Subgroups — C₁₃₉×#37300 #48031896

Order 35584.

2786 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2730×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2678×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2673×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2668×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2620×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2619×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2499×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	#537×C₁₃₉	—	2	8	no	—
24	#535×C₁₃₉	—	2	8	no	—
25	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
35	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
44	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
45	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
46	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
47	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	#399×C₁₃₉	C₂²	1	4	yes	complemented
53	#397×C₁₃₉	C₂²	1	4	yes	—
54	#397×C₁₃₉	C₂²	1	4	yes	complemented
55	#396×C₁₃₉	C₂²	1	4	yes	complemented
56	#394×C₁₃₉	C₂²	1	4	yes	—
57	#394×C₁₃₉	C₂²	1	4	yes	—
58	#394×C₁₃₉	C₂²	1	4	yes	complemented
59	#394×C₁₃₉	C₂²	1	4	yes	complemented
60	#392×C₁₃₉	C₂²	1	4	yes	—
61	#392×C₁₃₉	C₂²	1	4	yes	complemented
62	#392×C₁₃₉	C₂²	1	4	yes	complemented
63	#392×C₁₃₉	C₂²	1	4	yes	complemented
64	#391×C₁₃₉	C₂²	1	2	yes	complemented
65	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	#390×C₁₃₉	C₂²	1	2	yes	—
68	#390×C₁₃₉	C₂²	1	1	yes	characteristic
69	#390×C₁₃₉	C₂²	1	1	yes	characteristic
70	#390×C₁₃₉	C₂²	1	1	yes	characteristic
71	#390×C₁₃₉	C₂²	1	1	yes	characteristic
72	#390×C₁₃₉	C₂²	1	4	yes	complemented
73	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#388×C₁₃₉	C₂²	1	4	yes	complemented
76	#388×C₁₃₉	C₂²	1	4	yes	complemented
77	#387×C₁₃₉	C₂²	1	4	yes	complemented
78	#386×C₁₃₉	C₂²	1	2	yes	—
79	#386×C₁₃₉	C₂²	1	2	yes	complemented
80	#386×C₁₃₉	C₂²	1	4	yes	complemented
81	#386×C₁₃₉	C₂²	1	4	yes	complemented
82	#386×C₁₃₉	C₂²	1	4	yes	complemented
83	#386×C₁₃₉	C₂²	1	4	yes	complemented
84	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
85	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
87	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
88	#379×C₁₃₉	C₂²	1	4	yes	—
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
93	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
94	C₂×#41×C₁₃₉	—	2	4	no	—
95	C₂×#41×C₁₃₉	—	4	2	no	—
96	C₂×#41×C₁₃₉	—	4	2	no	—
97	C₂×#41×C₁₃₉	—	4	2	no	—
98	C₂×#41×C₁₃₉	—	4	2	no	—
99	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
100	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃₉	—	2	4	no	—
103	C₂²×D₄×C₁₃₉	—	4	2	no	—
104	C₂²×D₄×C₁₃₉	—	4	2	no	—
105	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
127	#127×C₁₃₉	—	2	8	no	—
128	#127×C₁₃₉	—	4	2	no	—
129	#127×C₁₃₉	—	4	2	no	—
130	#124×C₁₃₉	—	2	8	no	—
131	#124×C₁₃₉	—	4	2	no	—
132	#124×C₁₃₉	—	4	2	no	—
133	#123×C₁₃₉	—	4	8	no	—
134	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
135	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
136	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
137	#121×C₁₃₉	—	2	8	no	—
138	#121×C₁₃₉	—	2	8	no	—
139	#121×C₁₃₉	—	2	8	no	—
140	#121×C₁₃₉	—	2	4	no	—
141	#121×C₁₃₉	—	2	4	no	—
142	#121×C₁₃₉	—	2	4	no	—
143	#121×C₁₃₉	—	2	4	no	—
144	#121×C₁₃₉	—	2	4	no	—
145	#121×C₁₃₉	—	2	4	no	—
146	#121×C₁₃₉	—	4	8	no	—
147	#120×C₁₃₉	—	2	8	no	—
148	#120×C₁₃₉	—	2	8	no	—
149	#120×C₁₃₉	—	4	8	no	—
150	#117×C₁₃₉	—	2	4	no	—
151	#117×C₁₃₉	—	4	2	no	—
152	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
185	C₂×C₄²×C₁₃₉	—	4	2	no	—
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	#95×C₁₃₉	C₂³	1	4	yes	—
194	#95×C₁₃₉	C₂³	1	4	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	4	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	C₂⁴×C₁₃₉	—	2	4	no	—
201	C₂⁴×C₁₃₉	—	4	2	no	—
202	C₂⁴×C₁₃₉	—	4	2	no	—
203	C₂⁴×C₁₃₉	—	4	4	no	—
204	C₂⁴×C₁₃₉	—	4	4	no	—
205	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	#41×C₁₃₉	—	4	16	no	—
212	#41×C₁₃₉	—	4	16	no	—
213	C₂×Q₈×C₁₃₉	—	2	2	no	—
214	C₂×Q₈×C₁₃₉	—	2	2	no	—
215	C₂×Q₈×C₁₃₉	—	2	2	no	—
216	C₂×Q₈×C₁₃₉	—	4	1	no	—
217	C₂×Q₈×C₁₃₉	—	4	1	no	—
218	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	4	no	—
224	C₂×D₄×C₁₃₉	—	2	4	no	—
225	C₂×D₄×C₁₃₉	—	2	4	no	—
226	C₂×D₄×C₁₃₉	—	2	2	no	—
227	C₂×D₄×C₁₃₉	—	2	2	no	—
228	C₂×D₄×C₁₃₉	—	2	2	no	—
229	C₂×D₄×C₁₃₉	—	2	4	no	—
230	C₂×D₄×C₁₃₉	—	2	2	no	—
231	C₂×D₄×C₁₃₉	—	2	2	no	—
232	C₂×D₄×C₁₃₉	—	2	2	no	—
233	C₂×D₄×C₁₃₉	—	2	2	no	—
234	C₂×D₄×C₁₃₉	—	2	2	no	—
235	C₂×D₄×C₁₃₉	—	2	2	no	—
236	C₂×D₄×C₁₃₉	—	2	8	no	—
237	C₂×D₄×C₁₃₉	—	4	2	no	—
238	C₂×D₄×C₁₃₉	—	4	2	no	—
239	C₂×D₄×C₁₃₉	—	4	1	no	—
240	C₂×D₄×C₁₃₉	—	4	1	no	—
241	C₂×D₄×C₁₃₉	—	4	1	no	—
242	C₂×D₄×C₁₃₉	—	4	1	no	—
243	C₂×D₄×C₁₃₉	—	4	1	no	—
244	C₂×D₄×C₁₃₉	—	4	1	no	—
245	C₂×D₄×C₁₃₉	—	4	2	no	—
246	C₂×D₄×C₁₃₉	—	4	2	no	—
247	C₂×D₄×C₁₃₉	—	4	16	no	—
248	C₂×D₄×C₁₃₉	—	4	4	no	—
249	C₂×D₄×C₁₃₉	—	4	4	no	—
250	C₂×D₄×C₁₃₉	—	4	4	no	—
251	C₂×D₄×C₁₃₉	—	4	4	no	—
252	C₂×D₄×C₁₃₉	—	4	4	no	—
253	C₂×D₄×C₁₃₉	—	4	4	no	—
254	C₂×D₄×C₁₃₉	—	4	4	no	—
255	C₂×D₄×C₁₃₉	—	4	4	no	—
256	C₂×D₄×C₁₃₉	—	4	4	no	—
257	C₂×D₄×C₁₃₉	—	4	4	no	—
258	C₂×D₄×C₁₃₉	—	4	4	no	—
259	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
261	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
262	C₂²×C₄×C₁₃₉	—	2	2	no	—
263	C₂²×C₄×C₁₃₉	—	2	2	no	—
264	C₂²×C₄×C₁₃₉	—	2	2	no	—
265	C₂²×C₄×C₁₃₉	—	2	2	no	—
266	C₂²×C₄×C₁₃₉	—	2	2	no	—
267	C₂²×C₄×C₁₃₉	—	2	2	no	—
268	C₂²×C₄×C₁₃₉	—	2	4	no	—
269	C₂²×C₄×C₁₃₉	—	2	4	no	—
270	C₂²×C₄×C₁₃₉	—	2	4	no	—
271	C₂²×C₄×C₁₃₉	—	4	2	no	—
272	C₂²×C₄×C₁₃₉	—	4	2	no	—
273	C₂²×C₄×C₁₃₉	—	4	2	no	—
274	C₂²×C₄×C₁₃₉	—	4	2	no	—
275	C₂²×C₄×C₁₃₉	—	4	4	no	—
276	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
278	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
279	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₁₃₉	—	2	4	no	—
293	C₄⋊C₄×C₁₃₉	—	2	2	no	—
294	C₄⋊C₄×C₁₃₉	—	2	2	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	2	2	no	—
297	C₄⋊C₄×C₁₃₉	—	2	4	no	—
298	C₄⋊C₄×C₁₃₉	—	2	4	no	—
299	C₄⋊C₄×C₁₃₉	—	2	8	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
315	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
316	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
318	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
319	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
320	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
321	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
322	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
323	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
324	C₄²×C₁₃₉	—	2	4	no	—
325	C₄²×C₁₃₉	—	2	2	no	—
326	C₄²×C₁₃₉	—	2	2	no	—
327	C₄²×C₁₃₉	—	2	2	no	—
328	C₄²×C₁₃₉	—	2	2	no	—
329	C₄²×C₁₃₉	—	4	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	1	no	—
333	C₂³×C₁₃₉	—	2	1	no	—
334	C₂³×C₁₃₉	—	2	1	no	—
335	C₂³×C₁₃₉	—	2	1	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	1	no	—
338	C₂³×C₁₃₉	—	2	1	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	2	no	—
342	C₂³×C₁₃₉	—	2	2	no	—
343	C₂³×C₁₃₉	—	2	2	no	—
344	C₂³×C₁₃₉	—	2	2	no	—
345	C₂³×C₁₃₉	—	2	4	no	—
346	C₂³×C₁₃₉	—	2	2	no	—
347	C₂³×C₁₃₉	—	2	2	no	—
348	C₂³×C₁₃₉	—	2	4	no	—
349	C₂³×C₁₃₉	—	2	4	no	—
350	C₂³×C₁₃₉	—	2	2	no	—
351	C₂³×C₁₃₉	—	2	2	no	—
352	C₂³×C₁₃₉	—	2	2	no	—
353	C₂³×C₁₃₉	—	2	2	no	—
354	C₂³×C₁₃₉	—	2	4	no	—
355	C₂³×C₁₃₉	—	2	4	no	—
356	C₂³×C₁₃₉	—	2	4	no	—
357	C₂³×C₁₃₉	—	4	8	no	—
358	C₂³×C₁₃₉	—	8	4	no	—
359	C₂³×C₁₃₉	—	8	4	no	—
360	C₂³×C₁₃₉	—	8	8	no	—
361	C₂³×C₁₃₉	—	8	8	no	—
362	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
363	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
364	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
365	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
366	Q₈×C₁₃₉	—	4	4	no	—
367	Q₈×C₁₃₉	—	4	4	no	—
368	D₄×C₁₃₉	—	4	4	no	—
369	D₄×C₁₃₉	—	4	4	no	—
370	D₄×C₁₃₉	—	4	4	no	—
371	D₄×C₁₃₉	—	4	8	no	—
372	D₄×C₁₃₉	—	4	8	no	—
373	D₄×C₁₃₉	—	4	4	no	—
374	D₄×C₁₃₉	—	4	4	no	—
375	D₄×C₁₃₉	—	4	4	no	—
376	D₄×C₁₃₉	—	8	8	no	—
377	D₄×C₁₃₉	—	8	4	no	—
378	D₄×C₁₃₉	—	8	4	no	—
379	D₄×C₁₃₉	—	8	4	no	—
380	D₄×C₁₃₉	—	8	4	no	—
381	D₄×C₁₃₉	—	8	4	no	—
382	D₄×C₁₃₉	—	8	4	no	—
383	D₄×C₁₃₉	—	8	8	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	1	no	—
388	C₂×C₄×C₁₃₉	—	2	1	no	—
389	C₂×C₄×C₁₃₉	—	2	1	no	—
390	C₂×C₄×C₁₃₉	—	2	1	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	8	no	—
393	C₂×C₄×C₁₃₉	—	2	8	no	—
394	C₂×C₄×C₁₃₉	—	2	8	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	2	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	2	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	2	no	—
404	C₂×C₄×C₁₃₉	—	2	2	no	—
405	C₂×C₄×C₁₃₉	—	2	4	no	—
406	C₂×C₄×C₁₃₉	—	2	2	no	—
407	C₂×C₄×C₁₃₉	—	2	4	no	—
408	C₂×C₄×C₁₃₉	—	2	2	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	4	no	—
411	C₂×C₄×C₁₃₉	—	2	2	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	2	4	no	—
414	C₂×C₄×C₁₃₉	—	2	2	no	—
415	C₂×C₄×C₁₃₉	—	4	8	no	—
416	C₂×C₄×C₁₃₉	—	4	8	no	—
417	C₂×C₄×C₁₃₉	—	8	4	no	—
418	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
423	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
425	C₂²×C₁₃₉	—	2	2	no	—
426	C₂²×C₁₃₉	—	2	2	no	—
427	C₂²×C₁₃₉	—	2	2	no	—
428	C₂²×C₁₃₉	—	2	2	no	—
429	C₂²×C₁₃₉	—	2	2	no	—
430	C₂²×C₁₃₉	—	2	2	no	—
431	C₂²×C₁₃₉	—	2	2	no	—
432	C₂²×C₁₃₉	—	2	2	no	—
433	C₂²×C₁₃₉	—	2	2	no	—
434	C₂²×C₁₃₉	—	4	2	no	—
435	C₂²×C₁₃₉	—	4	2	no	—
436	C₂²×C₁₃₉	—	4	2	no	—
437	C₂²×C₁₃₉	—	4	2	no	—
438	C₂²×C₁₃₉	—	4	2	no	—
439	C₂²×C₁₃₉	—	4	2	no	—
440	C₂²×C₁₃₉	—	4	2	no	—
441	C₂²×C₁₃₉	—	4	2	no	—
442	C₂²×C₁₃₉	—	4	2	no	—
443	C₂²×C₁₃₉	—	4	2	no	—
444	C₂²×C₁₃₉	—	4	2	no	—
445	C₂²×C₁₃₉	—	4	2	no	—
446	C₂²×C₁₃₉	—	4	2	no	—
447	C₂²×C₁₃₉	—	4	2	no	—
448	C₂²×C₁₃₉	—	4	2	no	—
449	C₂²×C₁₃₉	—	4	4	no	—
450	C₂²×C₁₃₉	—	4	4	no	—
451	C₂²×C₁₃₉	—	4	4	no	—
452	C₂²×C₁₃₉	—	4	4	no	—
453	C₂²×C₁₃₉	—	4	4	no	—
454	C₂²×C₁₃₉	—	4	4	no	—
455	C₂²×C₁₃₉	—	8	16	no	—
456	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
457	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
460	C₂²×C₁₃₉	#585	1	2	yes	—
461	C₄×C₁₃₉	—	2	2	no	—
462	C₄×C₁₃₉	—	2	2	no	—
463	C₄×C₁₃₉	—	2	2	no	—
464	C₄×C₁₃₉	—	2	4	no	—
465	C₄×C₁₃₉	—	4	2	no	—
466	C₄×C₁₃₉	—	4	2	no	—
467	C₄×C₁₃₉	—	4	2	no	—
468	C₄×C₁₃₉	—	4	2	no	—
469	C₄×C₁₃₉	—	4	2	no	—
470	C₄×C₁₃₉	—	4	2	no	—
471	C₄×C₁₃₉	—	4	2	no	—
472	C₄×C₁₃₉	—	4	2	no	—
473	C₄×C₁₃₉	#534	1	4	yes	—
474	C₂×C₁₃₉	—	4	2	no	—
475	C₂×C₁₃₉	—	4	2	no	—
476	C₂×C₁₃₉	—	4	2	no	—
477	C₂×C₁₃₉	—	8	2	no	—
478	C₂×C₁₃₉	—	8	2	no	—
479	C₂×C₁₃₉	—	8	2	no	—
480	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
481	C₂×C₁₃₉	#3498	1	1	yes	characteristic
482	C₂×C₁₃₉	#3500	1	1	yes	characteristic
483	C₂×C₁₃₉	#3542	1	2	yes	—
484	C₂×C₁₃₉	#3546	1	2	yes	—
485	#37300	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₁₃₉	#37300	1	1	yes	characteristic, direct product factor, Sylow
487	C₂×#537	C₂×C₁₃₉	1	1	yes	characteristic, complemented
488	C₂×#535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
489	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
490	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
491	#2730	C₂×C₁₃₉	1	4	yes	complemented
492	#2678	C₂×C₁₃₉	1	4	yes	complemented
493	#2673	C₂×C₁₃₉	1	4	yes	complemented
494	#2668	C₂×C₁₃₉	1	4	yes	complemented
495	#2620	C₂×C₁₃₉	1	1	yes	characteristic, complemented
496	#2619	C₂×C₁₃₉	1	1	yes	characteristic, complemented
497	#2504	C₂×C₁₃₉	1	1	yes	characteristic, complemented
498	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
499	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
500	#2499	C₂×C₁₃₉	1	1	yes	characteristic, complemented
501	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
502	#2433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
503	#2431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
504	#2431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
505	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
506	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
508	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
509	#537	—	2	8	no	—
510	#535	—	2	8	no	—
511	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
512	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
513	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
515	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
516	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
517	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
518	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
519	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
520	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
521	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
522	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
523	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
524	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
525	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
526	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
529	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
530	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
531	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
532	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
533	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
534	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
535	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
536	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
537	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
538	#399	C₂²×C₁₃₉	1	4	yes	complemented
539	#397	C₂²×C₁₃₉	1	4	yes	—
540	#397	C₂²×C₁₃₉	1	4	yes	complemented
541	#396	C₂²×C₁₃₉	1	4	yes	complemented
542	#394	C₂²×C₁₃₉	1	4	yes	—
543	#394	C₂²×C₁₃₉	1	4	yes	—
544	#394	C₂²×C₁₃₉	1	4	yes	complemented
545	#394	C₂²×C₁₃₉	1	4	yes	complemented
546	#392	C₂²×C₁₃₉	1	4	yes	—
547	#392	C₂²×C₁₃₉	1	4	yes	complemented
548	#392	C₂²×C₁₃₉	1	4	yes	complemented
549	#392	C₂²×C₁₃₉	1	4	yes	complemented
550	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
551	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
552	#391	C₂²×C₁₃₉	1	2	yes	complemented
553	#390	C₂²×C₁₃₉	1	1	yes	characteristic
554	#390	C₂²×C₁₃₉	1	1	yes	characteristic
555	#390	C₂²×C₁₃₉	1	1	yes	characteristic
556	#390	C₂²×C₁₃₉	1	1	yes	characteristic
557	#390	C₂²×C₁₃₉	1	2	yes	—
558	#390	C₂²×C₁₃₉	1	4	yes	complemented
559	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
560	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
561	#388	C₂²×C₁₃₉	1	4	yes	complemented
562	#388	C₂²×C₁₃₉	1	4	yes	complemented
563	#387	C₂²×C₁₃₉	1	4	yes	complemented
564	#386	C₂²×C₁₃₉	1	2	yes	—
565	#386	C₂²×C₁₃₉	1	4	yes	complemented
566	#386	C₂²×C₁₃₉	1	4	yes	complemented
567	#386	C₂²×C₁₃₉	1	4	yes	complemented
568	#386	C₂²×C₁₃₉	1	2	yes	complemented
569	#386	C₂²×C₁₃₉	1	4	yes	complemented
570	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
571	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
572	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
573	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
574	#379	C₂²×C₁₃₉	1	4	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
578	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
579	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
580	C₂×#41	—	2	4	no	—
581	C₂×#41	—	4	2	no	—
582	C₂×#41	—	4	2	no	—
583	C₂×#41	—	4	2	no	—
584	C₂×#41	—	4	2	no	—
585	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
586	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂²×D₄	—	2	4	no	—
589	C₂²×D₄	—	4	2	no	—
590	C₂²×D₄	—	4	2	no	—
591	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
600	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
604	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
613	#127	—	2	8	no	—
614	#127	—	4	2	no	—
615	#127	—	4	2	no	—
616	#124	—	2	8	no	—
617	#124	—	4	2	no	—
618	#124	—	4	2	no	—
619	#123	—	4	8	no	—
620	C₂²⋊Q₈	—	2	8	no	—
621	C₂²⋊Q₈	—	2	4	no	—
622	C₂²⋊Q₈	—	2	4	no	—
623	#121	—	2	8	no	—
624	#121	—	2	8	no	—
625	#121	—	2	8	no	—
626	#121	—	2	4	no	—
627	#121	—	2	4	no	—
628	#121	—	2	4	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	4	8	no	—
633	#120	—	2	8	no	—
634	#120	—	2	8	no	—
635	#120	—	4	8	no	—
636	#117	—	2	4	no	—
637	#117	—	4	2	no	—
638	C₂×C₄⋊C₄	—	2	4	no	—
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
671	C₂×C₄²	—	4	2	no	—
672	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
678	#95	C₂³×C₁₃₉	1	2	yes	—
679	#95	C₂³×C₁₃₉	1	2	yes	—
680	#95	C₂³×C₁₃₉	1	2	yes	—
681	#95	C₂³×C₁₃₉	1	2	yes	—
682	#95	C₂³×C₁₃₉	1	4	yes	—
683	#95	C₂³×C₁₃₉	1	4	yes	—
684	#95	C₂³×C₁₃₉	1	4	yes	—
685	#95	C₂³×C₁₃₉	1	4	yes	—
686	C₂⁴	—	2	4	no	—
687	C₂⁴	—	4	2	no	—
688	C₂⁴	—	4	2	no	—
689	C₂⁴	—	4	4	no	—
690	C₂⁴	—	4	4	no	—
691	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
692	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
695	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
696	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	#41	—	4	16	no	—
698	#41	—	4	16	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	4	1	no	—
703	C₂×Q₈	—	4	1	no	—
704	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	8	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	1	no	—
726	C₂×D₄	—	4	1	no	—
727	C₂×D₄	—	4	1	no	—
728	C₂×D₄	—	4	1	no	—
729	C₂×D₄	—	4	1	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	16	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	4	4	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
746	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
747	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	4	no	—
762	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
763	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
764	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	8	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	8	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	4	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	4	no	—
805	C₂²⋊C₄	—	4	4	no	—
806	C₂²⋊C₄	—	4	4	no	—
807	C₂²⋊C₄	—	4	4	no	—
808	C₂²⋊C₄	—	4	4	no	—
809	C₂²⋊C₄	—	4	4	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	4	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	4	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	4	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	4	8	no	—
844	C₂³	—	8	4	no	—
845	C₂³	—	8	4	no	—
846	C₂³	—	8	8	no	—
847	C₂³	—	8	8	no	—
848	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
849	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
850	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
851	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
852	Q₈	—	4	4	no	—
853	Q₈	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	4	no	—
856	D₄	—	4	4	no	—
857	D₄	—	4	8	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	8	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	4	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	D₄	—	8	4	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	8	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	8	no	—
879	C₂×C₄	—	2	8	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	4	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	4	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	4	8	no	—
902	C₂×C₄	—	4	8	no	—
903	C₂×C₄	—	8	4	no	—
904	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
905	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
908	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
909	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
910	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	4	no	—
927	C₂²	—	4	4	no	—
928	C₂²	—	4	4	no	—
929	C₂²	—	4	4	no	—
930	C₂²	—	4	4	no	—
931	C₂²	—	4	4	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	8	16	no	—
942	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
943	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
944	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
945	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
946	C₂²	#585×C₁₃₉	1	2	yes	—
947	C₄	—	2	4	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	#534×C₁₃₉	1	4	yes	—
960	C₂	—	4	2	no	—
961	C₂	—	4	2	no	—
962	C₂	—	4	2	no	—
963	C₂	—	8	2	no	—
964	C₂	—	8	2	no	—
965	C₂	—	8	2	no	—
966	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
967	C₂	#3498×C₁₃₉	1	1	yes	characteristic
968	C₂	#3500×C₁₃₉	1	1	yes	characteristic
969	C₂	#3542×C₁₃₉	1	2	yes	—
970	C₂	#3546×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×#537×C₁₃₉	C₂	semidirect
2. C₂×#535×C₁₃₉	C₂	semidirect
3. #2856×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2730×C₁₃₉	C₂	semidirect
6. #2678×C₁₃₉	C₂	semidirect
7. #2673×C₁₃₉	C₂	semidirect
8. #2668×C₁₃₉	C₂	semidirect
9. #2620×C₁₃₉	C₂	semidirect
10. #2619×C₁₃₉	C₂	semidirect
11. #2504×C₁₃₉	C₂	semidirect
12. #2501×C₁₃₉	C₂	semidirect
13. #2500×C₁₃₉	C₂	semidirect
14. #2499×C₁₃₉	C₂	semidirect
15. #2435×C₁₃₉	C₂	semidirect
16. #2433×C₁₃₉	C₂	semidirect
17. #2431×C₁₃₉	C₂	semidirect
18. #2431×C₁₃₉	C₂	semidirect
19. #2297×C₁₃₉	C₂	semidirect
21. C₂²×#41×C₁₃₉	C₂²	semidirect
31. C₂×#123×C₁₃₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
42. C₂×#121×C₁₃₉	C₂²	semidirect
43. C₂×#121×C₁₃₉	C₂²	semidirect
44. C₂×#121×C₁₃₉	C₂²	semidirect
49. C₂×#117×C₁₃₉	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
51. C₂²×C₄²×C₁₃₉	C₂²	semidirect
52. #399×C₁₃₉	C₂²	semidirect
54. #397×C₁₃₉	C₂²	semidirect
55. #396×C₁₃₉	C₂²	semidirect
58. #394×C₁₃₉	C₂²	semidirect
59. #394×C₁₃₉	C₂²	semidirect
61. #392×C₁₃₉	C₂²	semidirect
62. #392×C₁₃₉	C₂²	semidirect
63. #392×C₁₃₉	C₂²	semidirect
64. #391×C₁₃₉	C₂²	semidirect
65. #391×C₁₃₉	C₂²	semidirect
66. #391×C₁₃₉	C₂²	semidirect
72. #390×C₁₃₉	C₂²	semidirect
73. #390×C₁₃₉	C₂²	semidirect
74. #390×C₁₃₉	C₂²	semidirect
75. #388×C₁₃₉	C₂²	semidirect
76. #388×C₁₃₉	C₂²	semidirect
77. #387×C₁₃₉	C₂²	semidirect
79. #386×C₁₃₉	C₂²	semidirect
80. #386×C₁₃₉	C₂²	semidirect
81. #386×C₁₃₉	C₂²	semidirect
82. #386×C₁₃₉	C₂²	semidirect
83. #386×C₁₃₉	C₂²	semidirect
84. #384×C₁₃₉	C₂²	semidirect
85. #384×C₁₃₉	C₂²	semidirect
86. #382×C₁₃₉	C₂²	semidirect
87. #382×C₁₃₉	C₂²	semidirect
91. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
92. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
99. C₂×#41×C₁₃₉	D₄	semidirect
485. #37300	C₁₃₉	direct (N × H)
486. C₁₃₉	#37300	direct (N × H)
487. C₂×#537	C₂×C₁₃₉	semidirect
488. C₂×#535	C₂×C₁₃₉	semidirect
489. #2856	C₂×C₁₃₉	semidirect
490. #2850	C₂×C₁₃₉	semidirect
491. #2730	C₂×C₁₃₉	semidirect
492. #2678	C₂×C₁₃₉	semidirect
493. #2673	C₂×C₁₃₉	semidirect
494. #2668	C₂×C₁₃₉	semidirect
495. #2620	C₂×C₁₃₉	semidirect
496. #2619	C₂×C₁₃₉	semidirect
497. #2504	C₂×C₁₃₉	semidirect
498. #2501	C₂×C₁₃₉	semidirect
499. #2500	C₂×C₁₃₉	semidirect
500. #2499	C₂×C₁₃₉	semidirect
501. #2435	C₂×C₁₃₉	semidirect
502. #2433	C₂×C₁₃₉	semidirect
503. #2431	C₂×C₁₃₉	semidirect
504. #2431	C₂×C₁₃₉	semidirect
505. #2297	C₂×C₁₃₉	semidirect
507. C₂²×#41	C₂²×C₁₃₉	semidirect
517. C₂×#123	C₂²×C₁₃₉	semidirect
519. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
520. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
528. C₂×#121	C₂²×C₁₃₉	semidirect
529. C₂×#121	C₂²×C₁₃₉	semidirect
530. C₂×#121	C₂²×C₁₃₉	semidirect
535. C₂×#117	C₂²×C₁₃₉	semidirect
536. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
537. C₂²×C₄²	C₂²×C₁₃₉	semidirect
538. #399	C₂²×C₁₃₉	semidirect
540. #397	C₂²×C₁₃₉	semidirect
541. #396	C₂²×C₁₃₉	semidirect
544. #394	C₂²×C₁₃₉	semidirect
545. #394	C₂²×C₁₃₉	semidirect
547. #392	C₂²×C₁₃₉	semidirect
548. #392	C₂²×C₁₃₉	semidirect
549. #392	C₂²×C₁₃₉	semidirect
550. #391	C₂²×C₁₃₉	semidirect
551. #391	C₂²×C₁₃₉	semidirect
552. #391	C₂²×C₁₃₉	semidirect
558. #390	C₂²×C₁₃₉	semidirect
559. #390	C₂²×C₁₃₉	semidirect
560. #390	C₂²×C₁₃₉	semidirect
561. #388	C₂²×C₁₃₉	semidirect
562. #388	C₂²×C₁₃₉	semidirect
563. #387	C₂²×C₁₃₉	semidirect
565. #386	C₂²×C₁₃₉	semidirect
566. #386	C₂²×C₁₃₉	semidirect
567. #386	C₂²×C₁₃₉	semidirect
568. #386	C₂²×C₁₃₉	semidirect
569. #386	C₂²×C₁₃₉	semidirect
570. #384	C₂²×C₁₃₉	semidirect
571. #384	C₂²×C₁₃₉	semidirect
572. #382	C₂²×C₁₃₉	semidirect
573. #382	C₂²×C₁₃₉	semidirect
577. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
578. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
585. C₂×#41	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×#537×C₁₃₉	2
C₂×#535×C₁₃₉	2
#2856×C₁₃₉	2
#2850×C₁₃₉	2
#2730×C₁₃₉	2
#2678×C₁₃₉	2
#2673×C₁₃₉	2
#2668×C₁₃₉	2
#2620×C₁₃₉	2
#2619×C₁₃₉	2
#2504×C₁₃₉	2
#2501×C₁₃₉	2
#2500×C₁₃₉	2
#2499×C₁₃₉	2
#2435×C₁₃₉	2
#2433×C₁₃₉	2
#2431×C₁₃₉	2
#2297×C₁₃₉	2
#37300	139

Subgroups — C139×#37300 #48031896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37300 #48031896