Subgroups — C₁₃₉×#36103 #48030699

Order 35584.

3522 conjugacy classes of subgroups.

The subgroup lattice has 860 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	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2847×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2449×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2443×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2440×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2416×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2406×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
21	#547×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	#525×C₁₃₉	—	2	16	no	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
34	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#120×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	4	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₁₃₉	—	2	8	no	—
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	#399×C₁₃₉	C₂²	1	4	yes	complemented
52	#398×C₁₃₉	C₂²	1	4	yes	complemented
53	#398×C₁₃₉	C₂²	1	2	yes	complemented
54	#397×C₁₃₉	C₂²	1	2	yes	complemented
55	#396×C₁₃₉	C₂²	1	4	yes	complemented
56	#395×C₁₃₉	C₂²	1	4	yes	complemented
57	#394×C₁₃₉	C₂²	1	4	yes	complemented
58	#390×C₁₃₉	C₂²	1	2	yes	complemented
59	#389×C₁₃₉	C₂²	1	2	yes	complemented
60	#389×C₁₃₉	C₂²	1	4	yes	complemented
61	#389×C₁₃₉	C₂²	1	2	yes	complemented
62	#388×C₁₃₉	C₂²	1	4	yes	complemented
63	#387×C₁₃₉	C₂²	1	4	yes	complemented
64	#386×C₁₃₉	C₂²	1	1	yes	characteristic
65	#386×C₁₃₉	C₂²	1	2	yes	—
66	#386×C₁₃₉	C₂²	1	2	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	1	yes	characteristic
71	#385×C₁₃₉	C₂²	1	2	yes	—
72	#385×C₁₃₉	C₂²	1	4	yes	—
73	#385×C₁₃₉	C₂²	1	4	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	complemented
75	#385×C₁₃₉	C₂²	1	4	yes	complemented
76	#384×C₁₃₉	C₂²	1	2	yes	complemented
77	#381×C₁₃₉	C₂²	1	2	yes	—
78	#381×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	complemented
82	#379×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
86	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂×#41×C₁₃₉	—	2	8	no	—
89	C₂×#41×C₁₃₉	—	4	4	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	—	2	4	no	—
98	C₂³×C₄×C₁₃₉	—	2	8	no	—
99	C₂³×C₄×C₁₃₉	—	2	8	no	—
100	C₂³×C₄×C₁₃₉	—	2	8	no	—
101	C₂³×C₄×C₁₃₉	—	4	4	no	—
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	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
114	#123×C₁₃₉	—	2	8	no	—
115	#123×C₁₃₉	—	2	8	no	—
116	#123×C₁₃₉	—	2	8	no	—
117	#123×C₁₃₉	—	2	8	no	—
118	#123×C₁₃₉	—	4	4	no	—
119	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
120	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
121	#121×C₁₃₉	—	2	16	no	—
122	#121×C₁₃₉	—	2	4	no	—
123	#121×C₁₃₉	—	2	8	no	—
124	#121×C₁₃₉	—	2	4	no	—
125	#120×C₁₃₉	—	2	8	no	—
126	#120×C₁₃₉	D₄	1	8	yes	complemented
127	C₄×D₄×C₁₃₉	—	2	16	no	—
128	C₄×D₄×C₁₃₉	—	2	4	no	—
129	C₄×D₄×C₁₃₉	—	2	8	no	—
130	C₄×D₄×C₁₃₉	—	2	4	no	—
131	C₄×D₄×C₁₃₉	—	2	16	no	—
132	#117×C₁₃₉	—	2	8	no	—
133	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
134	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
136	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
137	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
138	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊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	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	4	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	4	yes	—
186	C₂⁴×C₁₃₉	—	2	2	no	—
187	C₂⁴×C₁₃₉	—	2	4	no	—
188	C₂⁴×C₁₃₉	—	2	2	no	—
189	C₂⁴×C₁₃₉	—	2	4	no	—
190	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
191	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
195	#41×C₁₃₉	—	4	32	no	—
196	C₂×Q₈×C₁₃₉	—	2	4	no	—
197	C₂×Q₈×C₁₃₉	—	2	4	no	—
198	C₂×Q₈×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	—	2	2	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	4	no	—
203	C₂×D₄×C₁₃₉	—	2	8	no	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	8	no	—
208	C₂×D₄×C₁₃₉	—	2	4	no	—
209	C₂×D₄×C₁₃₉	—	2	8	no	—
210	C₂×D₄×C₁₃₉	—	2	2	no	—
211	C₂×D₄×C₁₃₉	—	2	4	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	4	2	no	—
214	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
215	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₁₃₉	—	2	32	no	—
217	C₂²×C₄×C₁₃₉	—	2	2	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	4	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	2	4	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	8	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	8	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	8	no	—
234	C₂²×C₄×C₁₃₉	—	2	8	no	—
235	C₂²×C₄×C₁₃₉	—	2	2	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	4	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	4	no	—
240	C₂²×C₄×C₁₃₉	—	4	4	no	—
241	C₂²×C₄×C₁₃₉	—	4	4	no	—
242	C₂²×C₄×C₁₃₉	—	4	2	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	—	4	32	no	—
245	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
247	C₂²×C₄×C₁₃₉	#41	1	8	yes	complemented
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₄⋊C₄×C₁₃₉	—	2	8	no	—
262	C₄⋊C₄×C₁₃₉	—	2	8	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	2	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	8	no	—
268	C₄⋊C₄×C₁₃₉	—	2	2	no	—
269	C₄⋊C₄×C₁₃₉	—	2	8	no	—
270	C₄⋊C₄×C₁₃₉	—	2	8	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	4	4	no	—
275	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
293	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
294	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
295	C₄²×C₁₃₉	—	2	8	no	—
296	C₄²×C₁₃₉	—	2	2	no	—
297	C₄²×C₁₃₉	—	2	4	no	—
298	C₂³×C₁₃₉	—	2	8	no	—
299	C₂³×C₁₃₉	—	2	8	no	—
300	C₂³×C₁₃₉	—	2	16	no	—
301	C₂³×C₁₃₉	—	2	8	no	—
302	C₂³×C₁₃₉	—	2	16	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	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	—	2	1	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	4	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	4	no	—
318	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
319	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
320	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
321	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
322	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
323	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
324	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
325	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃₉	—	4	8	no	—
327	D₄×C₁₃₉	—	2	8	no	—
328	D₄×C₁₃₉	—	2	16	no	—
329	D₄×C₁₃₉	—	4	8	no	—
330	D₄×C₁₃₉	—	4	8	no	—
331	D₄×C₁₃₉	—	4	16	no	—
332	D₄×C₁₃₉	—	4	4	no	—
333	C₂×C₄×C₁₃₉	—	2	16	no	—
334	C₂×C₄×C₁₃₉	—	2	8	no	—
335	C₂×C₄×C₁₃₉	—	2	16	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	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	8	no	—
348	C₂×C₄×C₁₃₉	—	2	16	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	4	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	4	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	4	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	4	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
365	C₂×C₄×C₁₃₉	—	4	8	no	—
366	C₂×C₄×C₁₃₉	—	4	16	no	—
367	C₂×C₄×C₁₃₉	—	4	16	no	—
368	C₂×C₄×C₁₃₉	—	4	8	no	—
369	C₂×C₄×C₁₃₉	—	4	8	no	—
370	C₂×C₄×C₁₃₉	—	4	4	no	—
371	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
372	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
378	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
379	C₂²×C₁₃₉	—	2	32	no	—
380	C₂²×C₁₃₉	—	2	2	no	—
381	C₂²×C₁₃₉	—	2	4	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	4	no	—
384	C₂²×C₁₃₉	—	2	4	no	—
385	C₂²×C₁₃₉	—	2	2	no	—
386	C₂²×C₁₃₉	—	2	4	no	—
387	C₂²×C₁₃₉	—	2	4	no	—
388	C₂²×C₁₃₉	—	2	4	no	—
389	C₂²×C₁₃₉	—	2	4	no	—
390	C₂²×C₁₃₉	—	2	2	no	—
391	C₂²×C₁₃₉	—	2	4	no	—
392	C₂²×C₁₃₉	—	4	1	no	—
393	C₂²×C₁₃₉	—	4	1	no	—
394	C₂²×C₁₃₉	—	4	2	no	—
395	C₂²×C₁₃₉	—	4	2	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	—	4	4	no	—
398	C₂²×C₁₃₉	—	4	2	no	—
399	C₂²×C₁₃₉	—	4	4	no	—
400	C₂²×C₁₃₉	D₄²	1	4	yes	—
401	C₂²×C₁₃₉	#547	1	8	yes	complemented
402	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
403	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
404	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
405	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
406	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
407	C₄×C₁₃₉	—	2	2	no	—
408	C₄×C₁₃₉	—	2	4	no	—
409	C₄×C₁₃₉	—	2	4	no	—
410	C₄×C₁₃₉	—	2	4	no	—
411	C₄×C₁₃₉	—	2	2	no	—
412	C₄×C₁₃₉	—	2	4	no	—
413	C₄×C₁₃₉	—	4	1	no	—
414	C₄×C₁₃₉	—	4	4	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₄×C₁₃₉	—	4	4	no	—
417	C₄×C₁₃₉	—	4	1	no	—
418	C₄×C₁₃₉	—	4	2	no	—
419	C₄×C₁₃₉	#525	1	4	yes	complemented
420	C₂×C₁₃₉	—	2	4	no	—
421	C₂×C₁₃₉	—	2	8	no	—
422	C₂×C₁₃₉	—	4	2	no	—
423	C₂×C₁₃₉	—	8	2	no	—
424	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
425	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
426	C₂×C₁₃₉	C₂×#547	1	2	yes	—
427	C₂×C₁₃₉	#3486	1	1	yes	characteristic
428	C₂×C₁₃₉	#3492	1	2	yes	—
429	#36103	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₁₃₉	#36103	1	1	yes	characteristic, direct product factor, Sylow
431	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂×#525	C₂×C₁₃₉	1	2	yes	complemented
433	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
434	#2849	C₂×C₁₃₉	1	2	yes	complemented
435	#2847	C₂×C₁₃₉	1	1	yes	characteristic, complemented
436	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
437	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
438	#2449	C₂×C₁₃₉	1	4	yes	complemented
439	#2443	C₂×C₁₃₉	1	4	yes	complemented
440	#2440	C₂×C₁₃₉	1	2	yes	complemented
441	#2416	C₂×C₁₃₉	1	2	yes	complemented
442	#2413	C₂×C₁₃₉	1	2	yes	complemented
443	#2406	C₂×C₁₃₉	1	2	yes	complemented
444	#2361	C₂×C₁₃₉	1	2	yes	complemented
445	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
446	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic, complemented
448	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
449	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
451	#547	—	2	8	no	—
452	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
453	#525	—	2	16	no	—
454	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
455	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
456	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
457	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
458	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
459	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
460	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
461	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
462	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
464	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
465	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
466	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
468	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
469	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
470	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
472	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
473	C₂²×C₄⋊C₄	—	2	8	no	—
474	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
475	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
476	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
477	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
478	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
481	#399	C₂²×C₁₃₉	1	4	yes	complemented
482	#398	C₂²×C₁₃₉	1	4	yes	complemented
483	#398	C₂²×C₁₃₉	1	2	yes	complemented
484	#397	C₂²×C₁₃₉	1	2	yes	complemented
485	#396	C₂²×C₁₃₉	1	4	yes	complemented
486	#395	C₂²×C₁₃₉	1	4	yes	complemented
487	#394	C₂²×C₁₃₉	1	4	yes	complemented
488	#390	C₂²×C₁₃₉	1	2	yes	complemented
489	#389	C₂²×C₁₃₉	1	2	yes	complemented
490	#389	C₂²×C₁₃₉	1	4	yes	complemented
491	#389	C₂²×C₁₃₉	1	2	yes	complemented
492	#388	C₂²×C₁₃₉	1	4	yes	complemented
493	#387	C₂²×C₁₃₉	1	4	yes	complemented
494	#386	C₂²×C₁₃₉	1	2	yes	—
495	#386	C₂²×C₁₃₉	1	4	yes	—
496	#386	C₂²×C₁₃₉	1	4	yes	—
497	#386	C₂²×C₁₃₉	1	4	yes	—
498	#386	C₂²×C₁₃₉	1	1	yes	characteristic
499	#386	C₂²×C₁₃₉	1	2	yes	—
500	#385	C₂²×C₁₃₉	1	4	yes	—
501	#385	C₂²×C₁₃₉	1	4	yes	—
502	#385	C₂²×C₁₃₉	1	1	yes	characteristic
503	#385	C₂²×C₁₃₉	1	2	yes	—
504	#385	C₂²×C₁₃₉	1	4	yes	complemented
505	#385	C₂²×C₁₃₉	1	4	yes	complemented
506	#384	C₂²×C₁₃₉	1	2	yes	complemented
507	#381	C₂²×C₁₃₉	1	2	yes	—
508	#381	C₂²×C₁₃₉	1	2	yes	—
509	#380	C₂²×C₁₃₉	1	1	yes	characteristic
510	#380	C₂²×C₁₃₉	1	2	yes	—
511	#380	C₂²×C₁₃₉	1	2	yes	complemented
512	#379	C₂²×C₁₃₉	1	1	yes	characteristic
513	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
514	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
515	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
516	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×#41	—	2	8	no	—
518	C₂×#41	—	2	8	no	—
519	C₂×#41	—	4	4	no	—
520	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂³×C₄	—	2	4	no	—
528	C₂³×C₄	—	2	8	no	—
529	C₂³×C₄	—	2	8	no	—
530	C₂³×C₄	—	2	8	no	—
531	C₂³×C₄	—	4	4	no	—
532	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
537	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
538	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₄⋊Q₈	—	2	4	no	—
544	#123	—	2	8	no	—
545	#123	—	2	8	no	—
546	#123	—	2	8	no	—
547	#123	—	2	8	no	—
548	#123	—	4	4	no	—
549	C₂²⋊Q₈	—	2	8	no	—
550	C₂²⋊Q₈	—	2	16	no	—
551	#121	—	2	16	no	—
552	#121	—	2	4	no	—
553	#121	—	2	8	no	—
554	#121	—	2	4	no	—
555	#120	—	2	8	no	—
556	#120	D₄×C₁₃₉	1	8	yes	complemented
557	C₄×D₄	—	2	16	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	8	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	16	no	—
562	#117	—	2	8	no	—
563	C₂×C₄⋊C₄	—	2	8	no	—
564	C₂×C₄⋊C₄	—	2	4	no	—
565	C₂×C₄⋊C₄	—	2	8	no	—
566	C₂×C₄⋊C₄	—	2	8	no	—
567	C₂×C₄⋊C₄	—	2	16	no	—
568	C₂×C₄⋊C₄	—	2	4	no	—
569	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
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	4	yes	—
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	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
605	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	4	yes	—
611	#95	C₂³×C₁₃₉	1	4	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	4	yes	—
614	#95	C₂³×C₁₃₉	1	4	yes	—
615	#95	C₂³×C₁₃₉	1	4	yes	—
616	C₂⁴	—	2	2	no	—
617	C₂⁴	—	2	4	no	—
618	C₂⁴	—	2	2	no	—
619	C₂⁴	—	2	4	no	—
620	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
621	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
622	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
625	#41	—	4	32	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	4	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	8	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	8	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	8	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
645	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
646	C₂²×C₄	—	2	32	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	8	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	8	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	2	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	32	no	—
675	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
676	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
677	C₂²×C₄	#41×C₁₃₉	1	8	yes	complemented
678	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
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	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	2	8	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	8	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	8	no	—
700	C₄⋊C₄	—	2	8	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	4	4	no	—
705	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
706	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
707	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	8	no	—
710	C₂²⋊C₄	—	2	8	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	8	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	8	no	—
722	C₂²⋊C₄	—	4	4	no	—
723	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
724	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
725	C₄²	—	2	8	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	4	no	—
728	C₂³	—	2	8	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	2	16	no	—
731	C₂³	—	2	8	no	—
732	C₂³	—	2	16	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	4	no	—
748	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
749	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
750	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
751	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
752	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
753	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
754	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
755	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
756	Q₈	—	4	8	no	—
757	D₄	—	2	8	no	—
758	D₄	—	2	16	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	16	no	—
762	D₄	—	4	4	no	—
763	C₂×C₄	—	2	16	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	16	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	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	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	8	no	—
778	C₂×C₄	—	2	16	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	16	no	—
797	C₂×C₄	—	4	16	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
802	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
804	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
807	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
808	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
809	C₂²	—	2	32	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	4	no	—
830	C₂²	D₄²×C₁₃₉	1	4	yes	—
831	C₂²	#547×C₁₃₉	1	8	yes	complemented
832	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
833	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
834	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
835	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
836	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	4	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	4	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	4	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	#525×C₁₃₉	1	4	yes	complemented
850	C₂	—	2	4	no	—
851	C₂	—	2	8	no	—
852	C₂	—	4	2	no	—
853	C₂	—	8	2	no	—
854	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
855	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
856	C₂	C₂×#547×C₁₃₉	1	2	yes	—
857	C₂	#3486×C₁₃₉	1	1	yes	characteristic
858	C₂	#3492×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×#525×C₁₃₉	C₂	semidirect
3. C₂³×C₄⋊C₄×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2847×C₁₃₉	C₂	semidirect
6. #2501×C₁₃₉	C₂	semidirect
7. #2486×C₁₃₉	C₂	semidirect
8. #2449×C₁₃₉	C₂	semidirect
9. #2443×C₁₃₉	C₂	semidirect
10. #2440×C₁₃₉	C₂	semidirect
11. #2416×C₁₃₉	C₂	semidirect
12. #2413×C₁₃₉	C₂	semidirect
13. #2406×C₁₃₉	C₂	semidirect
14. #2361×C₁₃₉	C₂	semidirect
15. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
16. #2344×C₁₃₉	C₂	semidirect
17. C₄×#120×C₁₃₉	C₂	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×#123×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×#121×C₁₃₉	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
51. #399×C₁₃₉	C₂²	semidirect
52. #398×C₁₃₉	C₂²	semidirect
53. #398×C₁₃₉	C₂²	semidirect
54. #397×C₁₃₉	C₂²	semidirect
55. #396×C₁₃₉	C₂²	semidirect
56. #395×C₁₃₉	C₂²	semidirect
57. #394×C₁₃₉	C₂²	semidirect
58. #390×C₁₃₉	C₂²	semidirect
59. #389×C₁₃₉	C₂²	semidirect
60. #389×C₁₃₉	C₂²	semidirect
61. #389×C₁₃₉	C₂²	semidirect
62. #388×C₁₃₉	C₂²	semidirect
63. #387×C₁₃₉	C₂²	semidirect
74. #385×C₁₃₉	C₂²	semidirect
75. #385×C₁₃₉	C₂²	semidirect
76. #384×C₁₃₉	C₂²	semidirect
81. #380×C₁₃₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
126. #120×C₁₃₉	D₄	semidirect
139. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
247. C₂²×C₄×C₁₃₉	#41	semidirect
401. C₂²×C₁₃₉	#547	semidirect
419. C₄×C₁₃₉	#525	semidirect
429. #36103	C₁₃₉	direct (N × H)
430. C₁₃₉	#36103	direct (N × H)
431. C₂×#547	C₂×C₁₃₉	semidirect
432. C₂×#525	C₂×C₁₃₉	semidirect
433. C₂³×C₄⋊C₄	C₂×C₁₃₉	semidirect
434. #2849	C₂×C₁₃₉	semidirect
435. #2847	C₂×C₁₃₉	semidirect
436. #2501	C₂×C₁₃₉	semidirect
437. #2486	C₂×C₁₃₉	semidirect
438. #2449	C₂×C₁₃₉	semidirect
439. #2443	C₂×C₁₃₉	semidirect
440. #2440	C₂×C₁₃₉	semidirect
441. #2416	C₂×C₁₃₉	semidirect
442. #2413	C₂×C₁₃₉	semidirect
443. #2406	C₂×C₁₃₉	semidirect
444. #2361	C₂×C₁₃₉	semidirect
445. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
446. #2344	C₂×C₁₃₉	semidirect
447. C₄×#120	C₂×C₁₃₉	semidirect
452. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
458. C₂×#123	C₂²×C₁₃₉	semidirect
460. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
464. C₂×#121	C₂²×C₁₃₉	semidirect
471. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
480. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
481. #399	C₂²×C₁₃₉	semidirect
482. #398	C₂²×C₁₃₉	semidirect
483. #398	C₂²×C₁₃₉	semidirect
484. #397	C₂²×C₁₃₉	semidirect
485. #396	C₂²×C₁₃₉	semidirect
486. #395	C₂²×C₁₃₉	semidirect
487. #394	C₂²×C₁₃₉	semidirect
488. #390	C₂²×C₁₃₉	semidirect
489. #389	C₂²×C₁₃₉	semidirect
490. #389	C₂²×C₁₃₉	semidirect
491. #389	C₂²×C₁₃₉	semidirect
492. #388	C₂²×C₁₃₉	semidirect
493. #387	C₂²×C₁₃₉	semidirect
504. #385	C₂²×C₁₃₉	semidirect
505. #385	C₂²×C₁₃₉	semidirect
506. #384	C₂²×C₁₃₉	semidirect
511. #380	C₂²×C₁₃₉	semidirect
513. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
556. #120	D₄×C₁₃₉	semidirect
569. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
677. C₂²×C₄	#41×C₁₃₉	semidirect
831. C₂²	#547×C₁₃₉	semidirect
849. C₄	#525×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×#525×C₁₃₉	2
C₂³×C₄⋊C₄×C₁₃₉	2
#2849×C₁₃₉	2
#2847×C₁₃₉	2
#2501×C₁₃₉	2
#2486×C₁₃₉	2
#2449×C₁₃₉	2
#2443×C₁₃₉	2
#2440×C₁₃₉	2
#2416×C₁₃₉	2
#2413×C₁₃₉	2
#2406×C₁₃₉	2
#2361×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36103	139

Subgroups — C139×#36103 #48030699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36103 #48030699