Subgroups — C₁₃₉×#36020 #48030616

Order 35584.

3002 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2621×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2618×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2543×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2536×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2486×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2429×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2425×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2413×C₁₃₉	C₂	1	4	yes	maximal, complemented
14	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#398×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2339×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
20	#547×C₁₃₉	—	2	16	no	—
21	#547×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
32	#520×C₁₃₉	—	2	8	no	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	#398×C₁₃₉	C₂²	1	2	yes	—
49	#398×C₁₃₉	C₂²	1	2	yes	—
50	#398×C₁₃₉	C₂²	1	2	yes	—
51	#398×C₁₃₉	C₂²	1	2	yes	—
52	#398×C₁₃₉	C₂²	1	2	yes	—
53	#398×C₁₃₉	C₂²	1	1	yes	characteristic
54	#398×C₁₃₉	C₂²	1	4	yes	—
55	#398×C₁₃₉	C₂²	1	4	yes	—
56	#397×C₁₃₉	C₂²	1	2	yes	—
57	#397×C₁₃₉	C₂²	1	2	yes	—
58	#397×C₁₃₉	C₂²	1	1	yes	characteristic
59	#396×C₁₃₉	C₂²	1	4	yes	—
60	#396×C₁₃₉	C₂²	1	4	yes	—
61	#396×C₁₃₉	C₂²	1	2	yes	—
62	#394×C₁₃₉	C₂²	1	2	yes	—
63	#394×C₁₃₉	C₂²	1	1	yes	characteristic
64	#394×C₁₃₉	C₂²	1	2	yes	—
65	#392×C₁₃₉	C₂²	1	1	yes	characteristic
66	#391×C₁₃₉	C₂²	1	2	yes	—
67	#391×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	4	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	4	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#388×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#386×C₁₃₉	C₂²	1	4	yes	—
75	#386×C₁₃₉	C₂²	1	4	yes	—
76	#385×C₁₃₉	C₂²	1	4	yes	—
77	#382×C₁₃₉	C₂²	1	1	yes	characteristic
78	#381×C₁₃₉	C₂²	1	4	yes	—
79	#380×C₁₃₉	C₂²	1	2	yes	—
80	#380×C₁₃₉	C₂²	1	2	yes	—
81	#380×C₁₃₉	C₂²	1	4	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
85	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
86	C₂×#41×C₁₃₉	—	2	4	no	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂×#41×C₁₃₉	—	2	8	no	—
89	C₂×#41×C₁₃₉	—	2	4	no	—
90	C₂×#41×C₁₃₉	—	2	8	no	—
91	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
92	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
108	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
109	#123×C₁₃₉	—	2	16	no	—
110	#123×C₁₃₉	—	2	16	no	—
111	#123×C₁₃₉	—	2	16	no	—
112	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
113	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
114	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	16	no	—
116	#121×C₁₃₉	—	2	8	no	—
117	C₄×Q₈×C₁₃₉	—	2	4	no	—
118	C₄×Q₈×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
126	#117×C₁₃₉	—	2	8	no	—
127	#117×C₁₃₉	—	2	4	no	—
128	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
129	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
130	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
131	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	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	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	1	yes	characteristic
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
185	#41×C₁₃₉	—	2	32	no	—
186	#41×C₁₃₉	—	4	32	no	—
187	C₂×Q₈×C₁₃₉	—	2	2	no	—
188	C₂×Q₈×C₁₃₉	—	2	4	no	—
189	C₂×Q₈×C₁₃₉	—	2	4	no	—
190	C₂×Q₈×C₁₃₉	—	2	2	no	—
191	C₂×Q₈×C₁₃₉	—	2	4	no	—
192	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
193	C₂×D₄×C₁₃₉	—	2	4	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	8	no	—
197	C₂×D₄×C₁₃₉	—	2	8	no	—
198	C₂×D₄×C₁₃₉	—	2	8	no	—
199	C₂×D₄×C₁₃₉	—	2	2	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	4	2	no	—
202	C₂×D₄×C₁₃₉	—	4	2	no	—
203	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
204	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
205	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
206	C₂×D₄×C₁₃₉	#41	1	4	yes	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	8	no	—
212	C₂²×C₄×C₁₃₉	—	2	8	no	—
213	C₂²×C₄×C₁₃₉	—	2	8	no	—
214	C₂²×C₄×C₁₃₉	—	2	8	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	8	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	4	4	no	—
222	C₂²×C₄×C₁₃₉	—	4	4	no	—
223	C₂²×C₄×C₁₃₉	—	4	4	no	—
224	C₂²×C₄×C₁₃₉	—	4	4	no	—
225	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
226	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	2	no	—
249	C₄⋊C₄×C₁₃₉	—	2	8	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	8	no	—
252	C₄⋊C₄×C₁₃₉	—	2	8	no	—
253	C₄⋊C₄×C₁₃₉	—	2	8	no	—
254	C₄⋊C₄×C₁₃₉	—	2	2	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	8	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	4	4	no	—
260	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	2	2	no	—
278	C₄²×C₁₃₉	—	2	4	no	—
279	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	4	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
294	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
295	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
296	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
297	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
298	Q₈×C₁₃₉	—	2	8	no	—
299	Q₈×C₁₃₉	—	4	8	no	—
300	D₄×C₁₃₉	—	2	16	no	—
301	D₄×C₁₃₉	—	4	8	no	—
302	D₄×C₁₃₉	—	4	4	no	—
303	D₄×C₁₃₉	—	4	16	no	—
304	D₄×C₁₃₉	#121	1	16	yes	—
305	C₂×C₄×C₁₃₉	—	2	16	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	4	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	8	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	4	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	4	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	4	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	4	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	4	8	no	—
335	C₂×C₄×C₁₃₉	—	4	16	no	—
336	C₂×C₄×C₁₃₉	—	4	16	no	—
337	C₂×C₄×C₁₃₉	—	4	8	no	—
338	C₂×C₄×C₁₃₉	—	8	4	no	—
339	C₂×C₄×C₁₃₉	—	8	4	no	—
340	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	2	8	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	2	8	no	—
353	C₂²×C₁₃₉	—	2	2	no	—
354	C₂²×C₁₃₉	—	2	4	no	—
355	C₂²×C₁₃₉	—	4	1	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	C₂×#121	1	8	yes	—
366	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
367	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
368	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
369	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
370	C₂²×C₁₃₉	#585	1	2	yes	—
371	C₄×C₁₃₉	—	2	2	no	—
372	C₄×C₁₃₉	—	2	4	no	—
373	C₄×C₁₃₉	—	2	2	no	—
374	C₄×C₁₃₉	—	2	4	no	—
375	C₄×C₁₃₉	—	2	4	no	—
376	C₄×C₁₃₉	—	2	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	4	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	1	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	4	no	—
383	C₄×C₁₃₉	—	4	1	no	—
384	C₄×C₁₃₉	C₂×#121	1	4	yes	—
385	C₂×C₁₃₉	—	2	8	no	—
386	C₂×C₁₃₉	—	4	2	no	—
387	C₂×C₁₃₉	—	8	2	no	—
388	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
389	C₂×C₁₃₉	#3485	1	1	yes	characteristic
390	C₂×C₁₃₉	#3489	1	2	yes	—
391	C₂×C₁₃₉	#3499	1	1	yes	characteristic
392	C₂×C₁₃₉	#3515	1	2	yes	—
393	#36020	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₁₃₉	#36020	1	1	yes	characteristic, direct product factor, Sylow
395	C₂×#547	C₂×C₁₃₉	1	2	yes	complemented
396	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	#2621	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2618	C₂×C₁₃₉	1	2	yes	complemented
400	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
401	#2543	C₂×C₁₃₉	1	2	yes	complemented
402	#2536	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	#2486	C₂×C₁₃₉	1	2	yes	complemented
404	#2429	C₂×C₁₃₉	1	2	yes	complemented
405	#2425	C₂×C₁₃₉	1	4	yes	complemented
406	#2417	C₂×C₁₃₉	1	2	yes	complemented
407	#2413	C₂×C₁₃₉	1	4	yes	complemented
408	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	C₂×#398	C₂×C₁₃₉	1	2	yes	complemented
410	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	#2339	C₂×C₁₃₉	1	2	yes	complemented
412	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
413	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
414	#547	—	2	16	no	—
415	#547	—	2	8	no	—
416	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
418	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
419	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
420	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
422	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
423	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
425	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
426	#520	—	2	8	no	—
427	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
434	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
438	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
440	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
442	#398	C₂²×C₁₃₉	1	2	yes	—
443	#398	C₂²×C₁₃₉	1	2	yes	—
444	#398	C₂²×C₁₃₉	1	2	yes	—
445	#398	C₂²×C₁₃₉	1	1	yes	characteristic
446	#398	C₂²×C₁₃₉	1	4	yes	—
447	#398	C₂²×C₁₃₉	1	4	yes	—
448	#398	C₂²×C₁₃₉	1	2	yes	—
449	#398	C₂²×C₁₃₉	1	2	yes	—
450	#397	C₂²×C₁₃₉	1	2	yes	—
451	#397	C₂²×C₁₃₉	1	2	yes	—
452	#397	C₂²×C₁₃₉	1	1	yes	characteristic
453	#396	C₂²×C₁₃₉	1	4	yes	—
454	#396	C₂²×C₁₃₉	1	4	yes	—
455	#396	C₂²×C₁₃₉	1	2	yes	—
456	#394	C₂²×C₁₃₉	1	1	yes	characteristic
457	#394	C₂²×C₁₃₉	1	2	yes	—
458	#394	C₂²×C₁₃₉	1	2	yes	—
459	#392	C₂²×C₁₃₉	1	1	yes	characteristic
460	#391	C₂²×C₁₃₉	1	2	yes	—
461	#391	C₂²×C₁₃₉	1	2	yes	—
462	#389	C₂²×C₁₃₉	1	2	yes	—
463	#389	C₂²×C₁₃₉	1	4	yes	—
464	#389	C₂²×C₁₃₉	1	4	yes	—
465	#388	C₂²×C₁₃₉	1	4	yes	—
466	#388	C₂²×C₁₃₉	1	4	yes	—
467	#386	C₂²×C₁₃₉	1	4	yes	—
468	#386	C₂²×C₁₃₉	1	4	yes	—
469	#386	C₂²×C₁₃₉	1	4	yes	—
470	#385	C₂²×C₁₃₉	1	4	yes	—
471	#382	C₂²×C₁₃₉	1	1	yes	characteristic
472	#381	C₂²×C₁₃₉	1	4	yes	—
473	#380	C₂²×C₁₃₉	1	2	yes	—
474	#380	C₂²×C₁₃₉	1	2	yes	—
475	#380	C₂²×C₁₃₉	1	4	yes	—
476	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
478	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
479	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
480	C₂×#41	—	2	4	no	—
481	C₂×#41	—	2	8	no	—
482	C₂×#41	—	2	8	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	8	no	—
485	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
486	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
487	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₄⋊Q₈	—	2	8	no	—
502	C₄⋊Q₈	—	2	4	no	—
503	#123	—	2	16	no	—
504	#123	—	2	16	no	—
505	#123	—	2	16	no	—
506	C₂²⋊Q₈	—	2	8	no	—
507	C₂²⋊Q₈	—	2	8	no	—
508	C₂²⋊Q₈	—	2	8	no	—
509	#121	—	2	16	no	—
510	#121	—	2	8	no	—
511	C₄×Q₈	—	2	4	no	—
512	C₄×Q₈	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	8	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	8	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
520	#117	—	2	8	no	—
521	#117	—	2	4	no	—
522	C₂×C₄⋊C₄	—	2	8	no	—
523	C₂×C₄⋊C₄	—	2	16	no	—
524	C₂×C₄⋊C₄	—	2	8	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
564	#95	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	1	yes	characteristic
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	4	yes	—
569	#95	C₂³×C₁₃₉	1	4	yes	—
570	#95	C₂³×C₁₃₉	1	4	yes	—
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	1	yes	characteristic
573	#95	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	4	yes	—
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
578	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
579	#41	—	2	32	no	—
580	#41	—	4	32	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	4	no	—
586	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
598	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
599	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
600	C₂×D₄	#41×C₁₃₉	1	4	yes	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	8	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	2	8	no	—
608	C₂²×C₄	—	2	8	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
620	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
621	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	8	no	—
646	C₄⋊C₄	—	2	8	no	—
647	C₄⋊C₄	—	2	8	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	8	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	4	4	no	—
654	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	8	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	8	no	—
664	C₂²⋊C₄	—	2	8	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
688	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
689	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
690	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
691	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
692	Q₈	—	2	8	no	—
693	Q₈	—	4	8	no	—
694	D₄	—	2	16	no	—
695	D₄	—	4	8	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	16	no	—
698	D₄	#121×C₁₃₉	1	16	yes	—
699	C₂×C₄	—	2	16	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	16	no	—
730	C₂×C₄	—	4	16	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
737	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
739	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
741	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
742	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	8	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	8	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	C₂×#121×C₁₃₉	1	8	yes	—
760	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
761	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
762	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
763	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
764	C₂²	#585×C₁₃₉	1	2	yes	—
765	C₄	—	2	2	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	4	no	—
770	C₄	—	2	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	4	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	4	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	1	no	—
778	C₄	C₂×#121×C₁₃₉	1	4	yes	—
779	C₂	—	2	8	no	—
780	C₂	—	4	2	no	—
781	C₂	—	8	2	no	—
782	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
783	C₂	#3485×C₁₃₉	1	1	yes	characteristic
784	C₂	#3489×C₁₃₉	1	2	yes	—
785	C₂	#3499×C₁₃₉	1	1	yes	characteristic
786	C₂	#3515×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×#547×C₁₃₉	C₂	semidirect
2. C₂×#547×C₁₃₉	C₂	semidirect
3. C₂×#520×C₁₃₉	C₂	semidirect
4. #2621×C₁₃₉	C₂	semidirect
5. #2618×C₁₃₉	C₂	semidirect
6. #2546×C₁₃₉	C₂	semidirect
7. #2543×C₁₃₉	C₂	semidirect
8. #2536×C₁₃₉	C₂	semidirect
9. #2486×C₁₃₉	C₂	semidirect
10. #2429×C₁₃₉	C₂	semidirect
11. #2425×C₁₃₉	C₂	semidirect
12. #2417×C₁₃₉	C₂	semidirect
13. #2413×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. C₂×#398×C₁₃₉	C₂	semidirect
16. #2349×C₁₃₉	C₂	semidirect
17. #2339×C₁₃₉	C₂	semidirect
91. C₂×#41×C₁₃₉	D₄	semidirect
125. C₄×D₄×C₁₃₉	D₄	semidirect
393. #36020	C₁₃₉	direct (N × H)
394. C₁₃₉	#36020	direct (N × H)
395. C₂×#547	C₂×C₁₃₉	semidirect
396. C₂×#547	C₂×C₁₃₉	semidirect
397. C₂×#520	C₂×C₁₃₉	semidirect
398. #2621	C₂×C₁₃₉	semidirect
399. #2618	C₂×C₁₃₉	semidirect
400. #2546	C₂×C₁₃₉	semidirect
401. #2543	C₂×C₁₃₉	semidirect
402. #2536	C₂×C₁₃₉	semidirect
403. #2486	C₂×C₁₃₉	semidirect
404. #2429	C₂×C₁₃₉	semidirect
405. #2425	C₂×C₁₃₉	semidirect
406. #2417	C₂×C₁₃₉	semidirect
407. #2413	C₂×C₁₃₉	semidirect
408. #2392	C₂×C₁₃₉	semidirect
409. C₂×#398	C₂×C₁₃₉	semidirect
410. #2349	C₂×C₁₃₉	semidirect
411. #2339	C₂×C₁₃₉	semidirect
485. C₂×#41	D₄×C₁₃₉	semidirect
519. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2621×C₁₃₉	2
#2618×C₁₃₉	2
#2546×C₁₃₉	2
#2543×C₁₃₉	2
#2536×C₁₃₉	2
#2486×C₁₃₉	2
#2429×C₁₃₉	2
#2425×C₁₃₉	2
#2417×C₁₃₉	2
#2413×C₁₃₉	2
#2392×C₁₃₉	2
C₂×#398×C₁₃₉	2
#2349×C₁₃₉	2
#2339×C₁₃₉	2
#36020	139

Subgroups — C139×#36020 #48030616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36020 #48030616