Subgroups — C₁₃₉×#36279 #48030875

Order 35584.

1832 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2863×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2612×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2605×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2586×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2520×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2511×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2505×C₁₃₉	C₂	1	2	yes	maximal
10	#2451×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2446×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2446×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2440×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2438×C₁₃₉	C₂	1	2	yes	maximal
15	#2434×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2368×C₁₃₉	C₂	1	2	yes	maximal
17	#2360×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2343×C₁₃₉	C₂	1	2	yes	maximal
19	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#400×C₁₃₉	C₂²	1	2	yes	—
40	#400×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	#395×C₁₃₉	C₂²	1	2	yes	—
46	#395×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	1	yes	characteristic
50	#391×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	1	yes	characteristic
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	1	yes	characteristic
55	#391×C₁₃₉	C₂²	1	2	yes	—
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	#391×C₁₃₉	C₂²	1	1	yes	characteristic
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#391×C₁₃₉	C₂²	1	2	yes	—
62	#391×C₁₃₉	C₂²	1	1	yes	characteristic
63	#391×C₁₃₉	C₂²	1	1	yes	characteristic
64	#391×C₁₃₉	C₂²	1	2	yes	—
65	#391×C₁₃₉	C₂²	1	2	yes	—
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	1	yes	characteristic
70	#389×C₁₃₉	C₂²	1	2	yes	—
71	#389×C₁₃₉	C₂²	1	2	yes	—
72	#389×C₁₃₉	C₂²	1	2	yes	—
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	#385×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	1	yes	characteristic
96	#383×C₁₃₉	C₂²	1	2	yes	—
97	#382×C₁₃₉	C₂²	1	2	yes	—
98	#382×C₁₃₉	C₂²	1	2	yes	—
99	#381×C₁₃₉	C₂²	1	2	yes	—
100	#380×C₁₃₉	C₂²	1	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
116	#376×C₁₃₉	C₂²	1	1	yes	characteristic
117	#376×C₁₃₉	C₂²	1	1	yes	characteristic
118	#376×C₁₃₉	C₂²	1	2	yes	—
119	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
120	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
121	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	—	2	4	no	—
124	C₂²×Q₈×C₁₃₉	—	2	4	no	—
125	C₂²×Q₈×C₁₃₉	—	4	2	no	—
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
129	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
137	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
138	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
139	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
140	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
141	C₄×Q₈×C₁₃₉	—	2	4	no	—
142	C₄×Q₈×C₁₃₉	—	4	2	no	—
143	C₄×Q₈×C₁₃₉	—	4	2	no	—
144	#117×C₁₃₉	—	2	4	no	—
145	#117×C₁₃₉	Q₈	1	8	yes	complemented
146	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	—	2	4	no	—
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	#95×C₁₃₉	C₂³	1	1	yes	characteristic
201	#95×C₁₃₉	C₂³	1	1	yes	characteristic
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	1	yes	characteristic
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	2	yes	—
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	2	yes	—
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	#95×C₁₃₉	C₂³	1	2	yes	—
235	#95×C₁₃₉	C₂³	1	2	yes	—
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂×Q₈×C₁₃₉	—	2	2	no	—
239	C₂×Q₈×C₁₃₉	—	2	2	no	—
240	C₂×Q₈×C₁₃₉	—	2	2	no	—
241	C₂×Q₈×C₁₃₉	—	2	4	no	—
242	C₂×Q₈×C₁₃₉	—	2	4	no	—
243	C₂×Q₈×C₁₃₉	—	2	2	no	—
244	C₂×Q₈×C₁₃₉	—	2	2	no	—
245	C₂×Q₈×C₁₃₉	—	2	4	no	—
246	C₂×Q₈×C₁₃₉	—	2	2	no	—
247	C₂×Q₈×C₁₃₉	—	2	2	no	—
248	C₂×Q₈×C₁₃₉	—	2	2	no	—
249	C₂×Q₈×C₁₃₉	—	4	2	no	—
250	C₂×Q₈×C₁₃₉	—	4	2	no	—
251	C₂×Q₈×C₁₃₉	—	4	2	no	—
252	C₂×Q₈×C₁₃₉	—	4	16	no	—
253	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
254	C₂²×C₄×C₁₃₉	—	2	2	no	—
255	C₂²×C₄×C₁₃₉	—	2	2	no	—
256	C₂²×C₄×C₁₃₉	—	2	2	no	—
257	C₂²×C₄×C₁₃₉	—	2	2	no	—
258	C₂²×C₄×C₁₃₉	—	2	2	no	—
259	C₂²×C₄×C₁₃₉	—	2	4	no	—
260	C₂²×C₄×C₁₃₉	—	2	4	no	—
261	C₂²×C₄×C₁₃₉	—	2	4	no	—
262	C₂²×C₄×C₁₃₉	—	2	2	no	—
263	C₂²×C₄×C₁₃₉	—	4	1	no	—
264	C₂²×C₄×C₁₃₉	—	4	2	no	—
265	C₂²×C₄×C₁₃₉	—	4	2	no	—
266	C₂²×C₄×C₁₃₉	—	4	2	no	—
267	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
268	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₁₃₉	—	2	2	no	—
292	C₄⋊C₄×C₁₃₉	—	2	2	no	—
293	C₄⋊C₄×C₁₃₉	—	2	4	no	—
294	C₄⋊C₄×C₁₃₉	—	2	2	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	2	4	no	—
297	C₄⋊C₄×C₁₃₉	—	2	4	no	—
298	C₄⋊C₄×C₁₃₉	—	2	4	no	—
299	C₄⋊C₄×C₁₃₉	—	2	4	no	—
300	C₄⋊C₄×C₁₃₉	—	2	4	no	—
301	C₄⋊C₄×C₁₃₉	—	2	4	no	—
302	C₄⋊C₄×C₁₃₉	—	2	2	no	—
303	C₄⋊C₄×C₁₃₉	—	2	2	no	—
304	C₄⋊C₄×C₁₃₉	—	2	2	no	—
305	C₄⋊C₄×C₁₃₉	—	2	4	no	—
306	C₄⋊C₄×C₁₃₉	—	4	2	no	—
307	C₄⋊C₄×C₁₃₉	—	4	2	no	—
308	C₄⋊C₄×C₁₃₉	—	4	2	no	—
309	C₄⋊C₄×C₁₃₉	—	4	2	no	—
310	C₄⋊C₄×C₁₃₉	—	4	2	no	—
311	C₄⋊C₄×C₁₃₉	—	4	2	no	—
312	C₄⋊C₄×C₁₃₉	—	4	2	no	—
313	C₄⋊C₄×C₁₃₉	—	4	2	no	—
314	C₄⋊C₄×C₁₃₉	—	4	2	no	—
315	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
316	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
317	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
318	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
319	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
320	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
321	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
322	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
323	C₄²×C₁₃₉	—	2	2	no	—
324	C₄²×C₁₃₉	—	2	2	no	—
325	C₄²×C₁₃₉	—	2	2	no	—
326	C₄²×C₁₃₉	—	2	2	no	—
327	C₄²×C₁₃₉	—	2	2	no	—
328	C₄²×C₁₃₉	—	2	2	no	—
329	C₄²×C₁₃₉	—	2	4	no	—
330	C₄²×C₁₃₉	—	2	2	no	—
331	C₄²×C₁₃₉	—	2	2	no	—
332	C₄²×C₁₃₉	—	2	2	no	—
333	C₄²×C₁₃₉	—	2	2	no	—
334	C₄²×C₁₃₉	—	2	2	no	—
335	C₄²×C₁₃₉	—	2	2	no	—
336	C₄²×C₁₃₉	—	4	1	no	—
337	C₄²×C₁₃₉	—	4	2	no	—
338	C₄²×C₁₃₉	—	4	1	no	—
339	C₄²×C₁₃₉	—	4	2	no	—
340	C₄²×C₁₃₉	—	4	2	no	—
341	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	complemented
342	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	complemented
343	C₂³×C₁₃₉	—	2	1	no	—
344	C₂³×C₁₃₉	—	2	1	no	—
345	C₂³×C₁₃₉	—	2	1	no	—
346	C₂³×C₁₃₉	—	2	1	no	—
347	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
348	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
351	Q₈×C₁₃₉	—	2	8	no	—
352	Q₈×C₁₃₉	—	4	8	no	—
353	Q₈×C₁₃₉	—	4	4	no	—
354	Q₈×C₁₃₉	—	4	4	no	—
355	Q₈×C₁₃₉	—	8	4	no	—
356	C₂×C₄×C₁₃₉	—	2	8	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	1	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	1	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	8	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	1	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	2	no	—
394	C₂×C₄×C₁₃₉	—	2	1	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	2	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	1	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	1	no	—
404	C₂×C₄×C₁₃₉	—	2	2	no	—
405	C₂×C₄×C₁₃₉	—	2	1	no	—
406	C₂×C₄×C₁₃₉	—	2	2	no	—
407	C₂×C₄×C₁₃₉	—	2	1	no	—
408	C₂×C₄×C₁₃₉	—	2	2	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	4	4	no	—
411	C₂×C₄×C₁₃₉	—	4	8	no	—
412	C₂×C₄×C₁₃₉	—	8	4	no	—
413	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
414	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
415	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
416	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
417	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
418	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
419	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
420	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
421	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
423	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
425	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
426	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
427	C₂²×C₁₃₉	—	2	2	no	—
428	C₂²×C₁₃₉	—	2	2	no	—
429	C₂²×C₁₃₉	—	2	2	no	—
430	C₂²×C₁₃₉	—	2	2	no	—
431	C₂²×C₁₃₉	—	2	2	no	—
432	C₂²×C₁₃₉	—	2	2	no	—
433	C₂²×C₁₃₉	#533	1	4	yes	—
434	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
435	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂²×C₁₃₉	#585	1	1	yes	characteristic
441	C₄×C₁₃₉	—	2	2	no	—
442	C₄×C₁₃₉	—	2	2	no	—
443	C₄×C₁₃₉	—	2	2	no	—
444	C₄×C₁₃₉	—	2	4	no	—
445	C₄×C₁₃₉	—	2	2	no	—
446	C₄×C₁₃₉	—	2	2	no	—
447	C₄×C₁₃₉	—	2	2	no	—
448	C₄×C₁₃₉	—	2	2	no	—
449	C₄×C₁₃₉	—	2	2	no	—
450	C₄×C₁₃₉	—	2	2	no	—
451	C₄×C₁₃₉	—	2	2	no	—
452	C₄×C₁₃₉	—	4	2	no	—
453	C₄×C₁₃₉	—	4	2	no	—
454	C₄×C₁₃₉	—	4	1	no	—
455	C₄×C₁₃₉	—	4	2	no	—
456	C₄×C₁₃₉	—	4	2	no	—
457	C₄×C₁₃₉	—	4	1	no	—
458	C₄×C₁₃₉	—	4	1	no	—
459	C₄×C₁₃₉	—	4	2	no	—
460	C₄×C₁₃₉	—	4	2	no	—
461	C₄×C₁₃₉	—	4	2	no	—
462	C₄×C₁₃₉	#551	1	4	yes	—
463	C₂×C₁₃₉	—	2	4	no	—
464	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
465	C₂×C₁₃₉	C₂×#551	1	1	yes	characteristic
466	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
467	C₂×C₁₃₉	#3482	1	1	yes	characteristic
468	C₂×C₁₃₉	#3495	1	1	yes	characteristic
469	C₂×C₁₃₉	#3503	1	1	yes	characteristic
470	C₂×C₁₃₉	#3514	1	1	yes	characteristic
471	#36279	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₁₃₉	#36279	1	1	yes	characteristic, direct product factor, Sylow
473	#2863	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2855	C₂×C₁₃₉	1	1	yes	characteristic
476	#2612	C₂×C₁₃₉	1	2	yes	complemented
477	#2605	C₂×C₁₃₉	1	2	yes	complemented
478	#2586	C₂×C₁₃₉	1	2	yes	complemented
479	#2520	C₂×C₁₃₉	1	2	yes	complemented
480	#2511	C₂×C₁₃₉	1	1	yes	characteristic, complemented
481	#2505	C₂×C₁₃₉	1	2	yes	—
482	#2451	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	#2446	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	#2446	C₂×C₁₃₉	1	1	yes	characteristic, complemented
485	#2440	C₂×C₁₃₉	1	1	yes	characteristic
486	#2438	C₂×C₁₃₉	1	2	yes	—
487	#2434	C₂×C₁₃₉	1	1	yes	characteristic
488	#2368	C₂×C₁₃₉	1	2	yes	—
489	#2360	C₂×C₁₃₉	1	1	yes	characteristic
490	#2343	C₂×C₁₃₉	1	2	yes	—
491	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
492	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
493	#2295	C₂×C₁₃₉	1	1	yes	characteristic, complemented
494	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic
495	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic
496	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
500	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
501	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
502	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
503	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
505	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
508	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
509	#400	C₂²×C₁₃₉	1	2	yes	—
510	#400	C₂²×C₁₃₉	1	2	yes	—
511	#400	C₂²×C₁₃₉	1	2	yes	—
512	#400	C₂²×C₁₃₉	1	2	yes	—
513	#398	C₂²×C₁₃₉	1	2	yes	—
514	#398	C₂²×C₁₃₉	1	2	yes	—
515	#398	C₂²×C₁₃₉	1	2	yes	—
516	#398	C₂²×C₁₃₉	1	2	yes	—
517	#395	C₂²×C₁₃₉	1	2	yes	—
518	#395	C₂²×C₁₃₉	1	2	yes	—
519	#395	C₂²×C₁₃₉	1	2	yes	—
520	#395	C₂²×C₁₃₉	1	2	yes	—
521	#391	C₂²×C₁₃₉	1	1	yes	characteristic
522	#391	C₂²×C₁₃₉	1	1	yes	characteristic
523	#391	C₂²×C₁₃₉	1	2	yes	—
524	#391	C₂²×C₁₃₉	1	2	yes	—
525	#391	C₂²×C₁₃₉	1	2	yes	—
526	#391	C₂²×C₁₃₉	1	2	yes	—
527	#391	C₂²×C₁₃₉	1	1	yes	characteristic
528	#391	C₂²×C₁₃₉	1	1	yes	characteristic
529	#391	C₂²×C₁₃₉	1	1	yes	characteristic
530	#391	C₂²×C₁₃₉	1	2	yes	—
531	#391	C₂²×C₁₃₉	1	2	yes	—
532	#391	C₂²×C₁₃₉	1	2	yes	—
533	#391	C₂²×C₁₃₉	1	1	yes	characteristic
534	#391	C₂²×C₁₃₉	1	1	yes	characteristic
535	#391	C₂²×C₁₃₉	1	1	yes	characteristic
536	#391	C₂²×C₁₃₉	1	1	yes	characteristic
537	#391	C₂²×C₁₃₉	1	1	yes	characteristic
538	#391	C₂²×C₁₃₉	1	1	yes	characteristic
539	#389	C₂²×C₁₃₉	1	2	yes	—
540	#389	C₂²×C₁₃₉	1	2	yes	—
541	#389	C₂²×C₁₃₉	1	2	yes	—
542	#389	C₂²×C₁₃₉	1	1	yes	characteristic
543	#389	C₂²×C₁₃₉	1	1	yes	characteristic
544	#389	C₂²×C₁₃₉	1	1	yes	characteristic
545	#389	C₂²×C₁₃₉	1	1	yes	characteristic
546	#389	C₂²×C₁₃₉	1	1	yes	characteristic
547	#387	C₂²×C₁₃₉	1	2	yes	—
548	#387	C₂²×C₁₃₉	1	2	yes	—
549	#387	C₂²×C₁₃₉	1	2	yes	—
550	#387	C₂²×C₁₃₉	1	2	yes	—
551	#387	C₂²×C₁₃₉	1	2	yes	—
552	#387	C₂²×C₁₃₉	1	2	yes	—
553	#387	C₂²×C₁₃₉	1	2	yes	—
554	#387	C₂²×C₁₃₉	1	2	yes	—
555	#387	C₂²×C₁₃₉	1	2	yes	—
556	#387	C₂²×C₁₃₉	1	2	yes	—
557	#387	C₂²×C₁₃₉	1	2	yes	—
558	#387	C₂²×C₁₃₉	1	2	yes	—
559	#387	C₂²×C₁₃₉	1	2	yes	—
560	#387	C₂²×C₁₃₉	1	2	yes	—
561	#387	C₂²×C₁₃₉	1	2	yes	—
562	#385	C₂²×C₁₃₉	1	2	yes	—
563	#385	C₂²×C₁₃₉	1	2	yes	—
564	#385	C₂²×C₁₃₉	1	2	yes	—
565	#385	C₂²×C₁₃₉	1	2	yes	—
566	#385	C₂²×C₁₃₉	1	2	yes	—
567	#384	C₂²×C₁₃₉	1	1	yes	characteristic
568	#383	C₂²×C₁₃₉	1	2	yes	—
569	#382	C₂²×C₁₃₉	1	2	yes	—
570	#382	C₂²×C₁₃₉	1	2	yes	—
571	#381	C₂²×C₁₃₉	1	2	yes	—
572	#380	C₂²×C₁₃₉	1	1	yes	characteristic
573	#380	C₂²×C₁₃₉	1	2	yes	—
574	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
578	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
585	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
586	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
588	#376	C₂²×C₁₃₉	1	2	yes	—
589	#376	C₂²×C₁₃₉	1	1	yes	characteristic
590	#376	C₂²×C₁₃₉	1	1	yes	characteristic
591	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
592	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
593	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
594	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂²×Q₈	—	2	4	no	—
596	C₂²×Q₈	—	2	4	no	—
597	C₂²×Q₈	—	4	2	no	—
598	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
601	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
602	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
603	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₄⋊Q₈	—	2	4	no	—
609	C₄⋊Q₈	—	4	2	no	—
610	C₄⋊Q₈	—	4	2	no	—
611	C₂²⋊Q₈	—	2	4	no	—
612	C₂²⋊Q₈	—	2	8	no	—
613	C₄×Q₈	—	2	4	no	—
614	C₄×Q₈	—	4	2	no	—
615	C₄×Q₈	—	4	2	no	—
616	#117	—	2	4	no	—
617	#117	Q₈×C₁₃₉	1	8	yes	complemented
618	C₂×C₄⋊C₄	—	4	2	no	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂×C₄²	—	2	4	no	—
652	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
657	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
666	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
667	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
670	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
672	#95	C₂³×C₁₃₉	1	2	yes	—
673	#95	C₂³×C₁₃₉	1	2	yes	—
674	#95	C₂³×C₁₃₉	1	2	yes	—
675	#95	C₂³×C₁₃₉	1	2	yes	—
676	#95	C₂³×C₁₃₉	1	2	yes	—
677	#95	C₂³×C₁₃₉	1	2	yes	—
678	#95	C₂³×C₁₃₉	1	2	yes	—
679	#95	C₂³×C₁₃₉	1	2	yes	—
680	#95	C₂³×C₁₃₉	1	1	yes	characteristic
681	#95	C₂³×C₁₃₉	1	1	yes	characteristic
682	#95	C₂³×C₁₃₉	1	1	yes	characteristic
683	#95	C₂³×C₁₃₉	1	1	yes	characteristic
684	#95	C₂³×C₁₃₉	1	1	yes	characteristic
685	#95	C₂³×C₁₃₉	1	1	yes	characteristic
686	#95	C₂³×C₁₃₉	1	1	yes	characteristic
687	#95	C₂³×C₁₃₉	1	1	yes	characteristic
688	#95	C₂³×C₁₃₉	1	2	yes	—
689	#95	C₂³×C₁₃₉	1	2	yes	—
690	#95	C₂³×C₁₃₉	1	2	yes	—
691	#95	C₂³×C₁₃₉	1	2	yes	—
692	#95	C₂³×C₁₃₉	1	2	yes	—
693	#95	C₂³×C₁₃₉	1	2	yes	—
694	#95	C₂³×C₁₃₉	1	2	yes	—
695	#95	C₂³×C₁₃₉	1	2	yes	—
696	#95	C₂³×C₁₃₉	1	2	yes	—
697	#95	C₂³×C₁₃₉	1	2	yes	—
698	#95	C₂³×C₁₃₉	1	2	yes	—
699	#95	C₂³×C₁₃₉	1	2	yes	—
700	#95	C₂³×C₁₃₉	1	2	yes	—
701	#95	C₂³×C₁₃₉	1	2	yes	—
702	#95	C₂³×C₁₃₉	1	2	yes	—
703	#95	C₂³×C₁₃₉	1	2	yes	—
704	#95	C₂³×C₁₃₉	1	2	yes	—
705	#95	C₂³×C₁₃₉	1	2	yes	—
706	#95	C₂³×C₁₃₉	1	2	yes	—
707	#95	C₂³×C₁₃₉	1	2	yes	—
708	#95	C₂³×C₁₃₉	1	2	yes	—
709	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	2	4	no	—
714	C₂×Q₈	—	2	4	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	4	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	4	2	no	—
722	C₂×Q₈	—	4	2	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×Q₈	—	4	16	no	—
725	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
740	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
788	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
793	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
794	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	4	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	4	1	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	1	no	—
811	C₄²	—	4	2	no	—
812	C₄²	—	4	2	no	—
813	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	complemented
814	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	complemented
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
820	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
821	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
822	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
823	Q₈	—	2	8	no	—
824	Q₈	—	4	8	no	—
825	Q₈	—	4	4	no	—
826	Q₈	—	4	4	no	—
827	Q₈	—	8	4	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	8	4	no	—
885	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
886	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
887	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
888	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
889	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
890	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
891	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
892	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
893	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
894	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
895	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
896	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
897	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
898	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	#533×C₁₃₉	1	4	yes	—
906	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
907	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
908	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
909	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
910	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
911	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
912	C₂²	#585×C₁₃₉	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	#551×C₁₃₉	1	4	yes	—
935	C₂	—	2	4	no	—
936	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
937	C₂	C₂×#551×C₁₃₉	1	1	yes	characteristic
938	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
939	C₂	#3482×C₁₃₉	1	1	yes	characteristic
940	C₂	#3495×C₁₃₉	1	1	yes	characteristic
941	C₂	#3503×C₁₃₉	1	1	yes	characteristic
942	C₂	#3514×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
1. #2863×C₁₃₉	C₂	semidirect
2. #2862×C₁₃₉	C₂	semidirect
4. #2612×C₁₃₉	C₂	semidirect
5. #2605×C₁₃₉	C₂	semidirect
6. #2586×C₁₃₉	C₂	semidirect
7. #2520×C₁₃₉	C₂	semidirect
8. #2511×C₁₃₉	C₂	semidirect
10. #2451×C₁₃₉	C₂	semidirect
11. #2446×C₁₃₉	C₂	semidirect
12. #2446×C₁₃₉	C₂	semidirect
20. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
21. #2295×C₁₃₉	C₂	semidirect
145. #117×C₁₃₉	Q₈	semidirect
315. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
316. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
341. C₄²×C₁₃₉	C₂×Q₈	semidirect
342. C₄²×C₁₃₉	C₂×Q₈	semidirect
471. #36279	C₁₃₉	direct (N × H)
472. C₁₃₉	#36279	direct (N × H)
473. #2863	C₂×C₁₃₉	semidirect
474. #2862	C₂×C₁₃₉	semidirect
476. #2612	C₂×C₁₃₉	semidirect
477. #2605	C₂×C₁₃₉	semidirect
478. #2586	C₂×C₁₃₉	semidirect
479. #2520	C₂×C₁₃₉	semidirect
480. #2511	C₂×C₁₃₉	semidirect
482. #2451	C₂×C₁₃₉	semidirect
483. #2446	C₂×C₁₃₉	semidirect
484. #2446	C₂×C₁₃₉	semidirect
492. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
493. #2295	C₂×C₁₃₉	semidirect
617. #117	Q₈×C₁₃₉	semidirect
787. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect
788. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect
813. C₄²	C₂×Q₈×C₁₃₉	semidirect
814. C₄²	C₂×Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2863×C₁₃₉	2
#2862×C₁₃₉	2
#2855×C₁₃₉	2
#2612×C₁₃₉	2
#2605×C₁₃₉	2
#2586×C₁₃₉	2
#2520×C₁₃₉	2
#2511×C₁₃₉	2
#2505×C₁₃₉	2
#2451×C₁₃₉	2
#2446×C₁₃₉	2
#2440×C₁₃₉	2
#2438×C₁₃₉	2
#2434×C₁₃₉	2
#2368×C₁₃₉	2
#2360×C₁₃₉	2
#2343×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2295×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₄×#117×C₁₃₉	2
#36279	139

Subgroups — C139×#36279 #48030875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36279 #48030875