Subgroups — C₁₃₉×#35705 #48030301

Order 35584.

1946 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2665×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2626×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2607×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2589×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2574×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2549×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2505×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2492×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2439×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2437×C₁₃₉	C₂	1	2	yes	maximal
12	#2434×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₂×#393×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2368×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2368×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2342×C₁₃₉	C₂	1	2	yes	maximal
18	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2273×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	#400×C₁₃₉	C₂²	1	2	yes	complemented
32	#400×C₁₃₉	C₂²	1	2	yes	complemented
33	#400×C₁₃₉	C₂²	1	2	yes	complemented
34	#399×C₁₃₉	C₂²	1	1	yes	characteristic
35	#399×C₁₃₉	C₂²	1	1	yes	characteristic
36	#399×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	complemented
38	#398×C₁₃₉	C₂²	1	2	yes	complemented
39	#396×C₁₃₉	C₂²	1	2	yes	—
40	#396×C₁₃₉	C₂²	1	2	yes	—
41	#396×C₁₃₉	C₂²	1	2	yes	—
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#395×C₁₃₉	C₂²	1	2	yes	complemented
44	#395×C₁₃₉	C₂²	1	2	yes	complemented
45	#395×C₁₃₉	C₂²	1	2	yes	complemented
46	#393×C₁₃₉	C₂²	1	1	yes	characteristic
47	#393×C₁₃₉	C₂²	1	2	yes	—
48	#393×C₁₃₉	C₂²	1	2	yes	—
49	#393×C₁₃₉	C₂²	1	2	yes	—
50	#393×C₁₃₉	C₂²	1	1	yes	characteristic
51	#393×C₁₃₉	C₂²	1	1	yes	characteristic
52	#393×C₁₃₉	C₂²	1	1	yes	characteristic
53	#393×C₁₃₉	C₂²	1	1	yes	characteristic
54	#393×C₁₃₉	C₂²	1	1	yes	characteristic
55	#391×C₁₃₉	C₂²	1	2	yes	complemented
56	#391×C₁₃₉	C₂²	1	2	yes	complemented
57	#391×C₁₃₉	C₂²	1	2	yes	complemented
58	#391×C₁₃₉	C₂²	1	2	yes	complemented
59	#391×C₁₃₉	C₂²	1	2	yes	complemented
60	#391×C₁₃₉	C₂²	1	2	yes	complemented
61	#391×C₁₃₉	C₂²	1	2	yes	complemented
62	#391×C₁₃₉	C₂²	1	2	yes	complemented
63	#389×C₁₃₉	C₂²	1	2	yes	complemented
64	#389×C₁₃₉	C₂²	1	2	yes	complemented
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	complemented
70	#387×C₁₃₉	C₂²	1	2	yes	complemented
71	#387×C₁₃₉	C₂²	1	2	yes	complemented
72	#387×C₁₃₉	C₂²	1	2	yes	complemented
73	#387×C₁₃₉	C₂²	1	2	yes	complemented
74	#387×C₁₃₉	C₂²	1	2	yes	complemented
75	#387×C₁₃₉	C₂²	1	2	yes	complemented
76	#387×C₁₃₉	C₂²	1	2	yes	complemented
77	#385×C₁₃₉	C₂²	1	2	yes	—
78	#385×C₁₃₉	C₂²	1	2	yes	—
79	#385×C₁₃₉	C₂²	1	2	yes	—
80	#385×C₁₃₉	C₂²	1	2	yes	—
81	#385×C₁₃₉	C₂²	1	2	yes	—
82	#385×C₁₃₉	C₂²	1	2	yes	—
83	#385×C₁₃₉	C₂²	1	2	yes	—
84	#382×C₁₃₉	C₂²	1	2	yes	complemented
85	#381×C₁₃₉	C₂²	1	2	yes	—
86	#380×C₁₃₉	C₂²	1	1	yes	characteristic
87	#380×C₁₃₉	C₂²	1	2	yes	—
88	#380×C₁₃₉	C₂²	1	2	yes	—
89	#380×C₁₃₉	C₂²	1	2	yes	—
90	#379×C₁₃₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	—	2	4	no	—
109	C₂²×Q₈×C₁₃₉	—	4	4	no	—
110	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
122	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
123	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
124	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
125	C₄×Q₈×C₁₃₉	—	4	4	no	—
126	#117×C₁₃₉	—	4	4	no	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
148	C₂×C₂²⋊C₄×C₁₃₉	Q₈	1	8	yes	complemented
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄²×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	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	1	yes	characteristic
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	1	yes	characteristic
193	#95×C₁₃₉	C₂³	1	1	yes	characteristic
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	C₂⁴×C₁₃₉	—	2	2	no	—
207	C₂⁴×C₁₃₉	—	2	2	no	—
208	C₂⁴×C₁₃₉	—	4	2	no	—
209	C₂⁴×C₁₃₉	—	4	2	no	—
210	C₂⁴×C₁₃₉	C₂×Q₈	1	4	yes	—
211	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₁₃₉	—	2	2	no	—
215	C₂×Q₈×C₁₃₉	—	2	4	no	—
216	C₂×Q₈×C₁₃₉	—	2	2	no	—
217	C₂×Q₈×C₁₃₉	—	2	2	no	—
218	C₂×Q₈×C₁₃₉	—	2	4	no	—
219	C₂×Q₈×C₁₃₉	—	2	4	no	—
220	C₂×Q₈×C₁₃₉	—	2	4	no	—
221	C₂×Q₈×C₁₃₉	—	4	2	no	—
222	C₂×Q₈×C₁₃₉	—	4	2	no	—
223	C₂×Q₈×C₁₃₉	—	4	2	no	—
224	C₂×Q₈×C₁₃₉	—	4	2	no	—
225	C₂×Q₈×C₁₃₉	—	4	2	no	—
226	C₂×Q₈×C₁₃₉	—	4	16	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	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	—	4	2	no	—
234	C₂²×C₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
242	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₁₃₉	—	2	2	no	—
260	C₄⋊C₄×C₁₃₉	—	2	4	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	4	2	no	—
268	C₄⋊C₄×C₁₃₉	—	4	2	no	—
269	C₄⋊C₄×C₁₃₉	—	4	2	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
293	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
294	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
295	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
296	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
297	C₄²×C₁₃₉	—	2	4	no	—
298	C₄²×C₁₃₉	—	4	2	no	—
299	C₄²×C₁₃₉	—	4	2	no	—
300	C₄²×C₁₃₉	—	4	2	no	—
301	C₄²×C₁₃₉	—	4	2	no	—
302	C₄²×C₁₃₉	—	4	2	no	—
303	C₄²×C₁₃₉	—	4	2	no	—
304	C₄²×C₁₃₉	—	4	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	1	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	1	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	8	no	—
316	C₂³×C₁₃₉	—	4	8	no	—
317	C₂³×C₁₃₉	—	8	2	no	—
318	C₂³×C₁₃₉	—	8	2	no	—
319	C₂³×C₁₃₉	—	8	4	no	—
320	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
321	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
322	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
323	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
324	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
325	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃₉	—	2	8	no	—
327	Q₈×C₁₃₉	—	4	8	no	—
328	Q₈×C₁₃₉	—	4	4	no	—
329	Q₈×C₁₃₉	—	8	2	no	—
330	Q₈×C₁₃₉	—	8	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	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	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	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	4	8	no	—
370	C₂×C₄×C₁₃₉	—	4	4	no	—
371	C₂×C₄×C₁₃₉	—	4	8	no	—
372	C₂×C₄×C₁₃₉	—	8	4	no	—
373	C₂×C₄×C₁₃₉	—	8	2	no	—
374	C₂×C₄×C₁₃₉	—	8	4	no	—
375	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
376	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
377	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
378	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
379	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
380	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
381	C₂²×C₁₃₉	—	2	2	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	2	no	—
384	C₂²×C₁₃₉	—	2	4	no	—
385	C₂²×C₁₃₉	—	2	2	no	—
386	C₂²×C₁₃₉	—	2	2	no	—
387	C₂²×C₁₃₉	—	2	4	no	—
388	C₂²×C₁₃₉	—	2	4	no	—
389	C₂²×C₁₃₉	—	4	1	no	—
390	C₂²×C₁₃₉	—	4	1	no	—
391	C₂²×C₁₃₉	—	4	1	no	—
392	C₂²×C₁₃₉	—	4	1	no	—
393	C₂²×C₁₃₉	—	4	2	no	—
394	C₂²×C₁₃₉	—	4	2	no	—
395	C₂²×C₁₃₉	—	8	8	no	—
396	C₂²×C₁₃₉	#533	1	4	yes	—
397	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
398	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
401	C₂²×C₁₃₉	#585	1	2	yes	—
402	C₄×C₁₃₉	—	2	2	no	—
403	C₄×C₁₃₉	—	2	2	no	—
404	C₄×C₁₃₉	—	2	4	no	—
405	C₄×C₁₃₉	—	2	4	no	—
406	C₄×C₁₃₉	—	2	4	no	—
407	C₄×C₁₃₉	—	2	4	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	1	no	—
412	C₄×C₁₃₉	—	4	1	no	—
413	C₄×C₁₃₉	—	4	2	no	—
414	C₄×C₁₃₉	—	4	2	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	2	no	—
417	C₄×C₁₃₉	—	4	2	no	—
418	C₂×C₁₃₉	—	2	4	no	—
419	C₂×C₁₃₉	—	4	2	no	—
420	C₂×C₁₃₉	—	4	2	no	—
421	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
422	C₂×C₁₃₉	#3490	1	1	yes	characteristic
423	C₂×C₁₃₉	#3501	1	2	yes	—
424	C₂×C₁₃₉	#3510	1	1	yes	characteristic
425	C₂×C₁₃₉	#3514	1	2	yes	—
426	#35705	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₁₃₉	#35705	1	1	yes	characteristic, direct product factor, Sylow
428	#2665	C₂×C₁₃₉	1	2	yes	complemented
429	#2626	C₂×C₁₃₉	1	1	yes	characteristic
430	#2607	C₂×C₁₃₉	1	2	yes	complemented
431	#2589	C₂×C₁₃₉	1	2	yes	complemented
432	#2574	C₂×C₁₃₉	1	2	yes	complemented
433	#2549	C₂×C₁₃₉	1	1	yes	characteristic, complemented
434	#2505	C₂×C₁₃₉	1	2	yes	complemented
435	#2492	C₂×C₁₃₉	1	2	yes	complemented
436	#2465	C₂×C₁₃₉	1	2	yes	complemented
437	#2439	C₂×C₁₃₉	1	2	yes	complemented
438	#2437	C₂×C₁₃₉	1	2	yes	—
439	#2434	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	#2396	C₂×C₁₃₉	1	2	yes	complemented
441	C₂×#393	C₂×C₁₃₉	1	1	yes	characteristic
442	#2368	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	#2368	C₂×C₁₃₉	1	2	yes	complemented
444	#2342	C₂×C₁₃₉	1	2	yes	—
445	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2273	C₂×C₁₃₉	1	1	yes	characteristic
447	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
449	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
452	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
453	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
454	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
457	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
458	#400	C₂²×C₁₃₉	1	2	yes	complemented
459	#400	C₂²×C₁₃₉	1	2	yes	complemented
460	#400	C₂²×C₁₃₉	1	2	yes	complemented
461	#399	C₂²×C₁₃₉	1	1	yes	characteristic
462	#399	C₂²×C₁₃₉	1	1	yes	characteristic
463	#399	C₂²×C₁₃₉	1	2	yes	—
464	#398	C₂²×C₁₃₉	1	2	yes	complemented
465	#398	C₂²×C₁₃₉	1	2	yes	complemented
466	#396	C₂²×C₁₃₉	1	2	yes	—
467	#396	C₂²×C₁₃₉	1	2	yes	—
468	#396	C₂²×C₁₃₉	1	2	yes	—
469	#396	C₂²×C₁₃₉	1	2	yes	—
470	#395	C₂²×C₁₃₉	1	2	yes	complemented
471	#395	C₂²×C₁₃₉	1	2	yes	complemented
472	#395	C₂²×C₁₃₉	1	2	yes	complemented
473	#393	C₂²×C₁₃₉	1	1	yes	characteristic
474	#393	C₂²×C₁₃₉	1	2	yes	—
475	#393	C₂²×C₁₃₉	1	2	yes	—
476	#393	C₂²×C₁₃₉	1	2	yes	—
477	#393	C₂²×C₁₃₉	1	1	yes	characteristic
478	#393	C₂²×C₁₃₉	1	1	yes	characteristic
479	#393	C₂²×C₁₃₉	1	1	yes	characteristic
480	#393	C₂²×C₁₃₉	1	1	yes	characteristic
481	#393	C₂²×C₁₃₉	1	1	yes	characteristic
482	#391	C₂²×C₁₃₉	1	2	yes	complemented
483	#391	C₂²×C₁₃₉	1	2	yes	complemented
484	#391	C₂²×C₁₃₉	1	2	yes	complemented
485	#391	C₂²×C₁₃₉	1	2	yes	complemented
486	#391	C₂²×C₁₃₉	1	2	yes	complemented
487	#391	C₂²×C₁₃₉	1	2	yes	complemented
488	#391	C₂²×C₁₃₉	1	2	yes	complemented
489	#391	C₂²×C₁₃₉	1	2	yes	complemented
490	#389	C₂²×C₁₃₉	1	2	yes	complemented
491	#389	C₂²×C₁₃₉	1	2	yes	complemented
492	#388	C₂²×C₁₃₉	1	2	yes	—
493	#388	C₂²×C₁₃₉	1	2	yes	—
494	#388	C₂²×C₁₃₉	1	2	yes	—
495	#388	C₂²×C₁₃₉	1	2	yes	—
496	#387	C₂²×C₁₃₉	1	2	yes	complemented
497	#387	C₂²×C₁₃₉	1	2	yes	complemented
498	#387	C₂²×C₁₃₉	1	2	yes	complemented
499	#387	C₂²×C₁₃₉	1	2	yes	complemented
500	#387	C₂²×C₁₃₉	1	2	yes	complemented
501	#387	C₂²×C₁₃₉	1	2	yes	complemented
502	#387	C₂²×C₁₃₉	1	2	yes	complemented
503	#387	C₂²×C₁₃₉	1	2	yes	complemented
504	#385	C₂²×C₁₃₉	1	2	yes	—
505	#385	C₂²×C₁₃₉	1	2	yes	—
506	#385	C₂²×C₁₃₉	1	2	yes	—
507	#385	C₂²×C₁₃₉	1	2	yes	—
508	#385	C₂²×C₁₃₉	1	2	yes	—
509	#385	C₂²×C₁₃₉	1	2	yes	—
510	#385	C₂²×C₁₃₉	1	2	yes	—
511	#382	C₂²×C₁₃₉	1	2	yes	complemented
512	#381	C₂²×C₁₃₉	1	2	yes	—
513	#380	C₂²×C₁₃₉	1	2	yes	—
514	#380	C₂²×C₁₃₉	1	1	yes	characteristic
515	#380	C₂²×C₁₃₉	1	2	yes	—
516	#380	C₂²×C₁₃₉	1	2	yes	—
517	#379	C₂²×C₁₃₉	1	2	yes	—
518	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
519	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
520	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
521	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
525	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
531	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
532	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
533	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
534	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂²×Q₈	—	2	4	no	—
536	C₂²×Q₈	—	4	4	no	—
537	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
539	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
540	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₄⋊Q₈	—	4	4	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	8	no	—
551	C₂²⋊Q₈	—	4	4	no	—
552	C₄×Q₈	—	4	4	no	—
553	#117	—	4	4	no	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
572	C₂×C₂²⋊C₄	—	2	4	no	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	C₂×C₂²⋊C₄	—	4	4	no	—
575	C₂×C₂²⋊C₄	Q₈×C₁₃₉	1	8	yes	complemented
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	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	1	yes	characteristic
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	1	yes	characteristic
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	2	yes	—
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
621	#95	C₂³×C₁₃₉	1	2	yes	—
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	2	yes	—
625	#95	C₂³×C₁₃₉	1	2	yes	—
626	#95	C₂³×C₁₃₉	1	1	yes	characteristic
627	#95	C₂³×C₁₃₉	1	1	yes	characteristic
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	2	yes	—
631	#95	C₂³×C₁₃₉	1	2	yes	—
632	#95	C₂³×C₁₃₉	1	2	yes	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	2	no	—
637	C₂⁴	C₂×Q₈×C₁₃₉	1	4	yes	—
638	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	2	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×Q₈	—	4	2	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	—	4	16	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
669	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
721	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
722	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
723	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
724	C₄²	—	2	4	no	—
725	C₄²	—	4	2	no	—
726	C₄²	—	4	2	no	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	2	no	—
731	C₄²	—	4	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	8	no	—
743	C₂³	—	4	8	no	—
744	C₂³	—	8	2	no	—
745	C₂³	—	8	2	no	—
746	C₂³	—	8	4	no	—
747	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
748	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
749	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
750	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
751	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
752	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
753	Q₈	—	2	8	no	—
754	Q₈	—	4	8	no	—
755	Q₈	—	4	4	no	—
756	Q₈	—	8	2	no	—
757	Q₈	—	8	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	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	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
803	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
804	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
805	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
806	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
807	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	8	no	—
823	C₂²	#533×C₁₃₉	1	4	yes	—
824	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
825	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
826	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
828	C₂²	#585×C₁₃₉	1	2	yes	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	4	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₂	—	2	4	no	—
846	C₂	—	4	2	no	—
847	C₂	—	4	2	no	—
848	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
849	C₂	#3490×C₁₃₉	1	1	yes	characteristic
850	C₂	#3501×C₁₃₉	1	2	yes	—
851	C₂	#3510×C₁₃₉	1	1	yes	characteristic
852	C₂	#3514×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂³
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. #2665×C₁₃₉	C₂	semidirect
3. #2607×C₁₃₉	C₂	semidirect
4. #2589×C₁₃₉	C₂	semidirect
5. #2574×C₁₃₉	C₂	semidirect
6. #2549×C₁₃₉	C₂	semidirect
7. #2505×C₁₃₉	C₂	semidirect
8. #2492×C₁₃₉	C₂	semidirect
9. #2465×C₁₃₉	C₂	semidirect
10. #2439×C₁₃₉	C₂	semidirect
12. #2434×C₁₃₉	C₂	semidirect
13. #2396×C₁₃₉	C₂	semidirect
15. #2368×C₁₃₉	C₂	semidirect
16. #2368×C₁₃₉	C₂	semidirect
18. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
31. #400×C₁₃₉	C₂²	semidirect
32. #400×C₁₃₉	C₂²	semidirect
33. #400×C₁₃₉	C₂²	semidirect
37. #398×C₁₃₉	C₂²	semidirect
38. #398×C₁₃₉	C₂²	semidirect
43. #395×C₁₃₉	C₂²	semidirect
44. #395×C₁₃₉	C₂²	semidirect
45. #395×C₁₃₉	C₂²	semidirect
55. #391×C₁₃₉	C₂²	semidirect
56. #391×C₁₃₉	C₂²	semidirect
57. #391×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
60. #391×C₁₃₉	C₂²	semidirect
61. #391×C₁₃₉	C₂²	semidirect
62. #391×C₁₃₉	C₂²	semidirect
63. #389×C₁₃₉	C₂²	semidirect
64. #389×C₁₃₉	C₂²	semidirect
69. #387×C₁₃₉	C₂²	semidirect
70. #387×C₁₃₉	C₂²	semidirect
71. #387×C₁₃₉	C₂²	semidirect
72. #387×C₁₃₉	C₂²	semidirect
73. #387×C₁₃₉	C₂²	semidirect
74. #387×C₁₃₉	C₂²	semidirect
75. #387×C₁₃₉	C₂²	semidirect
76. #387×C₁₃₉	C₂²	semidirect
84. #382×C₁₃₉	C₂²	semidirect
91. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
148. C₂×C₂²⋊C₄×C₁₃₉	Q₈	semidirect
241. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
295. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
426. #35705	C₁₃₉	direct (N × H)
427. C₁₃₉	#35705	direct (N × H)
428. #2665	C₂×C₁₃₉	semidirect
430. #2607	C₂×C₁₃₉	semidirect
431. #2589	C₂×C₁₃₉	semidirect
432. #2574	C₂×C₁₃₉	semidirect
433. #2549	C₂×C₁₃₉	semidirect
434. #2505	C₂×C₁₃₉	semidirect
435. #2492	C₂×C₁₃₉	semidirect
436. #2465	C₂×C₁₃₉	semidirect
437. #2439	C₂×C₁₃₉	semidirect
439. #2434	C₂×C₁₃₉	semidirect
440. #2396	C₂×C₁₃₉	semidirect
442. #2368	C₂×C₁₃₉	semidirect
443. #2368	C₂×C₁₃₉	semidirect
445. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
448. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
452. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
458. #400	C₂²×C₁₃₉	semidirect
459. #400	C₂²×C₁₃₉	semidirect
460. #400	C₂²×C₁₃₉	semidirect
464. #398	C₂²×C₁₃₉	semidirect
465. #398	C₂²×C₁₃₉	semidirect
470. #395	C₂²×C₁₃₉	semidirect
471. #395	C₂²×C₁₃₉	semidirect
472. #395	C₂²×C₁₃₉	semidirect
482. #391	C₂²×C₁₃₉	semidirect
483. #391	C₂²×C₁₃₉	semidirect
484. #391	C₂²×C₁₃₉	semidirect
485. #391	C₂²×C₁₃₉	semidirect
486. #391	C₂²×C₁₃₉	semidirect
487. #391	C₂²×C₁₃₉	semidirect
488. #391	C₂²×C₁₃₉	semidirect
489. #391	C₂²×C₁₃₉	semidirect
490. #389	C₂²×C₁₃₉	semidirect
491. #389	C₂²×C₁₃₉	semidirect
496. #387	C₂²×C₁₃₉	semidirect
497. #387	C₂²×C₁₃₉	semidirect
498. #387	C₂²×C₁₃₉	semidirect
499. #387	C₂²×C₁₃₉	semidirect
500. #387	C₂²×C₁₃₉	semidirect
501. #387	C₂²×C₁₃₉	semidirect
502. #387	C₂²×C₁₃₉	semidirect
503. #387	C₂²×C₁₃₉	semidirect
511. #382	C₂²×C₁₃₉	semidirect
518. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
519. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
520. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
575. C₂×C₂²⋊C₄	Q₈×C₁₃₉	semidirect
668. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
722. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2665×C₁₃₉	2
#2626×C₁₃₉	2
#2607×C₁₃₉	2
#2589×C₁₃₉	2
#2574×C₁₃₉	2
#2549×C₁₃₉	2
#2505×C₁₃₉	2
#2492×C₁₃₉	2
#2465×C₁₃₉	2
#2439×C₁₃₉	2
#2437×C₁₃₉	2
#2434×C₁₃₉	2
#2396×C₁₃₉	2
C₂×#393×C₁₃₉	2
#2368×C₁₃₉	2
#2342×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
#2273×C₁₃₉	2
#35705	139

Subgroups — C139×#35705 #48030301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35705 #48030301