Subgroups — C₁₃₉×#35888 #48030484

Order 35584.

1848 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2645×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2643×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2514×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2511×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2511×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2510×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2497×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2496×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2495×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2493×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2481×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2481×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2401×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#400×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2339×C₁₃₉	C₂	1	1	yes	maximal, characteristic
21	#2339×C₁₃₉	C₂	1	1	yes	maximal, characteristic
22	#2339×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	#401×C₁₃₉	C₂²	1	2	yes	—
35	#401×C₁₃₉	C₂²	1	2	yes	—
36	#401×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	#400×C₁₃₉	C₂²	1	2	yes	—
42	#400×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	2	yes	—
44	#400×C₁₃₉	C₂²	1	2	yes	—
45	#400×C₁₃₉	C₂²	1	1	yes	characteristic
46	#400×C₁₃₉	C₂²	1	2	yes	—
47	#400×C₁₃₉	C₂²	1	2	yes	—
48	#400×C₁₃₉	C₂²	1	2	yes	—
49	#400×C₁₃₉	C₂²	1	1	yes	characteristic
50	#400×C₁₃₉	C₂²	1	1	yes	characteristic
51	#397×C₁₃₉	C₂²	1	1	yes	characteristic
52	#397×C₁₃₉	C₂²	1	2	yes	—
53	#397×C₁₃₉	C₂²	1	1	yes	characteristic
54	#397×C₁₃₉	C₂²	1	2	yes	—
55	#397×C₁₃₉	C₂²	1	1	yes	characteristic
56	#396×C₁₃₉	C₂²	1	2	yes	—
57	#396×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	1	yes	characteristic
61	#391×C₁₃₉	C₂²	1	1	yes	characteristic
62	#391×C₁₃₉	C₂²	1	1	yes	characteristic
63	#391×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×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	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#387×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
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	#386×C₁₃₉	C₂²	1	2	yes	—
80	#386×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	2	yes	—
82	#386×C₁₃₉	C₂²	1	2	yes	—
83	#386×C₁₃₉	C₂²	1	2	yes	—
84	#386×C₁₃₉	C₂²	1	2	yes	—
85	#385×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#385×C₁₃₉	C₂²	1	2	yes	—
88	#385×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#384×C₁₃₉	C₂²	1	1	yes	characteristic
92	#384×C₁₃₉	C₂²	1	1	yes	characteristic
93	#383×C₁₃₉	C₂²	1	2	yes	—
94	#383×C₁₃₉	C₂²	1	2	yes	—
95	#382×C₁₃₉	C₂²	1	1	yes	characteristic
96	#381×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	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	1	yes	characteristic
103	#380×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	#376×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
119	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
120	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
121	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
122	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
123	C₂×#41×C₁₃₉	—	2	4	no	—
124	C₂×#41×C₁₃₉	—	2	4	no	—
125	C₂×#41×C₁₃₉	—	2	4	no	—
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
137	#126×C₁₃₉	—	4	4	no	—
138	C₄×D₄×C₁₃₉	—	2	4	no	—
139	C₄×D₄×C₁₃₉	—	2	4	no	—
140	C₄×D₄×C₁₃₉	—	2	4	no	—
141	C₄×D₄×C₁₃₉	—	2	4	no	—
142	C₄×D₄×C₁₃₉	—	2	4	no	—
143	C₄×D₄×C₁₃₉	—	2	4	no	—
144	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
145	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×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	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	1	yes	characteristic
194	#95×C₁₃₉	C₂³	1	1	yes	characteristic
195	#95×C₁₃₉	C₂³	1	1	yes	characteristic
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	1	yes	characteristic
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	1	yes	characteristic
201	#95×C₁₃₉	C₂³	1	1	yes	characteristic
202	#95×C₁₃₉	C₂³	1	1	yes	characteristic
203	#95×C₁₃₉	C₂³	1	1	yes	characteristic
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	1	yes	characteristic
206	#95×C₁₃₉	C₂³	1	1	yes	characteristic
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	1	yes	characteristic
210	#95×C₁₃₉	C₂³	1	1	yes	characteristic
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
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	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
236	#41×C₁₃₉	—	4	16	no	—
237	C₂×Q₈×C₁₃₉	—	2	2	no	—
238	C₂×Q₈×C₁₃₉	—	2	2	no	—
239	C₂×Q₈×C₁₃₉	—	2	2	no	—
240	C₂×D₄×C₁₃₉	—	2	4	no	—
241	C₂×D₄×C₁₃₉	—	2	4	no	—
242	C₂×D₄×C₁₃₉	—	2	4	no	—
243	C₂×D₄×C₁₃₉	#41	1	4	yes	—
244	C₂×D₄×C₁₃₉	#41	1	4	yes	—
245	C₂×D₄×C₁₃₉	#41	1	4	yes	—
246	C₂²×C₄×C₁₃₉	—	2	4	no	—
247	C₂²×C₄×C₁₃₉	—	2	4	no	—
248	C₂²×C₄×C₁₃₉	—	2	4	no	—
249	C₂²×C₄×C₁₃₉	—	2	4	no	—
250	C₂²×C₄×C₁₃₉	—	2	4	no	—
251	C₂²×C₄×C₁₃₉	—	2	4	no	—
252	C₂²×C₄×C₁₃₉	—	2	4	no	—
253	C₂²×C₄×C₁₃₉	—	2	4	no	—
254	C₂²×C₄×C₁₃₉	—	2	4	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	4	no	—
259	C₂²×C₄×C₁₃₉	—	2	4	no	—
260	C₂²×C₄×C₁₃₉	—	4	2	no	—
261	C₂²×C₄×C₁₃₉	—	4	2	no	—
262	C₂²×C₄×C₁₃₉	—	4	2	no	—
263	C₂²×C₄×C₁₃₉	—	4	2	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	—	4	2	no	—
268	C₂²×C₄×C₁₃₉	—	4	2	no	—
269	C₂²×C₄×C₁₃₉	—	4	2	no	—
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
282	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	no	—
294	C₄⋊C₄×C₁₃₉	—	2	2	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	2	2	no	—
297	C₄⋊C₄×C₁₃₉	—	2	2	no	—
298	C₄⋊C₄×C₁₃₉	—	2	2	no	—
299	C₄⋊C₄×C₁₃₉	—	2	4	no	—
300	C₄⋊C₄×C₁₃₉	—	2	4	no	—
301	C₄⋊C₄×C₁₃₉	—	2	2	no	—
302	C₄⋊C₄×C₁₃₉	—	2	2	no	—
303	C₄⋊C₄×C₁₃₉	—	4	2	no	—
304	C₄⋊C₄×C₁₃₉	—	4	2	no	—
305	C₄⋊C₄×C₁₃₉	—	4	2	no	—
306	C₄⋊C₄×C₁₃₉	—	4	2	no	—
307	C₄⋊C₄×C₁₃₉	—	4	1	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	1	no	—
312	C₄⋊C₄×C₁₃₉	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
316	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
317	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
318	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
319	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
320	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
321	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
322	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
323	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
324	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
325	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
326	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
327	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
328	C₄²×C₁₃₉	—	2	2	no	—
329	C₄²×C₁₃₉	—	2	2	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	—	4	2	no	—
335	C₄²×C₁₃₉	—	4	2	no	—
336	C₄²×C₁₃₉	—	4	2	no	—
337	C₂³×C₁₃₉	—	2	2	no	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	1	no	—
342	C₂³×C₁₃₉	—	2	1	no	—
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	—	2	1	no	—
348	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
349	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
350	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
351	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
352	Q₈×C₁₃₉	—	4	4	no	—
353	D₄×C₁₃₉	—	4	8	no	—
354	D₄×C₁₃₉	#126	1	16	yes	complemented
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	1	no	—
388	C₂×C₄×C₁₃₉	—	2	1	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	1	no	—
391	C₂×C₄×C₁₃₉	—	2	1	no	—
392	C₂×C₄×C₁₃₉	—	2	1	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	1	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	1	no	—
397	C₂×C₄×C₁₃₉	—	2	1	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	2	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	1	no	—
403	C₂×C₄×C₁₃₉	—	2	1	no	—
404	C₂×C₄×C₁₃₉	—	2	1	no	—
405	C₂×C₄×C₁₃₉	—	2	2	no	—
406	C₂×C₄×C₁₃₉	—	2	1	no	—
407	C₂×C₄×C₁₃₉	—	2	1	no	—
408	C₂×C₄×C₁₃₉	—	2	1	no	—
409	C₂×C₄×C₁₃₉	—	2	1	no	—
410	C₂×C₄×C₁₃₉	—	2	1	no	—
411	C₂×C₄×C₁₃₉	—	2	2	no	—
412	C₂×C₄×C₁₃₉	—	2	1	no	—
413	C₂×C₄×C₁₃₉	—	4	8	no	—
414	C₂×C₄×C₁₃₉	—	4	8	no	—
415	C₂×C₄×C₁₃₉	—	4	8	no	—
416	C₂×C₄×C₁₃₉	—	4	4	no	—
417	C₂×C₄×C₁₃₉	—	8	4	no	—
418	C₂×C₄×C₁₃₉	—	8	4	no	—
419	C₂×C₄×C₁₃₉	—	8	4	no	—
420	C₂×C₄×C₁₃₉	—	8	4	no	—
421	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
425	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
426	C₂²×C₁₃₉	—	2	4	no	—
427	C₂²×C₁₃₉	—	2	4	no	—
428	C₂²×C₁₃₉	—	2	4	no	—
429	C₂²×C₁₃₉	—	2	4	no	—
430	C₂²×C₁₃₉	—	2	4	no	—
431	C₂²×C₁₃₉	—	2	4	no	—
432	C₂²×C₁₃₉	—	4	1	no	—
433	C₂²×C₁₃₉	—	4	1	no	—
434	C₂²×C₁₃₉	—	4	1	no	—
435	C₂²×C₁₃₉	—	4	1	no	—
436	C₂²×C₁₃₉	—	4	1	no	—
437	C₂²×C₁₃₉	—	4	1	no	—
438	C₂²×C₁₃₉	—	4	1	no	—
439	C₂²×C₁₃₉	C₂×#126	1	8	yes	—
440	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
441	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
443	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂²×C₁₃₉	#585	1	1	yes	characteristic
446	C₂²×C₁₃₉	#585	1	1	yes	characteristic
447	C₄×C₁₃₉	—	2	2	no	—
448	C₄×C₁₃₉	—	2	2	no	—
449	C₄×C₁₃₉	—	4	1	no	—
450	C₄×C₁₃₉	—	4	2	no	—
451	C₄×C₁₃₉	—	4	2	no	—
452	C₄×C₁₃₉	—	4	2	no	—
453	C₄×C₁₃₉	—	4	1	no	—
454	C₄×C₁₃₉	—	4	2	no	—
455	C₄×C₁₃₉	—	4	2	no	—
456	C₄×C₁₃₉	—	4	1	no	—
457	C₄×C₁₃₉	—	4	1	no	—
458	C₄×C₁₃₉	—	4	1	no	—
459	C₄×C₁₃₉	—	4	1	no	—
460	C₄×C₁₃₉	—	4	1	no	—
461	C₄×C₁₃₉	—	4	1	no	—
462	C₄×C₁₃₉	—	4	1	no	—
463	C₄×C₁₃₉	—	4	2	no	—
464	C₄×C₁₃₉	—	4	1	no	—
465	C₄×C₁₃₉	—	4	2	no	—
466	C₄×C₁₃₉	—	4	1	no	—
467	C₄×C₁₃₉	C₂×#126	1	4	yes	—
468	C₂×C₁₃₉	—	2	8	no	—
469	C₂×C₁₃₉	—	8	1	no	—
470	C₂×C₁₃₉	C₂²×#126	1	1	yes	characteristic
471	C₂×C₁₃₉	#3513	1	1	yes	characteristic
472	C₂×C₁₃₉	#3514	1	1	yes	characteristic
473	C₂×C₁₃₉	#3515	1	1	yes	characteristic
474	C₂×C₁₃₉	#3515	1	1	yes	characteristic
475	C₂×C₁₃₉	#3520	1	1	yes	characteristic
476	C₂×C₁₃₉	#3521	1	1	yes	characteristic
477	#35888	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
478	C₁₃₉	#35888	1	1	yes	characteristic, direct product factor, Sylow
479	#2645	C₂×C₁₃₉	1	1	yes	characteristic, complemented
480	#2643	C₂×C₁₃₉	1	2	yes	complemented
481	#2514	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	#2511	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	#2511	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	#2510	C₂×C₁₃₉	1	2	yes	complemented
485	#2497	C₂×C₁₃₉	1	1	yes	characteristic, complemented
486	#2496	C₂×C₁₃₉	1	1	yes	characteristic, complemented
487	#2495	C₂×C₁₃₉	1	1	yes	characteristic, complemented
488	#2493	C₂×C₁₃₉	1	2	yes	complemented
489	#2493	C₂×C₁₃₉	1	2	yes	complemented
490	#2493	C₂×C₁₃₉	1	2	yes	complemented
491	#2481	C₂×C₁₃₉	1	2	yes	complemented
492	#2481	C₂×C₁₃₉	1	2	yes	complemented
493	#2401	C₂×C₁₃₉	1	1	yes	characteristic, complemented
494	C₂×#400	C₂×C₁₃₉	1	2	yes	complemented
495	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
496	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
497	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
498	#2339	C₂×C₁₃₉	1	1	yes	characteristic
499	#2339	C₂×C₁₃₉	1	1	yes	characteristic
500	#2339	C₂×C₁₃₉	1	1	yes	characteristic
501	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
502	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
503	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
504	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
510	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
511	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
512	#401	C₂²×C₁₃₉	1	2	yes	—
513	#401	C₂²×C₁₃₉	1	2	yes	—
514	#401	C₂²×C₁₃₉	1	1	yes	characteristic
515	#400	C₂²×C₁₃₉	1	2	yes	—
516	#400	C₂²×C₁₃₉	1	2	yes	—
517	#400	C₂²×C₁₃₉	1	2	yes	—
518	#400	C₂²×C₁₃₉	1	2	yes	—
519	#400	C₂²×C₁₃₉	1	2	yes	—
520	#400	C₂²×C₁₃₉	1	1	yes	characteristic
521	#400	C₂²×C₁₃₉	1	2	yes	—
522	#400	C₂²×C₁₃₉	1	2	yes	—
523	#400	C₂²×C₁₃₉	1	2	yes	—
524	#400	C₂²×C₁₃₉	1	2	yes	—
525	#400	C₂²×C₁₃₉	1	2	yes	—
526	#400	C₂²×C₁₃₉	1	2	yes	—
527	#400	C₂²×C₁₃₉	1	1	yes	characteristic
528	#400	C₂²×C₁₃₉	1	1	yes	characteristic
529	#397	C₂²×C₁₃₉	1	1	yes	characteristic
530	#397	C₂²×C₁₃₉	1	2	yes	—
531	#397	C₂²×C₁₃₉	1	2	yes	—
532	#397	C₂²×C₁₃₉	1	1	yes	characteristic
533	#397	C₂²×C₁₃₉	1	1	yes	characteristic
534	#396	C₂²×C₁₃₉	1	2	yes	—
535	#396	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	#391	C₂²×C₁₃₉	1	1	yes	characteristic
540	#391	C₂²×C₁₃₉	1	1	yes	characteristic
541	#391	C₂²×C₁₃₉	1	1	yes	characteristic
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	#389	C₂²×C₁₃₉	1	1	yes	characteristic
548	#388	C₂²×C₁₃₉	1	2	yes	—
549	#388	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	#386	C₂²×C₁₃₉	1	2	yes	—
558	#386	C₂²×C₁₃₉	1	2	yes	—
559	#386	C₂²×C₁₃₉	1	2	yes	—
560	#386	C₂²×C₁₃₉	1	2	yes	—
561	#386	C₂²×C₁₃₉	1	2	yes	—
562	#386	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	#385	C₂²×C₁₃₉	1	2	yes	—
568	#385	C₂²×C₁₃₉	1	2	yes	—
569	#384	C₂²×C₁₃₉	1	1	yes	characteristic
570	#384	C₂²×C₁₃₉	1	1	yes	characteristic
571	#383	C₂²×C₁₃₉	1	2	yes	—
572	#383	C₂²×C₁₃₉	1	2	yes	—
573	#382	C₂²×C₁₃₉	1	1	yes	characteristic
574	#381	C₂²×C₁₃₉	1	2	yes	—
575	#381	C₂²×C₁₃₉	1	2	yes	—
576	#381	C₂²×C₁₃₉	1	2	yes	—
577	#380	C₂²×C₁₃₉	1	1	yes	characteristic
578	#380	C₂²×C₁₃₉	1	1	yes	characteristic
579	#380	C₂²×C₁₃₉	1	1	yes	characteristic
580	#380	C₂²×C₁₃₉	1	2	yes	—
581	#380	C₂²×C₁₃₉	1	2	yes	—
582	#380	C₂²×C₁₃₉	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
592	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
594	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
595	#376	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
597	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
598	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
599	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
600	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
601	C₂×#41	—	2	4	no	—
602	C₂×#41	—	2	4	no	—
603	C₂×#41	—	2	4	no	—
604	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
615	#126	—	4	4	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	4	no	—
618	C₄×D₄	—	2	4	no	—
619	C₄×D₄	—	2	4	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₂×C₄⋊C₄	—	4	4	no	—
623	C₂×C₄⋊C₄	—	4	4	no	—
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
668	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	1	yes	characteristic
671	#95	C₂³×C₁₃₉	1	1	yes	characteristic
672	#95	C₂³×C₁₃₉	1	1	yes	characteristic
673	#95	C₂³×C₁₃₉	1	1	yes	characteristic
674	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
681	#95	C₂³×C₁₃₉	1	2	yes	—
682	#95	C₂³×C₁₃₉	1	2	yes	—
683	#95	C₂³×C₁₃₉	1	2	yes	—
684	#95	C₂³×C₁₃₉	1	2	yes	—
685	#95	C₂³×C₁₃₉	1	2	yes	—
686	#95	C₂³×C₁₃₉	1	2	yes	—
687	#95	C₂³×C₁₃₉	1	2	yes	—
688	#95	C₂³×C₁₃₉	1	2	yes	—
689	#95	C₂³×C₁₃₉	1	2	yes	—
690	#95	C₂³×C₁₃₉	1	1	yes	characteristic
691	#95	C₂³×C₁₃₉	1	1	yes	characteristic
692	#95	C₂³×C₁₃₉	1	1	yes	characteristic
693	#95	C₂³×C₁₃₉	1	1	yes	characteristic
694	#95	C₂³×C₁₃₉	1	1	yes	characteristic
695	#95	C₂³×C₁₃₉	1	1	yes	characteristic
696	#95	C₂³×C₁₃₉	1	1	yes	characteristic
697	#95	C₂³×C₁₃₉	1	1	yes	characteristic
698	#95	C₂³×C₁₃₉	1	1	yes	characteristic
699	#95	C₂³×C₁₃₉	1	1	yes	characteristic
700	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
710	#95	C₂³×C₁₃₉	1	2	yes	—
711	#95	C₂³×C₁₃₉	1	2	yes	—
712	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
713	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
714	#41	—	4	16	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	#41×C₁₃₉	1	4	yes	—
722	C₂×D₄	#41×C₁₃₉	1	4	yes	—
723	C₂×D₄	#41×C₁₃₉	1	4	yes	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	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	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	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	1	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	4	1	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	1	no	—
802	C₂²⋊C₄	—	4	1	no	—
803	C₂²⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
827	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
828	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
829	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
830	Q₈	—	4	4	no	—
831	D₄	—	4	8	no	—
832	D₄	#126×C₁₃₉	1	16	yes	complemented
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	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	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	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	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	1	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	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	—	8	4	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	—	8	4	no	—
899	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
900	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
901	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
902	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
903	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
904	C₂²	—	2	4	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	2	4	no	—
909	C₂²	—	2	4	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	C₂×#126×C₁₃₉	1	8	yes	—
918	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
919	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
920	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
921	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
922	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
923	C₂²	#585×C₁₃₉	1	1	yes	characteristic
924	C₂²	#585×C₁₃₉	1	1	yes	characteristic
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	1	no	—
945	C₄	C₂×#126×C₁₃₉	1	4	yes	—
946	C₂	—	2	8	no	—
947	C₂	—	8	1	no	—
948	C₂	C₂²×#126×C₁₃₉	1	1	yes	characteristic
949	C₂	#3513×C₁₃₉	1	1	yes	characteristic
950	C₂	#3514×C₁₃₉	1	1	yes	characteristic
951	C₂	#3515×C₁₃₉	1	1	yes	characteristic
952	C₂	#3515×C₁₃₉	1	1	yes	characteristic
953	C₂	#3520×C₁₃₉	1	1	yes	characteristic
954	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×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. #2645×C₁₃₉	C₂	semidirect
2. #2643×C₁₃₉	C₂	semidirect
3. #2514×C₁₃₉	C₂	semidirect
4. #2511×C₁₃₉	C₂	semidirect
5. #2511×C₁₃₉	C₂	semidirect
6. #2510×C₁₃₉	C₂	semidirect
7. #2497×C₁₃₉	C₂	semidirect
8. #2496×C₁₃₉	C₂	semidirect
9. #2495×C₁₃₉	C₂	semidirect
10. #2493×C₁₃₉	C₂	semidirect
11. #2493×C₁₃₉	C₂	semidirect
12. #2493×C₁₃₉	C₂	semidirect
13. #2481×C₁₃₉	C₂	semidirect
14. #2481×C₁₃₉	C₂	semidirect
15. #2401×C₁₃₉	C₂	semidirect
16. C₂×#400×C₁₃₉	C₂	semidirect
17. #2349×C₁₃₉	C₂	semidirect
18. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
19. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
23. #2275×C₁₃₉	C₂	semidirect
354. D₄×C₁₃₉	#126	semidirect
477. #35888	C₁₃₉	direct (N × H)
478. C₁₃₉	#35888	direct (N × H)
479. #2645	C₂×C₁₃₉	semidirect
480. #2643	C₂×C₁₃₉	semidirect
481. #2514	C₂×C₁₃₉	semidirect
482. #2511	C₂×C₁₃₉	semidirect
483. #2511	C₂×C₁₃₉	semidirect
484. #2510	C₂×C₁₃₉	semidirect
485. #2497	C₂×C₁₃₉	semidirect
486. #2496	C₂×C₁₃₉	semidirect
487. #2495	C₂×C₁₃₉	semidirect
488. #2493	C₂×C₁₃₉	semidirect
489. #2493	C₂×C₁₃₉	semidirect
490. #2493	C₂×C₁₃₉	semidirect
491. #2481	C₂×C₁₃₉	semidirect
492. #2481	C₂×C₁₃₉	semidirect
493. #2401	C₂×C₁₃₉	semidirect
494. C₂×#400	C₂×C₁₃₉	semidirect
495. #2349	C₂×C₁₃₉	semidirect
496. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
497. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
501. #2275	C₂×C₁₃₉	semidirect
832. D₄	#126×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2645×C₁₃₉	2
#2643×C₁₃₉	2
#2514×C₁₃₉	2
#2511×C₁₃₉	2
#2510×C₁₃₉	2
#2497×C₁₃₉	2
#2496×C₁₃₉	2
#2495×C₁₃₉	2
#2493×C₁₃₉	2
#2481×C₁₃₉	2
#2401×C₁₃₉	2
C₂×#400×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2339×C₁₃₉	2
#2275×C₁₃₉	2
#35888	139

Subgroups — C139×#35888 #48030484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35888 #48030484