Subgroups — C₁₃₉×#36259 #48030855

Order 35584.

3120 conjugacy classes of subgroups.

The subgroup lattice has 848 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×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2486×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2429×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2425×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2416×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2413×C₁₃₉	C₂	1	4	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2339×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#389×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	1	yes	characteristic
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
33	C₄×#41×C₁₃₉	—	2	8	no	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
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	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
49	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
50	#398×C₁₃₉	C₂²	1	4	yes	—
51	#398×C₁₃₉	C₂²	1	4	yes	—
52	#397×C₁₃₉	C₂²	1	4	yes	—
53	#396×C₁₃₉	C₂²	1	4	yes	—
54	#396×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	1	yes	characteristic
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	4	yes	—
66	#389×C₁₃₉	C₂²	1	4	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	4	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#386×C₁₃₉	C₂²	1	2	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#386×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	#384×C₁₃₉	C₂²	1	1	yes	characteristic
77	#381×C₁₃₉	C₂²	1	4	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	#380×C₁₃₉	C₂²	1	1	yes	characteristic
80	#380×C₁₃₉	C₂²	1	2	yes	—
81	#380×C₁₃₉	C₂²	1	2	yes	—
82	#380×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊C₄×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	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
109	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
110	#123×C₁₃₉	—	2	16	no	—
111	#123×C₁₃₉	—	2	16	no	—
112	#123×C₁₃₉	—	2	16	no	—
113	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
114	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
116	#121×C₁₃₉	—	2	16	no	—
117	#121×C₁₃₉	—	2	8	no	—
118	#121×C₁₃₉	—	2	4	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×Q₈×C₁₃₉	—	2	4	no	—
121	C₄×D₄×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	8	no	—
125	C₄×D₄×C₁₃₉	—	2	8	no	—
126	C₄×D₄×C₁₃₉	—	2	4	no	—
127	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
128	#117×C₁₃₉	—	2	4	no	—
129	#117×C₁₃₉	—	2	8	no	—
130	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
131	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
132	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	—	2	8	no	—
166	C₂×C₄²×C₁₃₉	—	2	4	no	—
167	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×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	4	yes	—
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	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	—	2	32	no	—
188	#41×C₁₃₉	—	4	32	no	—
189	C₂×Q₈×C₁₃₉	—	2	2	no	—
190	C₂×Q₈×C₁₃₉	—	2	4	no	—
191	C₂×Q₈×C₁₃₉	—	2	4	no	—
192	C₂×Q₈×C₁₃₉	—	2	2	no	—
193	C₂×Q₈×C₁₃₉	—	2	4	no	—
194	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	8	no	—
199	C₂×D₄×C₁₃₉	—	2	8	no	—
200	C₂×D₄×C₁₃₉	—	2	8	no	—
201	C₂×D₄×C₁₃₉	—	2	2	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	—	4	2	no	—
206	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
207	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
208	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
209	C₂×D₄×C₁₃₉	#41	1	4	yes	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	2	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	8	no	—
218	C₂²×C₄×C₁₃₉	—	2	8	no	—
219	C₂²×C₄×C₁₃₉	—	2	8	no	—
220	C₂²×C₄×C₁₃₉	—	2	8	no	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	4	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	8	no	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	4	1	no	—
232	C₂²×C₄×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	—	4	4	no	—
234	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
235	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
236	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
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	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	2	no	—
253	C₄⋊C₄×C₁₃₉	—	2	8	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	8	no	—
256	C₄⋊C₄×C₁₃₉	—	2	8	no	—
257	C₄⋊C₄×C₁₃₉	—	2	8	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	2	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	8	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	8	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	4	2	no	—
268	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
269	C₄⋊C₄×C₁₃₉	#41	1	4	yes	complemented
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
282	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
283	C₄²×C₁₃₉	—	2	2	no	—
284	C₄²×C₁₃₉	—	2	4	no	—
285	C₄²×C₁₃₉	—	2	2	no	—
286	C₄²×C₁₃₉	—	2	4	no	—
287	C₄²×C₁₃₉	—	2	2	no	—
288	C₄²×C₁₃₉	—	2	4	no	—
289	C₄²×C₁₃₉	—	2	4	no	—
290	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	1	no	—
296	C₂³×C₁₃₉	—	2	1	no	—
297	C₂³×C₁₃₉	—	2	1	no	—
298	C₂³×C₁₃₉	—	2	1	no	—
299	C₂³×C₁₃₉	—	2	1	no	—
300	C₂³×C₁₃₉	—	2	1	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
309	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
310	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
311	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
312	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
313	Q₈×C₁₃₉	—	2	8	no	—
314	Q₈×C₁₃₉	—	4	8	no	—
315	D₄×C₁₃₉	—	2	16	no	—
316	D₄×C₁₃₉	—	4	8	no	—
317	D₄×C₁₃₉	—	4	16	no	—
318	D₄×C₁₃₉	—	4	4	no	—
319	D₄×C₁₃₉	#121	1	16	yes	complemented
320	C₂×C₄×C₁₃₉	—	2	16	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	1	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	8	no	—
334	C₂×C₄×C₁₃₉	—	2	16	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	4	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	4	no	—
342	C₂×C₄×C₁₃₉	—	2	4	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	4	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	4	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	4	no	—
353	C₂×C₄×C₁₃₉	—	4	4	no	—
354	C₂×C₄×C₁₃₉	—	4	16	no	—
355	C₂×C₄×C₁₃₉	—	4	8	no	—
356	C₂×C₄×C₁₃₉	—	4	16	no	—
357	C₂×C₄×C₁₃₉	—	4	8	no	—
358	C₂×C₄×C₁₃₉	—	4	4	no	—
359	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
367	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
368	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
369	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
370	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
371	C₂²×C₁₃₉	—	2	4	no	—
372	C₂²×C₁₃₉	—	2	4	no	—
373	C₂²×C₁₃₉	—	2	4	no	—
374	C₂²×C₁₃₉	—	2	4	no	—
375	C₂²×C₁₃₉	—	2	4	no	—
376	C₂²×C₁₃₉	—	2	4	no	—
377	C₂²×C₁₃₉	—	2	2	no	—
378	C₂²×C₁₃₉	—	2	2	no	—
379	C₂²×C₁₃₉	—	2	2	no	—
380	C₂²×C₁₃₉	—	4	1	no	—
381	C₂²×C₁₃₉	—	4	1	no	—
382	C₂²×C₁₃₉	—	4	1	no	—
383	C₂²×C₁₃₉	—	4	1	no	—
384	C₂²×C₁₃₉	—	4	2	no	—
385	C₂²×C₁₃₉	—	4	2	no	—
386	C₂²×C₁₃₉	—	4	2	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	2	no	—
391	C₂²×C₁₃₉	C₂×#121	1	8	yes	—
392	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
393	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
394	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂²×C₁₃₉	#585	1	1	yes	characteristic
399	C₄×C₁₃₉	—	2	2	no	—
400	C₄×C₁₃₉	—	2	4	no	—
401	C₄×C₁₃₉	—	2	4	no	—
402	C₄×C₁₃₉	—	2	4	no	—
403	C₄×C₁₃₉	—	2	2	no	—
404	C₄×C₁₃₉	—	2	2	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	4	no	—
407	C₄×C₁₃₉	—	4	1	no	—
408	C₄×C₁₃₉	—	4	4	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	C₂×#121	1	4	yes	—
412	C₄×C₁₃₉	#547	1	4	yes	complemented
413	C₂×C₁₃₉	—	2	8	no	—
414	C₂×C₁₃₉	—	4	2	no	—
415	C₂×C₁₃₉	—	8	2	no	—
416	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
417	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
418	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
419	C₂×C₁₃₉	#3482	1	1	yes	characteristic
420	C₂×C₁₃₉	#3489	1	1	yes	characteristic
421	C₂×C₁₃₉	#3499	1	1	yes	characteristic
422	C₂×C₁₃₉	#3515	1	1	yes	characteristic
423	#36259	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₁₃₉	#36259	1	1	yes	characteristic, direct product factor, Sylow
425	C₂×#547	C₂×C₁₃₉	1	2	yes	complemented
426	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
427	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
428	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2854	C₂×C₁₃₉	1	2	yes	complemented
430	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
431	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
432	#2486	C₂×C₁₃₉	1	2	yes	complemented
433	#2429	C₂×C₁₃₉	1	2	yes	complemented
434	#2425	C₂×C₁₃₉	1	4	yes	complemented
435	#2416	C₂×C₁₃₉	1	2	yes	complemented
436	#2415	C₂×C₁₃₉	1	2	yes	complemented
437	#2413	C₂×C₁₃₉	1	4	yes	complemented
438	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2339	C₂×C₁₃₉	1	2	yes	complemented
440	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
441	C₂×#389	C₂×C₁₃₉	1	2	yes	complemented
442	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
443	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
444	#547	—	2	16	no	—
445	#547	—	2	8	no	—
446	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
448	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
449	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
450	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
454	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
455	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
457	C₄×#41	—	2	8	no	—
458	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
463	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
464	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
465	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
470	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
471	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
472	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
473	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
474	#398	C₂²×C₁₃₉	1	4	yes	—
475	#398	C₂²×C₁₃₉	1	4	yes	—
476	#397	C₂²×C₁₃₉	1	4	yes	—
477	#396	C₂²×C₁₃₉	1	4	yes	—
478	#396	C₂²×C₁₃₉	1	4	yes	—
479	#394	C₂²×C₁₃₉	1	4	yes	—
480	#391	C₂²×C₁₃₉	1	2	yes	—
481	#391	C₂²×C₁₃₉	1	2	yes	—
482	#390	C₂²×C₁₃₉	1	1	yes	characteristic
483	#390	C₂²×C₁₃₉	1	2	yes	—
484	#389	C₂²×C₁₃₉	1	2	yes	—
485	#389	C₂²×C₁₃₉	1	2	yes	—
486	#389	C₂²×C₁₃₉	1	2	yes	—
487	#389	C₂²×C₁₃₉	1	2	yes	—
488	#389	C₂²×C₁₃₉	1	4	yes	—
489	#389	C₂²×C₁₃₉	1	2	yes	—
490	#389	C₂²×C₁₃₉	1	4	yes	—
491	#389	C₂²×C₁₃₉	1	2	yes	—
492	#389	C₂²×C₁₃₉	1	1	yes	characteristic
493	#388	C₂²×C₁₃₉	1	4	yes	—
494	#388	C₂²×C₁₃₉	1	4	yes	—
495	#388	C₂²×C₁₃₉	1	2	yes	—
496	#386	C₂²×C₁₃₉	1	4	yes	—
497	#386	C₂²×C₁₃₉	1	4	yes	—
498	#386	C₂²×C₁₃₉	1	2	yes	—
499	#385	C₂²×C₁₃₉	1	4	yes	—
500	#384	C₂²×C₁₃₉	1	1	yes	characteristic
501	#381	C₂²×C₁₃₉	1	4	yes	—
502	#380	C₂²×C₁₃₉	1	2	yes	—
503	#380	C₂²×C₁₃₉	1	2	yes	—
504	#380	C₂²×C₁₃₉	1	2	yes	—
505	#380	C₂²×C₁₃₉	1	2	yes	—
506	#380	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
509	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
510	C₂×#41	—	2	4	no	—
511	C₂×#41	—	2	8	no	—
512	C₂×#41	—	2	8	no	—
513	C₂×#41	—	2	4	no	—
514	C₂×#41	—	2	8	no	—
515	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
516	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
517	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
527	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₄⋊Q₈	—	2	8	no	—
533	C₄⋊Q₈	—	2	4	no	—
534	#123	—	2	16	no	—
535	#123	—	2	16	no	—
536	#123	—	2	16	no	—
537	C₂²⋊Q₈	—	2	8	no	—
538	C₂²⋊Q₈	—	2	8	no	—
539	C₂²⋊Q₈	—	2	8	no	—
540	#121	—	2	16	no	—
541	#121	—	2	8	no	—
542	#121	—	2	4	no	—
543	C₄×Q₈	—	2	4	no	—
544	C₄×Q₈	—	2	4	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	8	no	—
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	8	no	—
549	C₄×D₄	—	2	8	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
552	#117	—	2	4	no	—
553	#117	—	2	8	no	—
554	C₂×C₄⋊C₄	—	2	16	no	—
555	C₂×C₄⋊C₄	—	2	8	no	—
556	C₂×C₄⋊C₄	—	2	8	no	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄²	—	2	8	no	—
590	C₂×C₄²	—	2	4	no	—
591	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	4	yes	—
601	#95	C₂³×C₁₃₉	1	4	yes	—
602	#95	C₂³×C₁₃₉	1	4	yes	—
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	4	yes	—
606	#95	C₂³×C₁₃₉	1	4	yes	—
607	#95	C₂³×C₁₃₉	1	4	yes	—
608	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
609	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
610	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
611	#41	—	2	32	no	—
612	#41	—	4	32	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	2	4	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	4	no	—
618	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	8	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
631	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
632	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
633	C₂×D₄	#41×C₁₃₉	1	4	yes	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	2	8	no	—
644	C₂²×C₄	—	2	8	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	8	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	4	1	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
659	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
660	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
667	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	8	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	8	no	—
680	C₄⋊C₄	—	2	8	no	—
681	C₄⋊C₄	—	2	8	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	8	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	8	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
693	C₄⋊C₄	#41×C₁₃₉	1	4	yes	complemented
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	8	no	—
702	C₂²⋊C₄	—	2	8	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	4	4	no	—
706	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	4	no	—
711	C₄²	—	2	2	no	—
712	C₄²	—	2	4	no	—
713	C₄²	—	2	4	no	—
714	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
733	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
734	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
735	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
736	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
737	Q₈	—	2	8	no	—
738	Q₈	—	4	8	no	—
739	D₄	—	2	16	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	16	no	—
742	D₄	—	4	4	no	—
743	D₄	#121×C₁₃₉	1	16	yes	complemented
744	C₂×C₄	—	2	16	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	16	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	16	no	—
779	C₂×C₄	—	4	8	no	—
780	C₂×C₄	—	4	16	no	—
781	C₂×C₄	—	4	8	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
787	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
788	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
790	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
791	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
792	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
793	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
794	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	C₂×#121×C₁₃₉	1	8	yes	—
816	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
817	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
818	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
819	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
820	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
821	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
822	C₂²	#585×C₁₃₉	1	1	yes	characteristic
823	C₄	—	2	2	no	—
824	C₄	—	2	4	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	4	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	4	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	C₂×#121×C₁₃₉	1	4	yes	—
836	C₄	#547×C₁₃₉	1	4	yes	complemented
837	C₂	—	2	8	no	—
838	C₂	—	4	2	no	—
839	C₂	—	8	2	no	—
840	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
841	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
842	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
843	C₂	#3482×C₁₃₉	1	1	yes	characteristic
844	C₂	#3489×C₁₃₉	1	1	yes	characteristic
845	C₂	#3499×C₁₃₉	1	1	yes	characteristic
846	C₂	#3515×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#547×C₁₃₉	C₂	semidirect
2. C₂×#547×C₁₃₉	C₂	semidirect
3. C₂×C₄×#41×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2854×C₁₃₉	C₂	semidirect
6. #2546×C₁₃₉	C₂	semidirect
7. #2538×C₁₃₉	C₂	semidirect
8. #2486×C₁₃₉	C₂	semidirect
9. #2429×C₁₃₉	C₂	semidirect
10. #2425×C₁₃₉	C₂	semidirect
11. #2416×C₁₃₉	C₂	semidirect
12. #2415×C₁₃₉	C₂	semidirect
13. #2413×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
15. #2339×C₁₃₉	C₂	semidirect
16. C₄×#121×C₁₃₉	C₂	semidirect
17. C₂×#389×C₁₃₉	C₂	semidirect
91. C₂×#41×C₁₃₉	D₄	semidirect
127. C₄×D₄×C₁₃₉	D₄	semidirect
269. C₄⋊C₄×C₁₃₉	#41	semidirect
319. D₄×C₁₃₉	#121	semidirect
412. C₄×C₁₃₉	#547	semidirect
423. #36259	C₁₃₉	direct (N × H)
424. C₁₃₉	#36259	direct (N × H)
425. C₂×#547	C₂×C₁₃₉	semidirect
426. C₂×#547	C₂×C₁₃₉	semidirect
427. C₂×C₄×#41	C₂×C₁₃₉	semidirect
428. #2857	C₂×C₁₃₉	semidirect
429. #2854	C₂×C₁₃₉	semidirect
430. #2546	C₂×C₁₃₉	semidirect
431. #2538	C₂×C₁₃₉	semidirect
432. #2486	C₂×C₁₃₉	semidirect
433. #2429	C₂×C₁₃₉	semidirect
434. #2425	C₂×C₁₃₉	semidirect
435. #2416	C₂×C₁₃₉	semidirect
436. #2415	C₂×C₁₃₉	semidirect
437. #2413	C₂×C₁₃₉	semidirect
438. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
439. #2339	C₂×C₁₃₉	semidirect
440. C₄×#121	C₂×C₁₃₉	semidirect
441. C₂×#389	C₂×C₁₃₉	semidirect
515. C₂×#41	D₄×C₁₃₉	semidirect
551. C₄×D₄	D₄×C₁₃₉	semidirect
693. C₄⋊C₄	#41×C₁₃₉	semidirect
743. D₄	#121×C₁₃₉	semidirect
836. C₄	#547×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×C₄×#41×C₁₃₉	2
#2857×C₁₃₉	2
#2854×C₁₃₉	2
#2546×C₁₃₉	2
#2538×C₁₃₉	2
#2486×C₁₃₉	2
#2429×C₁₃₉	2
#2425×C₁₃₉	2
#2416×C₁₃₉	2
#2415×C₁₃₉	2
#2413×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2339×C₁₃₉	2
C₄×#121×C₁₃₉	2
C₂×#389×C₁₃₉	2
#36259	139

Subgroups — C139×#36259 #48030855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36259 #48030855