Subgroups — C₁₃₉×#36216 #48030812

Order 35584.

2778 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2485×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2482×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2448×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2448×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2444×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2443×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2421×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2418×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2418×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	#2339×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#388×C₁₃₉	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	#546×C₁₃₉	—	2	8	no	—
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
35	C₄×#41×C₁₃₉	—	2	8	no	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
46	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
53	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	#400×C₁₃₉	C₂²	1	2	yes	complemented
55	#399×C₁₃₉	C₂²	1	2	yes	—
56	#399×C₁₃₉	C₂²	1	2	yes	complemented
57	#399×C₁₃₉	C₂²	1	2	yes	complemented
58	#398×C₁₃₉	C₂²	1	2	yes	complemented
59	#397×C₁₃₉	C₂²	1	2	yes	—
60	#397×C₁₃₉	C₂²	1	2	yes	complemented
61	#397×C₁₃₉	C₂²	1	2	yes	complemented
62	#397×C₁₃₉	C₂²	1	2	yes	complemented
63	#394×C₁₃₉	C₂²	1	2	yes	—
64	#394×C₁₃₉	C₂²	1	2	yes	complemented
65	#394×C₁₃₉	C₂²	1	2	yes	complemented
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	#390×C₁₃₉	C₂²	1	1	yes	characteristic
69	#390×C₁₃₉	C₂²	1	1	yes	characteristic
70	#390×C₁₃₉	C₂²	1	1	yes	characteristic
71	#390×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
76	#388×C₁₃₉	C₂²	1	1	yes	characteristic
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	1	yes	characteristic
81	#388×C₁₃₉	C₂²	1	2	yes	complemented
82	#388×C₁₃₉	C₂²	1	2	yes	complemented
83	#388×C₁₃₉	C₂²	1	2	yes	complemented
84	#388×C₁₃₉	C₂²	1	2	yes	complemented
85	#388×C₁₃₉	C₂²	1	2	yes	complemented
86	#388×C₁₃₉	C₂²	1	2	yes	complemented
87	#388×C₁₃₉	C₂²	1	2	yes	complemented
88	#388×C₁₃₉	C₂²	1	2	yes	complemented
89	#387×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
90	#387×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
91	#387×C₁₃₉	C₂²	1	2	yes	complemented
92	#387×C₁₃₉	C₂²	1	2	yes	complemented
93	#387×C₁₃₉	C₂²	1	2	yes	complemented
94	#386×C₁₃₉	C₂²	1	1	yes	characteristic
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#386×C₁₃₉	C₂²	1	2	yes	—
97	#386×C₁₃₉	C₂²	1	2	yes	—
98	#386×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	complemented
100	#386×C₁₃₉	C₂²	1	2	yes	complemented
101	#386×C₁₃₉	C₂²	1	2	yes	complemented
102	#385×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
103	#385×C₁₃₉	C₂²	1	2	yes	complemented
104	#385×C₁₃₉	C₂²	1	2	yes	complemented
105	#385×C₁₃₉	C₂²	1	2	yes	complemented
106	#385×C₁₃₉	C₂²	1	2	yes	complemented
107	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
108	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
109	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
110	#381×C₁₃₉	C₂²	1	2	yes	complemented
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
114	#380×C₁₃₉	C₂²	1	2	yes	complemented
115	#380×C₁₃₉	C₂²	1	2	yes	complemented
116	#379×C₁₃₉	C₂²	1	2	yes	—
117	#379×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
123	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
126	C₂×#41×C₁₃₉	—	2	4	no	—
127	C₂×#41×C₁₃₉	—	2	4	no	—
128	C₂×#41×C₁₃₉	D₄	1	8	yes	—
129	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	—	2	4	no	—
131	C₂²×D₄×C₁₃₉	—	2	4	no	—
132	C₂²×D₄×C₁₃₉	—	2	4	no	—
133	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
149	#124×C₁₃₉	—	2	4	no	—
150	#123×C₁₃₉	—	2	8	no	—
151	#123×C₁₃₉	—	2	4	no	—
152	#123×C₁₃₉	—	4	4	no	—
153	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
154	#121×C₁₃₉	—	2	8	no	—
155	#121×C₁₃₉	—	2	4	no	—
156	#120×C₁₃₉	—	2	8	no	—
157	C₄×Q₈×C₁₃₉	—	2	4	no	—
158	C₄×Q₈×C₁₃₉	—	2	4	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	C₄×D₄×C₁₃₉	—	2	4	no	—
161	C₄×D₄×C₁₃₉	—	2	4	no	—
162	C₄×D₄×C₁₃₉	—	2	8	no	—
163	C₄×D₄×C₁₃₉	—	2	8	no	—
164	C₄×D₄×C₁₃₉	—	2	4	no	—
165	C₄×D₄×C₁₃₉	—	2	4	no	—
166	C₄×D₄×C₁₃₉	—	2	4	no	—
167	#117×C₁₃₉	—	2	8	no	—
168	#117×C₁₃₉	—	2	4	no	—
169	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
191	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊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	2	yes	—
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	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₉	—	2	8	no	—
222	C₂×C₄²×C₁₃₉	—	2	4	no	—
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	#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	#95×C₁₃₉	C₂³	1	1	yes	characteristic
238	#95×C₁₃₉	C₂³	1	1	yes	characteristic
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	1	yes	characteristic
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	1	yes	characteristic
249	#95×C₁₃₉	C₂³	1	1	yes	characteristic
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	#95×C₁₃₉	C₂³	1	1	yes	characteristic
253	#95×C₁₃₉	C₂³	1	1	yes	characteristic
254	#95×C₁₃₉	C₂³	1	1	yes	characteristic
255	#95×C₁₃₉	C₂³	1	1	yes	characteristic
256	C₂⁴×C₁₃₉	—	2	4	no	—
257	C₂⁴×C₁₃₉	—	2	4	no	—
258	C₂⁴×C₁₃₉	—	2	4	no	—
259	C₂⁴×C₁₃₉	—	2	4	no	—
260	C₂⁴×C₁₃₉	—	4	2	no	—
261	C₂⁴×C₁₃₉	—	4	2	no	—
262	C₂⁴×C₁₃₉	—	4	2	no	—
263	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
267	#41×C₁₃₉	—	2	32	no	—
268	C₂×Q₈×C₁₃₉	—	2	2	no	—
269	C₂×Q₈×C₁₃₉	—	2	2	no	—
270	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
271	C₂×D₄×C₁₃₉	—	2	4	no	—
272	C₂×D₄×C₁₃₉	—	2	4	no	—
273	C₂×D₄×C₁₃₉	—	2	2	no	—
274	C₂×D₄×C₁₃₉	—	2	4	no	—
275	C₂×D₄×C₁₃₉	—	2	2	no	—
276	C₂×D₄×C₁₃₉	—	2	4	no	—
277	C₂×D₄×C₁₃₉	—	2	4	no	—
278	C₂×D₄×C₁₃₉	—	2	4	no	—
279	C₂×D₄×C₁₃₉	—	2	2	no	—
280	C₂×D₄×C₁₃₉	—	2	2	no	—
281	C₂×D₄×C₁₃₉	—	2	2	no	—
282	C₂×D₄×C₁₃₉	—	4	1	no	—
283	C₂×D₄×C₁₃₉	—	4	2	no	—
284	C₂×D₄×C₁₃₉	—	4	2	no	—
285	C₂×D₄×C₁₃₉	—	4	16	no	—
286	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
287	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
288	C₂×D₄×C₁₃₉	#41	1	4	yes	—
289	C₂×D₄×C₁₃₉	#41	1	4	yes	—
290	C₂²×C₄×C₁₃₉	—	2	4	no	—
291	C₂²×C₄×C₁₃₉	—	2	4	no	—
292	C₂²×C₄×C₁₃₉	—	2	2	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	2	2	no	—
295	C₂²×C₄×C₁₃₉	—	2	2	no	—
296	C₂²×C₄×C₁₃₉	—	2	4	no	—
297	C₂²×C₄×C₁₃₉	—	2	4	no	—
298	C₂²×C₄×C₁₃₉	—	2	4	no	—
299	C₂²×C₄×C₁₃₉	—	2	4	no	—
300	C₂²×C₄×C₁₃₉	—	2	4	no	—
301	C₂²×C₄×C₁₃₉	—	2	2	no	—
302	C₂²×C₄×C₁₃₉	—	2	4	no	—
303	C₂²×C₄×C₁₃₉	—	2	4	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	4	no	—
308	C₂²×C₄×C₁₃₉	—	2	2	no	—
309	C₂²×C₄×C₁₃₉	—	4	2	no	—
310	C₂²×C₄×C₁₃₉	—	4	1	no	—
311	C₂²×C₄×C₁₃₉	—	4	2	no	—
312	C₂²×C₄×C₁₃₉	—	4	2	no	—
313	C₂²×C₄×C₁₃₉	—	4	1	no	—
314	C₂²×C₄×C₁₃₉	—	4	2	no	—
315	C₂²×C₄×C₁₃₉	—	4	2	no	—
316	C₂²×C₄×C₁₃₉	—	4	2	no	—
317	C₂²×C₄×C₁₃₉	—	4	2	no	—
318	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
319	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₁₃₉	—	2	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	no	—
342	C₄⋊C₄×C₁₃₉	—	2	2	no	—
343	C₄⋊C₄×C₁₃₉	—	2	2	no	—
344	C₄⋊C₄×C₁₃₉	—	2	2	no	—
345	C₄⋊C₄×C₁₃₉	—	2	4	no	—
346	C₄⋊C₄×C₁₃₉	—	2	2	no	—
347	C₄⋊C₄×C₁₃₉	—	2	2	no	—
348	C₄⋊C₄×C₁₃₉	—	2	2	no	—
349	C₄⋊C₄×C₁₃₉	—	2	2	no	—
350	C₄⋊C₄×C₁₃₉	—	2	2	no	—
351	C₄⋊C₄×C₁₃₉	—	2	4	no	—
352	C₄⋊C₄×C₁₃₉	—	4	2	no	—
353	C₄⋊C₄×C₁₃₉	—	4	2	no	—
354	C₄⋊C₄×C₁₃₉	—	4	1	no	—
355	C₄⋊C₄×C₁₃₉	—	4	2	no	—
356	C₄⋊C₄×C₁₃₉	—	4	2	no	—
357	C₄⋊C₄×C₁₃₉	—	4	2	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
370	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
372	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
373	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
374	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
377	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
378	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
379	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
380	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
381	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
382	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
383	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
384	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
385	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
386	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	complemented
387	C₄²×C₁₃₉	—	2	2	no	—
388	C₄²×C₁₃₉	—	2	4	no	—
389	C₄²×C₁₃₉	—	2	2	no	—
390	C₄²×C₁₃₉	—	2	4	no	—
391	C₄²×C₁₃₉	—	2	4	no	—
392	C₄²×C₁₃₉	—	2	2	no	—
393	C₄²×C₁₃₉	—	2	2	no	—
394	C₄²×C₁₃₉	—	2	2	no	—
395	C₄²×C₁₃₉	—	2	2	no	—
396	C₄²×C₁₃₉	—	2	2	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	2	2	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	2	no	—
401	C₂³×C₁₃₉	—	2	1	no	—
402	C₂³×C₁₃₉	—	2	1	no	—
403	C₂³×C₁₃₉	—	2	1	no	—
404	C₂³×C₁₃₉	—	2	1	no	—
405	C₂³×C₁₃₉	—	2	1	no	—
406	C₂³×C₁₃₉	—	2	1	no	—
407	C₂³×C₁₃₉	—	2	1	no	—
408	C₂³×C₁₃₉	—	2	1	no	—
409	C₂³×C₁₃₉	—	2	1	no	—
410	C₂³×C₁₃₉	—	2	1	no	—
411	C₂³×C₁₃₉	—	2	1	no	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	2	2	no	—
414	C₂³×C₁₃₉	—	2	2	no	—
415	C₂³×C₁₃₉	—	2	2	no	—
416	C₂³×C₁₃₉	—	2	2	no	—
417	C₂³×C₁₃₉	—	2	2	no	—
418	C₂³×C₁₃₉	—	2	2	no	—
419	C₂³×C₁₃₉	—	2	2	no	—
420	C₂³×C₁₃₉	—	4	8	no	—
421	C₂³×C₁₃₉	—	4	8	no	—
422	C₂³×C₁₃₉	—	4	8	no	—
423	C₂³×C₁₃₉	—	4	8	no	—
424	C₂³×C₁₃₉	—	8	4	no	—
425	C₂³×C₁₃₉	—	8	4	no	—
426	C₂³×C₁₃₉	—	8	4	no	—
427	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
428	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
429	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
430	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
431	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
432	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
433	Q₈×C₁₃₉	—	2	8	no	—
434	D₄×C₁₃₉	—	2	16	no	—
435	D₄×C₁₃₉	—	4	4	no	—
436	D₄×C₁₃₉	—	4	8	no	—
437	D₄×C₁₃₉	—	4	4	no	—
438	D₄×C₁₃₉	—	8	4	no	—
439	D₄×C₁₃₉	#123	1	16	yes	complemented
440	C₂×C₄×C₁₃₉	—	2	16	no	—
441	C₂×C₄×C₁₃₉	—	2	1	no	—
442	C₂×C₄×C₁₃₉	—	2	1	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	1	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	2	no	—
448	C₂×C₄×C₁₃₉	—	2	1	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	1	no	—
451	C₂×C₄×C₁₃₉	—	2	8	no	—
452	C₂×C₄×C₁₃₉	—	2	2	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
459	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
465	C₂×C₄×C₁₃₉	—	2	2	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	2	2	no	—
468	C₂×C₄×C₁₃₉	—	2	2	no	—
469	C₂×C₄×C₁₃₉	—	2	1	no	—
470	C₂×C₄×C₁₃₉	—	2	1	no	—
471	C₂×C₄×C₁₃₉	—	2	1	no	—
472	C₂×C₄×C₁₃₉	—	2	2	no	—
473	C₂×C₄×C₁₃₉	—	2	1	no	—
474	C₂×C₄×C₁₃₉	—	2	2	no	—
475	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
480	C₂×C₄×C₁₃₉	—	2	1	no	—
481	C₂×C₄×C₁₃₉	—	2	1	no	—
482	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
488	C₂×C₄×C₁₃₉	—	2	1	no	—
489	C₂×C₄×C₁₃₉	—	2	1	no	—
490	C₂×C₄×C₁₃₉	—	2	2	no	—
491	C₂×C₄×C₁₃₉	—	4	8	no	—
492	C₂×C₄×C₁₃₉	—	4	4	no	—
493	C₂×C₄×C₁₃₉	—	4	8	no	—
494	C₂×C₄×C₁₃₉	—	4	8	no	—
495	C₂×C₄×C₁₃₉	—	4	4	no	—
496	C₂×C₄×C₁₃₉	—	4	4	no	—
497	C₂×C₄×C₁₃₉	—	8	4	no	—
498	C₂×C₄×C₁₃₉	—	8	4	no	—
499	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
501	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
503	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
504	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
505	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
506	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
507	C₂²×C₁₃₉	—	2	4	no	—
508	C₂²×C₁₃₉	—	2	4	no	—
509	C₂²×C₁₃₉	—	2	4	no	—
510	C₂²×C₁₃₉	—	2	4	no	—
511	C₂²×C₁₃₉	—	2	4	no	—
512	C₂²×C₁₃₉	—	2	4	no	—
513	C₂²×C₁₃₉	—	2	2	no	—
514	C₂²×C₁₃₉	—	2	2	no	—
515	C₂²×C₁₃₉	—	2	2	no	—
516	C₂²×C₁₃₉	—	2	2	no	—
517	C₂²×C₁₃₉	—	2	2	no	—
518	C₂²×C₁₃₉	—	2	2	no	—
519	C₂²×C₁₃₉	—	4	1	no	—
520	C₂²×C₁₃₉	—	4	1	no	—
521	C₂²×C₁₃₉	—	4	1	no	—
522	C₂²×C₁₃₉	—	4	1	no	—
523	C₂²×C₁₃₉	—	4	1	no	—
524	C₂²×C₁₃₉	—	4	1	no	—
525	C₂²×C₁₃₉	—	4	1	no	—
526	C₂²×C₁₃₉	—	4	1	no	—
527	C₂²×C₁₃₉	—	4	2	no	—
528	C₂²×C₁₃₉	—	4	2	no	—
529	C₂²×C₁₃₉	—	4	2	no	—
530	C₂²×C₁₃₉	—	4	2	no	—
531	C₂²×C₁₃₉	—	4	2	no	—
532	C₂²×C₁₃₉	—	4	2	no	—
533	C₂²×C₁₃₉	—	4	2	no	—
534	C₂²×C₁₃₉	—	8	16	no	—
535	C₂²×C₁₃₉	C₂×#123	1	8	yes	—
536	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
537	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
538	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
539	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
540	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂²×C₁₃₉	#585	1	1	yes	characteristic
542	C₂²×C₁₃₉	#585	1	1	yes	characteristic
543	C₄×C₁₃₉	—	2	2	no	—
544	C₄×C₁₃₉	—	2	4	no	—
545	C₄×C₁₃₉	—	2	2	no	—
546	C₄×C₁₃₉	—	2	2	no	—
547	C₄×C₁₃₉	—	2	2	no	—
548	C₄×C₁₃₉	—	4	1	no	—
549	C₄×C₁₃₉	—	4	2	no	—
550	C₄×C₁₃₉	—	4	1	no	—
551	C₄×C₁₃₉	—	4	1	no	—
552	C₄×C₁₃₉	—	4	1	no	—
553	C₄×C₁₃₉	—	4	2	no	—
554	C₄×C₁₃₉	—	4	2	no	—
555	C₄×C₁₃₉	—	4	1	no	—
556	C₄×C₁₃₉	—	4	1	no	—
557	C₄×C₁₃₉	—	4	2	no	—
558	C₄×C₁₃₉	—	4	2	no	—
559	C₄×C₁₃₉	—	4	1	no	—
560	C₄×C₁₃₉	—	4	1	no	—
561	C₄×C₁₃₉	C₂×#123	1	4	yes	—
562	C₂×C₁₃₉	—	2	8	no	—
563	C₂×C₁₃₉	—	4	2	no	—
564	C₂×C₁₃₉	—	4	2	no	—
565	C₂×C₁₃₉	—	8	2	no	—
566	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
567	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
568	C₂×C₁₃₉	#3475	1	1	yes	characteristic
569	C₂×C₁₃₉	#3481	1	1	yes	characteristic
570	C₂×C₁₃₉	#3488	1	1	yes	characteristic
571	C₂×C₁₃₉	#3514	1	1	yes	characteristic
572	C₂×C₁₃₉	#3521	1	1	yes	characteristic
573	#36216	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
574	C₁₃₉	#36216	1	1	yes	characteristic, direct product factor, Sylow
575	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
578	#2853	C₂×C₁₃₉	1	2	yes	complemented
579	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
580	#2498	C₂×C₁₃₉	1	2	yes	complemented
581	#2485	C₂×C₁₃₉	1	1	yes	characteristic, complemented
582	#2482	C₂×C₁₃₉	1	2	yes	complemented
583	#2448	C₂×C₁₃₉	1	1	yes	characteristic, complemented
584	#2448	C₂×C₁₃₉	1	1	yes	characteristic, complemented
585	#2444	C₂×C₁₃₉	1	2	yes	complemented
586	#2443	C₂×C₁₃₉	1	2	yes	complemented
587	#2423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
588	#2421	C₂×C₁₃₉	1	1	yes	characteristic, complemented
589	#2418	C₂×C₁₃₉	1	2	yes	complemented
590	#2418	C₂×C₁₃₉	1	2	yes	complemented
591	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
592	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
593	#2339	C₂×C₁₃₉	1	1	yes	characteristic, complemented
594	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
595	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
596	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
597	C₂×#388	C₂×C₁₃₉	1	2	yes	complemented
598	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
599	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
600	#546	—	2	8	no	—
601	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
603	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
604	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
605	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
606	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
607	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
608	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
609	C₄×#41	—	2	8	no	—
610	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
611	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
612	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
619	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
620	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
621	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
622	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
623	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
624	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
625	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
626	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
627	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
628	#400	C₂²×C₁₃₉	1	2	yes	complemented
629	#399	C₂²×C₁₃₉	1	2	yes	—
630	#399	C₂²×C₁₃₉	1	2	yes	complemented
631	#399	C₂²×C₁₃₉	1	2	yes	complemented
632	#398	C₂²×C₁₃₉	1	2	yes	complemented
633	#397	C₂²×C₁₃₉	1	2	yes	—
634	#397	C₂²×C₁₃₉	1	2	yes	complemented
635	#397	C₂²×C₁₃₉	1	2	yes	complemented
636	#397	C₂²×C₁₃₉	1	2	yes	complemented
637	#394	C₂²×C₁₃₉	1	2	yes	—
638	#394	C₂²×C₁₃₉	1	2	yes	complemented
639	#394	C₂²×C₁₃₉	1	2	yes	complemented
640	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
641	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
642	#390	C₂²×C₁₃₉	1	1	yes	characteristic
643	#390	C₂²×C₁₃₉	1	1	yes	characteristic
644	#390	C₂²×C₁₃₉	1	1	yes	characteristic
645	#390	C₂²×C₁₃₉	1	1	yes	characteristic
646	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
647	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
648	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
649	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
650	#388	C₂²×C₁₃₉	1	2	yes	—
651	#388	C₂²×C₁₃₉	1	2	yes	—
652	#388	C₂²×C₁₃₉	1	1	yes	characteristic
653	#388	C₂²×C₁₃₉	1	2	yes	—
654	#388	C₂²×C₁₃₉	1	1	yes	characteristic
655	#388	C₂²×C₁₃₉	1	2	yes	complemented
656	#388	C₂²×C₁₃₉	1	2	yes	complemented
657	#388	C₂²×C₁₃₉	1	2	yes	complemented
658	#388	C₂²×C₁₃₉	1	2	yes	complemented
659	#388	C₂²×C₁₃₉	1	2	yes	complemented
660	#388	C₂²×C₁₃₉	1	2	yes	complemented
661	#388	C₂²×C₁₃₉	1	2	yes	complemented
662	#388	C₂²×C₁₃₉	1	2	yes	complemented
663	#387	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
664	#387	C₂²×C₁₃₉	1	2	yes	complemented
665	#387	C₂²×C₁₃₉	1	2	yes	complemented
666	#387	C₂²×C₁₃₉	1	2	yes	complemented
667	#387	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
668	#386	C₂²×C₁₃₉	1	2	yes	—
669	#386	C₂²×C₁₃₉	1	2	yes	—
670	#386	C₂²×C₁₃₉	1	2	yes	—
671	#386	C₂²×C₁₃₉	1	2	yes	—
672	#386	C₂²×C₁₃₉	1	1	yes	characteristic
673	#386	C₂²×C₁₃₉	1	2	yes	complemented
674	#386	C₂²×C₁₃₉	1	2	yes	complemented
675	#386	C₂²×C₁₃₉	1	2	yes	complemented
676	#385	C₂²×C₁₃₉	1	2	yes	complemented
677	#385	C₂²×C₁₃₉	1	2	yes	complemented
678	#385	C₂²×C₁₃₉	1	2	yes	complemented
679	#385	C₂²×C₁₃₉	1	2	yes	complemented
680	#385	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
681	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
682	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
683	#381	C₂²×C₁₃₉	1	2	yes	complemented
684	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
685	#380	C₂²×C₁₃₉	1	1	yes	characteristic
686	#380	C₂²×C₁₃₉	1	1	yes	characteristic
687	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
688	#380	C₂²×C₁₃₉	1	2	yes	complemented
689	#380	C₂²×C₁₃₉	1	2	yes	complemented
690	#379	C₂²×C₁₃₉	1	2	yes	—
691	#379	C₂²×C₁₃₉	1	2	yes	—
692	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
693	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
694	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
695	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
696	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
697	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
698	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
699	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
700	C₂×#41	—	2	4	no	—
701	C₂×#41	—	2	4	no	—
702	C₂×#41	D₄×C₁₃₉	1	8	yes	—
703	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂²×D₄	—	2	4	no	—
705	C₂²×D₄	—	2	4	no	—
706	C₂²×D₄	—	2	4	no	—
707	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
708	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
709	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
711	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
712	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
713	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
714	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
715	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
716	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
723	#124	—	2	4	no	—
724	#123	—	2	8	no	—
725	#123	—	2	4	no	—
726	#123	—	4	4	no	—
727	C₂²⋊Q₈	—	2	4	no	—
728	#121	—	2	8	no	—
729	#121	—	2	4	no	—
730	#120	—	2	8	no	—
731	C₄×Q₈	—	2	4	no	—
732	C₄×Q₈	—	2	4	no	—
733	C₄×D₄	—	2	4	no	—
734	C₄×D₄	—	2	4	no	—
735	C₄×D₄	—	2	4	no	—
736	C₄×D₄	—	2	8	no	—
737	C₄×D₄	—	2	8	no	—
738	C₄×D₄	—	2	4	no	—
739	C₄×D₄	—	2	4	no	—
740	C₄×D₄	—	2	4	no	—
741	#117	—	2	8	no	—
742	#117	—	2	4	no	—
743	C₂×C₄⋊C₄	—	4	4	no	—
744	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
763	C₂×C₂²⋊C₄	—	2	8	no	—
764	C₂×C₂²⋊C₄	—	2	8	no	—
765	C₂×C₂²⋊C₄	—	4	4	no	—
766	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
795	C₂×C₄²	—	2	8	no	—
796	C₂×C₄²	—	2	4	no	—
797	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
799	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
805	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
806	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
807	#95	C₂³×C₁₃₉	1	1	yes	characteristic
808	#95	C₂³×C₁₃₉	1	1	yes	characteristic
809	#95	C₂³×C₁₃₉	1	2	yes	—
810	#95	C₂³×C₁₃₉	1	2	yes	—
811	#95	C₂³×C₁₃₉	1	2	yes	—
812	#95	C₂³×C₁₃₉	1	2	yes	—
813	#95	C₂³×C₁₃₉	1	2	yes	—
814	#95	C₂³×C₁₃₉	1	2	yes	—
815	#95	C₂³×C₁₃₉	1	1	yes	characteristic
816	#95	C₂³×C₁₃₉	1	1	yes	characteristic
817	#95	C₂³×C₁₃₉	1	1	yes	characteristic
818	#95	C₂³×C₁₃₉	1	1	yes	characteristic
819	#95	C₂³×C₁₃₉	1	1	yes	characteristic
820	#95	C₂³×C₁₃₉	1	1	yes	characteristic
821	#95	C₂³×C₁₃₉	1	1	yes	characteristic
822	#95	C₂³×C₁₃₉	1	1	yes	characteristic
823	#95	C₂³×C₁₃₉	1	2	yes	—
824	#95	C₂³×C₁₃₉	1	2	yes	—
825	#95	C₂³×C₁₃₉	1	2	yes	—
826	#95	C₂³×C₁₃₉	1	2	yes	—
827	#95	C₂³×C₁₃₉	1	2	yes	—
828	#95	C₂³×C₁₃₉	1	2	yes	—
829	#95	C₂³×C₁₃₉	1	2	yes	—
830	C₂⁴	—	2	4	no	—
831	C₂⁴	—	2	4	no	—
832	C₂⁴	—	2	4	no	—
833	C₂⁴	—	2	4	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	—	4	2	no	—
837	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
838	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
839	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
840	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
841	#41	—	2	32	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	2	4	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	4	1	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	16	no	—
860	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
861	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
862	C₂×D₄	#41×C₁₃₉	1	4	yes	—
863	C₂×D₄	#41×C₁₃₉	1	4	yes	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	2	4	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	2	4	no	—
872	C₂²×C₄	—	2	4	no	—
873	C₂²×C₄	—	2	4	no	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	4	no	—
877	C₂²×C₄	—	2	4	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	4	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	1	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	1	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	—	4	2	no	—
892	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
893	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
894	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
900	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	4	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	4	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	4	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	1	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	1	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	1	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	complemented
961	C₄²	—	2	2	no	—
962	C₄²	—	2	4	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	4	no	—
965	C₄²	—	2	4	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	4	8	no	—
995	C₂³	—	4	8	no	—
996	C₂³	—	4	8	no	—
997	C₂³	—	4	8	no	—
998	C₂³	—	8	4	no	—
999	C₂³	—	8	4	no	—
1000	C₂³	—	8	4	no	—
1001	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1002	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
1003	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1004	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
1005	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
1006	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1007	Q₈	—	2	8	no	—
1008	D₄	—	2	16	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	4	8	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	8	4	no	—
1013	D₄	#123×C₁₃₉	1	16	yes	complemented
1014	C₂×C₄	—	2	16	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	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	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	4	8	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	8	no	—
1068	C₂×C₄	—	4	8	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	8	4	no	—
1072	C₂×C₄	—	8	4	no	—
1073	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1075	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1076	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1077	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1078	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1079	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1080	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1081	C₂²	—	2	4	no	—
1082	C₂²	—	2	4	no	—
1083	C₂²	—	2	4	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	4	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	8	16	no	—
1109	C₂²	C₂×#123×C₁₃₉	1	8	yes	—
1110	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1111	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1112	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1113	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1114	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1115	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1116	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1117	C₄	—	2	2	no	—
1118	C₄	—	2	4	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	C₂×#123×C₁₃₉	1	4	yes	—
1136	C₂	—	2	8	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	2	no	—
1140	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
1141	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1142	C₂	#3475×C₁₃₉	1	1	yes	characteristic
1143	C₂	#3481×C₁₃₉	1	1	yes	characteristic
1144	C₂	#3488×C₁₃₉	1	1	yes	characteristic
1145	C₂	#3514×C₁₃₉	1	1	yes	characteristic
1146	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#546×C₁₃₉	C₂
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
2. C₂×C₄×#41×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2853×C₁₃₉	C₂	semidirect
5. #2500×C₁₃₉	C₂	semidirect
6. #2498×C₁₃₉	C₂	semidirect
7. #2485×C₁₃₉	C₂	semidirect
8. #2482×C₁₃₉	C₂	semidirect
9. #2448×C₁₃₉	C₂	semidirect
10. #2448×C₁₃₉	C₂	semidirect
11. #2444×C₁₃₉	C₂	semidirect
12. #2443×C₁₃₉	C₂	semidirect
13. #2423×C₁₃₉	C₂	semidirect
14. #2421×C₁₃₉	C₂	semidirect
15. #2418×C₁₃₉	C₂	semidirect
16. #2418×C₁₃₉	C₂	semidirect
17. #2349×C₁₃₉	C₂	semidirect
18. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
19. #2339×C₁₃₉	C₂	semidirect
20. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
21. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
22. C₄×#123×C₁₃₉	C₂	semidirect
23. C₂×#388×C₁₃₉	C₂	semidirect
30. C₂×#123×C₁₃₉	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
37. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
46. C₂×#117×C₁₃₉	C₂²	semidirect
47. C₂×#117×C₁₃₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
52. C₂²×C₄²×C₁₃₉	C₂²	semidirect
53. C₂²×C₄²×C₁₃₉	C₂²	semidirect
54. #400×C₁₃₉	C₂²	semidirect
56. #399×C₁₃₉	C₂²	semidirect
57. #399×C₁₃₉	C₂²	semidirect
58. #398×C₁₃₉	C₂²	semidirect
60. #397×C₁₃₉	C₂²	semidirect
61. #397×C₁₃₉	C₂²	semidirect
62. #397×C₁₃₉	C₂²	semidirect
64. #394×C₁₃₉	C₂²	semidirect
65. #394×C₁₃₉	C₂²	semidirect
66. #391×C₁₃₉	C₂²	semidirect
67. #391×C₁₃₉	C₂²	semidirect
72. #389×C₁₃₉	C₂²	semidirect
73. #389×C₁₃₉	C₂²	semidirect
74. #389×C₁₃₉	C₂²	semidirect
75. #389×C₁₃₉	C₂²	semidirect
81. #388×C₁₃₉	C₂²	semidirect
82. #388×C₁₃₉	C₂²	semidirect
83. #388×C₁₃₉	C₂²	semidirect
84. #388×C₁₃₉	C₂²	semidirect
85. #388×C₁₃₉	C₂²	semidirect
86. #388×C₁₃₉	C₂²	semidirect
87. #388×C₁₃₉	C₂²	semidirect
88. #388×C₁₃₉	C₂²	semidirect
89. #387×C₁₃₉	C₂²	semidirect
90. #387×C₁₃₉	C₂²	semidirect
91. #387×C₁₃₉	C₂²	semidirect
92. #387×C₁₃₉	C₂²	semidirect
93. #387×C₁₃₉	C₂²	semidirect
99. #386×C₁₃₉	C₂²	semidirect
100. #386×C₁₃₉	C₂²	semidirect
101. #386×C₁₃₉	C₂²	semidirect
102. #385×C₁₃₉	C₂²	semidirect
103. #385×C₁₃₉	C₂²	semidirect
104. #385×C₁₃₉	C₂²	semidirect
105. #385×C₁₃₉	C₂²	semidirect
106. #385×C₁₃₉	C₂²	semidirect
107. #384×C₁₃₉	C₂²	semidirect
108. #382×C₁₃₉	C₂²	semidirect
109. #381×C₁₃₉	C₂²	semidirect
110. #381×C₁₃₉	C₂²	semidirect
113. #380×C₁₃₉	C₂²	semidirect
114. #380×C₁₃₉	C₂²	semidirect
115. #380×C₁₃₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. C₂×#95×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
386. C₂²⋊C₄×C₁₃₉	#41	semidirect
439. D₄×C₁₃₉	#123	semidirect
573. #36216	C₁₃₉	direct (N × H)
574. C₁₃₉	#36216	direct (N × H)
576. C₂×C₄×#41	C₂×C₁₃₉	semidirect
577. #2854	C₂×C₁₃₉	semidirect
578. #2853	C₂×C₁₃₉	semidirect
579. #2500	C₂×C₁₃₉	semidirect
580. #2498	C₂×C₁₃₉	semidirect
581. #2485	C₂×C₁₃₉	semidirect
582. #2482	C₂×C₁₃₉	semidirect
583. #2448	C₂×C₁₃₉	semidirect
584. #2448	C₂×C₁₃₉	semidirect
585. #2444	C₂×C₁₃₉	semidirect
586. #2443	C₂×C₁₃₉	semidirect
587. #2423	C₂×C₁₃₉	semidirect
588. #2421	C₂×C₁₃₉	semidirect
589. #2418	C₂×C₁₃₉	semidirect
590. #2418	C₂×C₁₃₉	semidirect
591. #2349	C₂×C₁₃₉	semidirect
592. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
593. #2339	C₂×C₁₃₉	semidirect
594. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
595. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
596. C₄×#123	C₂×C₁₃₉	semidirect
597. C₂×#388	C₂×C₁₃₉	semidirect
604. C₂×#123	C₂²×C₁₃₉	semidirect
610. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
611. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
618. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
619. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
620. C₂×#117	C₂²×C₁₃₉	semidirect
621. C₂×#117	C₂²×C₁₃₉	semidirect
622. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
626. C₂²×C₄²	C₂²×C₁₃₉	semidirect
627. C₂²×C₄²	C₂²×C₁₃₉	semidirect
628. #400	C₂²×C₁₃₉	semidirect
630. #399	C₂²×C₁₃₉	semidirect
631. #399	C₂²×C₁₃₉	semidirect
632. #398	C₂²×C₁₃₉	semidirect
634. #397	C₂²×C₁₃₉	semidirect
635. #397	C₂²×C₁₃₉	semidirect
636. #397	C₂²×C₁₃₉	semidirect
638. #394	C₂²×C₁₃₉	semidirect
639. #394	C₂²×C₁₃₉	semidirect
640. #391	C₂²×C₁₃₉	semidirect
641. #391	C₂²×C₁₃₉	semidirect
646. #389	C₂²×C₁₃₉	semidirect
647. #389	C₂²×C₁₃₉	semidirect
648. #389	C₂²×C₁₃₉	semidirect
649. #389	C₂²×C₁₃₉	semidirect
655. #388	C₂²×C₁₃₉	semidirect
656. #388	C₂²×C₁₃₉	semidirect
657. #388	C₂²×C₁₃₉	semidirect
658. #388	C₂²×C₁₃₉	semidirect
659. #388	C₂²×C₁₃₉	semidirect
660. #388	C₂²×C₁₃₉	semidirect
661. #388	C₂²×C₁₃₉	semidirect
662. #388	C₂²×C₁₃₉	semidirect
663. #387	C₂²×C₁₃₉	semidirect
664. #387	C₂²×C₁₃₉	semidirect
665. #387	C₂²×C₁₃₉	semidirect
666. #387	C₂²×C₁₃₉	semidirect
667. #387	C₂²×C₁₃₉	semidirect
673. #386	C₂²×C₁₃₉	semidirect
674. #386	C₂²×C₁₃₉	semidirect
675. #386	C₂²×C₁₃₉	semidirect
676. #385	C₂²×C₁₃₉	semidirect
677. #385	C₂²×C₁₃₉	semidirect
678. #385	C₂²×C₁₃₉	semidirect
679. #385	C₂²×C₁₃₉	semidirect
680. #385	C₂²×C₁₃₉	semidirect
681. #384	C₂²×C₁₃₉	semidirect
682. #382	C₂²×C₁₃₉	semidirect
683. #381	C₂²×C₁₃₉	semidirect
684. #381	C₂²×C₁₃₉	semidirect
687. #380	C₂²×C₁₃₉	semidirect
688. #380	C₂²×C₁₃₉	semidirect
689. #380	C₂²×C₁₃₉	semidirect
692. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
693. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
696. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
697. C₂×#95	C₂²×C₁₃₉	semidirect
698. C₂×#95	C₂²×C₁₃₉	semidirect
960. C₂²⋊C₄	#41×C₁₃₉	semidirect
1013. D₄	#123×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2854×C₁₃₉	2
#2853×C₁₃₉	2
#2500×C₁₃₉	2
#2498×C₁₃₉	2
#2485×C₁₃₉	2
#2482×C₁₃₉	2
#2448×C₁₃₉	2
#2444×C₁₃₉	2
#2443×C₁₃₉	2
#2423×C₁₃₉	2
#2421×C₁₃₉	2
#2418×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2339×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₂×#388×C₁₃₉	2
#36216	139

Subgroups — C139×#36216 #48030812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36216 #48030812