Subgroups — C₁₃₉×#35741 #48030337

Order 35584.

3074 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2635×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2619×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2539×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2464×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2433×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2424×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2404×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2396×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2388×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2366×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	#550×C₁₃₉	—	2	8	no	—
21	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
28	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
29	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
30	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
31	#518×C₁₃₉	—	2	8	no	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
41	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
45	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	#399×C₁₃₉	C₂²	1	1	yes	characteristic
47	#399×C₁₃₉	C₂²	1	2	yes	complemented
48	#398×C₁₃₉	C₂²	1	2	yes	complemented
49	#396×C₁₃₉	C₂²	1	2	yes	—
50	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	#394×C₁₃₉	C₂²	1	2	yes	complemented
52	#394×C₁₃₉	C₂²	1	2	yes	complemented
53	#394×C₁₃₉	C₂²	1	4	yes	complemented
54	#394×C₁₃₉	C₂²	1	4	yes	complemented
55	#393×C₁₃₉	C₂²	1	1	yes	characteristic
56	#393×C₁₃₉	C₂²	1	2	yes	complemented
57	#392×C₁₃₉	C₂²	1	2	yes	—
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	4	yes	—
60	#392×C₁₃₉	C₂²	1	4	yes	—
61	#392×C₁₃₉	C₂²	1	2	yes	complemented
62	#392×C₁₃₉	C₂²	1	2	yes	complemented
63	#390×C₁₃₉	C₂²	1	4	yes	—
64	#390×C₁₃₉	C₂²	1	2	yes	—
65	#390×C₁₃₉	C₂²	1	2	yes	—
66	#390×C₁₃₉	C₂²	1	4	yes	complemented
67	#390×C₁₃₉	C₂²	1	2	yes	complemented
68	#390×C₁₃₉	C₂²	1	2	yes	complemented
69	#389×C₁₃₉	C₂²	1	2	yes	complemented
70	#388×C₁₃₉	C₂²	1	4	yes	complemented
71	#388×C₁₃₉	C₂²	1	4	yes	complemented
72	#386×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	complemented
74	#386×C₁₃₉	C₂²	1	4	yes	complemented
75	#386×C₁₃₉	C₂²	1	4	yes	complemented
76	#385×C₁₃₉	C₂²	1	4	yes	complemented
77	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
78	#381×C₁₃₉	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂×#41×C₁₃₉	—	4	8	no	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	—	2	4	no	—
91	C₂²×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	#127×C₁₃₉	—	2	8	no	—
110	#127×C₁₃₉	—	2	8	no	—
111	#127×C₁₃₉	—	2	4	no	—
112	#123×C₁₃₉	—	4	8	no	—
113	#121×C₁₃₉	—	2	8	no	—
114	#121×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	16	no	—
116	#121×C₁₃₉	—	4	8	no	—
117	#120×C₁₃₉	—	4	8	no	—
118	#120×C₁₃₉	—	4	8	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	4	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	4	no	—
123	C₄×D₄×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	8	no	—
125	C₄×D₄×C₁₃₉	—	2	4	no	—
126	C₄×D₄×C₁₃₉	—	4	8	no	—
127	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
128	#117×C₁₃₉	—	2	4	no	—
129	#117×C₁₃₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
142	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	1	yes	characteristic
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	C₂⁴×C₁₃₉	—	2	4	no	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	—	2	4	no	—
181	C₂⁴×C₁₃₉	—	4	4	no	—
182	C₂⁴×C₁₃₉	—	4	4	no	—
183	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
184	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
186	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
187	#41×C₁₃₉	—	4	32	no	—
188	C₂×Q₈×C₁₃₉	—	2	2	no	—
189	C₂×Q₈×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	32	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	8	no	—
195	C₂×D₄×C₁₃₉	—	2	8	no	—
196	C₂×D₄×C₁₃₉	—	2	8	no	—
197	C₂×D₄×C₁₃₉	—	2	8	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	2	4	no	—
202	C₂×D₄×C₁₃₉	—	2	4	no	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	2	2	no	—
205	C₂×D₄×C₁₃₉	—	2	2	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	4	no	—
208	C₂×D₄×C₁₃₉	—	2	8	no	—
209	C₂×D₄×C₁₃₉	—	2	8	no	—
210	C₂×D₄×C₁₃₉	—	4	4	no	—
211	C₂×D₄×C₁₃₉	—	4	4	no	—
212	C₂×D₄×C₁₃₉	—	4	4	no	—
213	C₂×D₄×C₁₃₉	—	4	4	no	—
214	C₂×D₄×C₁₃₉	—	4	4	no	—
215	C₂×D₄×C₁₃₉	—	4	4	no	—
216	C₂×D₄×C₁₃₉	—	4	4	no	—
217	C₂×D₄×C₁₃₉	—	4	4	no	—
218	C₂×D₄×C₁₃₉	—	4	4	no	—
219	C₂×D₄×C₁₃₉	—	4	4	no	—
220	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	8	no	—
226	C₂²×C₄×C₁₃₉	—	2	8	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	4	4	no	—
230	C₂²×C₄×C₁₃₉	—	4	4	no	—
231	C₂²×C₄×C₁₃₉	—	4	4	no	—
232	C₂²×C₄×C₁₃₉	—	4	4	no	—
233	C₂²×C₄×C₁₃₉	—	4	4	no	—
234	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
235	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₁₃₉	—	2	2	no	—
250	C₄⋊C₄×C₁₃₉	—	2	2	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	4	4	no	—
259	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
278	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	2	4	no	—
283	C₄²×C₁₃₉	—	4	4	no	—
284	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
285	C₂³×C₁₃₉	—	2	16	no	—
286	C₂³×C₁₃₉	—	2	1	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	—	2	4	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	4	no	—
297	C₂³×C₁₃₉	—	2	4	no	—
298	C₂³×C₁₃₉	—	2	4	no	—
299	C₂³×C₁₃₉	—	2	4	no	—
300	C₂³×C₁₃₉	—	2	4	no	—
301	C₂³×C₁₃₉	—	2	4	no	—
302	C₂³×C₁₃₉	—	2	4	no	—
303	C₂³×C₁₃₉	—	2	4	no	—
304	C₂³×C₁₃₉	—	2	4	no	—
305	C₂³×C₁₃₉	—	8	4	no	—
306	C₂³×C₁₃₉	—	8	4	no	—
307	C₂³×C₁₃₉	—	8	8	no	—
308	C₂³×C₁₃₉	—	8	8	no	—
309	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
310	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
311	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
312	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
313	Q₈×C₁₃₉	—	2	8	no	—
314	D₄×C₁₃₉	—	2	16	no	—
315	D₄×C₁₃₉	—	2	8	no	—
316	D₄×C₁₃₉	—	2	8	no	—
317	D₄×C₁₃₉	—	4	16	no	—
318	D₄×C₁₃₉	—	4	16	no	—
319	D₄×C₁₃₉	—	4	8	no	—
320	D₄×C₁₃₉	—	4	8	no	—
321	D₄×C₁₃₉	—	8	4	no	—
322	D₄×C₁₃₉	—	8	8	no	—
323	D₄×C₁₃₉	—	8	8	no	—
324	D₄×C₁₃₉	—	8	8	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	4	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	8	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	4	no	—
341	C₂×C₄×C₁₃₉	—	2	4	no	—
342	C₂×C₄×C₁₃₉	—	2	4	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	4	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	4	8	no	—
351	C₂×C₄×C₁₃₉	—	4	16	no	—
352	C₂×C₄×C₁₃₉	—	8	4	no	—
353	C₂×C₄×C₁₃₉	—	8	4	no	—
354	C₂×C₄×C₁₃₉	—	8	4	no	—
355	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
360	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
361	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
363	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
364	C₂²×C₁₃₉	—	2	2	no	—
365	C₂²×C₁₃₉	—	2	4	no	—
366	C₂²×C₁₃₉	—	2	4	no	—
367	C₂²×C₁₃₉	—	2	4	no	—
368	C₂²×C₁₃₉	—	2	4	no	—
369	C₂²×C₁₃₉	—	2	4	no	—
370	C₂²×C₁₃₉	—	2	8	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	1	no	—
373	C₂²×C₁₃₉	—	4	2	no	—
374	C₂²×C₁₃₉	—	4	1	no	—
375	C₂²×C₁₃₉	—	4	4	no	—
376	C₂²×C₁₃₉	—	4	4	no	—
377	C₂²×C₁₃₉	—	4	4	no	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	4	no	—
380	C₂²×C₁₃₉	—	4	4	no	—
381	C₂²×C₁₃₉	—	4	4	no	—
382	C₂²×C₁₃₉	—	4	4	no	—
383	C₂²×C₁₃₉	—	4	4	no	—
384	C₂²×C₁₃₉	—	4	4	no	—
385	C₂²×C₁₃₉	—	4	4	no	—
386	C₂²×C₁₃₉	—	8	16	no	—
387	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
388	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
389	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
391	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
392	C₄×C₁₃₉	—	2	2	no	—
393	C₄×C₁₃₉	—	2	4	no	—
394	C₄×C₁₃₉	—	2	2	no	—
395	C₄×C₁₃₉	—	2	4	no	—
396	C₄×C₁₃₉	—	2	2	no	—
397	C₄×C₁₃₉	—	2	4	no	—
398	C₄×C₁₃₉	—	4	1	no	—
399	C₄×C₁₃₉	—	4	2	no	—
400	C₄×C₁₃₉	—	4	1	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	4	no	—
403	C₄×C₁₃₉	—	4	2	no	—
404	C₄×C₁₃₉	#525	1	4	yes	—
405	C₂×C₁₃₉	—	4	4	no	—
406	C₂×C₁₃₉	—	4	4	no	—
407	C₂×C₁₃₉	—	4	2	no	—
408	C₂×C₁₃₉	—	8	4	no	—
409	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
410	C₂×C₁₃₉	#3484	1	1	yes	characteristic
411	C₂×C₁₃₉	#3498	1	1	yes	characteristic
412	C₂×C₁₃₉	#3508	1	2	yes	—
413	C₂×C₁₃₉	#3519	1	2	yes	—
414	#35741	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₁₃₉	#35741	1	1	yes	characteristic, direct product factor, Sylow
416	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	#2635	C₂×C₁₃₉	1	2	yes	complemented
419	#2619	C₂×C₁₃₉	1	1	yes	characteristic, complemented
420	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
421	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	#2539	C₂×C₁₃₉	1	2	yes	complemented
423	#2464	C₂×C₁₃₉	1	4	yes	complemented
424	#2445	C₂×C₁₃₉	1	2	yes	complemented
425	#2433	C₂×C₁₃₉	1	2	yes	complemented
426	#2424	C₂×C₁₃₉	1	4	yes	complemented
427	#2404	C₂×C₁₃₉	1	2	yes	complemented
428	#2396	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2388	C₂×C₁₃₉	1	2	yes	complemented
430	#2366	C₂×C₁₃₉	1	2	yes	complemented
431	#2363	C₂×C₁₃₉	1	2	yes	complemented
432	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
434	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
435	#550	—	2	8	no	—
436	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
437	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
438	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
439	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
440	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
441	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
442	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
443	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
444	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
445	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
446	#518	—	2	8	no	—
447	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
448	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
451	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
453	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
455	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
456	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
459	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
460	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
461	#399	C₂²×C₁₃₉	1	1	yes	characteristic
462	#399	C₂²×C₁₃₉	1	2	yes	complemented
463	#398	C₂²×C₁₃₉	1	2	yes	complemented
464	#396	C₂²×C₁₃₉	1	2	yes	—
465	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
466	#394	C₂²×C₁₃₉	1	2	yes	complemented
467	#394	C₂²×C₁₃₉	1	2	yes	complemented
468	#394	C₂²×C₁₃₉	1	4	yes	complemented
469	#394	C₂²×C₁₃₉	1	4	yes	complemented
470	#393	C₂²×C₁₃₉	1	1	yes	characteristic
471	#393	C₂²×C₁₃₉	1	2	yes	complemented
472	#392	C₂²×C₁₃₉	1	2	yes	—
473	#392	C₂²×C₁₃₉	1	2	yes	—
474	#392	C₂²×C₁₃₉	1	4	yes	—
475	#392	C₂²×C₁₃₉	1	4	yes	—
476	#392	C₂²×C₁₃₉	1	2	yes	complemented
477	#392	C₂²×C₁₃₉	1	2	yes	complemented
478	#390	C₂²×C₁₃₉	1	2	yes	—
479	#390	C₂²×C₁₃₉	1	2	yes	—
480	#390	C₂²×C₁₃₉	1	4	yes	—
481	#390	C₂²×C₁₃₉	1	2	yes	complemented
482	#390	C₂²×C₁₃₉	1	2	yes	complemented
483	#390	C₂²×C₁₃₉	1	4	yes	complemented
484	#389	C₂²×C₁₃₉	1	2	yes	complemented
485	#388	C₂²×C₁₃₉	1	4	yes	complemented
486	#388	C₂²×C₁₃₉	1	4	yes	complemented
487	#386	C₂²×C₁₃₉	1	4	yes	—
488	#386	C₂²×C₁₃₉	1	4	yes	complemented
489	#386	C₂²×C₁₃₉	1	4	yes	complemented
490	#386	C₂²×C₁₃₉	1	4	yes	complemented
491	#385	C₂²×C₁₃₉	1	4	yes	complemented
492	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
493	#381	C₂²×C₁₃₉	1	2	yes	complemented
494	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
495	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
496	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
497	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
499	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
500	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
501	C₂×#41	—	2	8	no	—
502	C₂×#41	—	4	8	no	—
503	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
524	#127	—	2	8	no	—
525	#127	—	2	8	no	—
526	#127	—	2	4	no	—
527	#123	—	4	8	no	—
528	#121	—	2	8	no	—
529	#121	—	2	8	no	—
530	#121	—	2	16	no	—
531	#121	—	4	8	no	—
532	#120	—	4	8	no	—
533	#120	—	4	8	no	—
534	C₄×Q₈	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	8	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	8	no	—
539	C₄×D₄	—	2	8	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	—	4	8	no	—
542	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
543	#117	—	2	4	no	—
544	#117	—	2	4	no	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	—	2	8	no	—
557	C₂×C₂²⋊C₄	—	2	8	no	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
582	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	1	yes	characteristic
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	4	yes	—
588	#95	C₂³×C₁₃₉	1	1	yes	characteristic
589	#95	C₂³×C₁₃₉	1	4	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	C₂⁴	—	2	4	no	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	4	4	no	—
597	C₂⁴	—	4	4	no	—
598	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
599	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
602	#41	—	4	32	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	4	no	—
605	C₂×D₄	—	2	32	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	8	no	—
609	C₂×D₄	—	2	8	no	—
610	C₂×D₄	—	2	8	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	8	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
636	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	4	no	—
648	C₂²×C₄	—	4	4	no	—
649	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
650	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
651	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	4	4	no	—
674	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	8	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	4	4	no	—
691	C₂²⋊C₄	—	4	4	no	—
692	C₂²⋊C₄	—	4	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	—	2	4	no	—
698	C₄²	—	4	4	no	—
699	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
700	C₂³	—	2	16	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	4	no	—
719	C₂³	—	2	4	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	4	no	—
722	C₂³	—	8	8	no	—
723	C₂³	—	8	8	no	—
724	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
725	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
726	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
727	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
728	Q₈	—	2	8	no	—
729	D₄	—	2	16	no	—
730	D₄	—	2	8	no	—
731	D₄	—	2	8	no	—
732	D₄	—	4	16	no	—
733	D₄	—	4	16	no	—
734	D₄	—	4	8	no	—
735	D₄	—	4	8	no	—
736	D₄	—	8	4	no	—
737	D₄	—	8	8	no	—
738	D₄	—	8	8	no	—
739	D₄	—	8	8	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	8	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	4	8	no	—
766	C₂×C₄	—	4	16	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	—	8	4	no	—
770	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
771	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
774	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
775	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
776	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
777	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
778	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	8	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	4	4	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	8	16	no	—
802	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
803	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
804	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
805	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
806	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
807	C₄	—	2	2	no	—
808	C₄	—	2	4	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	4	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	4	no	—
818	C₄	—	4	2	no	—
819	C₄	#525×C₁₃₉	1	4	yes	—
820	C₂	—	4	2	no	—
821	C₂	—	4	4	no	—
822	C₂	—	4	4	no	—
823	C₂	—	8	4	no	—
824	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
825	C₂	#3484×C₁₃₉	1	1	yes	characteristic
826	C₂	#3498×C₁₃₉	1	1	yes	characteristic
827	C₂	#3508×C₁₃₉	1	2	yes	—
828	C₂	#3519×C₁₃₉	1	2	yes	—

	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×#550×C₁₃₉	C₂	semidirect
2. C₂×#518×C₁₃₉	C₂	semidirect
3. #2635×C₁₃₉	C₂	semidirect
4. #2619×C₁₃₉	C₂	semidirect
5. #2580×C₁₃₉	C₂	semidirect
6. #2541×C₁₃₉	C₂	semidirect
7. #2539×C₁₃₉	C₂	semidirect
8. #2464×C₁₃₉	C₂	semidirect
9. #2445×C₁₃₉	C₂	semidirect
10. #2433×C₁₃₉	C₂	semidirect
11. #2424×C₁₃₉	C₂	semidirect
12. #2404×C₁₃₉	C₂	semidirect
13. #2396×C₁₃₉	C₂	semidirect
14. #2388×C₁₃₉	C₂	semidirect
15. #2366×C₁₃₉	C₂	semidirect
16. #2363×C₁₃₉	C₂	semidirect
17. #2357×C₁₃₉	C₂	semidirect
18. C₂²×#41×C₁₃₉	C₂²	semidirect
23. C₂×#127×C₁₃₉	C₂²	semidirect
24. C₂×#123×C₁₃₉	C₂²	semidirect
26. C₂×#121×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
28. C₂×#121×C₁₃₉	C₂²	semidirect
32. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
40. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
45. #400×C₁₃₉	C₂²	semidirect
47. #399×C₁₃₉	C₂²	semidirect
48. #398×C₁₃₉	C₂²	semidirect
50. #395×C₁₃₉	C₂²	semidirect
51. #394×C₁₃₉	C₂²	semidirect
52. #394×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
56. #393×C₁₃₉	C₂²	semidirect
61. #392×C₁₃₉	C₂²	semidirect
62. #392×C₁₃₉	C₂²	semidirect
66. #390×C₁₃₉	C₂²	semidirect
67. #390×C₁₃₉	C₂²	semidirect
68. #390×C₁₃₉	C₂²	semidirect
69. #389×C₁₃₉	C₂²	semidirect
70. #388×C₁₃₉	C₂²	semidirect
71. #388×C₁₃₉	C₂²	semidirect
73. #386×C₁₃₉	C₂²	semidirect
74. #386×C₁₃₉	C₂²	semidirect
75. #386×C₁₃₉	C₂²	semidirect
76. #385×C₁₃₉	C₂²	semidirect
77. #382×C₁₃₉	C₂²	semidirect
78. #381×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
127. C₄×D₄×C₁₃₉	D₄	semidirect
221. C₂×D₄×C₁₃₉	#41	semidirect
235. C₂²×C₄×C₁₃₉	#41	semidirect
414. #35741	C₁₃₉	direct (N × H)
415. C₁₃₉	#35741	direct (N × H)
416. C₂×#550	C₂×C₁₃₉	semidirect
417. C₂×#518	C₂×C₁₃₉	semidirect
418. #2635	C₂×C₁₃₉	semidirect
419. #2619	C₂×C₁₃₉	semidirect
420. #2580	C₂×C₁₃₉	semidirect
421. #2541	C₂×C₁₃₉	semidirect
422. #2539	C₂×C₁₃₉	semidirect
423. #2464	C₂×C₁₃₉	semidirect
424. #2445	C₂×C₁₃₉	semidirect
425. #2433	C₂×C₁₃₉	semidirect
426. #2424	C₂×C₁₃₉	semidirect
427. #2404	C₂×C₁₃₉	semidirect
428. #2396	C₂×C₁₃₉	semidirect
429. #2388	C₂×C₁₃₉	semidirect
430. #2366	C₂×C₁₃₉	semidirect
431. #2363	C₂×C₁₃₉	semidirect
432. #2357	C₂×C₁₃₉	semidirect
433. C₂²×#41	C₂²×C₁₃₉	semidirect
438. C₂×#127	C₂²×C₁₃₉	semidirect
439. C₂×#123	C₂²×C₁₃₉	semidirect
441. C₂×#121	C₂²×C₁₃₉	semidirect
442. C₂×#121	C₂²×C₁₃₉	semidirect
443. C₂×#121	C₂²×C₁₃₉	semidirect
447. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
454. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
455. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
460. #400	C₂²×C₁₃₉	semidirect
462. #399	C₂²×C₁₃₉	semidirect
463. #398	C₂²×C₁₃₉	semidirect
465. #395	C₂²×C₁₃₉	semidirect
466. #394	C₂²×C₁₃₉	semidirect
467. #394	C₂²×C₁₃₉	semidirect
468. #394	C₂²×C₁₃₉	semidirect
469. #394	C₂²×C₁₃₉	semidirect
471. #393	C₂²×C₁₃₉	semidirect
476. #392	C₂²×C₁₃₉	semidirect
477. #392	C₂²×C₁₃₉	semidirect
481. #390	C₂²×C₁₃₉	semidirect
482. #390	C₂²×C₁₃₉	semidirect
483. #390	C₂²×C₁₃₉	semidirect
484. #389	C₂²×C₁₃₉	semidirect
485. #388	C₂²×C₁₃₉	semidirect
486. #388	C₂²×C₁₃₉	semidirect
488. #386	C₂²×C₁₃₉	semidirect
489. #386	C₂²×C₁₃₉	semidirect
490. #386	C₂²×C₁₃₉	semidirect
491. #385	C₂²×C₁₃₉	semidirect
492. #382	C₂²×C₁₃₉	semidirect
493. #381	C₂²×C₁₃₉	semidirect
494. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
495. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
496. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
498. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
499. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
542. C₄×D₄	D₄×C₁₃₉	semidirect
636. C₂×D₄	#41×C₁₃₉	semidirect
650. 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×#550×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2635×C₁₃₉	2
#2619×C₁₃₉	2
#2580×C₁₃₉	2
#2541×C₁₃₉	2
#2539×C₁₃₉	2
#2464×C₁₃₉	2
#2445×C₁₃₉	2
#2433×C₁₃₉	2
#2424×C₁₃₉	2
#2404×C₁₃₉	2
#2396×C₁₃₉	2
#2388×C₁₃₉	2
#2366×C₁₃₉	2
#2363×C₁₃₉	2
#2357×C₁₃₉	2
#35741	139

Subgroups — C139×#35741 #48030337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35741 #48030337