	—	4	2	no	—
180	C₂×Q₈×C₁₃₉	—	4	4	no	—
181	C₂×Q₈×C₁₃₉	—	4	2	no	—
182	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
183	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
184	C₂²×C₄×C₁₃₉	—	2	4	no	—
185	C₂²×C₄×C₁₃₉	—	2	8	no	—
186	C₂²×C₄×C₁₃₉	—	2	4	no	—
187	C₂²×C₄×C₁₃₉	—	2	4	no	—
188	C₂²×C₄×C₁₃₉	—	4	4	no	—
189	C₂²×C₄×C₁₃₉	—	4	4	no	—
190	C₂²×C₄×C₁₃₉	—	4	4	no	—
191	C₂²×C₄×C₁₃₉	—	4	2	no	—
192	C₂²×C₄×C₁₃₉	—	4	4	no	—
193	C₂²×C₄×C₁₃₉	—	4	4	no	—
194	C₂²×C₄×C₁₃₉	—	4	4	no	—
195	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
196	C₂²×C₄×C₁₃₉	C₂×Q₈	1	16	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₄⋊C₄×C₁₃₉	—	2	2	no	—
214	C₄⋊C₄×C₁₃₉	—	2	2	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	—	2	8	no	—
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	4	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	2	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	8	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	8	no	—
231	C₄⋊C₄×C₁₃₉	—	4	4	no	—
232	C₄⋊C₄×C₁₃₉	—	4	4	no	—
233	C₄⋊C₄×C₁₃₉	—	4	2	no	—
234	C₄⋊C₄×C₁₃₉	—	4	4	no	—
235	C₄⋊C₄×C₁₃₉	—	4	4	no	—
236	C₄⋊C₄×C₁₃₉	—	4	2	no	—
237	C₄⋊C₄×C₁₃₉	—	4	2	no	—
238	C₄⋊C₄×C₁₃₉	—	4	4	no	—
239	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
240	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
241	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
245	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	16	yes	—
246	C₄²×C₁₃₉	—	2	4	no	—
247	C₄²×C₁₃₉	—	2	2	no	—
248	C₄²×C₁₃₉	—	2	2	no	—
249	C₄²×C₁₃₉	—	4	4	no	—
250	C₄²×C₁₃₉	—	4	2	no	—
251	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
252	C₄²×C₁₃₉	C₂×Q₈	1	8	yes	—
253	C₂³×C₁₃₉	—	2	2	no	—
254	C₂³×C₁₃₉	—	2	4	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
257	C₂³×C₁₃₉	C₂²×Q₈	1	8	yes	—
258	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
259	Q₈×C₁₃₉	—	4	4	no	—
260	Q₈×C₁₃₉	—	4	4	no	—
261	Q₈×C₁₃₉	—	8	4	no	—
262	Q₈×C₁₃₉	—	8	4	no	—
263	D₄×C₁₃₉	C₄⋊Q₈	1	16	yes	complemented
264	C₂×C₄×C₁₃₉	—	2	1	no	—
265	C₂×C₄×C₁₃₉	—	2	1	no	—
266	C₂×C₄×C₁₃₉	—	2	4	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	2	4	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	1	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	1	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	4	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	4	8	no	—
298	C₂×C₄×C₁₃₉	—	4	16	no	—
299	C₂×C₄×C₁₃₉	—	4	8	no	—
300	C₂×C₄×C₁₃₉	—	8	4	no	—
301	C₂×C₄×C₁₃₉	—	8	8	no	—
302	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
307	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
308	C₂×C₄×C₁₃₉	C₂²×Q₈	1	8	yes	—
309	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
310	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
311	C₂²×C₁₃₉	—	2	4	no	—
312	C₂²×C₁₃₉	—	2	4	no	—
313	C₂²×C₁₃₉	—	2	8	no	—
314	C₂²×C₁₃₉	—	2	8	no	—
315	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	8	yes	—
316	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
317	C₂²×C₁₃₉	C₂³×Q₈	1	2	yes	—
318	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²×C₁₃₉	#585	1	2	yes	—
320	C₂²×C₁₃₉	#585	1	1	yes	characteristic
321	C₄×C₁₃₉	—	2	2	no	—
322	C₄×C₁₃₉	—	2	4	no	—
323	C₄×C₁₃₉	—	2	2	no	—
324	C₄×C₁₃₉	—	2	2	no	—
325	C₄×C₁₃₉	—	2	4	no	—
326	C₄×C₁₃₉	—	2	8	no	—
327	C₄×C₁₃₉	—	2	4	no	—
328	C₄×C₁₃₉	—	4	1	no	—
329	C₄×C₁₃₉	—	4	2	no	—
330	C₄×C₁₃₉	—	4	2	no	—
331	C₄×C₁₃₉	—	4	1	no	—
332	C₄×C₁₃₉	—	4	2	no	—
333	C₄×C₁₃₉	—	4	2	no	—
334	C₄×C₁₃₉	—	4	4	no	—
335	C₄×C₁₃₉	—	4	1	no	—
336	C₄×C₁₃₉	C₂×C₄⋊Q₈	1	4	yes	—
337	C₂×C₁₃₉	—	2	8	no	—
338	C₂×C₁₃₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
339	C₂×C₁₃₉	#3485	1	1	yes	characteristic
340	C₂×C₁₃₉	#3488	1	1	yes	characteristic
341	C₂×C₁₃₉	#3501	1	2	yes	—
342	C₂×C₁₃₉	#3504	1	2	yes	—
343	#35950	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₁₃₉	#35950	1	1	yes	characteristic, direct product factor, Sylow
345	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
346	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
347	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
348	#2659	C₂×C₁₃₉	1	2	yes	complemented
349	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
350	#2583	C₂×C₁₃₉	1	2	yes	complemented
351	#2552	C₂×C₁₃₉	1	2	yes	complemented
352	#2550	C₂×C₁₃₉	1	2	yes	complemented
353	#2549	C₂×C₁₃₉	1	4	yes	complemented
354	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
355	#2502	C₂×C₁₃₉	1	2	yes	complemented
356	#2440	C₂×C₁₃₉	1	4	yes	complemented
357	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
358	C₂×#398	C₂×C₁₃₉	1	2	yes	complemented
359	#2349	C₂×C₁₃₉	1	2	yes	—
360	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	—
361	#2275	C₂×C₁₃₉	1	1	yes	characteristic
362	#554	—	2	8	no	—
363	#554	—	2	8	no	—
364	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
367	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
369	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
370	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
371	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
372	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
373	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
374	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
375	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
376	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
377	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
378	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
379	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
382	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
383	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
384	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
385	#398	C₂²×C₁₃₉	1	2	yes	—
386	#398	C₂²×C₁₃₉	1	2	yes	—
387	#398	C₂²×C₁₃₉	1	2	yes	—
388	#398	C₂²×C₁₃₉	1	1	yes	characteristic
389	#398	C₂²×C₁₃₉	1	2	yes	—
390	#398	C₂²×C₁₃₉	1	4	yes	—
391	#398	C₂²×C₁₃₉	1	4	yes	—
392	#398	C₂²×C₁₃₉	1	1	yes	characteristic
393	#398	C₂²×C₁₃₉	1	2	yes	—
394	#398	C₂²×C₁₃₉	1	4	yes	—
395	#398	C₂²×C₁₃₉	1	2	yes	—
396	#395	C₂²×C₁₃₉	1	1	yes	characteristic
397	#395	C₂²×C₁₃₉	1	2	yes	—
398	#395	C₂²×C₁₃₉	1	1	yes	characteristic
399	#395	C₂²×C₁₃₉	1	2	yes	—
400	#395	C₂²×C₁₃₉	1	4	yes	—
401	#395	C₂²×C₁₃₉	1	4	yes	—
402	#391	C₂²×C₁₃₉	1	4	yes	—
403	#391	C₂²×C₁₃₉	1	2	yes	—
404	#389	C₂²×C₁₃₉	1	4	yes	—
405	#389	C₂²×C₁₃₉	1	4	yes	—
406	#389	C₂²×C₁₃₉	1	2	yes	—
407	#389	C₂²×C₁₃₉	1	2	yes	—
408	#389	C₂²×C₁₃₉	1	4	yes	—
409	#389	C₂²×C₁₃₉	1	2	yes	—
410	#389	C₂²×C₁₃₉	1	2	yes	—
411	#385	C₂²×C₁₃₉	1	4	yes	—
412	#385	C₂²×C₁₃₉	1	4	yes	—
413	#385	C₂²×C₁₃₉	1	4	yes	—
414	#385	C₂²×C₁₃₉	1	4	yes	—
415	#384	C₂²×C₁₃₉	1	2	yes	—
416	#384	C₂²×C₁₃₉	1	4	yes	—
417	#382	C₂²×C₁₃₉	1	2	yes	—
418	#380	C₂²×C₁₃₉	1	4	yes	—
419	#380	C₂²×C₁₃₉	1	4	yes	—
420	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
426	#376	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
428	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
429	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
432	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
433	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
435	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
436	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
437	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
438	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
439	C₄⋊Q₈	—	2	4	no	—
440	C₄⋊Q₈	—	2	4	no	—
441	C₄⋊Q₈	—	4	4	no	—
442	#125	—	2	4	no	—
443	#125	—	2	8	no	—
444	#125	—	2	4	no	—
445	C₂²⋊Q₈	—	2	8	no	—
446	C₂²⋊Q₈	—	2	8	no	—
447	C₂²⋊Q₈	—	2	16	no	—
448	C₂²⋊Q₈	—	2	8	no	—
449	C₂²⋊Q₈	—	2	8	no	—
450	C₄×Q₈	—	2	4	no	—
451	C₄×Q₈	—	2	4	no	—
452	C₄×D₄	—	2	8	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	—	2	4	no	—
455	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
456	C₄×D₄	Q₈×C₁₃₉	1	16	yes	complemented
457	C₂×C₄⋊C₄	—	2	8	no	—
458	C₂×C₄⋊C₄	—	2	8	no	—
459	C₂×C₄⋊C₄	—	4	8	no	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
500	#95	C₂³×C₁₃₉	1	1	yes	characteristic
501	#95	C₂³×C₁₃₉	1	2	yes	—
502	#95	C₂³×C₁₃₉	1	2	yes	—
503	#95	C₂³×C₁₃₉	1	4	yes	—
504	#95	C₂³×C₁₃₉	1	4	yes	—
505	#95	C₂³×C₁₃₉	1	4	yes	—
506	#95	C₂³×C₁₃₉	1	4	yes	—
507	#95	C₂³×C₁₃₉	1	2	yes	—
508	#95	C₂³×C₁₃₉	1	1	yes	characteristic
509	#95	C₂³×C₁₃₉	1	2	yes	—
510	#95	C₂³×C₁₃₉	1	2	yes	—
511	#95	C₂³×C₁₃₉	1	2	yes	—
512	#95	C₂³×C₁₃₉	1	4	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	4	yes	—
515	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	4	1	no	—
522	C₂×Q₈	—	4	2	no	—
523	C₂×Q₈	—	4	2	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
527	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	4	4	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
540	C₂²×C₄	C₂×Q₈×C₁₃₉	1	16	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	8	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
584	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
589	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	16	yes	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	4	4	no	—
594	C₄²	—	4	2	no	—
595	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
596	C₄²	C₂×Q₈×C₁₃₉	1	8	yes	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	2	no	—
600	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
601	C₂³	C₂²×Q₈×C₁₃₉	1	8	yes	—
602	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
603	Q₈	—	4	4	no	—
604	Q₈	—	4	4	no	—
605	Q₈	—	8	4	no	—
606	Q₈	—	8	4	no	—
607	D₄	C₄⋊Q₈×C₁₃₉	1	16	yes	complemented
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	8	no	—
642	C₂×C₄	—	4	16	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	8	4	no	—
645	C₂×C₄	—	8	8	no	—
646	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
650	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
651	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
652	C₂×C₄	C₂²×Q₈×C₁₃₉	1	8	yes	—
653	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
654	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	8	yes	—
660	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
661	C₂²	C₂³×Q₈×C₁₃₉	1	2	yes	—
662	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
663	C₂²	#585×C₁₃₉	1	2	yes	—
664	C₂²	#585×C₁₃₉	1	1	yes	characteristic
665	C₄	—	2	2	no	—
666	C₄	—	2	4	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	2	8	no	—
671	C₄	—	2	4	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	1	no	—
680	C₄	C₂×C₄⋊Q₈×C₁₃₉	1	4	yes	—
681	C₂	—	2	8	no	—
682	C₂	C₂²×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
683	C₂	#3485×C₁₃₉	1	1	yes	characteristic
684	C₂	#3488×C₁₃₉	1	1	yes	characteristic
685	C₂	#3501×C₁₃₉	1	2	yes	—
686	C₂	#3504×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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
3. #2660×C₁₃₉	C₂	semidirect
4. #2659×C₁₃₉	C₂	semidirect
5. #2584×C₁₃₉	C₂	semidirect
6. #2583×C₁₃₉	C₂	semidirect
7. #2552×C₁₃₉	C₂	semidirect
8. #2550×C₁₃₉	C₂	semidirect
9. #2549×C₁₃₉	C₂	semidirect
10. #2546×C₁₃₉	C₂	semidirect
11. #2502×C₁₃₉	C₂	semidirect
12. #2440×C₁₃₉	C₂	semidirect
13. #2399×C₁₃₉	C₂	semidirect
14. C₂×#398×C₁₃₉	C₂	semidirect
112. C₄×D₄×C₁₃₉	Q₈	semidirect
263. D₄×C₁₃₉	C₄⋊Q₈	semidirect
343. #35950	C₁₃₉	direct (N × H)
344. C₁₃₉	#35950	direct (N × H)
347. #2660	C₂×C₁₃₉	semidirect
348. #2659	C₂×C₁₃₉	semidirect
349. #2584	C₂×C₁₃₉	semidirect
350. #2583	C₂×C₁₃₉	semidirect
351. #2552	C₂×C₁₃₉	semidirect
352. #2550	C₂×C₁₃₉	semidirect
353. #2549	C₂×C₁₃₉	semidirect
354. #2546	C₂×C₁₃₉	semidirect
355. #2502	C₂×C₁₃₉	semidirect
356. #2440	C₂×C₁₃₉	semidirect
357. #2399	C₂×C₁₃₉	semidirect
358. C₂×#398	C₂×C₁₃₉	semidirect
456. C₄×D₄	Q₈×C₁₃₉	semidirect
607. D₄	C₄⋊Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
#2660×C₁₃₉	2
#2659×C₁₃₉	2
#2584×C₁₃₉	2
#2583×C₁₃₉	2
#2552×C₁₃₉	2
#2550×C₁₃₉	2
#2549×C₁₃₉	2
#2546×C₁₃₉	2
#2502×C₁₃₉	2
#2440×C₁₃₉	2
#2399×C₁₃₉	2
C₂×#398×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35950	139

Subgroups — C139×#35950 #48030546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35950 #48030546