Subgroups — C₁₃₉×#36117 #48030713

Order 35584.

2440 conjugacy classes of subgroups.

The subgroup lattice has 758 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	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2501×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2479×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2448×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2425×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2366×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2354×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
19	#529×C₁₃₉	—	2	16	no	—
20	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
39	#399×C₁₃₉	C₂²	1	4	yes	—
40	#399×C₁₃₉	C₂²	1	4	yes	—
41	#398×C₁₃₉	C₂²	1	4	yes	—
42	#397×C₁₃₉	C₂²	1	4	yes	—
43	#396×C₁₃₉	C₂²	1	4	yes	—
44	#394×C₁₃₉	C₂²	1	4	yes	—
45	#391×C₁₃₉	C₂²	1	1	yes	characteristic
46	#390×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	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	1	yes	characteristic
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	4	yes	—
59	#388×C₁₃₉	C₂²	1	4	yes	—
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#387×C₁₃₉	C₂²	1	2	yes	—
64	#386×C₁₃₉	C₂²	1	4	yes	—
65	#386×C₁₃₉	C₂²	1	4	yes	—
66	#385×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	4	yes	—
68	#384×C₁₃₉	C₂²	1	2	yes	—
69	#384×C₁₃₉	C₂²	1	1	yes	characteristic
70	#384×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	1	yes	characteristic
72	#380×C₁₃₉	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	#127×C₁₃₉	—	2	4	no	—
96	#126×C₁₃₉	—	2	16	no	—
97	#125×C₁₃₉	—	2	8	no	—
98	#124×C₁₃₉	—	2	8	no	—
99	#123×C₁₃₉	—	2	16	no	—
100	#123×C₁₃₉	—	4	8	no	—
101	C₂²⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
102	#121×C₁₃₉	—	2	8	no	—
103	#121×C₁₃₉	—	2	8	no	—
104	#121×C₁₃₉	—	4	4	no	—
105	C₄×Q₈×C₁₃₉	—	2	8	no	—
106	C₄×Q₈×C₁₃₉	—	2	4	no	—
107	C₄×D₄×C₁₃₉	—	2	8	no	—
108	C₄×D₄×C₁₃₉	—	2	8	no	—
109	C₄×D₄×C₁₃₉	—	2	16	no	—
110	#117×C₁₃₉	—	2	16	no	—
111	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	2	yes	—
145	C₂×C₄²×C₁₃₉	—	2	8	no	—
146	C₂×C₄²×C₁₃₉	—	2	4	no	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	2	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	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
170	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₁₃₉	—	2	2	no	—
172	C₂×Q₈×C₁₃₉	—	2	2	no	—
173	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
174	C₂×D₄×C₁₃₉	—	2	8	no	—
175	C₂×D₄×C₁₃₉	—	2	8	no	—
176	C₂×D₄×C₁₃₉	—	2	8	no	—
177	C₂×D₄×C₁₃₉	—	2	4	no	—
178	C₂×D₄×C₁₃₉	—	2	4	no	—
179	C₂×D₄×C₁₃₉	—	2	4	no	—
180	C₂×D₄×C₁₃₉	—	2	4	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	—	4	2	no	—
185	C₂×D₄×C₁₃₉	—	4	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	8	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	8	no	—
199	C₂²×C₄×C₁₃₉	—	4	4	no	—
200	C₂²×C₄×C₁₃₉	—	4	2	no	—
201	C₂²×C₄×C₁₃₉	—	4	1	no	—
202	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₁₃₉	—	2	8	no	—
220	C₄⋊C₄×C₁₃₉	—	2	8	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	8	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	2	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	2	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	2	no	—
232	C₄⋊C₄×C₁₃₉	—	4	2	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	C₂×D₄	1	8	yes	—
237	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
238	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
239	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	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	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₄²×C₁₃₉	—	2	4	no	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	2	4	no	—
255	C₄²×C₁₃₉	—	2	8	no	—
256	C₄²×C₁₃₉	—	2	2	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	2	2	no	—
259	C₄²×C₁₃₉	—	2	4	no	—
260	C₄²×C₁₃₉	—	2	4	no	—
261	C₄²×C₁₃₉	#41	1	4	yes	—
262	C₂³×C₁₃₉	—	2	1	no	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	1	no	—
265	C₂³×C₁₃₉	—	2	1	no	—
266	C₂³×C₁₃₉	—	2	4	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	4	no	—
272	C₂³×C₁₃₉	—	2	4	no	—
273	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
274	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
275	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
276	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
277	Q₈×C₁₃₉	—	2	8	no	—
278	D₄×C₁₃₉	—	4	16	no	—
279	D₄×C₁₃₉	—	4	8	no	—
280	D₄×C₁₃₉	—	4	8	no	—
281	D₄×C₁₃₉	—	8	4	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	1	no	—
284	C₂×C₄×C₁₃₉	—	2	1	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	1	no	—
289	C₂×C₄×C₁₃₉	—	2	1	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	8	no	—
295	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	4	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	4	16	no	—
318	C₂×C₄×C₁₃₉	—	4	8	no	—
319	C₂×C₄×C₁₃₉	—	4	4	no	—
320	C₂×C₄×C₁₃₉	—	4	8	no	—
321	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
327	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
328	C₂×C₄×C₁₃₉	C₂×#41	1	2	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	2₋¹⁺⁴	1	2	yes	—
333	C₂²×C₁₃₉	—	2	2	no	—
334	C₂²×C₁₃₉	—	2	2	no	—
335	C₂²×C₁₃₉	—	2	2	no	—
336	C₂²×C₁₃₉	—	2	2	no	—
337	C₂²×C₁₃₉	—	2	2	no	—
338	C₂²×C₁₃₉	—	2	2	no	—
339	C₂²×C₁₃₉	—	4	4	no	—
340	C₂²×C₁₃₉	—	4	4	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	#550	1	4	yes	—
347	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
348	C₂²×C₁₃₉	C₂²×#41	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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂²×C₁₃₉	#585	1	1	yes	characteristic
354	C₄×C₁₃₉	—	2	2	no	—
355	C₄×C₁₃₉	—	2	2	no	—
356	C₄×C₁₃₉	—	2	4	no	—
357	C₄×C₁₃₉	—	2	4	no	—
358	C₄×C₁₃₉	—	2	4	no	—
359	C₄×C₁₃₉	—	2	2	no	—
360	C₄×C₁₃₉	—	4	2	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	4	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	—	4	2	no	—
365	C₄×C₁₃₉	—	4	1	no	—
366	C₄×C₁₃₉	—	4	2	no	—
367	C₄×C₁₃₉	#529	1	4	yes	complemented
368	C₄×C₁₃₉	#547	1	4	yes	—
369	C₂×C₁₃₉	—	2	4	no	—
370	C₂×C₁₃₉	—	8	4	no	—
371	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
372	C₂×C₁₃₉	C₂×#547	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	#3494	1	1	yes	characteristic
376	C₂×C₁₃₉	#3507	1	1	yes	characteristic
377	C₂×C₁₃₉	#3522	1	1	yes	characteristic
378	#36117	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₁₃₉	#36117	1	1	yes	characteristic, direct product factor, Sylow
380	C₂×#529	C₂×C₁₃₉	1	2	yes	complemented
381	#2856	C₂×C₁₃₉	1	1	yes	characteristic
382	#2854	C₂×C₁₃₉	1	2	yes	complemented
383	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	#2512	C₂×C₁₃₉	1	2	yes	complemented
386	#2501	C₂×C₁₃₉	1	2	yes	complemented
387	#2479	C₂×C₁₃₉	1	4	yes	complemented
388	#2454	C₂×C₁₃₉	1	2	yes	complemented
389	#2448	C₂×C₁₃₉	1	2	yes	complemented
390	#2425	C₂×C₁₃₉	1	4	yes	complemented
391	#2366	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	#2361	C₂×C₁₃₉	1	2	yes	complemented
393	#2354	C₂×C₁₃₉	1	2	yes	complemented
394	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
398	#529	—	2	16	no	—
399	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
400	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
401	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
402	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
403	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
406	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
407	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
408	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
409	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
412	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
414	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
417	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
418	#399	C₂²×C₁₃₉	1	4	yes	—
419	#399	C₂²×C₁₃₉	1	4	yes	—
420	#398	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	#391	C₂²×C₁₃₉	1	1	yes	characteristic
425	#390	C₂²×C₁₃₉	1	2	yes	—
426	#390	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	#389	C₂²×C₁₃₉	1	2	yes	—
434	#389	C₂²×C₁₃₉	1	2	yes	—
435	#389	C₂²×C₁₃₉	1	4	yes	—
436	#389	C₂²×C₁₃₉	1	2	yes	—
437	#389	C₂²×C₁₃₉	1	1	yes	characteristic
438	#388	C₂²×C₁₃₉	1	4	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	#386	C₂²×C₁₃₉	1	4	yes	—
444	#386	C₂²×C₁₃₉	1	4	yes	—
445	#385	C₂²×C₁₃₉	1	4	yes	—
446	#385	C₂²×C₁₃₉	1	2	yes	—
447	#384	C₂²×C₁₃₉	1	1	yes	characteristic
448	#384	C₂²×C₁₃₉	1	2	yes	—
449	#384	C₂²×C₁₃₉	1	2	yes	—
450	#380	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	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
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	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
462	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
463	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
465	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
468	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
470	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
474	#127	—	2	4	no	—
475	#126	—	2	16	no	—
476	#125	—	2	8	no	—
477	#124	—	2	8	no	—
478	#123	—	2	16	no	—
479	#123	—	4	8	no	—
480	C₂²⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
481	#121	—	2	8	no	—
482	#121	—	2	8	no	—
483	#121	—	4	4	no	—
484	C₄×Q₈	—	2	8	no	—
485	C₄×Q₈	—	2	4	no	—
486	C₄×D₄	—	2	8	no	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	2	16	no	—
489	#117	—	2	16	no	—
490	C₂×C₄⋊C₄	—	2	4	no	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	2	yes	—
524	C₂×C₄²	—	2	8	no	—
525	C₂×C₄²	—	2	4	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	2	yes	—
530	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
537	#95	C₂³×C₁₃₉	1	2	yes	—
538	#95	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
543	#95	C₂³×C₁₃₉	1	4	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	4	yes	—
548	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
549	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	8	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	4	4	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	1	no	—
581	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
582	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
583	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₄⋊C₄	—	4	4	no	—
615	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
616	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
617	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	8	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	C₂×D₄×C₁₃₉	1	8	yes	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	8	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	#41×C₁₃₉	1	4	yes	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	4	no	—
652	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
653	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
654	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
655	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
656	Q₈	—	2	8	no	—
657	D₄	—	4	16	no	—
658	D₄	—	4	8	no	—
659	D₄	—	4	8	no	—
660	D₄	—	8	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	8	no	—
674	C₂×C₄	—	2	8	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	16	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
702	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
703	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
704	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
705	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
706	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
707	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
708	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
709	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
711	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	#550×C₁₃₉	1	4	yes	—
726	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
727	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
728	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
729	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
730	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
731	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
732	C₂²	#585×C₁₃₉	1	1	yes	characteristic
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	#529×C₁₃₉	1	4	yes	complemented
747	C₄	#547×C₁₃₉	1	4	yes	—
748	C₂	—	2	4	no	—
749	C₂	—	8	4	no	—
750	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
751	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
752	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
753	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
754	C₂	#3494×C₁₃₉	1	1	yes	characteristic
755	C₂	#3507×C₁₃₉	1	1	yes	characteristic
756	C₂	#3522×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2856×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
3. #2854×C₁₃₉	C₂	semidirect
4. #2552×C₁₃₉	C₂	semidirect
5. #2548×C₁₃₉	C₂	semidirect
6. #2512×C₁₃₉	C₂	semidirect
7. #2501×C₁₃₉	C₂	semidirect
8. #2479×C₁₃₉	C₂	semidirect
9. #2454×C₁₃₉	C₂	semidirect
10. #2448×C₁₃₉	C₂	semidirect
11. #2425×C₁₃₉	C₂	semidirect
12. #2366×C₁₃₉	C₂	semidirect
13. #2361×C₁₃₉	C₂	semidirect
14. #2354×C₁₃₉	C₂	semidirect
15. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
101. C₂²⋊Q₈×C₁₃₉	D₄	semidirect
367. C₄×C₁₃₉	#529	semidirect
378. #36117	C₁₃₉	direct (N × H)
379. C₁₃₉	#36117	direct (N × H)
380. C₂×#529	C₂×C₁₃₉	semidirect
382. #2854	C₂×C₁₃₉	semidirect
383. #2552	C₂×C₁₃₉	semidirect
384. #2548	C₂×C₁₃₉	semidirect
385. #2512	C₂×C₁₃₉	semidirect
386. #2501	C₂×C₁₃₉	semidirect
387. #2479	C₂×C₁₃₉	semidirect
388. #2454	C₂×C₁₃₉	semidirect
389. #2448	C₂×C₁₃₉	semidirect
390. #2425	C₂×C₁₃₉	semidirect
391. #2366	C₂×C₁₃₉	semidirect
392. #2361	C₂×C₁₃₉	semidirect
393. #2354	C₂×C₁₃₉	semidirect
394. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
395. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
396. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
480. C₂²⋊Q₈	D₄×C₁₃₉	semidirect
746. 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
#2856×C₁₃₉	2
#2854×C₁₃₉	2
#2552×C₁₃₉	2
#2548×C₁₃₉	2
#2512×C₁₃₉	2
#2501×C₁₃₉	2
#2479×C₁₃₉	2
#2454×C₁₃₉	2
#2448×C₁₃₉	2
#2425×C₁₃₉	2
#2366×C₁₃₉	2
#2361×C₁₃₉	2
#2354×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36117	139

Subgroups — C139×#36117 #48030713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36117 #48030713