Subgroups — C₁₃₉×#37303 #48031899

Order 35584.

2078 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×#544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#542×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2721×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2680×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2677×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2674×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2640×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2565×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2499×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₁₃₉	—	2	8	no	—
21	#542×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
40	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	#399×C₁₃₉	C₂²	1	4	yes	—
47	#399×C₁₃₉	C₂²	1	4	yes	—
48	#398×C₁₃₉	C₂²	1	4	yes	—
49	#398×C₁₃₉	C₂²	1	4	yes	—
50	#398×C₁₃₉	C₂²	1	4	yes	—
51	#397×C₁₃₉	C₂²	1	4	yes	—
52	#397×C₁₃₉	C₂²	1	4	yes	—
53	#396×C₁₃₉	C₂²	1	4	yes	—
54	#395×C₁₃₉	C₂²	1	4	yes	—
55	#395×C₁₃₉	C₂²	1	4	yes	—
56	#394×C₁₃₉	C₂²	1	4	yes	—
57	#393×C₁₃₉	C₂²	1	4	yes	—
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic
60	#391×C₁₃₉	C₂²	1	1	yes	characteristic
61	#391×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	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	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	4	yes	—
75	#387×C₁₃₉	C₂²	1	4	yes	—
76	#385×C₁₃₉	C₂²	1	4	yes	—
77	#385×C₁₃₉	C₂²	1	4	yes	—
78	#384×C₁₃₉	C₂²	1	1	yes	characteristic
79	#384×C₁₃₉	C₂²	1	1	yes	characteristic
80	#384×C₁₃₉	C₂²	1	1	yes	characteristic
81	#384×C₁₃₉	C₂²	1	1	yes	characteristic
82	#384×C₁₃₉	C₂²	1	1	yes	characteristic
83	#384×C₁₃₉	C₂²	1	1	yes	characteristic
84	#384×C₁₃₉	C₂²	1	4	yes	—
85	#382×C₁₃₉	C₂²	1	1	yes	characteristic
86	#382×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
91	#376×C₁₃₉	C₂²	1	1	yes	characteristic
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
103	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
104	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
105	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
106	C₄⋊Q₈×C₁₃₉	—	4	8	no	—
107	#126×C₁₃₉	—	2	8	no	—
108	#125×C₁₃₉	—	2	8	no	—
109	#125×C₁₃₉	—	2	4	no	—
110	#125×C₁₃₉	—	2	4	no	—
111	#124×C₁₃₉	—	2	8	no	—
112	#124×C₁₃₉	—	2	4	no	—
113	#123×C₁₃₉	—	2	8	no	—
114	#123×C₁₃₉	—	4	8	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
116	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
118	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
119	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
120	#121×C₁₃₉	—	2	4	no	—
121	C₄×Q₈×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	—	2	4	no	—
123	#117×C₁₃₉	—	2	4	no	—
124	#117×C₁₃₉	D₄	1	8	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	4	yes	—
184	#95×C₁₃₉	C₂³	1	4	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₂×Q₈×C₁₃₉	—	2	2	no	—
191	C₂×Q₈×C₁₃₉	—	2	4	no	—
192	C₂×Q₈×C₁₃₉	—	2	4	no	—
193	C₂×Q₈×C₁₃₉	—	2	4	no	—
194	C₂×Q₈×C₁₃₉	—	2	2	no	—
195	C₂×Q₈×C₁₃₉	—	2	2	no	—
196	C₂×Q₈×C₁₃₉	—	4	4	no	—
197	C₂×Q₈×C₁₃₉	—	4	4	no	—
198	C₂×Q₈×C₁₃₉	—	4	4	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	2	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	4	4	no	—
209	C₂²×C₄×C₁₃₉	—	4	4	no	—
210	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	2	no	—
230	C₄⋊C₄×C₁₃₉	—	2	2	no	—
231	C₄⋊C₄×C₁₃₉	—	2	2	no	—
232	C₄⋊C₄×C₁₃₉	—	2	2	no	—
233	C₄⋊C₄×C₁₃₉	—	2	2	no	—
234	C₄⋊C₄×C₁₃₉	—	2	2	no	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	8	no	—
246	C₄⋊C₄×C₁₃₉	—	2	8	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	4	4	no	—
249	C₄⋊C₄×C₁₃₉	—	4	4	no	—
250	C₄⋊C₄×C₁₃₉	—	4	4	no	—
251	C₄⋊C₄×C₁₃₉	—	4	4	no	—
252	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
267	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃₉	—	2	4	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	2	2	no	—
273	C₄²×C₁₃₉	—	2	2	no	—
274	C₄²×C₁₃₉	—	2	2	no	—
275	C₄²×C₁₃₉	—	2	2	no	—
276	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	1	no	—
281	C₂³×C₁₃₉	—	2	1	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	4	no	—
284	C₂³×C₁₃₉	—	2	4	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
288	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
289	Q₈×C₁₃₉	—	4	4	no	—
290	Q₈×C₁₃₉	—	8	4	no	—
291	Q₈×C₁₃₉	—	8	4	no	—
292	Q₈×C₁₃₉	—	8	4	no	—
293	D₄×C₁₃₉	—	4	4	no	—
294	D₄×C₁₃₉	—	8	4	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	8	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	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	—	2	4	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	2	4	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	8	4	no	—
328	C₂×C₄×C₁₃₉	—	8	4	no	—
329	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
336	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
337	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
338	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
339	C₂²×C₁₃₉	—	2	2	no	—
340	C₂²×C₁₃₉	—	2	2	no	—
341	C₂²×C₁₃₉	—	2	2	no	—
342	C₂²×C₁₃₉	—	4	2	no	—
343	C₂²×C₁₃₉	—	4	2	no	—
344	C₂²×C₁₃₉	—	4	2	no	—
345	C₂²×C₁₃₉	—	4	2	no	—
346	C₂²×C₁₃₉	—	4	2	no	—
347	C₂²×C₁₃₉	—	4	4	no	—
348	C₂²×C₁₃₉	—	4	4	no	—
349	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
350	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
351	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
352	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
354	C₄×C₁₃₉	—	2	2	no	—
355	C₄×C₁₃₉	—	2	2	no	—
356	C₄×C₁₃₉	—	2	2	no	—
357	C₄×C₁₃₉	—	2	2	no	—
358	C₄×C₁₃₉	—	2	2	no	—
359	C₄×C₁₃₉	—	2	4	no	—
360	C₄×C₁₃₉	—	2	4	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	2	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	—	4	2	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	2	no	—
367	C₄×C₁₃₉	—	4	2	no	—
368	C₄×C₁₃₉	—	4	2	no	—
369	C₄×C₁₃₉	—	4	2	no	—
370	C₄×C₁₃₉	#536	1	4	yes	—
371	C₂×C₁₃₉	—	4	2	no	—
372	C₂×C₁₃₉	—	8	2	no	—
373	C₂×C₁₃₉	C₂×#536	1	1	yes	characteristic
374	C₂×C₁₃₉	#3498	1	1	yes	characteristic
375	C₂×C₁₃₉	#3499	1	1	yes	characteristic
376	C₂×C₁₃₉	#3544	1	2	yes	—
377	C₂×C₁₃₉	#3552	1	2	yes	—
378	#37303	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₁₃₉	#37303	1	1	yes	characteristic, direct product factor, Sylow
380	C₂×#544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	C₂×#542	C₂×C₁₃₉	1	1	yes	characteristic
382	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
383	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	#2721	C₂×C₁₃₉	1	4	yes	complemented
385	#2680	C₂×C₁₃₉	1	4	yes	complemented
386	#2677	C₂×C₁₃₉	1	4	yes	complemented
387	#2674	C₂×C₁₃₉	1	4	yes	complemented
388	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
389	#2640	C₂×C₁₃₉	1	1	yes	characteristic, complemented
390	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	#2565	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2501	C₂×C₁₃₉	1	1	yes	characteristic
396	#2500	C₂×C₁₃₉	1	1	yes	characteristic
397	#2499	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#544	—	2	8	no	—
400	#542	—	2	8	no	—
401	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
405	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
406	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
407	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
409	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
410	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
412	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
419	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
425	#399	C₂²×C₁₃₉	1	4	yes	—
426	#399	C₂²×C₁₃₉	1	4	yes	—
427	#398	C₂²×C₁₃₉	1	4	yes	—
428	#398	C₂²×C₁₃₉	1	4	yes	—
429	#398	C₂²×C₁₃₉	1	4	yes	—
430	#397	C₂²×C₁₃₉	1	4	yes	—
431	#397	C₂²×C₁₃₉	1	4	yes	—
432	#396	C₂²×C₁₃₉	1	4	yes	—
433	#395	C₂²×C₁₃₉	1	4	yes	—
434	#395	C₂²×C₁₃₉	1	4	yes	—
435	#394	C₂²×C₁₃₉	1	4	yes	—
436	#393	C₂²×C₁₃₉	1	4	yes	—
437	#391	C₂²×C₁₃₉	1	1	yes	characteristic
438	#391	C₂²×C₁₃₉	1	1	yes	characteristic
439	#391	C₂²×C₁₃₉	1	1	yes	characteristic
440	#391	C₂²×C₁₃₉	1	1	yes	characteristic
441	#390	C₂²×C₁₃₉	1	1	yes	characteristic
442	#390	C₂²×C₁₃₉	1	1	yes	characteristic
443	#390	C₂²×C₁₃₉	1	1	yes	characteristic
444	#390	C₂²×C₁₃₉	1	1	yes	characteristic
445	#389	C₂²×C₁₃₉	1	4	yes	—
446	#388	C₂²×C₁₃₉	1	4	yes	—
447	#388	C₂²×C₁₃₉	1	4	yes	—
448	#388	C₂²×C₁₃₉	1	2	yes	—
449	#388	C₂²×C₁₃₉	1	4	yes	—
450	#388	C₂²×C₁₃₉	1	2	yes	—
451	#387	C₂²×C₁₃₉	1	4	yes	—
452	#387	C₂²×C₁₃₉	1	2	yes	—
453	#387	C₂²×C₁₃₉	1	4	yes	—
454	#387	C₂²×C₁₃₉	1	2	yes	—
455	#385	C₂²×C₁₃₉	1	4	yes	—
456	#385	C₂²×C₁₃₉	1	4	yes	—
457	#384	C₂²×C₁₃₉	1	1	yes	characteristic
458	#384	C₂²×C₁₃₉	1	1	yes	characteristic
459	#384	C₂²×C₁₃₉	1	1	yes	characteristic
460	#384	C₂²×C₁₃₉	1	1	yes	characteristic
461	#384	C₂²×C₁₃₉	1	4	yes	—
462	#384	C₂²×C₁₃₉	1	1	yes	characteristic
463	#384	C₂²×C₁₃₉	1	1	yes	characteristic
464	#382	C₂²×C₁₃₉	1	1	yes	characteristic
465	#382	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
470	#376	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
474	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
475	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₄⋊Q₈	—	2	8	no	—
482	C₄⋊Q₈	—	2	4	no	—
483	C₄⋊Q₈	—	2	4	no	—
484	C₄⋊Q₈	—	2	4	no	—
485	C₄⋊Q₈	—	4	8	no	—
486	#126	—	2	8	no	—
487	#125	—	2	8	no	—
488	#125	—	2	4	no	—
489	#125	—	2	4	no	—
490	#124	—	2	8	no	—
491	#124	—	2	4	no	—
492	#123	—	2	8	no	—
493	#123	—	4	8	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	8	no	—
496	C₂²⋊Q₈	—	2	8	no	—
497	C₂²⋊Q₈	—	2	8	no	—
498	C₂²⋊Q₈	—	4	8	no	—
499	#121	—	2	4	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	#117	—	2	4	no	—
503	#117	D₄×C₁₃₉	1	8	yes	—
504	C₂×C₄⋊C₄	—	2	4	no	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	2	yes	—
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	4	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
568	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	4	no	—
577	C₂×Q₈	—	4	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	4	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	8	no	—
625	C₄⋊C₄	—	2	8	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	4	4	no	—
628	C₄⋊C₄	—	4	4	no	—
629	C₄⋊C₄	—	4	4	no	—
630	C₄⋊C₄	—	4	4	no	—
631	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
632	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
646	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
656	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
667	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
668	Q₈	—	4	4	no	—
669	Q₈	—	8	4	no	—
670	Q₈	—	8	4	no	—
671	Q₈	—	8	4	no	—
672	D₄	—	4	4	no	—
673	D₄	—	8	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	8	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	8	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
713	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
714	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
715	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
716	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
717	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
729	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
730	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
731	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
732	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
733	C₄	—	2	4	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	#536×C₁₃₉	1	4	yes	—
750	C₂	—	4	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₂×#536×C₁₃₉	1	1	yes	characteristic
753	C₂	#3498×C₁₃₉	1	1	yes	characteristic
754	C₂	#3499×C₁₃₉	1	1	yes	characteristic
755	C₂	#3544×C₁₃₉	1	2	yes	—
756	C₂	#3552×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×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×#544×C₁₃₉	C₂	semidirect
3. #2868×C₁₃₉	C₂	semidirect
4. #2861×C₁₃₉	C₂	semidirect
5. #2721×C₁₃₉	C₂	semidirect
6. #2680×C₁₃₉	C₂	semidirect
7. #2677×C₁₃₉	C₂	semidirect
8. #2674×C₁₃₉	C₂	semidirect
9. #2660×C₁₃₉	C₂	semidirect
10. #2640×C₁₃₉	C₂	semidirect
11. #2567×C₁₃₉	C₂	semidirect
12. #2566×C₁₃₉	C₂	semidirect
13. #2565×C₁₃₉	C₂	semidirect
14. #2542×C₁₃₉	C₂	semidirect
15. #2502×C₁₃₉	C₂	semidirect
18. #2499×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
378. #37303	C₁₃₉	direct (N × H)
379. C₁₃₉	#37303	direct (N × H)
380. C₂×#544	C₂×C₁₃₉	semidirect
382. #2868	C₂×C₁₃₉	semidirect
383. #2861	C₂×C₁₃₉	semidirect
384. #2721	C₂×C₁₃₉	semidirect
385. #2680	C₂×C₁₃₉	semidirect
386. #2677	C₂×C₁₃₉	semidirect
387. #2674	C₂×C₁₃₉	semidirect
388. #2660	C₂×C₁₃₉	semidirect
389. #2640	C₂×C₁₃₉	semidirect
390. #2567	C₂×C₁₃₉	semidirect
391. #2566	C₂×C₁₃₉	semidirect
392. #2565	C₂×C₁₃₉	semidirect
393. #2542	C₂×C₁₃₉	semidirect
394. #2502	C₂×C₁₃₉	semidirect
397. #2499	C₂×C₁₃₉	semidirect
398. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₁₃₉	2
C₂×#542×C₁₃₉	2
#2868×C₁₃₉	2
#2861×C₁₃₉	2
#2721×C₁₃₉	2
#2680×C₁₃₉	2
#2677×C₁₃₉	2
#2674×C₁₃₉	2
#2660×C₁₃₉	2
#2640×C₁₃₉	2
#2567×C₁₃₉	2
#2566×C₁₃₉	2
#2565×C₁₃₉	2
#2542×C₁₃₉	2
#2502×C₁₃₉	2
#2501×C₁₃₉	2
#2500×C₁₃₉	2
#2499×C₁₃₉	2
#2298×C₁₃₉	2
#37303	139

Subgroups — C139×#37303 #48031899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37303 #48031899