Subgroups — C₁₃₉×#36374 #48030970

Order 35584.

2692 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2592×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2581×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2477×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2474×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2459×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2444×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2430×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2416×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2415×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2409×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2407×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2364×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
20	#2352×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	#548×C₁₃₉	—	2	8	no	—
28	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₄×#41×C₁₃₉	—	2	8	no	—
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
58	#400×C₁₃₉	C₂²	1	2	yes	—
59	#397×C₁₃₉	C₂²	1	2	yes	—
60	#397×C₁₃₉	C₂²	1	2	yes	—
61	#396×C₁₃₉	C₂²	1	2	yes	—
62	#395×C₁₃₉	C₂²	1	2	yes	—
63	#395×C₁₃₉	C₂²	1	2	yes	—
64	#394×C₁₃₉	C₂²	1	2	yes	—
65	#394×C₁₃₉	C₂²	1	2	yes	—
66	#394×C₁₃₉	C₂²	1	2	yes	—
67	#393×C₁₃₉	C₂²	1	2	yes	—
68	#393×C₁₃₉	C₂²	1	2	yes	—
69	#392×C₁₃₉	C₂²	1	2	yes	—
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic
71	#391×C₁₃₉	C₂²	1	1	yes	characteristic
72	#391×C₁₃₉	C₂²	1	1	yes	characteristic
73	#391×C₁₃₉	C₂²	1	1	yes	characteristic
74	#391×C₁₃₉	C₂²	1	2	yes	—
75	#391×C₁₃₉	C₂²	1	2	yes	—
76	#391×C₁₃₉	C₂²	1	1	yes	characteristic
77	#391×C₁₃₉	C₂²	1	1	yes	characteristic
78	#390×C₁₃₉	C₂²	1	1	yes	characteristic
79	#390×C₁₃₉	C₂²	1	1	yes	characteristic
80	#390×C₁₃₉	C₂²	1	1	yes	characteristic
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic
82	#389×C₁₃₉	C₂²	1	1	yes	characteristic
83	#389×C₁₃₉	C₂²	1	1	yes	characteristic
84	#389×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#388×C₁₃₉	C₂²	1	2	yes	—
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	2	yes	—
97	#387×C₁₃₉	C₂²	1	2	yes	—
98	#387×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#386×C₁₃₉	C₂²	1	2	yes	—
102	#386×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#386×C₁₃₉	C₂²	1	2	yes	—
105	#386×C₁₃₉	C₂²	1	2	yes	—
106	#386×C₁₃₉	C₂²	1	2	yes	—
107	#386×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#385×C₁₃₉	C₂²	1	2	yes	—
110	#385×C₁₃₉	C₂²	1	2	yes	—
111	#385×C₁₃₉	C₂²	1	2	yes	—
112	#382×C₁₃₉	C₂²	1	1	yes	characteristic
113	#381×C₁₃₉	C₂²	1	2	yes	—
114	#380×C₁₃₉	C₂²	1	1	yes	characteristic
115	#380×C₁₃₉	C₂²	1	1	yes	characteristic
116	#380×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
123	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
125	C₂×#41×C₁₃₉	—	2	4	no	—
126	C₂×#41×C₁₃₉	—	2	4	no	—
127	C₂×#41×C₁₃₉	—	2	4	no	—
128	C₂×#41×C₁₃₉	—	2	4	no	—
129	C₂×#41×C₁₃₉	—	2	4	no	—
130	C₂×#41×C₁₃₉	—	4	2	no	—
131	C₂²×Q₈×C₁₃₉	—	2	4	no	—
132	C₂²×Q₈×C₁₃₉	—	2	4	no	—
133	C₂²×Q₈×C₁₃₉	—	4	2	no	—
134	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
157	#124×C₁₃₉	—	2	8	no	—
158	#124×C₁₃₉	—	2	4	no	—
159	#123×C₁₃₉	—	2	8	no	—
160	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
161	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
162	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
163	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
164	#121×C₁₃₉	—	2	8	no	—
165	#121×C₁₃₉	—	2	8	no	—
166	#121×C₁₃₉	—	2	4	no	—
167	#121×C₁₃₉	—	4	2	no	—
168	C₄×Q₈×C₁₃₉	—	2	4	no	—
169	C₄×Q₈×C₁₃₉	—	2	4	no	—
170	C₄×Q₈×C₁₃₉	—	2	4	no	—
171	C₄×D₄×C₁₃₉	—	2	4	no	—
172	C₄×D₄×C₁₃₉	—	2	4	no	—
173	C₄×D₄×C₁₃₉	—	2	4	no	—
174	C₄×D₄×C₁₃₉	—	2	4	no	—
175	C₄×D₄×C₁₃₉	—	2	4	no	—
176	C₄×D₄×C₁₃₉	—	2	8	no	—
177	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
178	#117×C₁₃₉	—	2	4	no	—
179	#117×C₁₃₉	—	2	4	no	—
180	#117×C₁₃₉	—	2	4	no	—
181	#117×C₁₃₉	—	4	2	no	—
182	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	—	2	4	no	—
226	C₂×C₄²×C₁₃₉	—	2	4	no	—
227	C₂×C₄²×C₁₃₉	—	2	4	no	—
228	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
239	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	2	yes	—
255	#95×C₁₃₉	C₂³	1	2	yes	—
256	#95×C₁₃₉	C₂³	1	2	yes	—
257	#95×C₁₃₉	C₂³	1	2	yes	—
258	#95×C₁₃₉	C₂³	1	2	yes	—
259	#95×C₁₃₉	C₂³	1	2	yes	—
260	#95×C₁₃₉	C₂³	1	2	yes	—
261	#95×C₁₃₉	C₂³	1	2	yes	—
262	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	#41×C₁₃₉	—	2	32	no	—
267	#41×C₁₃₉	—	4	16	no	—
268	C₂×Q₈×C₁₃₉	—	2	2	no	—
269	C₂×Q₈×C₁₃₉	—	2	2	no	—
270	C₂×Q₈×C₁₃₉	—	2	4	no	—
271	C₂×Q₈×C₁₃₉	—	2	2	no	—
272	C₂×Q₈×C₁₃₉	—	2	2	no	—
273	C₂×Q₈×C₁₃₉	—	2	2	no	—
274	C₂×Q₈×C₁₃₉	—	2	4	no	—
275	C₂×Q₈×C₁₃₉	—	2	2	no	—
276	C₂×Q₈×C₁₃₉	—	2	2	no	—
277	C₂×Q₈×C₁₃₉	—	2	2	no	—
278	C₂×Q₈×C₁₃₉	—	4	2	no	—
279	C₂×Q₈×C₁₃₉	—	4	16	no	—
280	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
281	C₂×D₄×C₁₃₉	—	2	2	no	—
282	C₂×D₄×C₁₃₉	—	2	2	no	—
283	C₂×D₄×C₁₃₉	—	2	2	no	—
284	C₂×D₄×C₁₃₉	—	2	2	no	—
285	C₂×D₄×C₁₃₉	—	2	2	no	—
286	C₂×D₄×C₁₃₉	—	2	2	no	—
287	C₂×D₄×C₁₃₉	—	2	4	no	—
288	C₂×D₄×C₁₃₉	—	2	4	no	—
289	C₂×D₄×C₁₃₉	—	2	4	no	—
290	C₂×D₄×C₁₃₉	—	2	4	no	—
291	C₂×D₄×C₁₃₉	—	2	4	no	—
292	C₂×D₄×C₁₃₉	—	2	2	no	—
293	C₂×D₄×C₁₃₉	—	2	2	no	—
294	C₂×D₄×C₁₃₉	—	2	4	no	—
295	C₂×D₄×C₁₃₉	—	2	2	no	—
296	C₂×D₄×C₁₃₉	—	2	2	no	—
297	C₂×D₄×C₁₃₉	—	4	2	no	—
298	C₂×D₄×C₁₃₉	—	4	2	no	—
299	C₂×D₄×C₁₃₉	—	4	2	no	—
300	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
301	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
302	C₂²×C₄×C₁₃₉	—	2	2	no	—
303	C₂²×C₄×C₁₃₉	—	2	2	no	—
304	C₂²×C₄×C₁₃₉	—	2	2	no	—
305	C₂²×C₄×C₁₃₉	—	2	2	no	—
306	C₂²×C₄×C₁₃₉	—	2	2	no	—
307	C₂²×C₄×C₁₃₉	—	2	2	no	—
308	C₂²×C₄×C₁₃₉	—	2	2	no	—
309	C₂²×C₄×C₁₃₉	—	2	2	no	—
310	C₂²×C₄×C₁₃₉	—	2	2	no	—
311	C₂²×C₄×C₁₃₉	—	2	2	no	—
312	C₂²×C₄×C₁₃₉	—	2	2	no	—
313	C₂²×C₄×C₁₃₉	—	2	2	no	—
314	C₂²×C₄×C₁₃₉	—	2	2	no	—
315	C₂²×C₄×C₁₃₉	—	2	2	no	—
316	C₂²×C₄×C₁₃₉	—	2	4	no	—
317	C₂²×C₄×C₁₃₉	—	2	4	no	—
318	C₂²×C₄×C₁₃₉	—	2	2	no	—
319	C₂²×C₄×C₁₃₉	—	2	2	no	—
320	C₂²×C₄×C₁₃₉	—	2	4	no	—
321	C₂²×C₄×C₁₃₉	—	2	2	no	—
322	C₂²×C₄×C₁₃₉	—	2	4	no	—
323	C₂²×C₄×C₁₃₉	—	2	4	no	—
324	C₂²×C₄×C₁₃₉	—	2	2	no	—
325	C₂²×C₄×C₁₃₉	—	2	2	no	—
326	C₂²×C₄×C₁₃₉	—	2	2	no	—
327	C₂²×C₄×C₁₃₉	—	2	2	no	—
328	C₂²×C₄×C₁₃₉	—	4	1	no	—
329	C₂²×C₄×C₁₃₉	—	4	1	no	—
330	C₂²×C₄×C₁₃₉	—	4	1	no	—
331	C₂²×C₄×C₁₃₉	—	4	2	no	—
332	C₂²×C₄×C₁₃₉	—	4	2	no	—
333	C₂²×C₄×C₁₃₉	—	4	2	no	—
334	C₂²×C₄×C₁₃₉	—	4	2	no	—
335	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
336	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
337	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
338	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₁₃₉	—	2	2	no	—
358	C₄⋊C₄×C₁₃₉	—	2	2	no	—
359	C₄⋊C₄×C₁₃₉	—	2	2	no	—
360	C₄⋊C₄×C₁₃₉	—	2	2	no	—
361	C₄⋊C₄×C₁₃₉	—	2	2	no	—
362	C₄⋊C₄×C₁₃₉	—	2	4	no	—
363	C₄⋊C₄×C₁₃₉	—	2	4	no	—
364	C₄⋊C₄×C₁₃₉	—	2	2	no	—
365	C₄⋊C₄×C₁₃₉	—	2	4	no	—
366	C₄⋊C₄×C₁₃₉	—	2	2	no	—
367	C₄⋊C₄×C₁₃₉	—	2	4	no	—
368	C₄⋊C₄×C₁₃₉	—	2	4	no	—
369	C₄⋊C₄×C₁₃₉	—	2	4	no	—
370	C₄⋊C₄×C₁₃₉	—	2	2	no	—
371	C₄⋊C₄×C₁₃₉	—	2	2	no	—
372	C₄⋊C₄×C₁₃₉	—	2	2	no	—
373	C₄⋊C₄×C₁₃₉	—	4	2	no	—
374	C₄⋊C₄×C₁₃₉	—	4	2	no	—
375	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
376	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
379	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
380	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
381	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
384	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
385	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
386	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
387	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
388	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
389	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
390	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
391	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
392	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
393	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
394	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
395	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
396	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
397	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
398	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
399	C₄²×C₁₃₉	—	2	2	no	—
400	C₄²×C₁₃₉	—	2	2	no	—
401	C₄²×C₁₃₉	—	2	2	no	—
402	C₄²×C₁₃₉	—	2	2	no	—
403	C₄²×C₁₃₉	—	2	2	no	—
404	C₄²×C₁₃₉	—	2	2	no	—
405	C₄²×C₁₃₉	—	2	2	no	—
406	C₄²×C₁₃₉	—	2	2	no	—
407	C₄²×C₁₃₉	—	2	2	no	—
408	C₄²×C₁₃₉	—	2	4	no	—
409	C₄²×C₁₃₉	—	4	2	no	—
410	C₄²×C₁₃₉	—	4	2	no	—
411	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	2	1	no	—
414	C₂³×C₁₃₉	—	2	1	no	—
415	C₂³×C₁₃₉	—	2	1	no	—
416	C₂³×C₁₃₉	—	2	1	no	—
417	C₂³×C₁₃₉	—	2	1	no	—
418	C₂³×C₁₃₉	—	2	1	no	—
419	C₂³×C₁₃₉	—	2	1	no	—
420	C₂³×C₁₃₉	—	2	1	no	—
421	C₂³×C₁₃₉	—	2	1	no	—
422	C₂³×C₁₃₉	—	2	1	no	—
423	C₂³×C₁₃₉	—	2	1	no	—
424	C₂³×C₁₃₉	—	2	1	no	—
425	C₂³×C₁₃₉	—	2	1	no	—
426	C₂³×C₁₃₉	—	2	1	no	—
427	C₂³×C₁₃₉	—	2	1	no	—
428	C₂³×C₁₃₉	—	2	2	no	—
429	C₂³×C₁₃₉	—	2	2	no	—
430	C₂³×C₁₃₉	—	2	2	no	—
431	C₂³×C₁₃₉	—	2	2	no	—
432	C₂³×C₁₃₉	—	2	2	no	—
433	C₂³×C₁₃₉	—	2	2	no	—
434	C₂³×C₁₃₉	—	2	2	no	—
435	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
436	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
437	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
438	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
439	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
440	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
441	Q₈×C₁₃₉	—	2	8	no	—
442	Q₈×C₁₃₉	—	2	8	no	—
443	Q₈×C₁₃₉	—	4	8	no	—
444	Q₈×C₁₃₉	—	4	4	no	—
445	D₄×C₁₃₉	—	2	8	no	—
446	D₄×C₁₃₉	—	2	8	no	—
447	D₄×C₁₃₉	—	2	8	no	—
448	D₄×C₁₃₉	—	4	8	no	—
449	D₄×C₁₃₉	—	4	8	no	—
450	D₄×C₁₃₉	—	4	4	no	—
451	D₄×C₁₃₉	—	8	4	no	—
452	C₂×C₄×C₁₃₉	—	2	8	no	—
453	C₂×C₄×C₁₃₉	—	2	8	no	—
454	C₂×C₄×C₁₃₉	—	2	8	no	—
455	C₂×C₄×C₁₃₉	—	2	1	no	—
456	C₂×C₄×C₁₃₉	—	2	1	no	—
457	C₂×C₄×C₁₃₉	—	2	1	no	—
458	C₂×C₄×C₁₃₉	—	2	1	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	1	no	—
461	C₂×C₄×C₁₃₉	—	2	1	no	—
462	C₂×C₄×C₁₃₉	—	2	1	no	—
463	C₂×C₄×C₁₃₉	—	2	1	no	—
464	C₂×C₄×C₁₃₉	—	2	1	no	—
465	C₂×C₄×C₁₃₉	—	2	1	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	2	1	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	2	no	—
470	C₂×C₄×C₁₃₉	—	2	1	no	—
471	C₂×C₄×C₁₃₉	—	2	1	no	—
472	C₂×C₄×C₁₃₉	—	2	1	no	—
473	C₂×C₄×C₁₃₉	—	2	8	no	—
474	C₂×C₄×C₁₃₉	—	2	8	no	—
475	C₂×C₄×C₁₃₉	—	2	1	no	—
476	C₂×C₄×C₁₃₉	—	2	1	no	—
477	C₂×C₄×C₁₃₉	—	2	1	no	—
478	C₂×C₄×C₁₃₉	—	2	2	no	—
479	C₂×C₄×C₁₃₉	—	2	2	no	—
480	C₂×C₄×C₁₃₉	—	2	2	no	—
481	C₂×C₄×C₁₃₉	—	2	2	no	—
482	C₂×C₄×C₁₃₉	—	2	2	no	—
483	C₂×C₄×C₁₃₉	—	2	2	no	—
484	C₂×C₄×C₁₃₉	—	2	2	no	—
485	C₂×C₄×C₁₃₉	—	2	1	no	—
486	C₂×C₄×C₁₃₉	—	2	2	no	—
487	C₂×C₄×C₁₃₉	—	2	2	no	—
488	C₂×C₄×C₁₃₉	—	2	2	no	—
489	C₂×C₄×C₁₃₉	—	2	2	no	—
490	C₂×C₄×C₁₃₉	—	2	2	no	—
491	C₂×C₄×C₁₃₉	—	2	1	no	—
492	C₂×C₄×C₁₃₉	—	2	2	no	—
493	C₂×C₄×C₁₃₉	—	2	2	no	—
494	C₂×C₄×C₁₃₉	—	2	2	no	—
495	C₂×C₄×C₁₃₉	—	2	1	no	—
496	C₂×C₄×C₁₃₉	—	2	1	no	—
497	C₂×C₄×C₁₃₉	—	2	2	no	—
498	C₂×C₄×C₁₃₉	—	2	2	no	—
499	C₂×C₄×C₁₃₉	—	2	1	no	—
500	C₂×C₄×C₁₃₉	—	2	1	no	—
501	C₂×C₄×C₁₃₉	—	2	2	no	—
502	C₂×C₄×C₁₃₉	—	4	4	no	—
503	C₂×C₄×C₁₃₉	—	4	8	no	—
504	C₂×C₄×C₁₃₉	—	4	4	no	—
505	C₂×C₄×C₁₃₉	—	4	4	no	—
506	C₂×C₄×C₁₃₉	—	4	8	no	—
507	C₂×C₄×C₁₃₉	—	4	4	no	—
508	C₂×C₄×C₁₃₉	—	8	4	no	—
509	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
515	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
516	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
517	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
518	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
519	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
521	C₂²×C₁₃₉	—	2	2	no	—
522	C₂²×C₁₃₉	—	2	2	no	—
523	C₂²×C₁₃₉	—	2	2	no	—
524	C₂²×C₁₃₉	—	2	2	no	—
525	C₂²×C₁₃₉	—	2	2	no	—
526	C₂²×C₁₃₉	—	2	2	no	—
527	C₂²×C₁₃₉	—	2	2	no	—
528	C₂²×C₁₃₉	—	2	2	no	—
529	C₂²×C₁₃₉	—	2	2	no	—
530	C₂²×C₁₃₉	—	2	2	no	—
531	C₂²×C₁₃₉	—	2	2	no	—
532	C₂²×C₁₃₉	—	2	2	no	—
533	C₂²×C₁₃₉	—	4	1	no	—
534	C₂²×C₁₃₉	—	4	1	no	—
535	C₂²×C₁₃₉	—	4	1	no	—
536	C₂²×C₁₃₉	—	4	1	no	—
537	C₂²×C₁₃₉	—	4	1	no	—
538	C₂²×C₁₃₉	—	4	1	no	—
539	C₂²×C₁₃₉	—	4	1	no	—
540	C₂²×C₁₃₉	—	4	1	no	—
541	C₂²×C₁₃₉	—	4	2	no	—
542	C₂²×C₁₃₉	—	4	2	no	—
543	C₂²×C₁₃₉	—	4	2	no	—
544	C₂²×C₁₃₉	—	4	2	no	—
545	C₂²×C₁₃₉	—	4	2	no	—
546	C₂²×C₁₃₉	—	4	2	no	—
547	C₂²×C₁₃₉	—	4	2	no	—
548	C₂²×C₁₃₉	#525	1	4	yes	—
549	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
550	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
551	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
552	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
553	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
555	C₂²×C₁₃₉	#585	1	1	yes	characteristic
556	C₄×C₁₃₉	—	2	2	no	—
557	C₄×C₁₃₉	—	2	2	no	—
558	C₄×C₁₃₉	—	2	2	no	—
559	C₄×C₁₃₉	—	2	2	no	—
560	C₄×C₁₃₉	—	2	2	no	—
561	C₄×C₁₃₉	—	2	2	no	—
562	C₄×C₁₃₉	—	2	4	no	—
563	C₄×C₁₃₉	—	2	2	no	—
564	C₄×C₁₃₉	—	2	2	no	—
565	C₄×C₁₃₉	—	4	2	no	—
566	C₄×C₁₃₉	—	4	1	no	—
567	C₄×C₁₃₉	—	4	2	no	—
568	C₄×C₁₃₉	—	4	2	no	—
569	C₄×C₁₃₉	—	4	1	no	—
570	C₄×C₁₃₉	—	4	1	no	—
571	C₄×C₁₃₉	—	4	2	no	—
572	C₄×C₁₃₉	—	4	2	no	—
573	C₄×C₁₃₉	—	4	2	no	—
574	C₄×C₁₃₉	#546	1	4	yes	—
575	C₂×C₁₃₉	—	2	4	no	—
576	C₂×C₁₃₉	—	4	2	no	—
577	C₂×C₁₃₉	—	4	2	no	—
578	C₂×C₁₃₉	—	8	2	no	—
579	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
580	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
581	C₂×C₁₃₉	#3480	1	1	yes	characteristic
582	C₂×C₁₃₉	#3482	1	1	yes	characteristic
583	C₂×C₁₃₉	#3489	1	1	yes	characteristic
584	C₂×C₁₃₉	#3511	1	1	yes	characteristic
585	C₂×C₁₃₉	#3514	1	1	yes	characteristic
586	#36374	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
587	C₁₃₉	#36374	1	1	yes	characteristic, direct product factor, Sylow
588	C₂×#548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
589	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
590	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
591	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
592	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
593	#2592	C₂×C₁₃₉	1	1	yes	characteristic, complemented
594	#2581	C₂×C₁₃₉	1	1	yes	characteristic, complemented
595	#2477	C₂×C₁₃₉	1	2	yes	complemented
596	#2474	C₂×C₁₃₉	1	2	yes	complemented
597	#2465	C₂×C₁₃₉	1	2	yes	complemented
598	#2459	C₂×C₁₃₉	1	2	yes	complemented
599	#2444	C₂×C₁₃₉	1	2	yes	complemented
600	#2430	C₂×C₁₃₉	1	2	yes	complemented
601	#2416	C₂×C₁₃₉	1	1	yes	characteristic, complemented
602	#2415	C₂×C₁₃₉	1	1	yes	characteristic, complemented
603	#2409	C₂×C₁₃₉	1	1	yes	characteristic, complemented
604	#2407	C₂×C₁₃₉	1	1	yes	characteristic, complemented
605	#2364	C₂×C₁₃₉	1	2	yes	complemented
606	#2359	C₂×C₁₃₉	1	2	yes	complemented
607	#2352	C₂×C₁₃₉	1	1	yes	characteristic, complemented
608	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
609	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
610	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
611	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
612	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
613	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
614	#548	—	2	8	no	—
615	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
616	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
617	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
619	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
620	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
621	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
622	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
623	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
624	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
625	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
626	C₄×#41	—	2	8	no	—
627	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
629	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
630	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
631	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
633	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
637	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
638	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
639	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
640	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
641	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
642	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
643	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
644	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
645	#400	C₂²×C₁₃₉	1	2	yes	—
646	#397	C₂²×C₁₃₉	1	2	yes	—
647	#397	C₂²×C₁₃₉	1	2	yes	—
648	#396	C₂²×C₁₃₉	1	2	yes	—
649	#395	C₂²×C₁₃₉	1	2	yes	—
650	#395	C₂²×C₁₃₉	1	2	yes	—
651	#394	C₂²×C₁₃₉	1	2	yes	—
652	#394	C₂²×C₁₃₉	1	2	yes	—
653	#394	C₂²×C₁₃₉	1	2	yes	—
654	#393	C₂²×C₁₃₉	1	2	yes	—
655	#393	C₂²×C₁₃₉	1	2	yes	—
656	#392	C₂²×C₁₃₉	1	2	yes	—
657	#391	C₂²×C₁₃₉	1	1	yes	characteristic
658	#391	C₂²×C₁₃₉	1	1	yes	characteristic
659	#391	C₂²×C₁₃₉	1	1	yes	characteristic
660	#391	C₂²×C₁₃₉	1	1	yes	characteristic
661	#391	C₂²×C₁₃₉	1	1	yes	characteristic
662	#391	C₂²×C₁₃₉	1	2	yes	—
663	#391	C₂²×C₁₃₉	1	2	yes	—
664	#391	C₂²×C₁₃₉	1	1	yes	characteristic
665	#390	C₂²×C₁₃₉	1	1	yes	characteristic
666	#390	C₂²×C₁₃₉	1	1	yes	characteristic
667	#390	C₂²×C₁₃₉	1	1	yes	characteristic
668	#389	C₂²×C₁₃₉	1	1	yes	characteristic
669	#389	C₂²×C₁₃₉	1	1	yes	characteristic
670	#389	C₂²×C₁₃₉	1	1	yes	characteristic
671	#389	C₂²×C₁₃₉	1	2	yes	—
672	#388	C₂²×C₁₃₉	1	2	yes	—
673	#388	C₂²×C₁₃₉	1	2	yes	—
674	#388	C₂²×C₁₃₉	1	2	yes	—
675	#388	C₂²×C₁₃₉	1	2	yes	—
676	#388	C₂²×C₁₃₉	1	2	yes	—
677	#388	C₂²×C₁₃₉	1	2	yes	—
678	#388	C₂²×C₁₃₉	1	2	yes	—
679	#388	C₂²×C₁₃₉	1	2	yes	—
680	#387	C₂²×C₁₃₉	1	2	yes	—
681	#387	C₂²×C₁₃₉	1	2	yes	—
682	#387	C₂²×C₁₃₉	1	2	yes	—
683	#387	C₂²×C₁₃₉	1	2	yes	—
684	#387	C₂²×C₁₃₉	1	2	yes	—
685	#387	C₂²×C₁₃₉	1	2	yes	—
686	#386	C₂²×C₁₃₉	1	2	yes	—
687	#386	C₂²×C₁₃₉	1	2	yes	—
688	#386	C₂²×C₁₃₉	1	2	yes	—
689	#386	C₂²×C₁₃₉	1	2	yes	—
690	#386	C₂²×C₁₃₉	1	2	yes	—
691	#386	C₂²×C₁₃₉	1	2	yes	—
692	#386	C₂²×C₁₃₉	1	2	yes	—
693	#386	C₂²×C₁₃₉	1	2	yes	—
694	#386	C₂²×C₁₃₉	1	2	yes	—
695	#385	C₂²×C₁₃₉	1	2	yes	—
696	#385	C₂²×C₁₃₉	1	2	yes	—
697	#385	C₂²×C₁₃₉	1	2	yes	—
698	#385	C₂²×C₁₃₉	1	2	yes	—
699	#382	C₂²×C₁₃₉	1	1	yes	characteristic
700	#381	C₂²×C₁₃₉	1	2	yes	—
701	#380	C₂²×C₁₃₉	1	1	yes	characteristic
702	#380	C₂²×C₁₃₉	1	1	yes	characteristic
703	#380	C₂²×C₁₃₉	1	1	yes	characteristic
704	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
705	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
706	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
707	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
708	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
709	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
710	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
711	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
712	C₂×#41	—	2	4	no	—
713	C₂×#41	—	2	4	no	—
714	C₂×#41	—	2	4	no	—
715	C₂×#41	—	2	4	no	—
716	C₂×#41	—	2	4	no	—
717	C₂×#41	—	4	2	no	—
718	C₂²×Q₈	—	2	4	no	—
719	C₂²×Q₈	—	2	4	no	—
720	C₂²×Q₈	—	4	2	no	—
721	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
724	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
725	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
726	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
731	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
732	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
733	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
741	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
743	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
744	#124	—	2	8	no	—
745	#124	—	2	4	no	—
746	#123	—	2	8	no	—
747	C₂²⋊Q₈	—	2	4	no	—
748	C₂²⋊Q₈	—	2	4	no	—
749	C₂²⋊Q₈	—	2	8	no	—
750	C₂²⋊Q₈	—	4	2	no	—
751	#121	—	2	8	no	—
752	#121	—	2	8	no	—
753	#121	—	2	4	no	—
754	#121	—	4	2	no	—
755	C₄×Q₈	—	2	4	no	—
756	C₄×Q₈	—	2	4	no	—
757	C₄×Q₈	—	2	4	no	—
758	C₄×D₄	—	2	4	no	—
759	C₄×D₄	—	2	4	no	—
760	C₄×D₄	—	2	4	no	—
761	C₄×D₄	—	2	4	no	—
762	C₄×D₄	—	2	4	no	—
763	C₄×D₄	—	2	8	no	—
764	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
765	#117	—	2	4	no	—
766	#117	—	2	4	no	—
767	#117	—	2	4	no	—
768	#117	—	4	2	no	—
769	C₂×C₄⋊C₄	—	4	2	no	—
770	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
774	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
775	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
783	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
784	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
785	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
787	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
790	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
812	C₂×C₄²	—	2	4	no	—
813	C₂×C₄²	—	2	4	no	—
814	C₂×C₄²	—	2	4	no	—
815	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
816	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
817	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
819	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
821	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
824	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
825	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
826	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
827	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
828	#95	C₂³×C₁₃₉	1	2	yes	—
829	#95	C₂³×C₁₃₉	1	2	yes	—
830	#95	C₂³×C₁₃₉	1	2	yes	—
831	#95	C₂³×C₁₃₉	1	2	yes	—
832	#95	C₂³×C₁₃₉	1	2	yes	—
833	#95	C₂³×C₁₃₉	1	2	yes	—
834	#95	C₂³×C₁₃₉	1	2	yes	—
835	#95	C₂³×C₁₃₉	1	2	yes	—
836	#95	C₂³×C₁₃₉	1	2	yes	—
837	#95	C₂³×C₁₃₉	1	2	yes	—
838	#95	C₂³×C₁₃₉	1	2	yes	—
839	#95	C₂³×C₁₃₉	1	2	yes	—
840	#95	C₂³×C₁₃₉	1	2	yes	—
841	#95	C₂³×C₁₃₉	1	2	yes	—
842	#95	C₂³×C₁₃₉	1	2	yes	—
843	#95	C₂³×C₁₃₉	1	2	yes	—
844	#95	C₂³×C₁₃₉	1	2	yes	—
845	#95	C₂³×C₁₃₉	1	2	yes	—
846	#95	C₂³×C₁₃₉	1	2	yes	—
847	#95	C₂³×C₁₃₉	1	2	yes	—
848	#95	C₂³×C₁₃₉	1	2	yes	—
849	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
850	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
851	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
852	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
853	#41	—	2	32	no	—
854	#41	—	4	16	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	4	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	4	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	4	16	no	—
867	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	4	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	2	no	—
887	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
888	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	2	4	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	4	no	—
910	C₂²×C₄	—	2	4	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	4	1	no	—
916	C₂²×C₄	—	4	1	no	—
917	C₂²×C₄	—	4	1	no	—
918	C₂²×C₄	—	4	2	no	—
919	C₂²×C₄	—	4	2	no	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
923	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
924	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
925	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	4	no	—
950	C₄⋊C₄	—	2	4	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	4	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	4	no	—
955	C₄⋊C₄	—	2	4	no	—
956	C₄⋊C₄	—	2	4	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	4	2	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	4	no	—
966	C₂²⋊C₄	—	2	4	no	—
967	C₂²⋊C₄	—	2	4	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	4	no	—
977	C₂²⋊C₄	—	2	4	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
985	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	4	no	—
996	C₄²	—	4	2	no	—
997	C₄²	—	4	2	no	—
998	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1023	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1024	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1025	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1026	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1027	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1028	Q₈	—	2	8	no	—
1029	Q₈	—	2	8	no	—
1030	Q₈	—	4	8	no	—
1031	Q₈	—	4	4	no	—
1032	D₄	—	2	8	no	—
1033	D₄	—	2	8	no	—
1034	D₄	—	2	8	no	—
1035	D₄	—	4	8	no	—
1036	D₄	—	4	8	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	8	4	no	—
1039	C₂×C₄	—	2	8	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	8	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	8	no	—
1061	C₂×C₄	—	2	8	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	8	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	4	8	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	8	4	no	—
1096	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1101	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1102	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1103	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1104	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1105	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1106	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1107	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	#525×C₁₃₉	1	4	yes	—
1136	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1137	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1138	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1139	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1140	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1141	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1142	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1143	C₄	—	2	2	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	4	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	#546×C₁₃₉	1	4	yes	—
1162	C₂	—	2	4	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	8	2	no	—
1166	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1167	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
1168	C₂	#3480×C₁₃₉	1	1	yes	characteristic
1169	C₂	#3482×C₁₃₉	1	1	yes	characteristic
1170	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1171	C₂	#3511×C₁₃₉	1	1	yes	characteristic
1172	C₂	#3514×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#548×C₁₃₉	C₂	semidirect
2. C₂×C₄×#41×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2592×C₁₃₉	C₂	semidirect
7. #2581×C₁₃₉	C₂	semidirect
8. #2477×C₁₃₉	C₂	semidirect
9. #2474×C₁₃₉	C₂	semidirect
10. #2465×C₁₃₉	C₂	semidirect
11. #2459×C₁₃₉	C₂	semidirect
12. #2444×C₁₃₉	C₂	semidirect
13. #2430×C₁₃₉	C₂	semidirect
14. #2416×C₁₃₉	C₂	semidirect
15. #2415×C₁₃₉	C₂	semidirect
16. #2409×C₁₃₉	C₂	semidirect
17. #2407×C₁₃₉	C₂	semidirect
18. #2364×C₁₃₉	C₂	semidirect
19. #2359×C₁₃₉	C₂	semidirect
20. #2352×C₁₃₉	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
22. #2297×C₁₃₉	C₂	semidirect
23. C₂×#391×C₁₃₉	C₂	semidirect
177. C₄×D₄×C₁₃₉	D₄	semidirect
280. C₂×Q₈×C₁₃₉	#41	semidirect
301. C₂×D₄×C₁₃₉	#41	semidirect
337. C₂²×C₄×C₁₃₉	#41	semidirect
586. #36374	C₁₃₉	direct (N × H)
587. C₁₃₉	#36374	direct (N × H)
588. C₂×#548	C₂×C₁₃₉	semidirect
589. C₂×C₄×#41	C₂×C₁₃₉	semidirect
590. #2855	C₂×C₁₃₉	semidirect
591. #2854	C₂×C₁₃₉	semidirect
592. #2850	C₂×C₁₃₉	semidirect
593. #2592	C₂×C₁₃₉	semidirect
594. #2581	C₂×C₁₃₉	semidirect
595. #2477	C₂×C₁₃₉	semidirect
596. #2474	C₂×C₁₃₉	semidirect
597. #2465	C₂×C₁₃₉	semidirect
598. #2459	C₂×C₁₃₉	semidirect
599. #2444	C₂×C₁₃₉	semidirect
600. #2430	C₂×C₁₃₉	semidirect
601. #2416	C₂×C₁₃₉	semidirect
602. #2415	C₂×C₁₃₉	semidirect
603. #2409	C₂×C₁₃₉	semidirect
604. #2407	C₂×C₁₃₉	semidirect
605. #2364	C₂×C₁₃₉	semidirect
606. #2359	C₂×C₁₃₉	semidirect
607. #2352	C₂×C₁₃₉	semidirect
608. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
609. #2297	C₂×C₁₃₉	semidirect
610. C₂×#391	C₂×C₁₃₉	semidirect
764. C₄×D₄	D₄×C₁₃₉	semidirect
867. C₂×Q₈	#41×C₁₃₉	semidirect
888. C₂×D₄	#41×C₁₃₉	semidirect
924. C₂²×C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2855×C₁₃₉	2
#2854×C₁₃₉	2
#2850×C₁₃₉	2
#2592×C₁₃₉	2
#2581×C₁₃₉	2
#2477×C₁₃₉	2
#2474×C₁₃₉	2
#2465×C₁₃₉	2
#2459×C₁₃₉	2
#2444×C₁₃₉	2
#2430×C₁₃₉	2
#2416×C₁₃₉	2
#2415×C₁₃₉	2
#2409×C₁₃₉	2
#2407×C₁₃₉	2
#2364×C₁₃₉	2
#2359×C₁₃₉	2
#2352×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#391×C₁₃₉	2
#36374	139

Subgroups — C139×#36374 #48030970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36374 #48030970