Subgroups — C₁₃₉×#35730 #48030326

Order 35584.

2838 conjugacy classes of subgroups.

The subgroup lattice has 804 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×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2638×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2457×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2418×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2408×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2404×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2388×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	#547×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
27	#518×C₁₃₉	—	2	8	no	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	#400×C₁₃₉	C₂²	1	2	yes	complemented
43	#399×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	#397×C₁₃₉	C₂²	1	1	yes	characteristic
46	#397×C₁₃₉	C₂²	1	2	yes	complemented
47	#397×C₁₃₉	C₂²	1	4	yes	complemented
48	#396×C₁₃₉	C₂²	1	2	yes	complemented
49	#395×C₁₃₉	C₂²	1	2	yes	complemented
50	#394×C₁₃₉	C₂²	1	4	yes	—
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	#394×C₁₃₉	C₂²	1	4	yes	complemented
54	#393×C₁₃₉	C₂²	1	2	yes	—
55	#393×C₁₃₉	C₂²	1	2	yes	complemented
56	#393×C₁₃₉	C₂²	1	2	yes	complemented
57	#392×C₁₃₉	C₂²	1	4	yes	—
58	#392×C₁₃₉	C₂²	1	1	yes	characteristic
59	#392×C₁₃₉	C₂²	1	2	yes	complemented
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	complemented
65	#388×C₁₃₉	C₂²	1	4	yes	complemented
66	#387×C₁₃₉	C₂²	1	4	yes	complemented
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	complemented
69	#386×C₁₃₉	C₂²	1	4	yes	complemented
70	#386×C₁₃₉	C₂²	1	4	yes	complemented
71	#385×C₁₃₉	C₂²	1	4	yes	complemented
72	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
73	#382×C₁₃₉	C₂²	1	2	yes	complemented
74	#381×C₁₃₉	C₂²	1	4	yes	complemented
75	#381×C₁₃₉	C₂²	1	2	yes	complemented
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	2	yes	complemented
78	#380×C₁₃₉	C₂²	1	4	yes	complemented
79	#379×C₁₃₉	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂×#41×C₁₃₉	—	4	8	no	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	—	2	4	no	—
91	C₂²×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	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	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
107	#123×C₁₃₉	—	2	16	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#121×C₁₃₉	—	2	8	no	—
111	#120×C₁₃₉	—	4	8	no	—
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	4	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	—	4	8	no	—
120	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
121	#117×C₁₃₉	—	2	4	no	—
122	#117×C₁₃₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
137	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	1	yes	characteristic
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	1	yes	characteristic
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	C₂⁴×C₁₃₉	—	2	4	no	—
176	C₂⁴×C₁₃₉	—	2	4	no	—
177	C₂⁴×C₁₃₉	—	2	4	no	—
178	C₂⁴×C₁₃₉	—	4	4	no	—
179	C₂⁴×C₁₃₉	—	4	4	no	—
180	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
184	#41×C₁₃₉	—	4	32	no	—
185	C₂×Q₈×C₁₃₉	—	2	4	no	—
186	C₂×Q₈×C₁₃₉	—	4	4	no	—
187	C₂×D₄×C₁₃₉	—	2	32	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	2	8	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	8	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	8	no	—
197	C₂×D₄×C₁₃₉	—	2	2	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	2	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂×D₄×C₁₃₉	—	4	2	no	—
205	C₂×D₄×C₁₃₉	—	4	4	no	—
206	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
207	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	8	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	8	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	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	—	4	4	no	—
219	C₂²×C₄×C₁₃₉	—	4	4	no	—
220	C₂²×C₄×C₁₃₉	—	4	4	no	—
221	C₂²×C₄×C₁₃₉	—	4	4	no	—
222	C₂²×C₄×C₁₃₉	—	4	4	no	—
223	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
224	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	1	yes	characteristic
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	8	no	—
240	C₄⋊C₄×C₁₃₉	—	2	2	no	—
241	C₄⋊C₄×C₁₃₉	—	2	2	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	4	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	4	no	—
249	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
250	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	2	no	—
272	C₄²×C₁₃₉	—	2	4	no	—
273	C₄²×C₁₃₉	—	4	4	no	—
274	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
275	C₂³×C₁₃₉	—	2	16	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	1	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	4	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	4	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	8	4	no	—
295	C₂³×C₁₃₉	—	8	8	no	—
296	C₂³×C₁₃₉	—	8	4	no	—
297	C₂³×C₁₃₉	—	8	8	no	—
298	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
299	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
300	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
301	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
302	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
303	Q₈×C₁₃₉	—	4	8	no	—
304	D₄×C₁₃₉	—	2	16	no	—
305	D₄×C₁₃₉	—	2	8	no	—
306	D₄×C₁₃₉	—	2	8	no	—
307	D₄×C₁₃₉	—	2	8	no	—
308	D₄×C₁₃₉	—	4	8	no	—
309	D₄×C₁₃₉	—	4	16	no	—
310	D₄×C₁₃₉	—	4	16	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	8	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	4	no	—
329	C₂×C₄×C₁₃₉	—	2	2	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	—	2	4	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	4	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	4	8	no	—
339	C₂×C₄×C₁₃₉	—	4	16	no	—
340	C₂×C₄×C₁₃₉	—	4	8	no	—
341	C₂×C₄×C₁₃₉	—	8	4	no	—
342	C₂×C₄×C₁₃₉	—	8	4	no	—
343	C₂×C₄×C₁₃₉	—	8	4	no	—
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	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	2	4	no	—
353	C₂²×C₁₃₉	—	2	4	no	—
354	C₂²×C₁₃₉	—	2	4	no	—
355	C₂²×C₁₃₉	—	2	4	no	—
356	C₂²×C₁₃₉	—	2	4	no	—
357	C₂²×C₁₃₉	—	2	4	no	—
358	C₂²×C₁₃₉	—	2	4	no	—
359	C₂²×C₁₃₉	—	2	4	no	—
360	C₂²×C₁₃₉	—	2	8	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	1	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	4	no	—
366	C₂²×C₁₃₉	—	4	4	no	—
367	C₂²×C₁₃₉	—	4	2	no	—
368	C₂²×C₁₃₉	—	4	2	no	—
369	C₂²×C₁₃₉	—	4	1	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	4	4	no	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	8	16	no	—
374	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
375	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
378	C₂²×C₁₃₉	#585	1	2	yes	—
379	C₄×C₁₃₉	—	2	2	no	—
380	C₄×C₁₃₉	—	2	4	no	—
381	C₄×C₁₃₉	—	2	2	no	—
382	C₄×C₁₃₉	—	2	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	—	4	4	no	—
385	C₄×C₁₃₉	—	4	1	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	—	4	1	no	—
390	C₄×C₁₃₉	—	4	4	no	—
391	C₄×C₁₃₉	#525	1	4	yes	—
392	C₂×C₁₃₉	—	4	4	no	—
393	C₂×C₁₃₉	—	4	4	no	—
394	C₂×C₁₃₉	—	4	4	no	—
395	C₂×C₁₃₉	—	4	2	no	—
396	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
397	C₂×C₁₃₉	#3484	1	1	yes	characteristic
398	C₂×C₁₃₉	#3494	1	2	yes	—
399	C₂×C₁₃₉	#3500	1	1	yes	characteristic
400	C₂×C₁₃₉	#3513	1	2	yes	—
401	#35730	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₁₃₉	#35730	1	1	yes	characteristic, direct product factor, Sylow
403	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2638	C₂×C₁₃₉	1	2	yes	complemented
406	#2628	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2561	C₂×C₁₃₉	1	2	yes	complemented
409	#2535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	#2457	C₂×C₁₃₉	1	4	yes	complemented
411	#2420	C₂×C₁₃₉	1	2	yes	complemented
412	#2418	C₂×C₁₃₉	1	4	yes	complemented
413	#2408	C₂×C₁₃₉	1	2	yes	complemented
414	#2404	C₂×C₁₃₉	1	2	yes	complemented
415	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2388	C₂×C₁₃₉	1	2	yes	complemented
417	#2361	C₂×C₁₃₉	1	2	yes	complemented
418	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
419	#2352	C₂×C₁₃₉	1	2	yes	complemented
420	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
421	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
422	#547	—	2	8	no	—
423	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
424	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
425	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
426	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
427	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
428	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
429	#518	—	2	8	no	—
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
436	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
438	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
439	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
441	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
442	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
444	#400	C₂²×C₁₃₉	1	2	yes	complemented
445	#399	C₂²×C₁₃₉	1	2	yes	—
446	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
447	#397	C₂²×C₁₃₉	1	1	yes	characteristic
448	#397	C₂²×C₁₃₉	1	2	yes	complemented
449	#397	C₂²×C₁₃₉	1	4	yes	complemented
450	#396	C₂²×C₁₃₉	1	2	yes	complemented
451	#395	C₂²×C₁₃₉	1	2	yes	complemented
452	#394	C₂²×C₁₃₉	1	4	yes	—
453	#394	C₂²×C₁₃₉	1	2	yes	—
454	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
455	#394	C₂²×C₁₃₉	1	4	yes	complemented
456	#393	C₂²×C₁₃₉	1	2	yes	—
457	#393	C₂²×C₁₃₉	1	2	yes	complemented
458	#393	C₂²×C₁₃₉	1	2	yes	complemented
459	#392	C₂²×C₁₃₉	1	4	yes	—
460	#392	C₂²×C₁₃₉	1	1	yes	characteristic
461	#392	C₂²×C₁₃₉	1	2	yes	complemented
462	#390	C₂²×C₁₃₉	1	2	yes	—
463	#390	C₂²×C₁₃₉	1	2	yes	—
464	#389	C₂²×C₁₃₉	1	2	yes	complemented
465	#388	C₂²×C₁₃₉	1	4	yes	—
466	#388	C₂²×C₁₃₉	1	4	yes	complemented
467	#388	C₂²×C₁₃₉	1	4	yes	complemented
468	#387	C₂²×C₁₃₉	1	4	yes	complemented
469	#386	C₂²×C₁₃₉	1	4	yes	—
470	#386	C₂²×C₁₃₉	1	4	yes	complemented
471	#386	C₂²×C₁₃₉	1	4	yes	complemented
472	#386	C₂²×C₁₃₉	1	4	yes	complemented
473	#385	C₂²×C₁₃₉	1	4	yes	complemented
474	#382	C₂²×C₁₃₉	1	2	yes	complemented
475	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
476	#381	C₂²×C₁₃₉	1	4	yes	complemented
477	#381	C₂²×C₁₃₉	1	2	yes	complemented
478	#380	C₂²×C₁₃₉	1	2	yes	—
479	#380	C₂²×C₁₃₉	1	4	yes	complemented
480	#380	C₂²×C₁₃₉	1	2	yes	complemented
481	#379	C₂²×C₁₃₉	1	4	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
484	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
485	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
486	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
487	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
488	C₂×#41	—	2	8	no	—
489	C₂×#41	—	4	8	no	—
490	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	—	2	4	no	—
493	C₂²×D₄	—	2	4	no	—
494	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₄⋊Q₈	—	2	4	no	—
509	#123	—	2	16	no	—
510	C₂²⋊Q₈	—	2	8	no	—
511	#121	—	2	8	no	—
512	#121	—	2	8	no	—
513	#120	—	4	8	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	8	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	4	8	no	—
522	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
523	#117	—	2	4	no	—
524	#117	—	2	4	no	—
525	C₂×C₄⋊C₄	—	2	8	no	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	—	2	8	no	—
539	C₂×C₂²⋊C₄	—	2	8	no	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
565	#95	C₂³×C₁₃₉	1	1	yes	characteristic
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	#95	C₂³×C₁₃₉	1	4	yes	—
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	1	yes	characteristic
572	#95	C₂³×C₁₃₉	1	4	yes	—
573	#95	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	4	yes	—
575	#95	C₂³×C₁₃₉	1	4	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	C₂⁴	—	2	4	no	—
578	C₂⁴	—	2	4	no	—
579	C₂⁴	—	2	4	no	—
580	C₂⁴	—	4	4	no	—
581	C₂⁴	—	4	4	no	—
582	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
583	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
586	#41	—	4	32	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×D₄	—	2	32	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	8	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
609	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	8	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
626	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	4	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	8	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	4	no	—
651	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	8	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	4	4	no	—
669	C₂²⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	4	4	no	—
676	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
677	C₂³	—	2	16	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	8	4	no	—
697	C₂³	—	8	8	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	8	no	—
700	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
701	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
702	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
703	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
704	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
705	Q₈	—	4	8	no	—
706	D₄	—	2	16	no	—
707	D₄	—	2	8	no	—
708	D₄	—	2	8	no	—
709	D₄	—	2	8	no	—
710	D₄	—	4	16	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	16	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	16	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
747	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
748	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
749	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
750	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
751	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
752	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	2	4	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	8	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	16	no	—
776	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
778	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
779	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
780	C₂²	#585×C₁₃₉	1	2	yes	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	4	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	4	no	—
793	C₄	#525×C₁₃₉	1	4	yes	—
794	C₂	—	4	2	no	—
795	C₂	—	4	4	no	—
796	C₂	—	4	4	no	—
797	C₂	—	4	4	no	—
798	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
799	C₂	#3484×C₁₃₉	1	1	yes	characteristic
800	C₂	#3494×C₁₃₉	1	2	yes	—
801	C₂	#3500×C₁₃₉	1	1	yes	characteristic
802	C₂	#3513×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×#518×C₁₃₉	C₂	semidirect
3. #2638×C₁₃₉	C₂	semidirect
4. #2628×C₁₃₉	C₂	semidirect
5. #2563×C₁₃₉	C₂	semidirect
6. #2561×C₁₃₉	C₂	semidirect
7. #2535×C₁₃₉	C₂	semidirect
8. #2457×C₁₃₉	C₂	semidirect
9. #2420×C₁₃₉	C₂	semidirect
10. #2418×C₁₃₉	C₂	semidirect
11. #2408×C₁₃₉	C₂	semidirect
12. #2404×C₁₃₉	C₂	semidirect
13. #2392×C₁₃₉	C₂	semidirect
14. #2388×C₁₃₉	C₂	semidirect
15. #2361×C₁₃₉	C₂	semidirect
16. #2357×C₁₃₉	C₂	semidirect
17. #2352×C₁₃₉	C₂	semidirect
18. C₂²×#41×C₁₃₉	C₂²	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×#123×C₁₃₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
42. #400×C₁₃₉	C₂²	semidirect
44. #398×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
47. #397×C₁₃₉	C₂²	semidirect
48. #396×C₁₃₉	C₂²	semidirect
49. #395×C₁₃₉	C₂²	semidirect
52. #394×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
55. #393×C₁₃₉	C₂²	semidirect
56. #393×C₁₃₉	C₂²	semidirect
59. #392×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
64. #388×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #387×C₁₃₉	C₂²	semidirect
68. #386×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
70. #386×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #382×C₁₃₉	C₂²	semidirect
73. #382×C₁₃₉	C₂²	semidirect
74. #381×C₁₃₉	C₂²	semidirect
75. #381×C₁₃₉	C₂²	semidirect
77. #380×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×D₄×C₁₃₉	D₄	semidirect
207. C₂×D₄×C₁₃₉	#41	semidirect
224. C₂²×C₄×C₁₃₉	#41	semidirect
401. #35730	C₁₃₉	direct (N × H)
402. C₁₃₉	#35730	direct (N × H)
403. C₂×#547	C₂×C₁₃₉	semidirect
404. C₂×#518	C₂×C₁₃₉	semidirect
405. #2638	C₂×C₁₃₉	semidirect
406. #2628	C₂×C₁₃₉	semidirect
407. #2563	C₂×C₁₃₉	semidirect
408. #2561	C₂×C₁₃₉	semidirect
409. #2535	C₂×C₁₃₉	semidirect
410. #2457	C₂×C₁₃₉	semidirect
411. #2420	C₂×C₁₃₉	semidirect
412. #2418	C₂×C₁₃₉	semidirect
413. #2408	C₂×C₁₃₉	semidirect
414. #2404	C₂×C₁₃₉	semidirect
415. #2392	C₂×C₁₃₉	semidirect
416. #2388	C₂×C₁₃₉	semidirect
417. #2361	C₂×C₁₃₉	semidirect
418. #2357	C₂×C₁₃₉	semidirect
419. #2352	C₂×C₁₃₉	semidirect
420. C₂²×#41	C₂²×C₁₃₉	semidirect
423. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
424. C₂×#123	C₂²×C₁₃₉	semidirect
425. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
437. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
438. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
441. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
444. #400	C₂²×C₁₃₉	semidirect
446. #398	C₂²×C₁₃₉	semidirect
448. #397	C₂²×C₁₃₉	semidirect
449. #397	C₂²×C₁₃₉	semidirect
450. #396	C₂²×C₁₃₉	semidirect
451. #395	C₂²×C₁₃₉	semidirect
454. #394	C₂²×C₁₃₉	semidirect
455. #394	C₂²×C₁₃₉	semidirect
457. #393	C₂²×C₁₃₉	semidirect
458. #393	C₂²×C₁₃₉	semidirect
461. #392	C₂²×C₁₃₉	semidirect
464. #389	C₂²×C₁₃₉	semidirect
466. #388	C₂²×C₁₃₉	semidirect
467. #388	C₂²×C₁₃₉	semidirect
468. #387	C₂²×C₁₃₉	semidirect
470. #386	C₂²×C₁₃₉	semidirect
471. #386	C₂²×C₁₃₉	semidirect
472. #386	C₂²×C₁₃₉	semidirect
473. #385	C₂²×C₁₃₉	semidirect
474. #382	C₂²×C₁₃₉	semidirect
475. #382	C₂²×C₁₃₉	semidirect
476. #381	C₂²×C₁₃₉	semidirect
477. #381	C₂²×C₁₃₉	semidirect
479. #380	C₂²×C₁₃₉	semidirect
480. #380	C₂²×C₁₃₉	semidirect
482. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
483. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
484. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
485. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
486. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
522. C₄×D₄	D₄×C₁₃₉	semidirect
609. C₂×D₄	#41×C₁₃₉	semidirect
626. C₂²×C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2638×C₁₃₉	2
#2628×C₁₃₉	2
#2563×C₁₃₉	2
#2561×C₁₃₉	2
#2535×C₁₃₉	2
#2457×C₁₃₉	2
#2420×C₁₃₉	2
#2418×C₁₃₉	2
#2408×C₁₃₉	2
#2404×C₁₃₉	2
#2392×C₁₃₉	2
#2388×C₁₃₉	2
#2361×C₁₃₉	2
#2357×C₁₃₉	2
#2352×C₁₃₉	2
#35730	139

Subgroups — C139×#35730 #48030326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35730 #48030326