Subgroups — C₁₃₉×#36022 #48030618

Order 35584.

2682 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2635×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2539×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2482×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2461×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2354×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#555×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
28	#518×C₁₃₉	—	2	8	no	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	2	yes	complemented
44	#399×C₁₃₉	C₂²	1	2	yes	—
45	#399×C₁₃₉	C₂²	1	2	yes	complemented
46	#399×C₁₃₉	C₂²	1	2	yes	complemented
47	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	#397×C₁₃₉	C₂²	1	1	yes	characteristic
49	#397×C₁₃₉	C₂²	1	2	yes	complemented
50	#397×C₁₃₉	C₂²	1	4	yes	complemented
51	#396×C₁₃₉	C₂²	1	2	yes	complemented
52	#395×C₁₃₉	C₂²	1	2	yes	complemented
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#394×C₁₃₉	C₂²	1	4	yes	complemented
57	#393×C₁₃₉	C₂²	1	2	yes	—
58	#392×C₁₃₉	C₂²	1	1	yes	characteristic
59	#392×C₁₃₉	C₂²	1	4	yes	—
60	#392×C₁₃₉	C₂²	1	2	yes	complemented
61	#390×C₁₃₉	C₂²	1	4	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	4	yes	complemented
65	#389×C₁₃₉	C₂²	1	2	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	complemented
68	#388×C₁₃₉	C₂²	1	4	yes	complemented
69	#388×C₁₃₉	C₂²	1	4	yes	complemented
70	#386×C₁₃₉	C₂²	1	4	yes	complemented
71	#386×C₁₃₉	C₂²	1	4	yes	complemented
72	#385×C₁₃₉	C₂²	1	4	yes	complemented
73	#384×C₁₃₉	C₂²	1	2	yes	complemented
74	#382×C₁₃₉	C₂²	1	1	yes	characteristic, 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	#379×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	—	2	4	no	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×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	4	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
104	#124×C₁₃₉	—	2	16	no	—
105	#123×C₁₃₉	—	4	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
107	#121×C₁₃₉	—	2	8	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#120×C₁₃₉	—	4	8	no	—
111	C₄×D₄×C₁₃₉	—	2	4	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	8	no	—
116	C₄×D₄×C₁₃₉	—	2	4	no	—
117	C₄×D₄×C₁₃₉	—	2	4	no	—
118	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
119	#117×C₁₃₉	—	2	8	no	—
120	#117×C₁₃₉	—	2	4	no	—
121	#117×C₁₃₉	—	2	8	no	—
122	#117×C₁₃₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	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	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×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	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	1	yes	characteristic
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂×Q₈×C₁₃₉	—	2	4	no	—
185	C₂×Q₈×C₁₃₉	—	4	4	no	—
186	C₂×D₄×C₁₃₉	—	2	32	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	8	no	—
191	C₂×D₄×C₁₃₉	—	2	8	no	—
192	C₂×D₄×C₁₃₉	—	2	2	no	—
193	C₂×D₄×C₁₃₉	—	2	2	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	2	no	—
196	C₂×D₄×C₁₃₉	—	2	2	no	—
197	C₂×D₄×C₁₃₉	—	2	2	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	4	2	no	—
200	C₂×D₄×C₁₃₉	—	4	2	no	—
201	C₂×D₄×C₁₃₉	—	4	4	no	—
202	C₂×D₄×C₁₃₉	—	4	4	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂×D₄×C₁₃₉	—	4	4	no	—
205	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
206	C₂×D₄×C₁₃₉	#41	1	4	yes	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	4	4	no	—
216	C₂²×C₄×C₁₃₉	—	4	4	no	—
217	C₂²×C₄×C₁₃₉	—	4	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	4	no	—
219	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
220	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₁₃₉	—	2	2	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	8	no	—
244	C₄⋊C₄×C₁₃₉	—	4	4	no	—
245	C₄⋊C₄×C₁₃₉	—	4	4	no	—
246	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
247	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
268	C₄²×C₁₃₉	—	2	8	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	2	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	4	4	no	—
273	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
274	C₂³×C₁₃₉	—	2	16	no	—
275	C₂³×C₁₃₉	—	2	1	no	—
276	C₂³×C₁₃₉	—	2	2	no	—
277	C₂³×C₁₃₉	—	2	1	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	4	no	—
282	C₂³×C₁₃₉	—	2	4	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	4	no	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	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	C₂⁵	1	1	yes	characteristic
302	Q₈×C₁₃₉	—	8	4	no	—
303	D₄×C₁₃₉	—	2	16	no	—
304	D₄×C₁₃₉	—	2	8	no	—
305	D₄×C₁₃₉	—	2	8	no	—
306	D₄×C₁₃₉	—	4	8	no	—
307	D₄×C₁₃₉	—	4	4	no	—
308	D₄×C₁₃₉	—	8	8	no	—
309	D₄×C₁₃₉	—	8	8	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	8	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	1	no	—
322	C₂×C₄×C₁₃₉	—	2	4	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	4	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	4	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	4	8	no	—
337	C₂×C₄×C₁₃₉	—	4	8	no	—
338	C₂×C₄×C₁₃₉	—	8	4	no	—
339	C₂×C₄×C₁₃₉	—	8	4	no	—
340	C₂×C₄×C₁₃₉	—	8	4	no	—
341	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
349	C₂²×C₁₃₉	—	2	2	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	2	4	no	—
353	C₂²×C₁₃₉	—	2	4	no	—
354	C₂²×C₁₃₉	—	2	4	no	—
355	C₂²×C₁₃₉	—	2	8	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	1	no	—
358	C₂²×C₁₃₉	—	4	4	no	—
359	C₂²×C₁₃₉	—	4	4	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	1	no	—
362	C₂²×C₁₃₉	—	4	4	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	2	no	—
366	C₂²×C₁₃₉	—	4	2	no	—
367	C₂²×C₁₃₉	—	4	2	no	—
368	C₂²×C₁₃₉	—	4	2	no	—
369	C₂²×C₁₃₉	—	4	2	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	8	16	no	—
372	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
373	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
376	C₂²×C₁₃₉	#585	1	2	yes	—
377	C₄×C₁₃₉	—	2	2	no	—
378	C₄×C₁₃₉	—	2	2	no	—
379	C₄×C₁₃₉	—	2	4	no	—
380	C₄×C₁₃₉	—	2	4	no	—
381	C₄×C₁₃₉	—	2	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	1	no	—
384	C₄×C₁₃₉	—	4	2	no	—
385	C₄×C₁₃₉	—	4	1	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	4	no	—
388	C₄×C₁₃₉	—	4	4	no	—
389	C₄×C₁₃₉	#525	1	4	yes	—
390	C₂×C₁₃₉	—	4	4	no	—
391	C₂×C₁₃₉	—	4	4	no	—
392	C₂×C₁₃₉	—	4	2	no	—
393	C₂×C₁₃₉	—	8	2	no	—
394	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
395	C₂×C₁₃₉	#3485	1	1	yes	characteristic
396	C₂×C₁₃₉	#3494	1	2	yes	—
397	C₂×C₁₃₉	#3498	1	1	yes	characteristic
398	C₂×C₁₃₉	#3514	1	2	yes	—
399	#36022	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₁₃₉	#36022	1	1	yes	characteristic, direct product factor, Sylow
401	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	#2635	C₂×C₁₃₉	1	2	yes	complemented
404	#2628	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2539	C₂×C₁₃₉	1	2	yes	complemented
407	#2535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2482	C₂×C₁₃₉	1	2	yes	complemented
409	#2472	C₂×C₁₃₉	1	4	yes	complemented
410	#2461	C₂×C₁₃₉	1	4	yes	complemented
411	#2422	C₂×C₁₃₉	1	2	yes	complemented
412	#2408	C₂×C₁₃₉	1	2	yes	complemented
413	#2395	C₂×C₁₃₉	1	2	yes	complemented
414	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	#2363	C₂×C₁₃₉	1	2	yes	complemented
416	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#2354	C₂×C₁₃₉	1	2	yes	complemented
418	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
419	#555	—	2	8	no	—
420	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
421	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
422	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
423	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
424	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
425	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
426	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
427	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
428	#518	—	2	8	no	—
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
437	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
440	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
441	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
442	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	#400	C₂²×C₁₃₉	1	2	yes	complemented
444	#399	C₂²×C₁₃₉	1	2	yes	—
445	#399	C₂²×C₁₃₉	1	2	yes	complemented
446	#399	C₂²×C₁₃₉	1	2	yes	complemented
447	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
448	#397	C₂²×C₁₃₉	1	1	yes	characteristic
449	#397	C₂²×C₁₃₉	1	4	yes	complemented
450	#397	C₂²×C₁₃₉	1	2	yes	complemented
451	#396	C₂²×C₁₃₉	1	2	yes	complemented
452	#395	C₂²×C₁₃₉	1	2	yes	complemented
453	#394	C₂²×C₁₃₉	1	2	yes	—
454	#394	C₂²×C₁₃₉	1	4	yes	—
455	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
456	#394	C₂²×C₁₃₉	1	4	yes	complemented
457	#393	C₂²×C₁₃₉	1	2	yes	—
458	#392	C₂²×C₁₃₉	1	4	yes	—
459	#392	C₂²×C₁₃₉	1	1	yes	characteristic
460	#392	C₂²×C₁₃₉	1	2	yes	complemented
461	#390	C₂²×C₁₃₉	1	4	yes	—
462	#390	C₂²×C₁₃₉	1	2	yes	—
463	#390	C₂²×C₁₃₉	1	2	yes	—
464	#390	C₂²×C₁₃₉	1	4	yes	complemented
465	#389	C₂²×C₁₃₉	1	2	yes	complemented
466	#388	C₂²×C₁₃₉	1	4	yes	—
467	#388	C₂²×C₁₃₉	1	4	yes	complemented
468	#388	C₂²×C₁₃₉	1	4	yes	complemented
469	#388	C₂²×C₁₃₉	1	4	yes	complemented
470	#386	C₂²×C₁₃₉	1	4	yes	complemented
471	#386	C₂²×C₁₃₉	1	4	yes	complemented
472	#385	C₂²×C₁₃₉	1	4	yes	complemented
473	#384	C₂²×C₁₃₉	1	2	yes	complemented
474	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
475	#381	C₂²×C₁₃₉	1	2	yes	complemented
476	#380	C₂²×C₁₃₉	1	2	yes	—
477	#380	C₂²×C₁₃₉	1	2	yes	complemented
478	#379	C₂²×C₁₃₉	1	4	yes	—
479	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
480	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
482	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
483	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
484	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
485	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
486	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
487	C₂²×D₄	—	2	4	no	—
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	—	2	4	no	—
490	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₄⋊Q₈	—	2	4	no	—
504	#124	—	2	16	no	—
505	#123	—	4	8	no	—
506	C₂²⋊Q₈	—	4	8	no	—
507	#121	—	2	8	no	—
508	#121	—	2	8	no	—
509	#121	—	2	8	no	—
510	#120	—	4	8	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	8	no	—
513	C₄×D₄	—	2	8	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	2	4	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
519	#117	—	2	8	no	—
520	#117	—	2	4	no	—
521	#117	—	2	8	no	—
522	#117	—	2	4	no	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	—	2	8	no	—
537	C₂×C₂²⋊C₄	—	2	8	no	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	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	2	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	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
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	2	yes	—
566	#95	C₂³×C₁₃₉	1	1	yes	characteristic
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	4	yes	—
570	#95	C₂³×C₁₃₉	1	4	yes	—
571	#95	C₂³×C₁₃₉	1	4	yes	—
572	#95	C₂³×C₁₃₉	1	1	yes	characteristic
573	#95	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	C₂⁴	—	2	4	no	—
576	C₂⁴	—	2	4	no	—
577	C₂⁴	—	2	4	no	—
578	C₂⁴	—	4	4	no	—
579	C₂⁴	—	4	4	no	—
580	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
581	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
582	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
583	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
584	C₂×Q₈	—	2	4	no	—
585	C₂×Q₈	—	4	4	no	—
586	C₂×D₄	—	2	32	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
606	C₂×D₄	#41×C₁₃₉	1	4	yes	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
620	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	4	4	no	—
645	C₄⋊C₄	—	4	4	no	—
646	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	8	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	4	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
668	C₄²	—	2	8	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	4	4	no	—
673	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
674	C₂³	—	2	16	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	8	4	no	—
695	C₂³	—	8	8	no	—
696	C₂³	—	8	4	no	—
697	C₂³	—	8	8	no	—
698	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
699	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
700	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
701	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
702	Q₈	—	8	4	no	—
703	D₄	—	2	16	no	—
704	D₄	—	2	8	no	—
705	D₄	—	2	8	no	—
706	D₄	—	4	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	8	8	no	—
709	D₄	—	8	8	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
742	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
743	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
744	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
745	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
746	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
747	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
748	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	8	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	4	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	8	16	no	—
772	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
773	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
774	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
775	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
776	C₂²	#585×C₁₃₉	1	2	yes	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	4	no	—
788	C₄	—	4	4	no	—
789	C₄	#525×C₁₃₉	1	4	yes	—
790	C₂	—	4	2	no	—
791	C₂	—	4	4	no	—
792	C₂	—	4	4	no	—
793	C₂	—	8	2	no	—
794	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
795	C₂	#3485×C₁₃₉	1	1	yes	characteristic
796	C₂	#3494×C₁₃₉	1	2	yes	—
797	C₂	#3498×C₁₃₉	1	1	yes	characteristic
798	C₂	#3514×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×#555×C₁₃₉	C₂	semidirect
2. C₂×#518×C₁₃₉	C₂	semidirect
3. #2635×C₁₃₉	C₂	semidirect
4. #2628×C₁₃₉	C₂	semidirect
5. #2542×C₁₃₉	C₂	semidirect
6. #2539×C₁₃₉	C₂	semidirect
7. #2535×C₁₃₉	C₂	semidirect
8. #2482×C₁₃₉	C₂	semidirect
9. #2472×C₁₃₉	C₂	semidirect
10. #2461×C₁₃₉	C₂	semidirect
11. #2422×C₁₃₉	C₂	semidirect
12. #2408×C₁₃₉	C₂	semidirect
13. #2395×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. #2363×C₁₃₉	C₂	semidirect
16. #2357×C₁₃₉	C₂	semidirect
17. #2354×C₁₃₉	C₂	semidirect
20. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
21. C₂×#124×C₁₃₉	C₂²	semidirect
22. C₂×#123×C₁₃₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×#121×C₁₃₉	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. C₂×#117×C₁₃₉	C₂²	semidirect
40. C₂×#117×C₁₃₉	C₂²	semidirect
43. #400×C₁₃₉	C₂²	semidirect
45. #399×C₁₃₉	C₂²	semidirect
46. #399×C₁₃₉	C₂²	semidirect
47. #398×C₁₃₉	C₂²	semidirect
49. #397×C₁₃₉	C₂²	semidirect
50. #397×C₁₃₉	C₂²	semidirect
51. #396×C₁₃₉	C₂²	semidirect
52. #395×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #394×C₁₃₉	C₂²	semidirect
60. #392×C₁₃₉	C₂²	semidirect
64. #390×C₁₃₉	C₂²	semidirect
65. #389×C₁₃₉	C₂²	semidirect
67. #388×C₁₃₉	C₂²	semidirect
68. #388×C₁₃₉	C₂²	semidirect
69. #388×C₁₃₉	C₂²	semidirect
70. #386×C₁₃₉	C₂²	semidirect
71. #386×C₁₃₉	C₂²	semidirect
72. #385×C₁₃₉	C₂²	semidirect
73. #384×C₁₃₉	C₂²	semidirect
74. #382×C₁₃₉	C₂²	semidirect
75. #381×C₁₃₉	C₂²	semidirect
77. #380×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×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
118. C₄×D₄×C₁₃₉	D₄	semidirect
399. #36022	C₁₃₉	direct (N × H)
400. C₁₃₉	#36022	direct (N × H)
401. C₂×#555	C₂×C₁₃₉	semidirect
402. C₂×#518	C₂×C₁₃₉	semidirect
403. #2635	C₂×C₁₃₉	semidirect
404. #2628	C₂×C₁₃₉	semidirect
405. #2542	C₂×C₁₃₉	semidirect
406. #2539	C₂×C₁₃₉	semidirect
407. #2535	C₂×C₁₃₉	semidirect
408. #2482	C₂×C₁₃₉	semidirect
409. #2472	C₂×C₁₃₉	semidirect
410. #2461	C₂×C₁₃₉	semidirect
411. #2422	C₂×C₁₃₉	semidirect
412. #2408	C₂×C₁₃₉	semidirect
413. #2395	C₂×C₁₃₉	semidirect
414. #2392	C₂×C₁₃₉	semidirect
415. #2363	C₂×C₁₃₉	semidirect
416. #2357	C₂×C₁₃₉	semidirect
417. #2354	C₂×C₁₃₉	semidirect
420. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
421. C₂×#124	C₂²×C₁₃₉	semidirect
422. C₂×#123	C₂²×C₁₃₉	semidirect
423. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
426. C₂×#121	C₂²×C₁₃₉	semidirect
436. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
439. C₂×#117	C₂²×C₁₃₉	semidirect
440. C₂×#117	C₂²×C₁₃₉	semidirect
443. #400	C₂²×C₁₃₉	semidirect
445. #399	C₂²×C₁₃₉	semidirect
446. #399	C₂²×C₁₃₉	semidirect
447. #398	C₂²×C₁₃₉	semidirect
449. #397	C₂²×C₁₃₉	semidirect
450. #397	C₂²×C₁₃₉	semidirect
451. #396	C₂²×C₁₃₉	semidirect
452. #395	C₂²×C₁₃₉	semidirect
455. #394	C₂²×C₁₃₉	semidirect
456. #394	C₂²×C₁₃₉	semidirect
460. #392	C₂²×C₁₃₉	semidirect
464. #390	C₂²×C₁₃₉	semidirect
465. #389	C₂²×C₁₃₉	semidirect
467. #388	C₂²×C₁₃₉	semidirect
468. #388	C₂²×C₁₃₉	semidirect
469. #388	C₂²×C₁₃₉	semidirect
470. #386	C₂²×C₁₃₉	semidirect
471. #386	C₂²×C₁₃₉	semidirect
472. #385	C₂²×C₁₃₉	semidirect
473. #384	C₂²×C₁₃₉	semidirect
474. #382	C₂²×C₁₃₉	semidirect
475. #381	C₂²×C₁₃₉	semidirect
477. #380	C₂²×C₁₃₉	semidirect
479. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
480. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
481. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
482. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
483. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
484. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
518. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2635×C₁₃₉	2
#2628×C₁₃₉	2
#2542×C₁₃₉	2
#2539×C₁₃₉	2
#2535×C₁₃₉	2
#2482×C₁₃₉	2
#2472×C₁₃₉	2
#2461×C₁₃₉	2
#2422×C₁₃₉	2
#2408×C₁₃₉	2
#2395×C₁₃₉	2
#2392×C₁₃₉	2
#2363×C₁₃₉	2
#2357×C₁₃₉	2
#2354×C₁₃₉	2
#36022	139

Subgroups — C139×#36022 #48030618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36022 #48030618