Subgroups — C₁₃₉×#35909 #48030505

Order 35584.

2272 conjugacy classes of subgroups.

The subgroup lattice has 720 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×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2664×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2640×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2611×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2603×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2560×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2540×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	#2452×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2429×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2276×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#556×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×#126×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
41	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	1	yes	characteristic
44	#400×C₁₃₉	C₂²	1	1	yes	characteristic
45	#399×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	4	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	4	yes	—
53	#396×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	1	yes	characteristic
56	#394×C₁₃₉	C₂²	1	1	yes	characteristic
57	#393×C₁₃₉	C₂²	1	4	yes	—
58	#393×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	2	yes	—
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#391×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	4	yes	—
63	#390×C₁₃₉	C₂²	1	4	yes	—
64	#390×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	4	yes	—
68	#389×C₁₃₉	C₂²	1	4	yes	—
69	#388×C₁₃₉	C₂²	1	4	yes	—
70	#388×C₁₃₉	C₂²	1	4	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#387×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	#376×C₁₃₉	C₂²	1	2	yes	—
84	#376×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×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	#126×C₁₃₉	—	2	8	no	—
99	#126×C₁₃₉	—	2	8	no	—
100	#125×C₁₃₉	—	2	8	no	—
101	#124×C₁₃₉	—	2	4	no	—
102	#124×C₁₃₉	—	2	4	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
107	#121×C₁₃₉	—	2	8	no	—
108	C₄×Q₈×C₁₃₉	—	2	4	no	—
109	C₄×Q₈×C₁₃₉	—	2	8	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	4	8	no	—
116	#117×C₁₃₉	—	2	8	no	—
117	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	2	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	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	1	yes	characteristic
163	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂×Q₈×C₁₃₉	—	2	2	no	—
176	C₂×Q₈×C₁₃₉	—	2	2	no	—
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	4	1	no	—
182	C₂×Q₈×C₁₃₉	—	4	2	no	—
183	C₂×Q₈×C₁₃₉	—	4	2	no	—
184	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	8	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	8	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	4	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
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	—	4	2	no	—
199	C₂²×C₄×C₁₃₉	—	4	4	no	—
200	C₂²×C₄×C₁₃₉	—	4	4	no	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	4	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₁₃₉	—	2	8	no	—
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	2	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	2	no	—
224	C₄⋊C₄×C₁₃₉	—	2	2	no	—
225	C₄⋊C₄×C₁₃₉	—	2	8	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	8	no	—
228	C₄⋊C₄×C₁₃₉	—	2	8	no	—
229	C₄⋊C₄×C₁₃₉	—	2	8	no	—
230	C₄⋊C₄×C₁₃₉	—	4	4	no	—
231	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
233	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
234	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	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	C₄²×C₁₃₉	—	2	4	no	—
250	C₄²×C₁₃₉	—	2	2	no	—
251	C₄²×C₁₃₉	—	2	2	no	—
252	C₄²×C₁₃₉	—	2	8	no	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	4	4	no	—
255	C₄²×C₁₃₉	—	4	2	no	—
256	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
257	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	2	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	4	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	4	no	—
268	C₂³×C₁₃₉	—	2	2	no	—
269	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
270	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
271	Q₈×C₁₃₉	—	2	8	no	—
272	Q₈×C₁₃₉	—	4	4	no	—
273	Q₈×C₁₃₉	—	4	4	no	—
274	Q₈×C₁₃₉	—	8	4	no	—
275	D₄×C₁₃₉	—	2	8	no	—
276	D₄×C₁₃₉	—	4	16	no	—
277	D₄×C₁₃₉	—	4	4	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	4	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	1	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	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	1	no	—
289	C₂×C₄×C₁₃₉	—	2	1	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	4	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	4	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	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	2	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	4	8	no	—
310	C₂×C₄×C₁₃₉	—	4	8	no	—
311	C₂×C₄×C₁₃₉	—	8	8	no	—
312	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
313	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
318	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
319	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
320	C₂²×C₁₃₉	—	2	4	no	—
321	C₂²×C₁₃₉	—	2	4	no	—
322	C₂²×C₁₃₉	—	2	4	no	—
323	C₂²×C₁₃₉	—	4	2	no	—
324	C₂²×C₁₃₉	—	4	2	no	—
325	C₂²×C₁₃₉	—	4	2	no	—
326	C₂²×C₁₃₉	—	4	2	no	—
327	C₂²×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	4	2	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	4	no	—
331	C₂²×C₁₃₉	—	4	4	no	—
332	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
333	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
334	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
336	C₂²×C₁₃₉	#585	1	1	yes	characteristic
337	C₄×C₁₃₉	—	2	4	no	—
338	C₄×C₁₃₉	—	2	2	no	—
339	C₄×C₁₃₉	—	2	2	no	—
340	C₄×C₁₃₉	—	2	4	no	—
341	C₄×C₁₃₉	—	2	2	no	—
342	C₄×C₁₃₉	—	2	8	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	1	no	—
346	C₄×C₁₃₉	—	4	1	no	—
347	C₄×C₁₃₉	—	4	4	no	—
348	C₄×C₁₃₉	—	4	1	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	2	no	—
351	C₄×C₁₃₉	#532	1	4	yes	—
352	C₂×C₁₃₉	—	4	4	no	—
353	C₂×C₁₃₉	—	8	2	no	—
354	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
355	C₂×C₁₃₉	#3486	1	1	yes	characteristic
356	C₂×C₁₃₉	#3488	1	1	yes	characteristic
357	C₂×C₁₃₉	#3516	1	2	yes	—
358	C₂×C₁₃₉	#3520	1	2	yes	—
359	#35909	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₁₃₉	#35909	1	1	yes	characteristic, direct product factor, Sylow
361	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
362	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
363	#2664	C₂×C₁₃₉	1	2	yes	complemented
364	#2640	C₂×C₁₃₉	1	1	yes	characteristic, complemented
365	#2611	C₂×C₁₃₉	1	2	yes	complemented
366	#2603	C₂×C₁₃₉	1	2	yes	complemented
367	#2560	C₂×C₁₃₉	1	4	yes	complemented
368	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	#2540	C₂×C₁₃₉	1	1	yes	characteristic
370	#2452	C₂×C₁₃₉	1	4	yes	complemented
371	#2429	C₂×C₁₃₉	1	2	yes	complemented
372	#2426	C₂×C₁₃₉	1	2	yes	complemented
373	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
374	#2392	C₂×C₁₃₉	1	2	yes	complemented
375	#2361	C₂×C₁₃₉	1	2	yes	complemented
376	#2360	C₂×C₁₃₉	1	2	yes	complemented
377	#2276	C₂×C₁₃₉	1	1	yes	characteristic, complemented
378	#556	—	2	8	no	—
379	#554	—	2	8	no	—
380	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
383	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
384	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
385	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
386	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
387	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
388	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
389	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
392	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
393	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
394	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
396	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
401	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
402	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
403	#400	C₂²×C₁₃₉	1	1	yes	characteristic
404	#400	C₂²×C₁₃₉	1	1	yes	characteristic
405	#399	C₂²×C₁₃₉	1	2	yes	—
406	#398	C₂²×C₁₃₉	1	4	yes	—
407	#398	C₂²×C₁₃₉	1	2	yes	—
408	#398	C₂²×C₁₃₉	1	2	yes	—
409	#397	C₂²×C₁₃₉	1	2	yes	—
410	#397	C₂²×C₁₃₉	1	2	yes	—
411	#397	C₂²×C₁₃₉	1	2	yes	—
412	#396	C₂²×C₁₃₉	1	4	yes	—
413	#396	C₂²×C₁₃₉	1	4	yes	—
414	#394	C₂²×C₁₃₉	1	4	yes	—
415	#394	C₂²×C₁₃₉	1	1	yes	characteristic
416	#394	C₂²×C₁₃₉	1	1	yes	characteristic
417	#393	C₂²×C₁₃₉	1	4	yes	—
418	#393	C₂²×C₁₃₉	1	2	yes	—
419	#392	C₂²×C₁₃₉	1	2	yes	—
420	#391	C₂²×C₁₃₉	1	2	yes	—
421	#391	C₂²×C₁₃₉	1	2	yes	—
422	#390	C₂²×C₁₃₉	1	4	yes	—
423	#390	C₂²×C₁₃₉	1	4	yes	—
424	#390	C₂²×C₁₃₉	1	2	yes	—
425	#389	C₂²×C₁₃₉	1	4	yes	—
426	#389	C₂²×C₁₃₉	1	4	yes	—
427	#389	C₂²×C₁₃₉	1	2	yes	—
428	#389	C₂²×C₁₃₉	1	2	yes	—
429	#388	C₂²×C₁₃₉	1	4	yes	—
430	#388	C₂²×C₁₃₉	1	4	yes	—
431	#388	C₂²×C₁₃₉	1	4	yes	—
432	#387	C₂²×C₁₃₉	1	4	yes	—
433	#386	C₂²×C₁₃₉	1	4	yes	—
434	#385	C₂²×C₁₃₉	1	4	yes	—
435	#385	C₂²×C₁₃₉	1	4	yes	—
436	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
437	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
441	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	#376	C₂²×C₁₃₉	1	2	yes	—
444	#376	C₂²×C₁₃₉	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
448	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
449	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
452	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
455	C₄⋊Q₈	—	2	4	no	—
456	C₄⋊Q₈	—	2	4	no	—
457	C₄⋊Q₈	—	4	4	no	—
458	#126	—	2	8	no	—
459	#126	—	2	8	no	—
460	#125	—	2	8	no	—
461	#124	—	2	4	no	—
462	#124	—	2	4	no	—
463	C₂²⋊Q₈	—	2	8	no	—
464	C₂²⋊Q₈	—	2	16	no	—
465	C₂²⋊Q₈	—	2	8	no	—
466	C₂²⋊Q₈	—	2	8	no	—
467	#121	—	2	8	no	—
468	C₄×Q₈	—	2	4	no	—
469	C₄×Q₈	—	2	8	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	8	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	4	8	no	—
476	#117	—	2	8	no	—
477	C₂×C₄⋊C₄	—	2	8	no	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
517	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
520	#95	C₂³×C₁₃₉	1	1	yes	characteristic
521	#95	C₂³×C₁₃₉	1	4	yes	—
522	#95	C₂³×C₁₃₉	1	2	yes	—
523	#95	C₂³×C₁₃₉	1	2	yes	—
524	#95	C₂³×C₁₃₉	1	1	yes	characteristic
525	#95	C₂³×C₁₃₉	1	2	yes	—
526	#95	C₂³×C₁₃₉	1	2	yes	—
527	#95	C₂³×C₁₃₉	1	4	yes	—
528	#95	C₂³×C₁₃₉	1	2	yes	—
529	#95	C₂³×C₁₃₉	1	2	yes	—
530	#95	C₂³×C₁₃₉	1	4	yes	—
531	#95	C₂³×C₁₃₉	1	4	yes	—
532	#95	C₂³×C₁₃₉	1	4	yes	—
533	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
534	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	4	no	—
538	C₂×Q₈	—	2	4	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	4	1	no	—
542	C₂×Q₈	—	4	2	no	—
543	C₂×Q₈	—	4	2	no	—
544	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	8	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	8	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
576	C₄⋊C₄	—	2	8	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	2	8	no	—
589	C₄⋊C₄	—	2	8	no	—
590	C₄⋊C₄	—	4	4	no	—
591	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
592	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
593	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	4	2	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	4	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	8	no	—
613	C₄²	—	2	4	no	—
614	C₄²	—	4	4	no	—
615	C₄²	—	4	2	no	—
616	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
617	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
630	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
631	Q₈	—	2	8	no	—
632	Q₈	—	4	4	no	—
633	Q₈	—	4	4	no	—
634	Q₈	—	8	4	no	—
635	D₄	—	2	8	no	—
636	D₄	—	4	16	no	—
637	D₄	—	4	4	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	—	4	8	no	—
671	C₂×C₄	—	8	8	no	—
672	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
673	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
675	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
677	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
678	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
679	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
693	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
694	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
695	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
696	C₂²	#585×C₁₃₉	1	1	yes	characteristic
697	C₄	—	2	4	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	4	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	8	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	4	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	#532×C₁₃₉	1	4	yes	—
712	C₂	—	4	4	no	—
713	C₂	—	8	2	no	—
714	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
715	C₂	#3486×C₁₃₉	1	1	yes	characteristic
716	C₂	#3488×C₁₃₉	1	1	yes	characteristic
717	C₂	#3516×C₁₃₉	1	2	yes	—
718	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2540×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×#556×C₁₃₉	C₂	semidirect
2. C₂×#554×C₁₃₉	C₂	semidirect
3. #2664×C₁₃₉	C₂	semidirect
4. #2640×C₁₃₉	C₂	semidirect
5. #2611×C₁₃₉	C₂	semidirect
6. #2603×C₁₃₉	C₂	semidirect
7. #2560×C₁₃₉	C₂	semidirect
8. #2546×C₁₃₉	C₂	semidirect
10. #2452×C₁₃₉	C₂	semidirect
11. #2429×C₁₃₉	C₂	semidirect
12. #2426×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. #2361×C₁₃₉	C₂	semidirect
16. #2360×C₁₃₉	C₂	semidirect
17. #2276×C₁₃₉	C₂	semidirect
111. C₄×Q₈×C₁₃₉	D₄	semidirect
359. #35909	C₁₃₉	direct (N × H)
360. C₁₃₉	#35909	direct (N × H)
361. C₂×#556	C₂×C₁₃₉	semidirect
362. C₂×#554	C₂×C₁₃₉	semidirect
363. #2664	C₂×C₁₃₉	semidirect
364. #2640	C₂×C₁₃₉	semidirect
365. #2611	C₂×C₁₃₉	semidirect
366. #2603	C₂×C₁₃₉	semidirect
367. #2560	C₂×C₁₃₉	semidirect
368. #2546	C₂×C₁₃₉	semidirect
370. #2452	C₂×C₁₃₉	semidirect
371. #2429	C₂×C₁₃₉	semidirect
372. #2426	C₂×C₁₃₉	semidirect
373. #2398	C₂×C₁₃₉	semidirect
374. #2392	C₂×C₁₃₉	semidirect
375. #2361	C₂×C₁₃₉	semidirect
376. #2360	C₂×C₁₃₉	semidirect
377. #2276	C₂×C₁₃₉	semidirect
471. C₄×Q₈	D₄×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×#554×C₁₃₉	2
#2664×C₁₃₉	2
#2640×C₁₃₉	2
#2611×C₁₃₉	2
#2603×C₁₃₉	2
#2560×C₁₃₉	2
#2546×C₁₃₉	2
#2540×C₁₃₉	2
#2452×C₁₃₉	2
#2429×C₁₃₉	2
#2426×C₁₃₉	2
#2398×C₁₃₉	2
#2392×C₁₃₉	2
#2361×C₁₃₉	2
#2360×C₁₃₉	2
#2276×C₁₃₉	2
#35909	139

Subgroups — C139×#35909 #48030505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35909 #48030505