Subgroups — C₁₃₉×#37135 #48031731

Order 35584.

1570 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2806×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2805×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2802×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2792×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2791×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2774×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2755×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2734×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2726×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2713×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2627×C₁₃₉	C₂	1	2	yes	maximal
14	#2569×C₁₃₉	C₂	1	2	yes	maximal
15	#2549×C₁₃₉	C₂	1	2	yes	maximal
16	#2442×C₁₃₉	C₂	1	2	yes	maximal
17	#2440×C₁₃₉	C₂	1	2	yes	maximal
18	#2313×C₁₃₉	C₂	1	2	yes	maximal
19	C₂×#389×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#400×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	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	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	2	yes	—
50	#395×C₁₃₉	C₂²	1	2	yes	—
51	#395×C₁₃₉	C₂²	1	2	yes	—
52	#395×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	2	yes	—
55	#391×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
59	#389×C₁₃₉	C₂²	1	1	yes	characteristic
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	2	yes	—
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#384×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	2	yes	—
97	#381×C₁₃₉	C₂²	1	2	yes	—
98	#381×C₁₃₉	C₂²	1	2	yes	—
99	#380×C₁₃₉	C₂²	1	2	yes	—
100	#380×C₁₃₉	C₂²	1	2	yes	—
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	2	yes	—
103	#380×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
116	#125×C₁₃₉	—	4	4	no	—
117	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
118	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
119	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
120	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
121	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
122	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	8	yes	complemented
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	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	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	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	—	4	2	no	—
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₁₃₉	—	2	2	no	—
205	C₂×Q₈×C₁₃₉	—	2	2	no	—
206	C₂×Q₈×C₁₃₉	—	4	1	no	—
207	C₂×Q₈×C₁₃₉	—	4	1	no	—
208	C₂×Q₈×C₁₃₉	—	4	2	no	—
209	C₂×Q₈×C₁₃₉	—	4	2	no	—
210	C₂×Q₈×C₁₃₉	—	4	1	no	—
211	C₂×Q₈×C₁₃₉	—	4	1	no	—
212	C₂×Q₈×C₁₃₉	—	4	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	2	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	2	no	—
219	C₂²×C₄×C₁₃₉	—	2	2	no	—
220	C₂²×C₄×C₁₃₉	—	4	2	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	—	4	1	no	—
223	C₂²×C₄×C₁₃₉	—	4	1	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	2	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	4	1	no	—
253	C₄⋊C₄×C₁₃₉	—	4	2	no	—
254	C₄⋊C₄×C₁₃₉	—	4	1	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	1	no	—
260	C₄⋊C₄×C₁₃₉	—	4	1	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	2	no	—
266	C₄⋊C₄×C₁₃₉	—	4	1	no	—
267	C₄⋊C₄×C₁₃₉	—	4	1	no	—
268	C₄⋊C₄×C₁₃₉	—	4	2	no	—
269	C₄⋊C₄×C₁₃₉	—	4	2	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
279	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
280	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄²×C₁₃₉	—	4	1	no	—
286	C₄²×C₁₃₉	—	4	1	no	—
287	C₄²×C₁₃₉	—	4	1	no	—
288	C₄²×C₁₃₉	—	4	1	no	—
289	C₄²×C₁₃₉	—	4	2	no	—
290	C₄²×C₁₃₉	—	4	2	no	—
291	C₄²×C₁₃₉	—	4	2	no	—
292	C₄²×C₁₃₉	—	4	2	no	—
293	C₂³×C₁₃₉	—	2	1	no	—
294	C₂³×C₁₃₉	—	2	1	no	—
295	C₂³×C₁₃₉	—	2	1	no	—
296	C₂³×C₁₃₉	—	2	1	no	—
297	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
298	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
299	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
300	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
301	Q₈×C₁₃₉	—	8	2	no	—
302	Q₈×C₁₃₉	—	8	2	no	—
303	Q₈×C₁₃₉	—	8	4	no	—
304	C₂×C₄×C₁₃₉	—	2	8	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	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	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	4	8	no	—
354	C₂×C₄×C₁₃₉	—	4	4	no	—
355	C₂×C₄×C₁₃₉	—	4	4	no	—
356	C₂×C₄×C₁₃₉	—	8	4	no	—
357	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
360	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
361	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
363	C₂²×C₁₃₉	—	2	2	no	—
364	C₂²×C₁₃₉	—	2	2	no	—
365	C₂²×C₁₃₉	—	2	2	no	—
366	C₂²×C₁₃₉	—	2	2	no	—
367	C₂²×C₁₃₉	—	2	2	no	—
368	C₂²×C₁₃₉	—	2	2	no	—
369	C₂²×C₁₃₉	#544	1	4	yes	—
370	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
371	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂²×C₁₃₉	#585	1	1	yes	characteristic
376	C₂²×C₁₃₉	#585	1	1	yes	characteristic
377	C₄×C₁₃₉	—	2	2	no	—
378	C₄×C₁₃₉	—	2	2	no	—
379	C₄×C₁₃₉	—	2	4	no	—
380	C₄×C₁₃₉	—	2	4	no	—
381	C₄×C₁₃₉	—	2	2	no	—
382	C₄×C₁₃₉	—	2	2	no	—
383	C₄×C₁₃₉	—	4	1	no	—
384	C₄×C₁₃₉	—	4	2	no	—
385	C₄×C₁₃₉	—	4	2	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	—	4	1	no	—
390	C₄×C₁₃₉	—	4	2	no	—
391	C₄×C₁₃₉	—	4	2	no	—
392	C₄×C₁₃₉	—	4	2	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₂×C₁₃₉	—	2	4	no	—
396	C₂×C₁₃₉	C₂×#544	1	1	yes	characteristic
397	C₂×C₁₃₉	#3501	1	1	yes	characteristic
398	C₂×C₁₃₉	#3502	1	1	yes	characteristic
399	C₂×C₁₃₉	#3534	1	1	yes	characteristic
400	C₂×C₁₃₉	#3535	1	1	yes	characteristic
401	C₂×C₁₃₉	#3552	1	1	yes	characteristic
402	C₂×C₁₃₉	#3553	1	1	yes	characteristic
403	#37135	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₁₃₉	#37135	1	1	yes	characteristic, direct product factor, Sylow
405	#2855	C₂×C₁₃₉	1	1	yes	characteristic
406	#2855	C₂×C₁₃₉	1	1	yes	characteristic
407	#2806	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2805	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	#2802	C₂×C₁₃₉	1	2	yes	complemented
410	#2792	C₂×C₁₃₉	1	2	yes	complemented
411	#2791	C₂×C₁₃₉	1	2	yes	complemented
412	#2774	C₂×C₁₃₉	1	2	yes	complemented
413	#2755	C₂×C₁₃₉	1	2	yes	complemented
414	#2734	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	#2726	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2713	C₂×C₁₃₉	1	2	yes	complemented
417	#2627	C₂×C₁₃₉	1	2	yes	—
418	#2569	C₂×C₁₃₉	1	2	yes	—
419	#2549	C₂×C₁₃₉	1	2	yes	—
420	#2442	C₂×C₁₃₉	1	2	yes	—
421	#2440	C₂×C₁₃₉	1	2	yes	—
422	#2313	C₂×C₁₃₉	1	2	yes	—
423	C₂×#389	C₂×C₁₃₉	1	1	yes	characteristic
424	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
425	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
429	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
431	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
433	#400	C₂²×C₁₃₉	1	2	yes	—
434	#400	C₂²×C₁₃₉	1	2	yes	—
435	#400	C₂²×C₁₃₉	1	2	yes	—
436	#400	C₂²×C₁₃₉	1	2	yes	—
437	#400	C₂²×C₁₃₉	1	2	yes	—
438	#400	C₂²×C₁₃₉	1	2	yes	—
439	#398	C₂²×C₁₃₉	1	2	yes	—
440	#398	C₂²×C₁₃₉	1	2	yes	—
441	#398	C₂²×C₁₃₉	1	2	yes	—
442	#398	C₂²×C₁₃₉	1	2	yes	—
443	#398	C₂²×C₁₃₉	1	2	yes	—
444	#398	C₂²×C₁₃₉	1	2	yes	—
445	#398	C₂²×C₁₃₉	1	2	yes	—
446	#398	C₂²×C₁₃₉	1	2	yes	—
447	#398	C₂²×C₁₃₉	1	2	yes	—
448	#398	C₂²×C₁₃₉	1	2	yes	—
449	#398	C₂²×C₁₃₉	1	2	yes	—
450	#398	C₂²×C₁₃₉	1	2	yes	—
451	#395	C₂²×C₁₃₉	1	2	yes	—
452	#395	C₂²×C₁₃₉	1	2	yes	—
453	#395	C₂²×C₁₃₉	1	2	yes	—
454	#395	C₂²×C₁₃₉	1	2	yes	—
455	#395	C₂²×C₁₃₉	1	2	yes	—
456	#395	C₂²×C₁₃₉	1	2	yes	—
457	#391	C₂²×C₁₃₉	1	1	yes	characteristic
458	#391	C₂²×C₁₃₉	1	1	yes	characteristic
459	#391	C₂²×C₁₃₉	1	1	yes	characteristic
460	#391	C₂²×C₁₃₉	1	1	yes	characteristic
461	#391	C₂²×C₁₃₉	1	2	yes	—
462	#391	C₂²×C₁₃₉	1	2	yes	—
463	#389	C₂²×C₁₃₉	1	1	yes	characteristic
464	#389	C₂²×C₁₃₉	1	1	yes	characteristic
465	#389	C₂²×C₁₃₉	1	1	yes	characteristic
466	#389	C₂²×C₁₃₉	1	1	yes	characteristic
467	#389	C₂²×C₁₃₉	1	2	yes	—
468	#389	C₂²×C₁₃₉	1	2	yes	—
469	#389	C₂²×C₁₃₉	1	2	yes	—
470	#389	C₂²×C₁₃₉	1	2	yes	—
471	#389	C₂²×C₁₃₉	1	2	yes	—
472	#389	C₂²×C₁₃₉	1	2	yes	—
473	#389	C₂²×C₁₃₉	1	1	yes	characteristic
474	#389	C₂²×C₁₃₉	1	1	yes	characteristic
475	#389	C₂²×C₁₃₉	1	2	yes	—
476	#389	C₂²×C₁₃₉	1	1	yes	characteristic
477	#389	C₂²×C₁₃₉	1	2	yes	—
478	#389	C₂²×C₁₃₉	1	1	yes	characteristic
479	#387	C₂²×C₁₃₉	1	2	yes	—
480	#387	C₂²×C₁₃₉	1	2	yes	—
481	#387	C₂²×C₁₃₉	1	2	yes	—
482	#387	C₂²×C₁₃₉	1	2	yes	—
483	#387	C₂²×C₁₃₉	1	2	yes	—
484	#387	C₂²×C₁₃₉	1	2	yes	—
485	#387	C₂²×C₁₃₉	1	2	yes	—
486	#387	C₂²×C₁₃₉	1	2	yes	—
487	#387	C₂²×C₁₃₉	1	2	yes	—
488	#387	C₂²×C₁₃₉	1	2	yes	—
489	#387	C₂²×C₁₃₉	1	2	yes	—
490	#387	C₂²×C₁₃₉	1	2	yes	—
491	#387	C₂²×C₁₃₉	1	2	yes	—
492	#387	C₂²×C₁₃₉	1	2	yes	—
493	#387	C₂²×C₁₃₉	1	2	yes	—
494	#387	C₂²×C₁₃₉	1	2	yes	—
495	#385	C₂²×C₁₃₉	1	2	yes	—
496	#385	C₂²×C₁₃₉	1	2	yes	—
497	#385	C₂²×C₁₃₉	1	2	yes	—
498	#385	C₂²×C₁₃₉	1	2	yes	—
499	#384	C₂²×C₁₃₉	1	2	yes	—
500	#382	C₂²×C₁₃₉	1	2	yes	—
501	#381	C₂²×C₁₃₉	1	2	yes	—
502	#381	C₂²×C₁₃₉	1	2	yes	—
503	#380	C₂²×C₁₃₉	1	2	yes	—
504	#380	C₂²×C₁₃₉	1	2	yes	—
505	#380	C₂²×C₁₃₉	1	1	yes	characteristic
506	#380	C₂²×C₁₃₉	1	2	yes	—
507	#380	C₂²×C₁₃₉	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
510	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
511	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₄⋊Q₈	—	4	4	no	—
520	#125	—	4	4	no	—
521	C₂²⋊Q₈	—	4	2	no	—
522	C₂²⋊Q₈	—	4	2	no	—
523	C₂²⋊Q₈	—	4	4	no	—
524	C₂×C₄⋊C₄	—	4	4	no	—
525	C₂×C₄⋊C₄	—	4	2	no	—
526	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	8	yes	complemented
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄²	—	4	2	no	—
567	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	#95	C₂³×C₁₃₉	1	2	yes	—
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	2	yes	—
596	#95	C₂³×C₁₃₉	1	2	yes	—
597	#95	C₂³×C₁₃₉	1	2	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	2	yes	—
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	4	1	no	—
611	C₂×Q₈	—	4	1	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	1	no	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
631	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	4	1	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	1	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	1	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
683	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
684	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₄²	—	4	1	no	—
690	C₄²	—	4	1	no	—
691	C₄²	—	4	1	no	—
692	C₄²	—	4	1	no	—
693	C₄²	—	4	2	no	—
694	C₄²	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
702	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
703	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
704	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
705	Q₈	—	8	2	no	—
706	Q₈	—	8	2	no	—
707	Q₈	—	8	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	8	4	no	—
761	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
762	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
763	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
764	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
765	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
766	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	#544×C₁₃₉	1	4	yes	—
774	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
775	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
776	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
777	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
778	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
779	C₂²	#585×C₁₃₉	1	1	yes	characteristic
780	C₂²	#585×C₁₃₉	1	1	yes	characteristic
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₂	—	2	4	no	—
800	C₂	C₂×#544×C₁₃₉	1	1	yes	characteristic
801	C₂	#3501×C₁₃₉	1	1	yes	characteristic
802	C₂	#3502×C₁₃₉	1	1	yes	characteristic
803	C₂	#3534×C₁₃₉	1	1	yes	characteristic
804	C₂	#3535×C₁₃₉	1	1	yes	characteristic
805	C₂	#3552×C₁₃₉	1	1	yes	characteristic
806	C₂	#3553×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
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. #2806×C₁₃₉	C₂	semidirect
4. #2805×C₁₃₉	C₂	semidirect
5. #2802×C₁₃₉	C₂	semidirect
6. #2792×C₁₃₉	C₂	semidirect
7. #2791×C₁₃₉	C₂	semidirect
8. #2774×C₁₃₉	C₂	semidirect
9. #2755×C₁₃₉	C₂	semidirect
10. #2734×C₁₃₉	C₂	semidirect
11. #2726×C₁₃₉	C₂	semidirect
12. #2713×C₁₃₉	C₂	semidirect
122. C₂×C₄⋊C₄×C₁₃₉	Q₈	semidirect
403. #37135	C₁₃₉	direct (N × H)
404. C₁₃₉	#37135	direct (N × H)
407. #2806	C₂×C₁₃₉	semidirect
408. #2805	C₂×C₁₃₉	semidirect
409. #2802	C₂×C₁₃₉	semidirect
410. #2792	C₂×C₁₃₉	semidirect
411. #2791	C₂×C₁₃₉	semidirect
412. #2774	C₂×C₁₃₉	semidirect
413. #2755	C₂×C₁₃₉	semidirect
414. #2734	C₂×C₁₃₉	semidirect
415. #2726	C₂×C₁₃₉	semidirect
416. #2713	C₂×C₁₃₉	semidirect
526. C₂×C₄⋊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
#2855×C₁₃₉	2
#2806×C₁₃₉	2
#2805×C₁₃₉	2
#2802×C₁₃₉	2
#2792×C₁₃₉	2
#2791×C₁₃₉	2
#2774×C₁₃₉	2
#2755×C₁₃₉	2
#2734×C₁₃₉	2
#2726×C₁₃₉	2
#2713×C₁₃₉	2
#2627×C₁₃₉	2
#2569×C₁₃₉	2
#2549×C₁₃₉	2
#2442×C₁₃₉	2
#2440×C₁₃₉	2
#2313×C₁₃₉	2
C₂×#389×C₁₃₉	2
#37135	139

Subgroups — C139×#37135 #48031731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37135 #48031731