Subgroups — C₁₃₉×#36009 #48030605

Order 35584.

3174 conjugacy classes of subgroups.

The subgroup lattice has 826 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×#546×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2621×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2617×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2543×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2486×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2425×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2412×C₁₃₉	C₂	1	4	yes	maximal, complemented
14	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#397×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2339×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	#547×C₁₃₉	—	2	8	no	—
21	#546×C₁₃₉	—	2	16	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
32	#518×C₁₃₉	—	2	8	no	—
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	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
45	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
47	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	2	yes	complemented
49	#398×C₁₃₉	C₂²	1	2	yes	complemented
50	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#397×C₁₃₉	C₂²	1	2	yes	—
53	#397×C₁₃₉	C₂²	1	1	yes	characteristic
54	#397×C₁₃₉	C₂²	1	4	yes	—
55	#397×C₁₃₉	C₂²	1	2	yes	complemented
56	#397×C₁₃₉	C₂²	1	2	yes	complemented
57	#397×C₁₃₉	C₂²	1	2	yes	complemented
58	#397×C₁₃₉	C₂²	1	4	yes	complemented
59	#396×C₁₃₉	C₂²	1	2	yes	complemented
60	#394×C₁₃₉	C₂²	1	4	yes	—
61	#394×C₁₃₉	C₂²	1	2	yes	—
62	#394×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
63	#394×C₁₃₉	C₂²	1	4	yes	complemented
64	#392×C₁₃₉	C₂²	1	1	yes	characteristic
65	#392×C₁₃₉	C₂²	1	2	yes	complemented
66	#391×C₁₃₉	C₂²	1	2	yes	complemented
67	#391×C₁₃₉	C₂²	1	2	yes	complemented
68	#389×C₁₃₉	C₂²	1	2	yes	complemented
69	#389×C₁₃₉	C₂²	1	4	yes	complemented
70	#388×C₁₃₉	C₂²	1	4	yes	complemented
71	#386×C₁₃₉	C₂²	1	4	yes	complemented
72	#386×C₁₃₉	C₂²	1	4	yes	complemented
73	#386×C₁₃₉	C₂²	1	4	yes	complemented
74	#386×C₁₃₉	C₂²	1	4	yes	complemented
75	#385×C₁₃₉	C₂²	1	4	yes	complemented
76	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#381×C₁₃₉	C₂²	1	4	yes	complemented
78	#380×C₁₃₉	C₂²	1	2	yes	complemented
79	#380×C₁₃₉	C₂²	1	4	yes	complemented
80	#380×C₁₃₉	C₂²	1	2	yes	complemented
81	#380×C₁₃₉	C₂²	1	4	yes	complemented
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
85	C₂×#95×C₁₃₉	C₂²	1	4	yes	complemented
86	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂×#41×C₁₃₉	—	2	8	no	—
89	C₂×#41×C₁₃₉	—	2	8	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×D₄×C₁₃₉	—	2	4	no	—
93	C₂²×D₄×C₁₃₉	D₄	1	8	yes	complemented
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
110	#124×C₁₃₉	—	2	8	no	—
111	#123×C₁₃₉	—	2	16	no	—
112	#123×C₁₃₉	—	2	16	no	—
113	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
114	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	8	no	—
116	#121×C₁₃₉	—	2	16	no	—
117	#121×C₁₃₉	—	2	8	no	—
118	#120×C₁₃₉	—	2	16	no	—
119	C₄×D₄×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	4	no	—
124	C₄×D₄×C₁₃₉	—	2	8	no	—
125	C₄×D₄×C₁₃₉	—	2	4	no	—
126	C₄×D₄×C₁₃₉	—	2	4	no	—
127	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
128	#117×C₁₃₉	—	2	4	no	—
129	#117×C₁₃₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
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	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
145	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
146	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
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	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	1	yes	characteristic
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	4	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	1	yes	characteristic
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	C₂⁴×C₁₃₉	—	2	4	no	—
183	C₂⁴×C₁₃₉	—	2	4	no	—
184	C₂⁴×C₁₃₉	—	4	4	no	—
185	C₂⁴×C₁₃₉	—	4	4	no	—
186	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
187	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
191	#41×C₁₃₉	—	4	32	no	—
192	C₂×Q₈×C₁₃₉	—	2	4	no	—
193	C₂×Q₈×C₁₃₉	—	2	4	no	—
194	C₂×Q₈×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	32	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	8	no	—
200	C₂×D₄×C₁₃₉	—	2	8	no	—
201	C₂×D₄×C₁₃₉	—	2	8	no	—
202	C₂×D₄×C₁₃₉	—	2	8	no	—
203	C₂×D₄×C₁₃₉	—	2	2	no	—
204	C₂×D₄×C₁₃₉	—	2	2	no	—
205	C₂×D₄×C₁₃₉	—	2	2	no	—
206	C₂×D₄×C₁₃₉	—	4	2	no	—
207	C₂×D₄×C₁₃₉	—	4	2	no	—
208	C₂×D₄×C₁₃₉	—	4	2	no	—
209	C₂×D₄×C₁₃₉	—	4	4	no	—
210	C₂×D₄×C₁₃₉	—	4	4	no	—
211	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
212	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
213	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
214	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
215	C₂×D₄×C₁₃₉	#41	1	4	yes	—
216	C₂²×C₄×C₁₃₉	—	2	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	2	no	—
218	C₂²×C₄×C₁₃₉	—	2	8	no	—
219	C₂²×C₄×C₁₃₉	—	2	8	no	—
220	C₂²×C₄×C₁₃₉	—	2	8	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	8	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	—	4	4	no	—
229	C₂²×C₄×C₁₃₉	—	4	4	no	—
230	C₂²×C₄×C₁₃₉	—	4	4	no	—
231	C₂²×C₄×C₁₃₉	—	4	4	no	—
232	C₂²×C₄×C₁₃₉	—	4	4	no	—
233	C₂²×C₄×C₁₃₉	—	4	4	no	—
234	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₁₃₉	—	2	2	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	8	no	—
252	C₄⋊C₄×C₁₃₉	—	2	2	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	2	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	8	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	4	no	—
261	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
280	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	2	2	no	—
283	C₄²×C₁₃₉	—	2	4	no	—
284	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	2	4	no	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	4	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	16	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	2	no	—
298	C₂³×C₁₃₉	—	2	2	no	—
299	C₂³×C₁₃₉	—	2	2	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	4	16	no	—
304	C₂³×C₁₃₉	—	8	4	no	—
305	C₂³×C₁₃₉	—	8	4	no	—
306	C₂³×C₁₃₉	—	8	8	no	—
307	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
309	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
310	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
311	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
312	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
313	Q₈×C₁₃₉	—	4	8	no	—
314	D₄×C₁₃₉	—	2	16	no	—
315	D₄×C₁₃₉	—	2	8	no	—
316	D₄×C₁₃₉	—	4	4	no	—
317	D₄×C₁₃₉	—	4	8	no	—
318	D₄×C₁₃₉	—	4	16	no	—
319	D₄×C₁₃₉	—	8	8	no	—
320	D₄×C₁₃₉	#121	1	16	yes	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	4	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	8	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	1	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	—	2	4	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	4	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	4	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	4	no	—
348	C₂×C₄×C₁₃₉	—	4	8	no	—
349	C₂×C₄×C₁₃₉	—	4	16	no	—
350	C₂×C₄×C₁₃₉	—	4	8	no	—
351	C₂×C₄×C₁₃₉	—	8	4	no	—
352	C₂×C₄×C₁₃₉	—	8	4	no	—
353	C₂×C₄×C₁₃₉	—	8	8	no	—
354	C₂×C₄×C₁₃₉	—	8	4	no	—
355	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
362	C₂²×C₁₃₉	—	2	4	no	—
363	C₂²×C₁₃₉	—	2	8	no	—
364	C₂²×C₁₃₉	—	2	4	no	—
365	C₂²×C₁₃₉	—	2	8	no	—
366	C₂²×C₁₃₉	—	2	2	no	—
367	C₂²×C₁₃₉	—	2	4	no	—
368	C₂²×C₁₃₉	—	2	4	no	—
369	C₂²×C₁₃₉	—	2	8	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	4	1	no	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	4	1	no	—
374	C₂²×C₁₃₉	—	4	4	no	—
375	C₂²×C₁₃₉	—	4	2	no	—
376	C₂²×C₁₃₉	—	4	2	no	—
377	C₂²×C₁₃₉	—	4	2	no	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	2	no	—
380	C₂²×C₁₃₉	—	4	2	no	—
381	C₂²×C₁₃₉	—	4	2	no	—
382	C₂²×C₁₃₉	—	4	2	no	—
383	C₂²×C₁₃₉	—	8	16	no	—
384	C₂²×C₁₃₉	C₂×#121	1	8	yes	—
385	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
386	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
387	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₁₃₉	#585	1	2	yes	—
389	C₂²×C₁₃₉	#585	1	2	yes	—
390	C₄×C₁₃₉	—	2	2	no	—
391	C₄×C₁₃₉	—	2	2	no	—
392	C₄×C₁₃₉	—	2	4	no	—
393	C₄×C₁₃₉	—	2	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₄×C₁₃₉	—	4	4	no	—
396	C₄×C₁₃₉	—	4	1	no	—
397	C₄×C₁₃₉	—	4	2	no	—
398	C₄×C₁₃₉	—	4	4	no	—
399	C₄×C₁₃₉	—	4	2	no	—
400	C₄×C₁₃₉	—	4	2	no	—
401	C₄×C₁₃₉	—	4	1	no	—
402	C₄×C₁₃₉	C₂×#121	1	4	yes	—
403	C₂×C₁₃₉	—	2	8	no	—
404	C₂×C₁₃₉	—	4	4	no	—
405	C₂×C₁₃₉	—	4	2	no	—
406	C₂×C₁₃₉	—	8	2	no	—
407	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
408	C₂×C₁₃₉	#3485	1	1	yes	characteristic
409	C₂×C₁₃₉	#3485	1	2	yes	—
410	C₂×C₁₃₉	#3500	1	1	yes	characteristic
411	C₂×C₁₃₉	#3521	1	2	yes	—
412	#36009	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₁₃₉	#36009	1	1	yes	characteristic, direct product factor, Sylow
414	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	C₂×#546	C₂×C₁₃₉	1	2	yes	complemented
416	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#2621	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	#2617	C₂×C₁₃₉	1	2	yes	complemented
419	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
420	#2543	C₂×C₁₃₉	1	2	yes	complemented
421	#2535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	#2486	C₂×C₁₃₉	1	2	yes	complemented
423	#2427	C₂×C₁₃₉	1	2	yes	complemented
424	#2425	C₂×C₁₃₉	1	4	yes	complemented
425	#2415	C₂×C₁₃₉	1	2	yes	complemented
426	#2412	C₂×C₁₃₉	1	4	yes	complemented
427	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
428	C₂×#397	C₂×C₁₃₉	1	2	yes	complemented
429	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
430	#2339	C₂×C₁₃₉	1	2	yes	complemented
431	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
432	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
433	#547	—	2	8	no	—
434	#546	—	2	16	no	—
435	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
436	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
437	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
438	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
439	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
440	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
441	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
442	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
443	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
444	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
445	#518	—	2	8	no	—
446	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
449	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
455	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
458	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
459	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
460	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
461	#398	C₂²×C₁₃₉	1	2	yes	complemented
462	#398	C₂²×C₁₃₉	1	2	yes	complemented
463	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
464	#397	C₂²×C₁₃₉	1	2	yes	—
465	#397	C₂²×C₁₃₉	1	2	yes	—
466	#397	C₂²×C₁₃₉	1	1	yes	characteristic
467	#397	C₂²×C₁₃₉	1	4	yes	—
468	#397	C₂²×C₁₃₉	1	2	yes	complemented
469	#397	C₂²×C₁₃₉	1	4	yes	complemented
470	#397	C₂²×C₁₃₉	1	2	yes	complemented
471	#397	C₂²×C₁₃₉	1	2	yes	complemented
472	#396	C₂²×C₁₃₉	1	2	yes	complemented
473	#394	C₂²×C₁₃₉	1	4	yes	—
474	#394	C₂²×C₁₃₉	1	2	yes	—
475	#394	C₂²×C₁₃₉	1	4	yes	complemented
476	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
477	#392	C₂²×C₁₃₉	1	1	yes	characteristic
478	#392	C₂²×C₁₃₉	1	2	yes	complemented
479	#391	C₂²×C₁₃₉	1	2	yes	complemented
480	#391	C₂²×C₁₃₉	1	2	yes	complemented
481	#389	C₂²×C₁₃₉	1	2	yes	complemented
482	#389	C₂²×C₁₃₉	1	4	yes	complemented
483	#388	C₂²×C₁₃₉	1	4	yes	complemented
484	#386	C₂²×C₁₃₉	1	4	yes	complemented
485	#386	C₂²×C₁₃₉	1	4	yes	complemented
486	#386	C₂²×C₁₃₉	1	4	yes	complemented
487	#386	C₂²×C₁₃₉	1	4	yes	complemented
488	#385	C₂²×C₁₃₉	1	4	yes	complemented
489	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
490	#381	C₂²×C₁₃₉	1	4	yes	complemented
491	#380	C₂²×C₁₃₉	1	2	yes	complemented
492	#380	C₂²×C₁₃₉	1	2	yes	complemented
493	#380	C₂²×C₁₃₉	1	4	yes	complemented
494	#380	C₂²×C₁₃₉	1	4	yes	complemented
495	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
496	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
497	C₂×#95	C₂²×C₁₃₉	1	4	yes	complemented
498	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
499	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
500	C₂×#41	—	2	8	no	—
501	C₂×#41	—	2	8	no	—
502	C₂×#41	—	2	8	no	—
503	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	D₄×C₁₃₉	1	8	yes	complemented
507	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₄⋊Q₈	—	2	4	no	—
523	#124	—	2	8	no	—
524	#123	—	2	16	no	—
525	#123	—	2	16	no	—
526	C₂²⋊Q₈	—	2	8	no	—
527	C₂²⋊Q₈	—	2	8	no	—
528	#121	—	2	8	no	—
529	#121	—	2	16	no	—
530	#121	—	2	8	no	—
531	#120	—	2	16	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	8	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
541	#117	—	2	4	no	—
542	#117	—	2	4	no	—
543	C₂×C₄⋊C₄	—	2	8	no	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	16	no	—
558	C₂×C₂²⋊C₄	—	2	8	no	—
559	C₂×C₂²⋊C₄	—	2	8	no	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	1	yes	characteristic
585	#95	C₂³×C₁₃₉	1	4	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	4	yes	—
588	#95	C₂³×C₁₃₉	1	4	yes	—
589	#95	C₂³×C₁₃₉	1	4	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	1	yes	characteristic
592	#95	C₂³×C₁₃₉	1	4	yes	—
593	#95	C₂³×C₁₃₉	1	4	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	2	4	no	—
597	C₂⁴	—	4	4	no	—
598	C₂⁴	—	4	4	no	—
599	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
600	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
601	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
602	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
603	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
604	#41	—	4	32	no	—
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	32	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
625	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
627	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
628	C₂×D₄	#41×C₁₃₉	1	4	yes	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	8	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	4	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
648	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
649	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	8	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	4	no	—
674	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	2	8	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	—	4	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	16	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	4	16	no	—
717	C₂³	—	8	4	no	—
718	C₂³	—	8	4	no	—
719	C₂³	—	8	8	no	—
720	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
721	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
722	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
723	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
724	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
725	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
726	Q₈	—	4	8	no	—
727	D₄	—	2	16	no	—
728	D₄	—	2	8	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	16	no	—
732	D₄	—	8	8	no	—
733	D₄	#121×C₁₃₉	1	16	yes	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	16	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	8	4	no	—
765	C₂×C₄	—	8	4	no	—
766	C₂×C₄	—	8	8	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
769	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
774	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	8	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	8	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	8	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	8	16	no	—
797	C₂²	C₂×#121×C₁₃₉	1	8	yes	—
798	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
799	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
800	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
801	C₂²	#585×C₁₃₉	1	2	yes	—
802	C₂²	#585×C₁₃₉	1	2	yes	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	4	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	4	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	1	no	—
815	C₄	C₂×#121×C₁₃₉	1	4	yes	—
816	C₂	—	2	8	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	4	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
821	C₂	#3485×C₁₃₉	1	1	yes	characteristic
822	C₂	#3485×C₁₃₉	1	2	yes	—
823	C₂	#3500×C₁₃₉	1	1	yes	characteristic
824	C₂	#3521×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×#546×C₁₃₉	C₂	semidirect
3. C₂×#518×C₁₃₉	C₂	semidirect
4. #2621×C₁₃₉	C₂	semidirect
5. #2617×C₁₃₉	C₂	semidirect
6. #2547×C₁₃₉	C₂	semidirect
7. #2543×C₁₃₉	C₂	semidirect
8. #2535×C₁₃₉	C₂	semidirect
9. #2486×C₁₃₉	C₂	semidirect
10. #2427×C₁₃₉	C₂	semidirect
11. #2425×C₁₃₉	C₂	semidirect
12. #2415×C₁₃₉	C₂	semidirect
13. #2412×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. C₂×#397×C₁₃₉	C₂	semidirect
16. #2349×C₁₃₉	C₂	semidirect
17. #2339×C₁₃₉	C₂	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
25. C₂×#123×C₁₃₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×#121×C₁₃₉	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
48. #398×C₁₃₉	C₂²	semidirect
49. #398×C₁₃₉	C₂²	semidirect
50. #398×C₁₃₉	C₂²	semidirect
55. #397×C₁₃₉	C₂²	semidirect
56. #397×C₁₃₉	C₂²	semidirect
57. #397×C₁₃₉	C₂²	semidirect
58. #397×C₁₃₉	C₂²	semidirect
59. #396×C₁₃₉	C₂²	semidirect
62. #394×C₁₃₉	C₂²	semidirect
63. #394×C₁₃₉	C₂²	semidirect
65. #392×C₁₃₉	C₂²	semidirect
66. #391×C₁₃₉	C₂²	semidirect
67. #391×C₁₃₉	C₂²	semidirect
68. #389×C₁₃₉	C₂²	semidirect
69. #389×C₁₃₉	C₂²	semidirect
70. #388×C₁₃₉	C₂²	semidirect
71. #386×C₁₃₉	C₂²	semidirect
72. #386×C₁₃₉	C₂²	semidirect
73. #386×C₁₃₉	C₂²	semidirect
74. #386×C₁₃₉	C₂²	semidirect
75. #385×C₁₃₉	C₂²	semidirect
76. #382×C₁₃₉	C₂²	semidirect
77. #381×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
79. #380×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
81. #380×C₁₃₉	C₂²	semidirect
82. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₂×#95×C₁₃₉	C₂²	semidirect
85. C₂×#95×C₁₃₉	C₂²	semidirect
93. C₂²×D₄×C₁₃₉	D₄	semidirect
127. C₄×D₄×C₁₃₉	D₄	semidirect
412. #36009	C₁₃₉	direct (N × H)
413. C₁₃₉	#36009	direct (N × H)
414. C₂×#547	C₂×C₁₃₉	semidirect
415. C₂×#546	C₂×C₁₃₉	semidirect
416. C₂×#518	C₂×C₁₃₉	semidirect
417. #2621	C₂×C₁₃₉	semidirect
418. #2617	C₂×C₁₃₉	semidirect
419. #2547	C₂×C₁₃₉	semidirect
420. #2543	C₂×C₁₃₉	semidirect
421. #2535	C₂×C₁₃₉	semidirect
422. #2486	C₂×C₁₃₉	semidirect
423. #2427	C₂×C₁₃₉	semidirect
424. #2425	C₂×C₁₃₉	semidirect
425. #2415	C₂×C₁₃₉	semidirect
426. #2412	C₂×C₁₃₉	semidirect
427. #2392	C₂×C₁₃₉	semidirect
428. C₂×#397	C₂×C₁₃₉	semidirect
429. #2349	C₂×C₁₃₉	semidirect
430. #2339	C₂×C₁₃₉	semidirect
435. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
438. C₂×#123	C₂²×C₁₃₉	semidirect
440. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
443. C₂×#121	C₂²×C₁₃₉	semidirect
454. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
457. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
461. #398	C₂²×C₁₃₉	semidirect
462. #398	C₂²×C₁₃₉	semidirect
463. #398	C₂²×C₁₃₉	semidirect
468. #397	C₂²×C₁₃₉	semidirect
469. #397	C₂²×C₁₃₉	semidirect
470. #397	C₂²×C₁₃₉	semidirect
471. #397	C₂²×C₁₃₉	semidirect
472. #396	C₂²×C₁₃₉	semidirect
475. #394	C₂²×C₁₃₉	semidirect
476. #394	C₂²×C₁₃₉	semidirect
478. #392	C₂²×C₁₃₉	semidirect
479. #391	C₂²×C₁₃₉	semidirect
480. #391	C₂²×C₁₃₉	semidirect
481. #389	C₂²×C₁₃₉	semidirect
482. #389	C₂²×C₁₃₉	semidirect
483. #388	C₂²×C₁₃₉	semidirect
484. #386	C₂²×C₁₃₉	semidirect
485. #386	C₂²×C₁₃₉	semidirect
486. #386	C₂²×C₁₃₉	semidirect
487. #386	C₂²×C₁₃₉	semidirect
488. #385	C₂²×C₁₃₉	semidirect
489. #382	C₂²×C₁₃₉	semidirect
490. #381	C₂²×C₁₃₉	semidirect
491. #380	C₂²×C₁₃₉	semidirect
492. #380	C₂²×C₁₃₉	semidirect
493. #380	C₂²×C₁₃₉	semidirect
494. #380	C₂²×C₁₃₉	semidirect
495. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
496. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
497. C₂×#95	C₂²×C₁₃₉	semidirect
498. C₂×#95	C₂²×C₁₃₉	semidirect
506. C₂²×D₄	D₄×C₁₃₉	semidirect
540. 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×#547×C₁₃₉	2
C₂×#546×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2621×C₁₃₉	2
#2617×C₁₃₉	2
#2547×C₁₃₉	2
#2543×C₁₃₉	2
#2535×C₁₃₉	2
#2486×C₁₃₉	2
#2427×C₁₃₉	2
#2425×C₁₃₉	2
#2415×C₁₃₉	2
#2412×C₁₃₉	2
#2392×C₁₃₉	2
C₂×#397×C₁₃₉	2
#2349×C₁₃₉	2
#2339×C₁₃₉	2
#36009	139

Subgroups — C139×#36009 #48030605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36009 #48030605