Subgroups — C₁₃₉×#36015 #48030611

Order 35584.

2202 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2661×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2620×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2558×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2554×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2490×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2489×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2415×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2414×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2367×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2363×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2362×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#553×C₁₃₉	—	2	8	no	—
25	#552×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	#400×C₁₃₉	C₂²	1	2	yes	—
54	#399×C₁₃₉	C₂²	1	2	yes	—
55	#398×C₁₃₉	C₂²	1	1	yes	characteristic
56	#398×C₁₃₉	C₂²	1	2	yes	—
57	#398×C₁₃₉	C₂²	1	2	yes	—
58	#397×C₁₃₉	C₂²	1	2	yes	—
59	#397×C₁₃₉	C₂²	1	2	yes	—
60	#397×C₁₃₉	C₂²	1	2	yes	—
61	#397×C₁₃₉	C₂²	1	1	yes	characteristic
62	#396×C₁₃₉	C₂²	1	1	yes	characteristic
63	#396×C₁₃₉	C₂²	1	2	yes	—
64	#396×C₁₃₉	C₂²	1	2	yes	—
65	#396×C₁₃₉	C₂²	1	1	yes	characteristic
66	#394×C₁₃₉	C₂²	1	1	yes	characteristic
67	#394×C₁₃₉	C₂²	1	2	yes	—
68	#394×C₁₃₉	C₂²	1	1	yes	characteristic
69	#394×C₁₃₉	C₂²	1	2	yes	—
70	#394×C₁₃₉	C₂²	1	2	yes	—
71	#394×C₁₃₉	C₂²	1	1	yes	characteristic
72	#394×C₁₃₉	C₂²	1	2	yes	—
73	#394×C₁₃₉	C₂²	1	2	yes	—
74	#392×C₁₃₉	C₂²	1	2	yes	—
75	#392×C₁₃₉	C₂²	1	2	yes	—
76	#392×C₁₃₉	C₂²	1	1	yes	characteristic
77	#391×C₁₃₉	C₂²	1	1	yes	characteristic
78	#391×C₁₃₉	C₂²	1	1	yes	characteristic
79	#390×C₁₃₉	C₂²	1	2	yes	—
80	#390×C₁₃₉	C₂²	1	2	yes	—
81	#390×C₁₃₉	C₂²	1	2	yes	—
82	#390×C₁₃₉	C₂²	1	2	yes	—
83	#390×C₁₃₉	C₂²	1	2	yes	—
84	#390×C₁₃₉	C₂²	1	2	yes	—
85	#390×C₁₃₉	C₂²	1	1	yes	characteristic
86	#390×C₁₃₉	C₂²	1	1	yes	characteristic
87	#389×C₁₃₉	C₂²	1	2	yes	—
88	#389×C₁₃₉	C₂²	1	2	yes	—
89	#389×C₁₃₉	C₂²	1	1	yes	characteristic
90	#389×C₁₃₉	C₂²	1	1	yes	characteristic
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#388×C₁₃₉	C₂²	1	2	yes	—
94	#388×C₁₃₉	C₂²	1	2	yes	—
95	#388×C₁₃₉	C₂²	1	2	yes	—
96	#388×C₁₃₉	C₂²	1	2	yes	—
97	#388×C₁₃₉	C₂²	1	2	yes	—
98	#388×C₁₃₉	C₂²	1	2	yes	—
99	#388×C₁₃₉	C₂²	1	2	yes	—
100	#388×C₁₃₉	C₂²	1	2	yes	—
101	#388×C₁₃₉	C₂²	1	2	yes	—
102	#387×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#385×C₁₃₉	C₂²	1	2	yes	—
105	#384×C₁₃₉	C₂²	1	2	yes	—
106	#384×C₁₃₉	C₂²	1	1	yes	characteristic
107	#382×C₁₃₉	C₂²	1	2	yes	—
108	#380×C₁₃₉	C₂²	1	1	yes	characteristic
109	#380×C₁₃₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	#126×C₁₃₉	—	2	8	no	—
139	#126×C₁₃₉	—	2	8	no	—
140	#125×C₁₃₉	—	2	8	no	—
141	#125×C₁₃₉	—	2	4	no	—
142	#125×C₁₃₉	—	2	4	no	—
143	#124×C₁₃₉	—	2	4	no	—
144	#123×C₁₃₉	—	2	8	no	—
145	#123×C₁₃₉	—	2	8	no	—
146	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
147	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
148	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
149	#121×C₁₃₉	—	2	8	no	—
150	#121×C₁₃₉	—	2	4	no	—
151	#121×C₁₃₉	—	2	4	no	—
152	#121×C₁₃₉	—	2	4	no	—
153	C₄×Q₈×C₁₃₉	—	2	4	no	—
154	C₄×D₄×C₁₃₉	—	2	4	no	—
155	C₄×D₄×C₁₃₉	—	2	8	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	4	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	#117×C₁₃₉	—	2	8	no	—
160	#117×C₁₃₉	—	2	4	no	—
161	#117×C₁₃₉	—	2	4	no	—
162	#117×C₁₃₉	—	2	4	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
224	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
233	#95×C₁₃₉	C₂³	1	1	yes	characteristic
234	#95×C₁₃₉	C₂³	1	1	yes	characteristic
235	#95×C₁₃₉	C₂³	1	2	yes	—
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	1	yes	characteristic
240	#95×C₁₃₉	C₂³	1	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	1	yes	characteristic
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	1	yes	characteristic
246	#95×C₁₃₉	C₂³	1	1	yes	characteristic
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₁₃₉	—	2	2	no	—
256	C₂×Q₈×C₁₃₉	—	2	2	no	—
257	C₂×Q₈×C₁₃₉	—	2	2	no	—
258	C₂×D₄×C₁₃₉	—	2	4	no	—
259	C₂×D₄×C₁₃₉	—	2	2	no	—
260	C₂×D₄×C₁₃₉	—	2	2	no	—
261	C₂×D₄×C₁₃₉	—	2	2	no	—
262	C₂×D₄×C₁₃₉	—	2	4	no	—
263	C₂×D₄×C₁₃₉	—	2	2	no	—
264	C₂×D₄×C₁₃₉	—	2	2	no	—
265	C₂×D₄×C₁₃₉	—	2	2	no	—
266	C₂×D₄×C₁₃₉	—	2	4	no	—
267	C₂×D₄×C₁₃₉	—	4	1	no	—
268	C₂×D₄×C₁₃₉	—	4	1	no	—
269	C₂×D₄×C₁₃₉	—	4	1	no	—
270	C₂×D₄×C₁₃₉	—	4	1	no	—
271	C₂×D₄×C₁₃₉	—	4	2	no	—
272	C₂×D₄×C₁₃₉	—	4	1	no	—
273	C₂×D₄×C₁₃₉	—	4	1	no	—
274	C₂×D₄×C₁₃₉	—	4	2	no	—
275	C₂×D₄×C₁₃₉	—	4	2	no	—
276	C₂×D₄×C₁₃₉	—	4	2	no	—
277	C₂×D₄×C₁₃₉	—	4	2	no	—
278	C₂×D₄×C₁₃₉	—	4	2	no	—
279	C₂²×C₄×C₁₃₉	—	2	2	no	—
280	C₂²×C₄×C₁₃₉	—	2	2	no	—
281	C₂²×C₄×C₁₃₉	—	2	2	no	—
282	C₂²×C₄×C₁₃₉	—	2	2	no	—
283	C₂²×C₄×C₁₃₉	—	2	2	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	2	no	—
287	C₂²×C₄×C₁₃₉	—	2	4	no	—
288	C₂²×C₄×C₁₃₉	—	4	2	no	—
289	C₂²×C₄×C₁₃₉	—	4	2	no	—
290	C₂²×C₄×C₁₃₉	—	4	2	no	—
291	C₂²×C₄×C₁₃₉	—	4	2	no	—
292	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
293	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
294	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₁₃₉	—	2	2	no	—
314	C₄⋊C₄×C₁₃₉	—	2	4	no	—
315	C₄⋊C₄×C₁₃₉	—	2	2	no	—
316	C₄⋊C₄×C₁₃₉	—	2	4	no	—
317	C₄⋊C₄×C₁₃₉	—	2	4	no	—
318	C₄⋊C₄×C₁₃₉	—	2	2	no	—
319	C₄⋊C₄×C₁₃₉	—	2	2	no	—
320	C₄⋊C₄×C₁₃₉	—	2	4	no	—
321	C₄⋊C₄×C₁₃₉	—	2	4	no	—
322	C₄⋊C₄×C₁₃₉	—	2	4	no	—
323	C₄⋊C₄×C₁₃₉	—	2	4	no	—
324	C₄⋊C₄×C₁₃₉	—	2	2	no	—
325	C₄⋊C₄×C₁₃₉	—	2	2	no	—
326	C₄⋊C₄×C₁₃₉	—	2	2	no	—
327	C₄⋊C₄×C₁₃₉	—	2	2	no	—
328	C₄⋊C₄×C₁₃₉	—	2	4	no	—
329	C₄⋊C₄×C₁₃₉	—	4	1	no	—
330	C₄⋊C₄×C₁₃₉	—	4	1	no	—
331	C₄⋊C₄×C₁₃₉	—	4	2	no	—
332	C₄⋊C₄×C₁₃₉	—	4	2	no	—
333	C₄⋊C₄×C₁₃₉	—	4	2	no	—
334	C₄⋊C₄×C₁₃₉	—	4	2	no	—
335	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
336	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
337	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
338	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
339	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
340	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
341	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
343	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
344	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
345	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
346	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
349	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
350	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
361	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
362	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
364	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
365	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
366	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
369	C₄²×C₁₃₉	—	2	4	no	—
370	C₄²×C₁₃₉	—	2	4	no	—
371	C₄²×C₁₃₉	—	2	4	no	—
372	C₄²×C₁₃₉	—	2	2	no	—
373	C₄²×C₁₃₉	—	2	2	no	—
374	C₄²×C₁₃₉	—	2	4	no	—
375	C₄²×C₁₃₉	—	2	2	no	—
376	C₄²×C₁₃₉	—	4	2	no	—
377	C₄²×C₁₃₉	—	4	2	no	—
378	C₄²×C₁₃₉	—	4	2	no	—
379	C₄²×C₁₃₉	—	4	2	no	—
380	C₄²×C₁₃₉	#41	1	4	yes	—
381	C₂³×C₁₃₉	—	2	1	no	—
382	C₂³×C₁₃₉	—	2	1	no	—
383	C₂³×C₁₃₉	—	2	1	no	—
384	C₂³×C₁₃₉	—	2	1	no	—
385	C₂³×C₁₃₉	—	2	1	no	—
386	C₂³×C₁₃₉	—	2	1	no	—
387	C₂³×C₁₃₉	—	2	1	no	—
388	C₂³×C₁₃₉	—	2	1	no	—
389	C₂³×C₁₃₉	—	2	2	no	—
390	C₂³×C₁₃₉	—	2	1	no	—
391	C₂³×C₁₃₉	—	2	2	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	2	no	—
395	C₂³×C₁₃₉	—	2	1	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	2	1	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	1	no	—
401	C₂³×C₁₃₉	—	2	1	no	—
402	C₂³×C₁₃₉	—	2	1	no	—
403	C₂³×C₁₃₉	—	2	2	no	—
404	C₂³×C₁₃₉	—	2	2	no	—
405	C₂³×C₁₃₉	—	2	1	no	—
406	C₂³×C₁₃₉	—	2	1	no	—
407	C₂³×C₁₃₉	—	2	1	no	—
408	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
409	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
410	Q₈×C₁₃₉	—	4	4	no	—
411	D₄×C₁₃₉	—	4	4	no	—
412	D₄×C₁₃₉	—	4	4	no	—
413	D₄×C₁₃₉	—	4	8	no	—
414	D₄×C₁₃₉	—	4	4	no	—
415	D₄×C₁₃₉	—	4	4	no	—
416	D₄×C₁₃₉	—	8	4	no	—
417	D₄×C₁₃₉	—	8	4	no	—
418	C₂×C₄×C₁₃₉	—	2	1	no	—
419	C₂×C₄×C₁₃₉	—	2	1	no	—
420	C₂×C₄×C₁₃₉	—	2	1	no	—
421	C₂×C₄×C₁₃₉	—	2	1	no	—
422	C₂×C₄×C₁₃₉	—	2	2	no	—
423	C₂×C₄×C₁₃₉	—	2	2	no	—
424	C₂×C₄×C₁₃₉	—	2	2	no	—
425	C₂×C₄×C₁₃₉	—	2	2	no	—
426	C₂×C₄×C₁₃₉	—	2	2	no	—
427	C₂×C₄×C₁₃₉	—	2	1	no	—
428	C₂×C₄×C₁₃₉	—	2	1	no	—
429	C₂×C₄×C₁₃₉	—	2	2	no	—
430	C₂×C₄×C₁₃₉	—	2	8	no	—
431	C₂×C₄×C₁₃₉	—	2	1	no	—
432	C₂×C₄×C₁₃₉	—	2	1	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	2	no	—
435	C₂×C₄×C₁₃₉	—	2	2	no	—
436	C₂×C₄×C₁₃₉	—	2	1	no	—
437	C₂×C₄×C₁₃₉	—	2	2	no	—
438	C₂×C₄×C₁₃₉	—	2	1	no	—
439	C₂×C₄×C₁₃₉	—	2	1	no	—
440	C₂×C₄×C₁₃₉	—	2	1	no	—
441	C₂×C₄×C₁₃₉	—	2	1	no	—
442	C₂×C₄×C₁₃₉	—	2	2	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	2	no	—
445	C₂×C₄×C₁₃₉	—	2	1	no	—
446	C₂×C₄×C₁₃₉	—	2	1	no	—
447	C₂×C₄×C₁₃₉	—	2	2	no	—
448	C₂×C₄×C₁₃₉	—	2	1	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	1	no	—
451	C₂×C₄×C₁₃₉	—	2	2	no	—
452	C₂×C₄×C₁₃₉	—	2	1	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	1	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	1	no	—
458	C₂×C₄×C₁₃₉	—	2	1	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	1	no	—
461	C₂×C₄×C₁₃₉	—	2	1	no	—
462	C₂×C₄×C₁₃₉	—	2	2	no	—
463	C₂×C₄×C₁₃₉	—	2	1	no	—
464	C₂×C₄×C₁₃₉	—	2	2	no	—
465	C₂×C₄×C₁₃₉	—	2	1	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	4	8	no	—
468	C₂×C₄×C₁₃₉	—	4	4	no	—
469	C₂×C₄×C₁₃₉	—	4	4	no	—
470	C₂×C₄×C₁₃₉	—	8	4	no	—
471	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
472	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
476	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
477	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
478	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
479	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
480	C₂²×C₁₃₉	—	2	2	no	—
481	C₂²×C₁₃₉	—	2	2	no	—
482	C₂²×C₁₃₉	—	2	2	no	—
483	C₂²×C₁₃₉	—	4	1	no	—
484	C₂²×C₁₃₉	—	4	1	no	—
485	C₂²×C₁₃₉	—	4	1	no	—
486	C₂²×C₁₃₉	—	4	1	no	—
487	C₂²×C₁₃₉	—	4	1	no	—
488	C₂²×C₁₃₉	—	4	1	no	—
489	C₂²×C₁₃₉	—	4	2	no	—
490	C₂²×C₁₃₉	—	4	2	no	—
491	C₂²×C₁₃₉	—	4	1	no	—
492	C₂²×C₁₃₉	—	4	1	no	—
493	C₂²×C₁₃₉	—	4	1	no	—
494	C₂²×C₁₃₉	—	4	2	no	—
495	C₂²×C₁₃₉	—	4	1	no	—
496	C₂²×C₁₃₉	—	4	1	no	—
497	C₂²×C₁₃₉	—	4	1	no	—
498	C₂²×C₁₃₉	—	4	2	no	—
499	C₂²×C₁₃₉	—	4	2	no	—
500	C₂²×C₁₃₉	—	4	1	no	—
501	C₂²×C₁₃₉	—	4	1	no	—
502	C₂²×C₁₃₉	—	4	1	no	—
503	C₂²×C₁₃₉	—	4	2	no	—
504	C₂²×C₁₃₉	—	4	1	no	—
505	C₂²×C₁₃₉	—	4	1	no	—
506	C₂²×C₁₃₉	—	4	2	no	—
507	C₂²×C₁₃₉	—	4	1	no	—
508	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
509	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
511	C₂²×C₁₃₉	#585	1	1	yes	characteristic
512	C₂²×C₁₃₉	#585	1	1	yes	characteristic
513	C₂²×C₁₃₉	#585	1	1	yes	characteristic
514	C₂²×C₁₃₉	#585	1	1	yes	characteristic
515	C₄×C₁₃₉	—	2	2	no	—
516	C₄×C₁₃₉	—	2	4	no	—
517	C₄×C₁₃₉	—	2	4	no	—
518	C₄×C₁₃₉	—	2	2	no	—
519	C₄×C₁₃₉	—	2	2	no	—
520	C₄×C₁₃₉	—	2	4	no	—
521	C₄×C₁₃₉	—	4	1	no	—
522	C₄×C₁₃₉	—	4	1	no	—
523	C₄×C₁₃₉	—	4	2	no	—
524	C₄×C₁₃₉	—	4	1	no	—
525	C₄×C₁₃₉	—	4	1	no	—
526	C₄×C₁₃₉	—	4	1	no	—
527	C₄×C₁₃₉	—	4	2	no	—
528	C₄×C₁₃₉	—	4	2	no	—
529	C₄×C₁₃₉	—	4	1	no	—
530	C₄×C₁₃₉	—	4	1	no	—
531	C₄×C₁₃₉	—	4	1	no	—
532	C₄×C₁₃₉	—	4	2	no	—
533	C₄×C₁₃₉	#532	1	4	yes	—
534	C₂×C₁₃₉	—	4	2	no	—
535	C₂×C₁₃₉	—	8	1	no	—
536	C₂×C₁₃₉	—	8	1	no	—
537	C₂×C₁₃₉	—	8	2	no	—
538	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
539	C₂×C₁₃₉	#3485	1	1	yes	characteristic
540	C₂×C₁₃₉	#3487	1	1	yes	characteristic
541	C₂×C₁₃₉	#3493	1	1	yes	characteristic
542	C₂×C₁₃₉	#3512	1	1	yes	characteristic
543	C₂×C₁₃₉	#3521	1	1	yes	characteristic
544	C₂×C₁₃₉	#3524	1	1	yes	characteristic
545	#36015	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₁₃₉	#36015	1	1	yes	characteristic, direct product factor, Sylow
547	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
548	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
549	#2661	C₂×C₁₃₉	1	2	yes	complemented
550	#2620	C₂×C₁₃₉	1	1	yes	characteristic, complemented
551	#2602	C₂×C₁₃₉	1	2	yes	complemented
552	#2558	C₂×C₁₃₉	1	2	yes	complemented
553	#2554	C₂×C₁₃₉	1	2	yes	complemented
554	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
555	#2540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
556	#2519	C₂×C₁₃₉	1	2	yes	complemented
557	#2512	C₂×C₁₃₉	1	2	yes	complemented
558	#2500	C₂×C₁₃₉	1	2	yes	complemented
559	#2490	C₂×C₁₃₉	1	1	yes	characteristic, complemented
560	#2489	C₂×C₁₃₉	1	1	yes	characteristic, complemented
561	#2415	C₂×C₁₃₉	1	1	yes	characteristic, complemented
562	#2414	C₂×C₁₃₉	1	1	yes	characteristic, complemented
563	#2395	C₂×C₁₃₉	1	2	yes	complemented
564	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
565	#2367	C₂×C₁₃₉	1	1	yes	characteristic, complemented
566	#2363	C₂×C₁₃₉	1	1	yes	characteristic, complemented
567	#2362	C₂×C₁₃₉	1	1	yes	characteristic, complemented
568	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
569	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
570	#553	—	2	8	no	—
571	#552	—	2	8	no	—
572	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
573	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
574	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
576	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
578	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
579	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
583	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
585	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
586	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
589	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
591	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
593	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
594	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
597	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
598	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
599	#400	C₂²×C₁₃₉	1	2	yes	—
600	#399	C₂²×C₁₃₉	1	2	yes	—
601	#398	C₂²×C₁₃₉	1	1	yes	characteristic
602	#398	C₂²×C₁₃₉	1	2	yes	—
603	#398	C₂²×C₁₃₉	1	2	yes	—
604	#397	C₂²×C₁₃₉	1	2	yes	—
605	#397	C₂²×C₁₃₉	1	1	yes	characteristic
606	#397	C₂²×C₁₃₉	1	2	yes	—
607	#397	C₂²×C₁₃₉	1	2	yes	—
608	#396	C₂²×C₁₃₉	1	2	yes	—
609	#396	C₂²×C₁₃₉	1	2	yes	—
610	#396	C₂²×C₁₃₉	1	1	yes	characteristic
611	#396	C₂²×C₁₃₉	1	1	yes	characteristic
612	#394	C₂²×C₁₃₉	1	1	yes	characteristic
613	#394	C₂²×C₁₃₉	1	2	yes	—
614	#394	C₂²×C₁₃₉	1	2	yes	—
615	#394	C₂²×C₁₃₉	1	1	yes	characteristic
616	#394	C₂²×C₁₃₉	1	1	yes	characteristic
617	#394	C₂²×C₁₃₉	1	2	yes	—
618	#394	C₂²×C₁₃₉	1	2	yes	—
619	#394	C₂²×C₁₃₉	1	2	yes	—
620	#392	C₂²×C₁₃₉	1	2	yes	—
621	#392	C₂²×C₁₃₉	1	1	yes	characteristic
622	#392	C₂²×C₁₃₉	1	2	yes	—
623	#391	C₂²×C₁₃₉	1	1	yes	characteristic
624	#391	C₂²×C₁₃₉	1	1	yes	characteristic
625	#390	C₂²×C₁₃₉	1	2	yes	—
626	#390	C₂²×C₁₃₉	1	2	yes	—
627	#390	C₂²×C₁₃₉	1	1	yes	characteristic
628	#390	C₂²×C₁₃₉	1	2	yes	—
629	#390	C₂²×C₁₃₉	1	1	yes	characteristic
630	#390	C₂²×C₁₃₉	1	2	yes	—
631	#390	C₂²×C₁₃₉	1	2	yes	—
632	#390	C₂²×C₁₃₉	1	2	yes	—
633	#389	C₂²×C₁₃₉	1	2	yes	—
634	#389	C₂²×C₁₃₉	1	1	yes	characteristic
635	#389	C₂²×C₁₃₉	1	1	yes	characteristic
636	#389	C₂²×C₁₃₉	1	2	yes	—
637	#388	C₂²×C₁₃₉	1	2	yes	—
638	#388	C₂²×C₁₃₉	1	2	yes	—
639	#388	C₂²×C₁₃₉	1	2	yes	—
640	#388	C₂²×C₁₃₉	1	2	yes	—
641	#388	C₂²×C₁₃₉	1	2	yes	—
642	#388	C₂²×C₁₃₉	1	2	yes	—
643	#388	C₂²×C₁₃₉	1	2	yes	—
644	#388	C₂²×C₁₃₉	1	2	yes	—
645	#388	C₂²×C₁₃₉	1	2	yes	—
646	#388	C₂²×C₁₃₉	1	2	yes	—
647	#388	C₂²×C₁₃₉	1	2	yes	—
648	#387	C₂²×C₁₃₉	1	2	yes	—
649	#386	C₂²×C₁₃₉	1	2	yes	—
650	#385	C₂²×C₁₃₉	1	2	yes	—
651	#384	C₂²×C₁₃₉	1	1	yes	characteristic
652	#384	C₂²×C₁₃₉	1	2	yes	—
653	#382	C₂²×C₁₃₉	1	2	yes	—
654	#380	C₂²×C₁₃₉	1	1	yes	characteristic
655	#380	C₂²×C₁₃₉	1	1	yes	characteristic
656	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
657	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
658	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
659	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
660	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
661	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
662	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
663	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
664	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
666	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
668	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
669	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
670	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
671	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
672	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
673	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
678	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
679	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
683	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
684	#126	—	2	8	no	—
685	#126	—	2	8	no	—
686	#125	—	2	8	no	—
687	#125	—	2	4	no	—
688	#125	—	2	4	no	—
689	#124	—	2	4	no	—
690	#123	—	2	8	no	—
691	#123	—	2	8	no	—
692	C₂²⋊Q₈	—	2	4	no	—
693	C₂²⋊Q₈	—	2	4	no	—
694	C₂²⋊Q₈	—	2	4	no	—
695	#121	—	2	8	no	—
696	#121	—	2	4	no	—
697	#121	—	2	4	no	—
698	#121	—	2	4	no	—
699	C₄×Q₈	—	2	4	no	—
700	C₄×D₄	—	2	4	no	—
701	C₄×D₄	—	2	8	no	—
702	C₄×D₄	—	2	4	no	—
703	C₄×D₄	—	2	4	no	—
704	C₄×D₄	—	2	4	no	—
705	#117	—	2	8	no	—
706	#117	—	2	4	no	—
707	#117	—	2	4	no	—
708	#117	—	2	4	no	—
709	#117	—	2	4	no	—
710	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
711	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
767	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
768	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
772	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
776	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
779	#95	C₂³×C₁₃₉	1	1	yes	characteristic
780	#95	C₂³×C₁₃₉	1	1	yes	characteristic
781	#95	C₂³×C₁₃₉	1	2	yes	—
782	#95	C₂³×C₁₃₉	1	2	yes	—
783	#95	C₂³×C₁₃₉	1	2	yes	—
784	#95	C₂³×C₁₃₉	1	2	yes	—
785	#95	C₂³×C₁₃₉	1	1	yes	characteristic
786	#95	C₂³×C₁₃₉	1	1	yes	characteristic
787	#95	C₂³×C₁₃₉	1	2	yes	—
788	#95	C₂³×C₁₃₉	1	2	yes	—
789	#95	C₂³×C₁₃₉	1	1	yes	characteristic
790	#95	C₂³×C₁₃₉	1	2	yes	—
791	#95	C₂³×C₁₃₉	1	2	yes	—
792	#95	C₂³×C₁₃₉	1	1	yes	characteristic
793	#95	C₂³×C₁₃₉	1	2	yes	—
794	#95	C₂³×C₁₃₉	1	2	yes	—
795	#95	C₂³×C₁₃₉	1	2	yes	—
796	#95	C₂³×C₁₃₉	1	2	yes	—
797	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
798	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
799	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
800	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	4	1	no	—
814	C₂×D₄	—	4	1	no	—
815	C₂×D₄	—	4	1	no	—
816	C₂×D₄	—	4	1	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	1	no	—
819	C₂×D₄	—	4	1	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	4	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
839	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
840	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	4	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	4	1	no	—
876	C₄⋊C₄	—	4	1	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
882	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
883	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
884	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	1	no	—
907	C₂²⋊C₄	—	4	1	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	1	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	1	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₄²	—	2	4	no	—
916	C₄²	—	2	4	no	—
917	C₄²	—	2	4	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	4	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	4	2	no	—
923	C₄²	—	4	2	no	—
924	C₄²	—	4	2	no	—
925	C₄²	—	4	2	no	—
926	C₄²	#41×C₁₃₉	1	4	yes	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
955	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
956	Q₈	—	4	4	no	—
957	D₄	—	4	4	no	—
958	D₄	—	4	4	no	—
959	D₄	—	4	8	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	4	no	—
962	D₄	—	8	4	no	—
963	D₄	—	8	4	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	8	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	4	8	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	8	4	no	—
1017	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1018	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1020	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1022	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1023	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1024	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1025	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	1	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	2	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1055	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1056	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1057	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1058	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1059	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1060	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	4	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	#532×C₁₃₉	1	4	yes	—
1080	C₂	—	4	2	no	—
1081	C₂	—	8	1	no	—
1082	C₂	—	8	1	no	—
1083	C₂	—	8	2	no	—
1084	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
1085	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1086	C₂	#3487×C₁₃₉	1	1	yes	characteristic
1087	C₂	#3493×C₁₃₉	1	1	yes	characteristic
1088	C₂	#3512×C₁₃₉	1	1	yes	characteristic
1089	C₂	#3521×C₁₃₉	1	1	yes	characteristic
1090	C₂	#3524×C₁₃₉	1	1	yes	characteristic

	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×#553×C₁₃₉	C₂	semidirect
2. C₂×#552×C₁₃₉	C₂	semidirect
3. #2661×C₁₃₉	C₂	semidirect
4. #2620×C₁₃₉	C₂	semidirect
5. #2602×C₁₃₉	C₂	semidirect
6. #2558×C₁₃₉	C₂	semidirect
7. #2554×C₁₃₉	C₂	semidirect
8. #2552×C₁₃₉	C₂	semidirect
9. #2540×C₁₃₉	C₂	semidirect
10. #2519×C₁₃₉	C₂	semidirect
11. #2512×C₁₃₉	C₂	semidirect
12. #2500×C₁₃₉	C₂	semidirect
13. #2490×C₁₃₉	C₂	semidirect
14. #2489×C₁₃₉	C₂	semidirect
15. #2415×C₁₃₉	C₂	semidirect
16. #2414×C₁₃₉	C₂	semidirect
17. #2395×C₁₃₉	C₂	semidirect
18. #2392×C₁₃₉	C₂	semidirect
19. #2367×C₁₃₉	C₂	semidirect
20. #2363×C₁₃₉	C₂	semidirect
21. #2362×C₁₃₉	C₂	semidirect
22. #2354×C₁₃₉	C₂	semidirect
23. #2274×C₁₃₉	C₂	semidirect
164. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
545. #36015	C₁₃₉	direct (N × H)
546. C₁₃₉	#36015	direct (N × H)
547. C₂×#553	C₂×C₁₃₉	semidirect
548. C₂×#552	C₂×C₁₃₉	semidirect
549. #2661	C₂×C₁₃₉	semidirect
550. #2620	C₂×C₁₃₉	semidirect
551. #2602	C₂×C₁₃₉	semidirect
552. #2558	C₂×C₁₃₉	semidirect
553. #2554	C₂×C₁₃₉	semidirect
554. #2552	C₂×C₁₃₉	semidirect
555. #2540	C₂×C₁₃₉	semidirect
556. #2519	C₂×C₁₃₉	semidirect
557. #2512	C₂×C₁₃₉	semidirect
558. #2500	C₂×C₁₃₉	semidirect
559. #2490	C₂×C₁₃₉	semidirect
560. #2489	C₂×C₁₃₉	semidirect
561. #2415	C₂×C₁₃₉	semidirect
562. #2414	C₂×C₁₃₉	semidirect
563. #2395	C₂×C₁₃₉	semidirect
564. #2392	C₂×C₁₃₉	semidirect
565. #2367	C₂×C₁₃₉	semidirect
566. #2363	C₂×C₁₃₉	semidirect
567. #2362	C₂×C₁₃₉	semidirect
568. #2354	C₂×C₁₃₉	semidirect
569. #2274	C₂×C₁₃₉	semidirect
710. C₂×C₄⋊C₄	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×#553×C₁₃₉	2
C₂×#552×C₁₃₉	2
#2661×C₁₃₉	2
#2620×C₁₃₉	2
#2602×C₁₃₉	2
#2558×C₁₃₉	2
#2554×C₁₃₉	2
#2552×C₁₃₉	2
#2540×C₁₃₉	2
#2519×C₁₃₉	2
#2512×C₁₃₉	2
#2500×C₁₃₉	2
#2490×C₁₃₉	2
#2489×C₁₃₉	2
#2415×C₁₃₉	2
#2414×C₁₃₉	2
#2395×C₁₃₉	2
#2392×C₁₃₉	2
#2367×C₁₃₉	2
#2363×C₁₃₉	2
#2362×C₁₃₉	2
#2354×C₁₃₉	2
#2274×C₁₃₉	2
#36015	139

Subgroups — C139×#36015 #48030611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36015 #48030611