Subgroups — C₁₃₉×#36004 #48030600

Order 35584.

2826 conjugacy classes of subgroups.

The subgroup lattice has 806 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	#2631×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2624×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2598×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2540×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2452×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2424×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2366×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, 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×#127×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
32	#518×C₁₃₉	—	2	8	no	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×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, complemented
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
40	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
43	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
45	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	#399×C₁₃₉	C₂²	1	2	yes	complemented
48	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	complemented
51	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	#396×C₁₃₉	C₂²	1	4	yes	complemented
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#394×C₁₃₉	C₂²	1	4	yes	complemented
57	#393×C₁₃₉	C₂²	1	4	yes	complemented
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	2	yes	—
60	#392×C₁₃₉	C₂²	1	2	yes	—
61	#392×C₁₃₉	C₂²	1	4	yes	complemented
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	4	yes	complemented
65	#390×C₁₃₉	C₂²	1	4	yes	complemented
66	#390×C₁₃₉	C₂²	1	2	yes	complemented
67	#389×C₁₃₉	C₂²	1	2	yes	complemented
68	#389×C₁₃₉	C₂²	1	2	yes	complemented
69	#388×C₁₃₉	C₂²	1	4	yes	—
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	#383×C₁₃₉	C₂²	1	2	yes	complemented
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	#379×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	—	2	8	no	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
104	#127×C₁₃₉	—	2	8	no	—
105	#124×C₁₃₉	—	2	8	no	—
106	#124×C₁₃₉	—	2	8	no	—
107	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	4	no	—
110	#121×C₁₃₉	—	2	4	no	—
111	#121×C₁₃₉	—	2	8	no	—
112	#121×C₁₃₉	—	4	8	no	—
113	#120×C₁₃₉	—	4	4	no	—
114	#120×C₁₃₉	—	4	8	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	—	2	8	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	4	8	no	—
122	#117×C₁₃₉	—	2	4	no	—
123	#117×C₁₃₉	—	2	4	no	—
124	#117×C₁₃₉	—	2	8	no	—
125	#117×C₁₃₉	D₄	1	8	yes	complemented
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	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	4	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	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	2	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	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	1	yes	characteristic
172	#95×C₁₃₉	C₂³	1	1	yes	characteristic
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	—	2	4	no	—
177	C₂⁴×C₁₃₉	—	2	8	no	—
178	C₂⁴×C₁₃₉	—	4	4	no	—
179	C₂⁴×C₁₃₉	—	4	2	no	—
180	C₂⁴×C₁₃₉	—	4	2	no	—
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
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	8	no	—
189	C₂×D₄×C₁₃₉	—	2	2	no	—
190	C₂×D₄×C₁₃₉	—	2	8	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	8	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	2	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	8	no	—
202	C₂×D₄×C₁₃₉	—	4	4	no	—
203	C₂×D₄×C₁₃₉	—	4	1	no	—
204	C₂×D₄×C₁₃₉	—	4	4	no	—
205	C₂×D₄×C₁₃₉	—	4	4	no	—
206	C₂×D₄×C₁₃₉	—	4	4	no	—
207	C₂×D₄×C₁₃₉	—	4	4	no	—
208	C₂×D₄×C₁₃₉	—	4	4	no	—
209	C₂×D₄×C₁₃₉	—	4	4	no	—
210	C₂×D₄×C₁₃₉	#41	1	8	yes	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	8	no	—
217	C₂²×C₄×C₁₃₉	—	2	8	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	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	4	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	2	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	2	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	8	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	4	4	no	—
247	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	8	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	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	2	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	4	no	—
272	C₄²×C₁₃₉	—	2	2	no	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	4	4	no	—
275	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
276	C₂³×C₁₃₉	—	2	16	no	—
277	C₂³×C₁₃₉	—	2	4	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	4	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	4	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	4	no	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	2	1	no	—
287	C₂³×C₁₃₉	—	2	1	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	2	no	—
293	C₂³×C₁₃₉	—	2	4	no	—
294	C₂³×C₁₃₉	—	2	1	no	—
295	C₂³×C₁₃₉	—	2	1	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	8	4	no	—
298	C₂³×C₁₃₉	—	8	4	no	—
299	C₂³×C₁₃₉	—	8	8	no	—
300	C₂³×C₁₃₉	—	8	8	no	—
301	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
302	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
303	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
304	Q₈×C₁₃₉	—	8	4	no	—
305	D₄×C₁₃₉	—	2	16	no	—
306	D₄×C₁₃₉	—	2	16	no	—
307	D₄×C₁₃₉	—	4	4	no	—
308	D₄×C₁₃₉	—	4	16	no	—
309	D₄×C₁₃₉	—	4	4	no	—
310	D₄×C₁₃₉	—	8	4	no	—
311	D₄×C₁₃₉	—	8	4	no	—
312	D₄×C₁₃₉	—	8	8	no	—
313	D₄×C₁₃₉	—	8	8	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	8	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	4	no	—
331	C₂×C₄×C₁₃₉	—	2	4	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	4	no	—
335	C₂×C₄×C₁₃₉	—	2	4	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	4	8	no	—
342	C₂×C₄×C₁₃₉	—	4	4	no	—
343	C₂×C₄×C₁₃₉	—	8	8	no	—
344	C₂×C₄×C₁₃₉	—	8	8	no	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
348	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
351	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	2	8	no	—
354	C₂²×C₁₃₉	—	2	2	no	—
355	C₂²×C₁₃₉	—	2	2	no	—
356	C₂²×C₁₃₉	—	2	8	no	—
357	C₂²×C₁₃₉	—	2	8	no	—
358	C₂²×C₁₃₉	—	4	4	no	—
359	C₂²×C₁₃₉	—	4	4	no	—
360	C₂²×C₁₃₉	—	4	4	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	4	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	1	no	—
365	C₂²×C₁₃₉	—	4	2	no	—
366	C₂²×C₁₃₉	—	4	2	no	—
367	C₂²×C₁₃₉	—	4	1	no	—
368	C₂²×C₁₃₉	—	4	1	no	—
369	C₂²×C₁₃₉	—	4	2	no	—
370	C₂²×C₁₃₉	—	4	4	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	4	no	—
373	C₂²×C₁₃₉	—	4	2	no	—
374	C₂²×C₁₃₉	—	8	16	no	—
375	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
376	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
377	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
379	C₂²×C₁₃₉	#585	1	1	yes	characteristic
380	C₄×C₁₃₉	—	2	2	no	—
381	C₄×C₁₃₉	—	2	2	no	—
382	C₄×C₁₃₉	—	2	4	no	—
383	C₄×C₁₃₉	—	2	4	no	—
384	C₄×C₁₃₉	—	2	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	2	no	—
391	C₄×C₁₃₉	—	4	4	no	—
392	C₄×C₁₃₉	#525	1	4	yes	—
393	C₂×C₁₃₉	—	4	8	no	—
394	C₂×C₁₃₉	—	4	2	no	—
395	C₂×C₁₃₉	—	8	1	no	—
396	C₂×C₁₃₉	—	8	2	no	—
397	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
398	C₂×C₁₃₉	#3488	1	1	yes	characteristic
399	C₂×C₁₃₉	#3498	1	1	yes	characteristic
400	C₂×C₁₃₉	#3514	1	2	yes	—
401	C₂×C₁₃₉	#3519	1	2	yes	—
402	#36004	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₁₃₉	#36004	1	1	yes	characteristic, direct product factor, Sylow
404	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2631	C₂×C₁₃₉	1	2	yes	complemented
407	#2624	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2598	C₂×C₁₃₉	1	2	yes	complemented
409	#2540	C₂×C₁₃₉	1	2	yes	complemented
410	#2472	C₂×C₁₃₉	1	4	yes	complemented
411	#2452	C₂×C₁₃₉	1	2	yes	complemented
412	#2433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2428	C₂×C₁₃₉	1	2	yes	complemented
414	#2424	C₂×C₁₃₉	1	4	yes	complemented
415	#2408	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#2392	C₂×C₁₃₉	1	2	yes	complemented
418	#2366	C₂×C₁₃₉	1	2	yes	complemented
419	#2363	C₂×C₁₃₉	1	2	yes	complemented
420	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
421	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
422	#555	—	2	8	no	—
423	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
424	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
425	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
426	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
427	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
428	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
429	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
431	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
433	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
434	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
435	#518	—	2	8	no	—
436	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
437	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
438	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
442	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
443	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
445	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
446	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
447	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
448	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
449	#399	C₂²×C₁₃₉	1	2	yes	complemented
450	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
451	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
452	#397	C₂²×C₁₃₉	1	2	yes	—
453	#397	C₂²×C₁₃₉	1	2	yes	complemented
454	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
455	#396	C₂²×C₁₃₉	1	4	yes	complemented
456	#394	C₂²×C₁₃₉	1	2	yes	—
457	#394	C₂²×C₁₃₉	1	4	yes	—
458	#394	C₂²×C₁₃₉	1	2	yes	—
459	#394	C₂²×C₁₃₉	1	4	yes	complemented
460	#393	C₂²×C₁₃₉	1	4	yes	complemented
461	#392	C₂²×C₁₃₉	1	2	yes	—
462	#392	C₂²×C₁₃₉	1	2	yes	—
463	#392	C₂²×C₁₃₉	1	2	yes	—
464	#392	C₂²×C₁₃₉	1	4	yes	complemented
465	#390	C₂²×C₁₃₉	1	2	yes	—
466	#390	C₂²×C₁₃₉	1	2	yes	—
467	#390	C₂²×C₁₃₉	1	4	yes	complemented
468	#390	C₂²×C₁₃₉	1	2	yes	complemented
469	#390	C₂²×C₁₃₉	1	4	yes	complemented
470	#389	C₂²×C₁₃₉	1	2	yes	complemented
471	#389	C₂²×C₁₃₉	1	2	yes	complemented
472	#388	C₂²×C₁₃₉	1	4	yes	—
473	#388	C₂²×C₁₃₉	1	4	yes	complemented
474	#386	C₂²×C₁₃₉	1	4	yes	complemented
475	#386	C₂²×C₁₃₉	1	4	yes	complemented
476	#386	C₂²×C₁₃₉	1	4	yes	complemented
477	#386	C₂²×C₁₃₉	1	4	yes	complemented
478	#385	C₂²×C₁₃₉	1	4	yes	complemented
479	#383	C₂²×C₁₃₉	1	2	yes	complemented
480	#380	C₂²×C₁₃₉	1	1	yes	characteristic
481	#379	C₂²×C₁₃₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
484	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
485	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
487	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
488	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
489	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
490	C₂²×D₄	—	2	8	no	—
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
497	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₄⋊Q₈	—	2	4	no	—
507	#127	—	2	8	no	—
508	#124	—	2	8	no	—
509	#124	—	2	8	no	—
510	C₂²⋊Q₈	—	4	8	no	—
511	#121	—	2	8	no	—
512	#121	—	2	4	no	—
513	#121	—	2	4	no	—
514	#121	—	2	8	no	—
515	#121	—	4	8	no	—
516	#120	—	4	4	no	—
517	#120	—	4	8	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	4	8	no	—
525	#117	—	2	4	no	—
526	#117	—	2	4	no	—
527	#117	—	2	8	no	—
528	#117	D₄×C₁₃₉	1	8	yes	complemented
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	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	16	no	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	1	yes	characteristic
570	#95	C₂³×C₁₃₉	1	1	yes	characteristic
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	4	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	4	yes	—
579	C₂⁴	—	2	4	no	—
580	C₂⁴	—	2	8	no	—
581	C₂⁴	—	4	4	no	—
582	C₂⁴	—	4	2	no	—
583	C₂⁴	—	4	2	no	—
584	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
585	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
587	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×D₄	—	2	32	no	—
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	2	2	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	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	1	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	#41×C₁₃₉	1	8	yes	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	8	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	8	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	4	4	no	—
650	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	8	no	—
655	C₂²⋊C₄	—	2	8	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	8	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	—	4	4	no	—
672	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	4	4	no	—
678	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
679	C₂³	—	2	16	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	8	4	no	—
701	C₂³	—	8	4	no	—
702	C₂³	—	8	8	no	—
703	C₂³	—	8	8	no	—
704	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
705	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
706	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
707	Q₈	—	8	4	no	—
708	D₄	—	2	16	no	—
709	D₄	—	2	16	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	16	no	—
712	D₄	—	4	4	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	8	no	—
716	D₄	—	8	8	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	8	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	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	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	8	8	no	—
747	C₂×C₄	—	8	8	no	—
748	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
749	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
750	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
752	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
753	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
754	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	8	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	8	no	—
760	C₂²	—	2	8	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	8	16	no	—
778	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
779	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
780	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
781	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
782	C₂²	#585×C₁₃₉	1	1	yes	characteristic
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	4	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	4	no	—
795	C₄	#525×C₁₃₉	1	4	yes	—
796	C₂	—	4	2	no	—
797	C₂	—	4	8	no	—
798	C₂	—	8	1	no	—
799	C₂	—	8	2	no	—
800	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
801	C₂	#3488×C₁₃₉	1	1	yes	characteristic
802	C₂	#3498×C₁₃₉	1	1	yes	characteristic
803	C₂	#3514×C₁₃₉	1	2	yes	—
804	C₂	#3519×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. #2631×C₁₃₉	C₂	semidirect
4. #2624×C₁₃₉	C₂	semidirect
5. #2598×C₁₃₉	C₂	semidirect
6. #2540×C₁₃₉	C₂	semidirect
7. #2472×C₁₃₉	C₂	semidirect
8. #2452×C₁₃₉	C₂	semidirect
9. #2433×C₁₃₉	C₂	semidirect
10. #2428×C₁₃₉	C₂	semidirect
11. #2424×C₁₃₉	C₂	semidirect
12. #2408×C₁₃₉	C₂	semidirect
13. #2395×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. #2366×C₁₃₉	C₂	semidirect
16. #2363×C₁₃₉	C₂	semidirect
17. #2347×C₁₃₉	C₂	semidirect
20. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
23. C₂×#124×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×#121×C₁₃₉	C₂²	semidirect
29. C₂×#121×C₁₃₉	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
42. C₂×#117×C₁₃₉	C₂²	semidirect
43. C₂×#117×C₁₃₉	C₂²	semidirect
45. #400×C₁₃₉	C₂²	semidirect
46. #399×C₁₃₉	C₂²	semidirect
47. #399×C₁₃₉	C₂²	semidirect
48. #398×C₁₃₉	C₂²	semidirect
50. #397×C₁₃₉	C₂²	semidirect
51. #397×C₁₃₉	C₂²	semidirect
52. #396×C₁₃₉	C₂²	semidirect
56. #394×C₁₃₉	C₂²	semidirect
57. #393×C₁₃₉	C₂²	semidirect
61. #392×C₁₃₉	C₂²	semidirect
64. #390×C₁₃₉	C₂²	semidirect
65. #390×C₁₃₉	C₂²	semidirect
66. #390×C₁₃₉	C₂²	semidirect
67. #389×C₁₃₉	C₂²	semidirect
68. #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. #383×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
125. #117×C₁₃₉	D₄	semidirect
402. #36004	C₁₃₉	direct (N × H)
403. C₁₃₉	#36004	direct (N × H)
404. C₂×#555	C₂×C₁₃₉	semidirect
405. C₂×#518	C₂×C₁₃₉	semidirect
406. #2631	C₂×C₁₃₉	semidirect
407. #2624	C₂×C₁₃₉	semidirect
408. #2598	C₂×C₁₃₉	semidirect
409. #2540	C₂×C₁₃₉	semidirect
410. #2472	C₂×C₁₃₉	semidirect
411. #2452	C₂×C₁₃₉	semidirect
412. #2433	C₂×C₁₃₉	semidirect
413. #2428	C₂×C₁₃₉	semidirect
414. #2424	C₂×C₁₃₉	semidirect
415. #2408	C₂×C₁₃₉	semidirect
416. #2395	C₂×C₁₃₉	semidirect
417. #2392	C₂×C₁₃₉	semidirect
418. #2366	C₂×C₁₃₉	semidirect
419. #2363	C₂×C₁₃₉	semidirect
420. #2347	C₂×C₁₃₉	semidirect
423. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
426. C₂×#124	C₂²×C₁₃₉	semidirect
427. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
431. C₂×#121	C₂²×C₁₃₉	semidirect
432. C₂×#121	C₂²×C₁₃₉	semidirect
441. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
442. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
445. C₂×#117	C₂²×C₁₃₉	semidirect
446. C₂×#117	C₂²×C₁₃₉	semidirect
448. #400	C₂²×C₁₃₉	semidirect
449. #399	C₂²×C₁₃₉	semidirect
450. #399	C₂²×C₁₃₉	semidirect
451. #398	C₂²×C₁₃₉	semidirect
453. #397	C₂²×C₁₃₉	semidirect
454. #397	C₂²×C₁₃₉	semidirect
455. #396	C₂²×C₁₃₉	semidirect
459. #394	C₂²×C₁₃₉	semidirect
460. #393	C₂²×C₁₃₉	semidirect
464. #392	C₂²×C₁₃₉	semidirect
467. #390	C₂²×C₁₃₉	semidirect
468. #390	C₂²×C₁₃₉	semidirect
469. #390	C₂²×C₁₃₉	semidirect
470. #389	C₂²×C₁₃₉	semidirect
471. #389	C₂²×C₁₃₉	semidirect
473. #388	C₂²×C₁₃₉	semidirect
474. #386	C₂²×C₁₃₉	semidirect
475. #386	C₂²×C₁₃₉	semidirect
476. #386	C₂²×C₁₃₉	semidirect
477. #386	C₂²×C₁₃₉	semidirect
478. #385	C₂²×C₁₃₉	semidirect
479. #383	C₂²×C₁₃₉	semidirect
482. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
483. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
484. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
486. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
487. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
528. #117	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
#2631×C₁₃₉	2
#2624×C₁₃₉	2
#2598×C₁₃₉	2
#2540×C₁₃₉	2
#2472×C₁₃₉	2
#2452×C₁₃₉	2
#2433×C₁₃₉	2
#2428×C₁₃₉	2
#2424×C₁₃₉	2
#2408×C₁₃₉	2
#2395×C₁₃₉	2
#2392×C₁₃₉	2
#2366×C₁₃₉	2
#2363×C₁₃₉	2
#2347×C₁₃₉	2
#36004	139

Subgroups — C139×#36004 #48030600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36004 #48030600