Subgroups — C₇₃×#59824 #32969228

Order 18688.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#552×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2721	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2673	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2554	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2554	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2490	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2471	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2467	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2363	C₂	1	2	yes	maximal, complemented
19	C₇₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#553×C₇₃	—	2	8	no	—
25	#552×C₇₃	—	2	8	no	—
26	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#126×C₇₃	C₂²	1	2	yes	—
28	C₂×#126×C₇₃	C₂²	1	2	yes	—
29	C₂×#125×C₇₃	C₂²	1	2	yes	—
30	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#123×C₇₃	C₂²	1	2	yes	—
33	C₂×#123×C₇₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×#121×C₇₃	C₂²	1	2	yes	—
39	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₇₃	C₂²	1	2	yes	—
42	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×#117×C₇₃	C₂²	1	2	yes	—
54	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
55	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
58	#399×C₇₃	C₂²	1	2	yes	—
59	#399×C₇₃	C₂²	1	2	yes	—
60	#398×C₇₃	C₂²	1	2	yes	—
61	#398×C₇₃	C₂²	1	2	yes	—
62	#397×C₇₃	C₂²	1	2	yes	—
63	#397×C₇₃	C₂²	1	2	yes	—
64	#396×C₇₃	C₂²	1	2	yes	—
65	#396×C₇₃	C₂²	1	2	yes	—
66	#394×C₇₃	C₂²	1	2	yes	—
67	#394×C₇₃	C₂²	1	2	yes	—
68	#394×C₇₃	C₂²	1	2	yes	—
69	#394×C₇₃	C₂²	1	2	yes	—
70	#392×C₇₃	C₂²	1	2	yes	—
71	#392×C₇₃	C₂²	1	2	yes	—
72	#392×C₇₃	C₂²	1	2	yes	—
73	#392×C₇₃	C₂²	1	2	yes	—
74	#391×C₇₃	C₂²	1	1	yes	characteristic
75	#390×C₇₃	C₂²	1	1	yes	characteristic
76	#390×C₇₃	C₂²	1	1	yes	characteristic
77	#390×C₇₃	C₂²	1	2	yes	—
78	#390×C₇₃	C₂²	1	1	yes	characteristic
79	#390×C₇₃	C₂²	1	2	yes	—
80	#390×C₇₃	C₂²	1	2	yes	—
81	#390×C₇₃	C₂²	1	2	yes	—
82	#390×C₇₃	C₂²	1	2	yes	—
83	#390×C₇₃	C₂²	1	1	yes	characteristic
84	#390×C₇₃	C₂²	1	1	yes	characteristic
85	#390×C₇₃	C₂²	1	1	yes	characteristic
86	#390×C₇₃	C₂²	1	1	yes	characteristic
87	#389×C₇₃	C₂²	1	2	yes	—
88	#389×C₇₃	C₂²	1	1	yes	characteristic
89	#389×C₇₃	C₂²	1	1	yes	characteristic
90	#388×C₇₃	C₂²	1	2	yes	—
91	#388×C₇₃	C₂²	1	2	yes	—
92	#388×C₇₃	C₂²	1	2	yes	—
93	#388×C₇₃	C₂²	1	2	yes	—
94	#388×C₇₃	C₂²	1	2	yes	—
95	#388×C₇₃	C₂²	1	2	yes	—
96	#388×C₇₃	C₂²	1	2	yes	—
97	#388×C₇₃	C₂²	1	2	yes	—
98	#387×C₇₃	C₂²	1	2	yes	—
99	#387×C₇₃	C₂²	1	2	yes	—
100	#387×C₇₃	C₂²	1	2	yes	—
101	#387×C₇₃	C₂²	1	2	yes	—
102	#386×C₇₃	C₂²	1	2	yes	—
103	#386×C₇₃	C₂²	1	2	yes	—
104	#386×C₇₃	C₂²	1	2	yes	—
105	#386×C₇₃	C₂²	1	2	yes	—
106	#386×C₇₃	C₂²	1	2	yes	—
107	#386×C₇₃	C₂²	1	2	yes	—
108	#384×C₇₃	C₂²	1	1	yes	characteristic
109	#382×C₇₃	C₂²	1	1	yes	characteristic
110	#382×C₇₃	C₂²	1	1	yes	characteristic
111	#380×C₇₃	C₂²	1	2	yes	—
112	#380×C₇₃	C₂²	1	1	yes	characteristic
113	#380×C₇₃	C₂²	1	1	yes	characteristic
114	#380×C₇₃	C₂²	1	1	yes	characteristic
115	#380×C₇₃	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
124	C₄³×C₇₃	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
144	#127×C₇₃	—	2	4	no	—
145	#126×C₇₃	—	2	8	no	—
146	#126×C₇₃	—	2	8	no	—
147	#125×C₇₃	—	2	8	no	—
148	#125×C₇₃	D₄	1	8	yes	complemented
149	#124×C₇₃	—	2	4	no	—
150	#123×C₇₃	—	2	8	no	—
151	#123×C₇₃	—	2	8	no	—
152	C₂²⋊Q₈×C₇₃	—	2	4	no	—
153	C₂²⋊Q₈×C₇₃	—	2	4	no	—
154	C₂²⋊Q₈×C₇₃	—	4	2	no	—
155	C₂²⋊Q₈×C₇₃	—	4	2	no	—
156	#121×C₇₃	—	2	8	no	—
157	#121×C₇₃	—	2	8	no	—
158	#121×C₇₃	—	2	4	no	—
159	#121×C₇₃	—	2	4	no	—
160	#121×C₇₃	—	4	2	no	—
161	#121×C₇₃	—	4	2	no	—
162	C₄×Q₈×C₇₃	—	2	4	no	—
163	C₄×D₄×C₇₃	—	2	8	no	—
164	C₄×D₄×C₇₃	—	2	4	no	—
165	C₄×D₄×C₇₃	—	2	4	no	—
166	C₄×D₄×C₇₃	—	2	4	no	—
167	C₄×D₄×C₇₃	—	2	4	no	—
168	C₄×D₄×C₇₃	—	2	4	no	—
169	C₄×D₄×C₇₃	—	4	2	no	—
170	C₄×D₄×C₇₃	—	4	2	no	—
171	#117×C₇₃	—	2	4	no	—
172	#117×C₇₃	—	2	8	no	—
173	#117×C₇₃	—	2	4	no	—
174	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
175	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
176	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
239	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
242	#95×C₇₃	C₂³	1	2	yes	—
243	#95×C₇₃	C₂³	1	2	yes	—
244	#95×C₇₃	C₂³	1	2	yes	—
245	#95×C₇₃	C₂³	1	2	yes	—
246	#95×C₇₃	C₂³	1	2	yes	—
247	#95×C₇₃	C₂³	1	2	yes	—
248	#95×C₇₃	C₂³	1	2	yes	—
249	#95×C₇₃	C₂³	1	2	yes	—
250	#95×C₇₃	C₂³	1	2	yes	—
251	#95×C₇₃	C₂³	1	2	yes	—
252	#95×C₇₃	C₂³	1	2	yes	—
253	#95×C₇₃	C₂³	1	2	yes	—
254	#95×C₇₃	C₂³	1	2	yes	—
255	#95×C₇₃	C₂³	1	2	yes	—
256	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
258	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂×Q₈×C₇₃	—	2	2	no	—
262	C₂×Q₈×C₇₃	—	2	2	no	—
263	C₂×Q₈×C₇₃	—	2	2	no	—
264	C₂×D₄×C₇₃	—	2	4	no	—
265	C₂×D₄×C₇₃	—	2	2	no	—
266	C₂×D₄×C₇₃	—	2	2	no	—
267	C₂×D₄×C₇₃	—	2	2	no	—
268	C₂×D₄×C₇₃	—	2	2	no	—
269	C₂×D₄×C₇₃	—	2	4	no	—
270	C₂×D₄×C₇₃	—	2	4	no	—
271	C₂×D₄×C₇₃	—	2	2	no	—
272	C₂×D₄×C₇₃	—	2	2	no	—
273	C₂×D₄×C₇₃	—	2	2	no	—
274	C₂×D₄×C₇₃	—	2	4	no	—
275	C₂×D₄×C₇₃	—	2	2	no	—
276	C₂×D₄×C₇₃	—	2	2	no	—
277	C₂×D₄×C₇₃	—	2	2	no	—
278	C₂×D₄×C₇₃	—	2	2	no	—
279	C₂×D₄×C₇₃	—	2	2	no	—
280	C₂×D₄×C₇₃	—	4	1	no	—
281	C₂×D₄×C₇₃	—	4	1	no	—
282	C₂×D₄×C₇₃	—	4	2	no	—
283	C₂×D₄×C₇₃	—	4	1	no	—
284	C₂×D₄×C₇₃	—	4	1	no	—
285	C₂×D₄×C₇₃	—	4	1	no	—
286	C₂×D₄×C₇₃	—	4	1	no	—
287	C₂×D₄×C₇₃	—	4	1	no	—
288	C₂×D₄×C₇₃	—	4	1	no	—
289	C₂×D₄×C₇₃	—	4	2	no	—
290	C₂×D₄×C₇₃	—	4	2	no	—
291	C₂×D₄×C₇₃	—	4	2	no	—
292	C₂×D₄×C₇₃	—	4	2	no	—
293	C₂×D₄×C₇₃	—	4	2	no	—
294	C₂×D₄×C₇₃	—	4	2	no	—
295	C₂×D₄×C₇₃	—	4	2	no	—
296	C₂×D₄×C₇₃	#41	1	4	yes	—
297	C₂²×C₄×C₇₃	—	2	4	no	—
298	C₂²×C₄×C₇₃	—	2	4	no	—
299	C₂²×C₄×C₇₃	—	2	2	no	—
300	C₂²×C₄×C₇₃	—	2	2	no	—
301	C₂²×C₄×C₇₃	—	2	2	no	—
302	C₂²×C₄×C₇₃	—	2	2	no	—
303	C₂²×C₄×C₇₃	—	2	2	no	—
304	C₂²×C₄×C₇₃	—	2	2	no	—
305	C₂²×C₄×C₇₃	—	2	2	no	—
306	C₂²×C₄×C₇₃	—	2	2	no	—
307	C₂²×C₄×C₇₃	—	2	2	no	—
308	C₂²×C₄×C₇₃	—	2	2	no	—
309	C₂²×C₄×C₇₃	—	2	2	no	—
310	C₂²×C₄×C₇₃	—	2	2	no	—
311	C₂²×C₄×C₇₃	—	2	4	no	—
312	C₂²×C₄×C₇₃	—	2	4	no	—
313	C₂²×C₄×C₇₃	—	4	2	no	—
314	C₂²×C₄×C₇₃	—	4	2	no	—
315	C₂²×C₄×C₇₃	—	4	2	no	—
316	C₂²×C₄×C₇₃	—	4	2	no	—
317	C₂²×C₄×C₇₃	—	4	2	no	—
318	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
336	C₄⋊C₄×C₇₃	—	2	2	no	—
337	C₄⋊C₄×C₇₃	—	2	2	no	—
338	C₄⋊C₄×C₇₃	—	2	4	no	—
339	C₄⋊C₄×C₇₃	—	2	4	no	—
340	C₄⋊C₄×C₇₃	—	2	4	no	—
341	C₄⋊C₄×C₇₃	—	2	2	no	—
342	C₄⋊C₄×C₇₃	—	2	2	no	—
343	C₄⋊C₄×C₇₃	—	2	4	no	—
344	C₄⋊C₄×C₇₃	—	2	4	no	—
345	C₄⋊C₄×C₇₃	—	2	2	no	—
346	C₄⋊C₄×C₇₃	—	2	2	no	—
347	C₄⋊C₄×C₇₃	—	2	4	no	—
348	C₄⋊C₄×C₇₃	—	2	2	no	—
349	C₄⋊C₄×C₇₃	—	2	2	no	—
350	C₄⋊C₄×C₇₃	—	4	2	no	—
351	C₄⋊C₄×C₇₃	—	4	1	no	—
352	C₄⋊C₄×C₇₃	—	4	1	no	—
353	C₄⋊C₄×C₇₃	—	4	2	no	—
354	C₄⋊C₄×C₇₃	—	4	2	no	—
355	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
356	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
357	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
358	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
359	C₂²⋊C₄×C₇₃	—	2	4	no	—
360	C₂²⋊C₄×C₇₃	—	2	2	no	—
361	C₂²⋊C₄×C₇₃	—	2	4	no	—
362	C₂²⋊C₄×C₇₃	—	2	4	no	—
363	C₂²⋊C₄×C₇₃	—	2	4	no	—
364	C₂²⋊C₄×C₇₃	—	2	2	no	—
365	C₂²⋊C₄×C₇₃	—	2	4	no	—
366	C₂²⋊C₄×C₇₃	—	2	4	no	—
367	C₂²⋊C₄×C₇₃	—	2	2	no	—
368	C₂²⋊C₄×C₇₃	—	2	2	no	—
369	C₂²⋊C₄×C₇₃	—	2	4	no	—
370	C₂²⋊C₄×C₇₃	—	2	4	no	—
371	C₂²⋊C₄×C₇₃	—	2	2	no	—
372	C₂²⋊C₄×C₇₃	—	2	2	no	—
373	C₂²⋊C₄×C₇₃	—	2	2	no	—
374	C₂²⋊C₄×C₇₃	—	2	2	no	—
375	C₂²⋊C₄×C₇₃	—	2	4	no	—
376	C₂²⋊C₄×C₇₃	—	2	4	no	—
377	C₂²⋊C₄×C₇₃	—	2	4	no	—
378	C₂²⋊C₄×C₇₃	—	4	2	no	—
379	C₂²⋊C₄×C₇₃	—	4	2	no	—
380	C₂²⋊C₄×C₇₃	—	4	2	no	—
381	C₂²⋊C₄×C₇₃	—	4	2	no	—
382	C₂²⋊C₄×C₇₃	—	4	1	no	—
383	C₂²⋊C₄×C₇₃	—	4	1	no	—
384	C₂²⋊C₄×C₇₃	—	4	1	no	—
385	C₂²⋊C₄×C₇₃	—	4	1	no	—
386	C₂²⋊C₄×C₇₃	—	4	2	no	—
387	C₂²⋊C₄×C₇₃	—	4	2	no	—
388	C₂²⋊C₄×C₇₃	—	4	2	no	—
389	C₂²⋊C₄×C₇₃	—	4	2	no	—
390	C₄²×C₇₃	—	2	4	no	—
391	C₄²×C₇₃	—	2	4	no	—
392	C₄²×C₇₃	—	2	4	no	—
393	C₄²×C₇₃	—	2	2	no	—
394	C₄²×C₇₃	—	2	2	no	—
395	C₄²×C₇₃	—	4	1	no	—
396	C₄²×C₇₃	—	4	2	no	—
397	C₄²×C₇₃	—	4	2	no	—
398	C₄²×C₇₃	—	4	1	no	—
399	C₄²×C₇₃	—	4	1	no	—
400	C₄²×C₇₃	C₂×D₄	1	4	yes	—
401	C₄²×C₇₃	#41	1	4	yes	—
402	C₂³×C₇₃	—	2	1	no	—
403	C₂³×C₇₃	—	2	1	no	—
404	C₂³×C₇₃	—	2	1	no	—
405	C₂³×C₇₃	—	2	1	no	—
406	C₂³×C₇₃	—	2	1	no	—
407	C₂³×C₇₃	—	2	1	no	—
408	C₂³×C₇₃	—	2	1	no	—
409	C₂³×C₇₃	—	2	1	no	—
410	C₂³×C₇₃	—	2	1	no	—
411	C₂³×C₇₃	—	2	1	no	—
412	C₂³×C₇₃	—	2	1	no	—
413	C₂³×C₇₃	—	2	1	no	—
414	C₂³×C₇₃	—	2	1	no	—
415	C₂³×C₇₃	—	2	1	no	—
416	C₂³×C₇₃	—	2	2	no	—
417	C₂³×C₇₃	—	2	2	no	—
418	C₂³×C₇₃	—	2	1	no	—
419	C₂³×C₇₃	—	2	1	no	—
420	C₂³×C₇₃	—	2	2	no	—
421	C₂³×C₇₃	—	2	1	no	—
422	C₂³×C₇₃	—	2	1	no	—
423	C₂³×C₇₃	—	2	1	no	—
424	C₂³×C₇₃	—	2	2	no	—
425	C₂³×C₇₃	—	2	1	no	—
426	C₂³×C₇₃	—	2	1	no	—
427	C₂³×C₇₃	—	2	1	no	—
428	C₂³×C₇₃	—	2	2	no	—
429	C₂³×C₇₃	—	2	2	no	—
430	C₂³×C₇₃	—	2	2	no	—
431	C₂³×C₇₃	—	2	1	no	—
432	C₂³×C₇₃	—	2	1	no	—
433	C₂³×C₇₃	—	2	1	no	—
434	C₂³×C₇₃	—	2	1	no	—
435	C₂³×C₇₃	C₂×#41	1	2	yes	—
436	C₂³×C₇₃	C₂×#41	1	2	yes	—
437	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
438	Q₈×C₇₃	—	4	4	no	—
439	D₄×C₇₃	—	4	4	no	—
440	D₄×C₇₃	—	4	8	no	—
441	D₄×C₇₃	—	4	4	no	—
442	D₄×C₇₃	—	4	4	no	—
443	D₄×C₇₃	—	4	4	no	—
444	D₄×C₇₃	—	4	4	no	—
445	D₄×C₇₃	—	4	4	no	—
446	D₄×C₇₃	—	4	4	no	—
447	D₄×C₇₃	—	8	4	no	—
448	D₄×C₇₃	—	8	4	no	—
449	D₄×C₇₃	—	8	4	no	—
450	C₂×C₄×C₇₃	—	2	1	no	—
451	C₂×C₄×C₇₃	—	2	1	no	—
452	C₂×C₄×C₇₃	—	2	2	no	—
453	C₂×C₄×C₇₃	—	2	1	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	—	2	1	no	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	2	2	no	—
459	C₂×C₄×C₇₃	—	2	2	no	—
460	C₂×C₄×C₇₃	—	2	1	no	—
461	C₂×C₄×C₇₃	—	2	1	no	—
462	C₂×C₄×C₇₃	—	2	1	no	—
463	C₂×C₄×C₇₃	—	2	2	no	—
464	C₂×C₄×C₇₃	—	2	1	no	—
465	C₂×C₄×C₇₃	—	2	1	no	—
466	C₂×C₄×C₇₃	—	2	2	no	—
467	C₂×C₄×C₇₃	—	2	2	no	—
468	C₂×C₄×C₇₃	—	2	2	no	—
469	C₂×C₄×C₇₃	—	2	1	no	—
470	C₂×C₄×C₇₃	—	2	1	no	—
471	C₂×C₄×C₇₃	—	2	2	no	—
472	C₂×C₄×C₇₃	—	2	2	no	—
473	C₂×C₄×C₇₃	—	2	1	no	—
474	C₂×C₄×C₇₃	—	2	1	no	—
475	C₂×C₄×C₇₃	—	2	1	no	—
476	C₂×C₄×C₇₃	—	2	1	no	—
477	C₂×C₄×C₇₃	—	2	2	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	2	1	no	—
480	C₂×C₄×C₇₃	—	2	1	no	—
481	C₂×C₄×C₇₃	—	2	2	no	—
482	C₂×C₄×C₇₃	—	2	2	no	—
483	C₂×C₄×C₇₃	—	2	2	no	—
484	C₂×C₄×C₇₃	—	2	1	no	—
485	C₂×C₄×C₇₃	—	2	1	no	—
486	C₂×C₄×C₇₃	—	2	1	no	—
487	C₂×C₄×C₇₃	—	2	2	no	—
488	C₂×C₄×C₇₃	—	2	2	no	—
489	C₂×C₄×C₇₃	—	2	1	no	—
490	C₂×C₄×C₇₃	—	2	2	no	—
491	C₂×C₄×C₇₃	—	2	2	no	—
492	C₂×C₄×C₇₃	—	2	2	no	—
493	C₂×C₄×C₇₃	—	2	2	no	—
494	C₂×C₄×C₇₃	—	4	8	no	—
495	C₂×C₄×C₇₃	—	4	4	no	—
496	C₂×C₄×C₇₃	—	4	4	no	—
497	C₂×C₄×C₇₃	—	4	4	no	—
498	C₂×C₄×C₇₃	—	4	4	no	—
499	C₂×C₄×C₇₃	—	8	4	no	—
500	C₂×C₄×C₇₃	—	8	4	no	—
501	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
503	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
504	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
507	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
508	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
509	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
511	C₂²×C₇₃	—	2	2	no	—
512	C₂²×C₇₃	—	2	2	no	—
513	C₂²×C₇₃	—	2	2	no	—
514	C₂²×C₇₃	—	2	2	no	—
515	C₂²×C₇₃	—	2	2	no	—
516	C₂²×C₇₃	—	2	2	no	—
517	C₂²×C₇₃	—	4	1	no	—
518	C₂²×C₇₃	—	4	1	no	—
519	C₂²×C₇₃	—	4	1	no	—
520	C₂²×C₇₃	—	4	1	no	—
521	C₂²×C₇₃	—	4	1	no	—
522	C₂²×C₇₃	—	4	1	no	—
523	C₂²×C₇₃	—	4	1	no	—
524	C₂²×C₇₃	—	4	1	no	—
525	C₂²×C₇₃	—	4	1	no	—
526	C₂²×C₇₃	—	4	1	no	—
527	C₂²×C₇₃	—	4	2	no	—
528	C₂²×C₇₃	—	4	1	no	—
529	C₂²×C₇₃	—	4	2	no	—
530	C₂²×C₇₃	—	4	1	no	—
531	C₂²×C₇₃	—	4	1	no	—
532	C₂²×C₇₃	—	4	1	no	—
533	C₂²×C₇₃	—	4	2	no	—
534	C₂²×C₇₃	—	4	2	no	—
535	C₂²×C₇₃	—	4	1	no	—
536	C₂²×C₇₃	—	4	1	no	—
537	C₂²×C₇₃	—	4	1	no	—
538	C₂²×C₇₃	—	4	1	no	—
539	C₂²×C₇₃	—	4	2	no	—
540	C₂²×C₇₃	—	4	2	no	—
541	C₂²×C₇₃	—	4	1	no	—
542	C₂²×C₇₃	—	4	1	no	—
543	C₂²×C₇₃	—	4	1	no	—
544	C₂²×C₇₃	—	4	2	no	—
545	C₂²×C₇₃	—	4	1	no	—
546	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
547	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
548	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
549	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂²×C₇₃	#585	1	1	yes	characteristic
551	C₂²×C₇₃	#585	1	1	yes	characteristic
552	C₂²×C₇₃	#585	1	1	yes	characteristic
553	C₄×C₇₃	—	2	4	no	—
554	C₄×C₇₃	—	2	2	no	—
555	C₄×C₇₃	—	2	2	no	—
556	C₄×C₇₃	—	2	2	no	—
557	C₄×C₇₃	—	2	4	no	—
558	C₄×C₇₃	—	2	2	no	—
559	C₄×C₇₃	—	2	2	no	—
560	C₄×C₇₃	—	4	1	no	—
561	C₄×C₇₃	—	4	1	no	—
562	C₄×C₇₃	—	4	1	no	—
563	C₄×C₇₃	—	4	1	no	—
564	C₄×C₇₃	—	4	2	no	—
565	C₄×C₇₃	—	4	2	no	—
566	C₄×C₇₃	—	4	2	no	—
567	C₄×C₇₃	—	4	2	no	—
568	C₄×C₇₃	—	4	1	no	—
569	C₄×C₇₃	—	4	2	no	—
570	C₄×C₇₃	#550	1	4	yes	—
571	#59824	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂×C₇₃	—	4	2	no	—
573	C₂×C₇₃	—	4	2	no	—
574	C₂×C₇₃	—	8	1	no	—
575	C₂×C₇₃	—	8	1	no	—
576	C₂×C₇₃	—	8	2	no	—
577	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
578	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
579	C₂×C₇₃	#3475	1	1	yes	characteristic
580	C₂×C₇₃	#3500	1	1	yes	characteristic
581	C₂×C₇₃	#3505	1	1	yes	characteristic
582	C₂×C₇₃	#3512	1	1	yes	characteristic
583	C₂×C₇₃	#3551	1	1	yes	characteristic
584	C₂×#553	C₂×C₇₃	1	1	yes	characteristic, complemented
585	C₂×#552	C₂×C₇₃	1	1	yes	characteristic, complemented
586	#2721	C₂×C₇₃	1	2	yes	complemented
587	#2673	C₂×C₇₃	1	2	yes	complemented
588	#2554	C₂×C₇₃	1	2	yes	complemented
589	#2554	C₂×C₇₃	1	2	yes	complemented
590	#2540	C₂×C₇₃	1	1	yes	characteristic, complemented
591	#2540	C₂×C₇₃	1	1	yes	characteristic, complemented
592	#2536	C₂×C₇₃	1	1	yes	characteristic, complemented
593	#2535	C₂×C₇₃	1	1	yes	characteristic, complemented
594	#2490	C₂×C₇₃	1	2	yes	complemented
595	#2471	C₂×C₇₃	1	2	yes	complemented
596	#2467	C₂×C₇₃	1	2	yes	complemented
597	#2417	C₂×C₇₃	1	1	yes	characteristic, complemented
598	#2416	C₂×C₇₃	1	1	yes	characteristic, complemented
599	#2415	C₂×C₇₃	1	1	yes	characteristic, complemented
600	#2414	C₂×C₇₃	1	1	yes	characteristic, complemented
601	#2363	C₂×C₇₃	1	2	yes	complemented
602	#2352	C₂×C₇₃	1	1	yes	characteristic, complemented
603	#2352	C₂×C₇₃	1	1	yes	characteristic, complemented
604	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
605	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
606	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
607	C₇₃	#59824	1	1	yes	characteristic, direct product factor, Sylow
608	#553	—	2	8	no	—
609	#552	—	2	8	no	—
610	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
611	C₂×#126	C₂²×C₇₃	1	2	yes	—
612	C₂×#126	C₂²×C₇₃	1	2	yes	—
613	C₂×#125	C₂²×C₇₃	1	2	yes	—
614	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
615	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
616	C₂×#123	C₂²×C₇₃	1	2	yes	—
617	C₂×#123	C₂²×C₇₃	1	2	yes	—
618	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
619	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
620	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
621	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
622	C₂×#121	C₂²×C₇₃	1	2	yes	—
623	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
624	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
625	C₂×#121	C₂²×C₇₃	1	2	yes	—
626	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
627	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
628	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
629	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
630	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
631	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
632	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
633	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
634	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
637	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
638	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
639	C₂×#117	C₂²×C₇₃	1	2	yes	—
640	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
641	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
642	#399	C₂²×C₇₃	1	2	yes	—
643	#399	C₂²×C₇₃	1	2	yes	—
644	#398	C₂²×C₇₃	1	2	yes	—
645	#398	C₂²×C₇₃	1	2	yes	—
646	#397	C₂²×C₇₃	1	2	yes	—
647	#397	C₂²×C₇₃	1	2	yes	—
648	#396	C₂²×C₇₃	1	2	yes	—
649	#396	C₂²×C₇₃	1	2	yes	—
650	#394	C₂²×C₇₃	1	2	yes	—
651	#394	C₂²×C₇₃	1	2	yes	—
652	#394	C₂²×C₇₃	1	2	yes	—
653	#394	C₂²×C₇₃	1	2	yes	—
654	#392	C₂²×C₇₃	1	2	yes	—
655	#392	C₂²×C₇₃	1	2	yes	—
656	#392	C₂²×C₇₃	1	2	yes	—
657	#392	C₂²×C₇₃	1	2	yes	—
658	#391	C₂²×C₇₃	1	1	yes	characteristic
659	#390	C₂²×C₇₃	1	1	yes	characteristic
660	#390	C₂²×C₇₃	1	1	yes	characteristic
661	#390	C₂²×C₇₃	1	1	yes	characteristic
662	#390	C₂²×C₇₃	1	1	yes	characteristic
663	#390	C₂²×C₇₃	1	1	yes	characteristic
664	#390	C₂²×C₇₃	1	1	yes	characteristic
665	#390	C₂²×C₇₃	1	2	yes	—
666	#390	C₂²×C₇₃	1	2	yes	—
667	#390	C₂²×C₇₃	1	1	yes	characteristic
668	#390	C₂²×C₇₃	1	2	yes	—
669	#390	C₂²×C₇₃	1	2	yes	—
670	#390	C₂²×C₇₃	1	2	yes	—
671	#389	C₂²×C₇₃	1	1	yes	characteristic
672	#389	C₂²×C₇₃	1	1	yes	characteristic
673	#389	C₂²×C₇₃	1	2	yes	—
674	#388	C₂²×C₇₃	1	2	yes	—
675	#388	C₂²×C₇₃	1	2	yes	—
676	#388	C₂²×C₇₃	1	2	yes	—
677	#388	C₂²×C₇₃	1	2	yes	—
678	#388	C₂²×C₇₃	1	2	yes	—
679	#388	C₂²×C₇₃	1	2	yes	—
680	#388	C₂²×C₇₃	1	2	yes	—
681	#388	C₂²×C₇₃	1	2	yes	—
682	#387	C₂²×C₇₃	1	2	yes	—
683	#387	C₂²×C₇₃	1	2	yes	—
684	#387	C₂²×C₇₃	1	2	yes	—
685	#387	C₂²×C₇₃	1	2	yes	—
686	#386	C₂²×C₇₃	1	2	yes	—
687	#386	C₂²×C₇₃	1	2	yes	—
688	#386	C₂²×C₇₃	1	2	yes	—
689	#386	C₂²×C₇₃	1	2	yes	—
690	#386	C₂²×C₇₃	1	2	yes	—
691	#386	C₂²×C₇₃	1	2	yes	—
692	#384	C₂²×C₇₃	1	1	yes	characteristic
693	#382	C₂²×C₇₃	1	1	yes	characteristic
694	#382	C₂²×C₇₃	1	1	yes	characteristic
695	#380	C₂²×C₇₃	1	1	yes	characteristic
696	#380	C₂²×C₇₃	1	1	yes	characteristic
697	#380	C₂²×C₇₃	1	1	yes	characteristic
698	#380	C₂²×C₇₃	1	1	yes	characteristic
699	#380	C₂²×C₇₃	1	2	yes	—
700	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
701	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
702	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
703	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
704	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
705	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
706	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
707	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
708	C₄³	C₂²×C₇₃	1	1	yes	characteristic
709	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
714	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
715	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
716	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
717	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
718	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
719	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
720	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
722	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
726	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
727	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
728	#127	—	2	4	no	—
729	#126	—	2	8	no	—
730	#126	—	2	8	no	—
731	#125	—	2	8	no	—
732	#125	D₄×C₇₃	1	8	yes	complemented
733	#124	—	2	4	no	—
734	#123	—	2	8	no	—
735	#123	—	2	8	no	—
736	C₂²⋊Q₈	—	2	4	no	—
737	C₂²⋊Q₈	—	2	4	no	—
738	C₂²⋊Q₈	—	4	2	no	—
739	C₂²⋊Q₈	—	4	2	no	—
740	#121	—	2	8	no	—
741	#121	—	2	8	no	—
742	#121	—	2	4	no	—
743	#121	—	2	4	no	—
744	#121	—	4	2	no	—
745	#121	—	4	2	no	—
746	C₄×Q₈	—	2	4	no	—
747	C₄×D₄	—	2	8	no	—
748	C₄×D₄	—	2	4	no	—
749	C₄×D₄	—	2	4	no	—
750	C₄×D₄	—	2	4	no	—
751	C₄×D₄	—	2	4	no	—
752	C₄×D₄	—	2	4	no	—
753	C₄×D₄	—	4	2	no	—
754	C₄×D₄	—	4	2	no	—
755	#117	—	2	4	no	—
756	#117	—	2	8	no	—
757	#117	—	2	4	no	—
758	C₂×C₄⋊C₄	—	2	4	no	—
759	C₂×C₄⋊C₄	—	2	4	no	—
760	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
763	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
764	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
766	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
775	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
781	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
796	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
804	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
805	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
814	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
815	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
816	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
817	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
821	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
823	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
824	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
825	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
826	#95	C₂³×C₇₃	1	2	yes	—
827	#95	C₂³×C₇₃	1	2	yes	—
828	#95	C₂³×C₇₃	1	2	yes	—
829	#95	C₂³×C₇₃	1	2	yes	—
830	#95	C₂³×C₇₃	1	2	yes	—
831	#95	C₂³×C₇₃	1	2	yes	—
832	#95	C₂³×C₇₃	1	2	yes	—
833	#95	C₂³×C₇₃	1	2	yes	—
834	#95	C₂³×C₇₃	1	2	yes	—
835	#95	C₂³×C₇₃	1	2	yes	—
836	#95	C₂³×C₇₃	1	2	yes	—
837	#95	C₂³×C₇₃	1	2	yes	—
838	#95	C₂³×C₇₃	1	2	yes	—
839	#95	C₂³×C₇₃	1	2	yes	—
840	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
841	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
842	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
843	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
844	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	4	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	4	1	no	—
865	C₂×D₄	—	4	1	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	4	1	no	—
868	C₂×D₄	—	4	1	no	—
869	C₂×D₄	—	4	1	no	—
870	C₂×D₄	—	4	1	no	—
871	C₂×D₄	—	4	1	no	—
872	C₂×D₄	—	4	1	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	4	2	no	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	4	2	no	—
877	C₂×D₄	—	4	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	—	4	2	no	—
880	C₂×D₄	#41×C₇₃	1	4	yes	—
881	C₂²×C₄	—	2	4	no	—
882	C₂²×C₄	—	2	4	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	4	2	no	—
898	C₂²×C₄	—	4	2	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
916	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	4	no	—
923	C₄⋊C₄	—	2	4	no	—
924	C₄⋊C₄	—	2	4	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	4	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	4	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	1	no	—
936	C₄⋊C₄	—	4	1	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
940	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
941	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
942	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	1	no	—
967	C₂²⋊C₄	—	4	1	no	—
968	C₂²⋊C₄	—	4	1	no	—
969	C₂²⋊C₄	—	4	1	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₄²	—	2	4	no	—
975	C₄²	—	2	4	no	—
976	C₄²	—	2	4	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	4	1	no	—
980	C₄²	—	4	2	no	—
981	C₄²	—	4	2	no	—
982	C₄²	—	4	1	no	—
983	C₄²	—	4	1	no	—
984	C₄²	C₂×D₄×C₇₃	1	4	yes	—
985	C₄²	#41×C₇₃	1	4	yes	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	C₂×#41×C₇₃	1	2	yes	—
1020	C₂³	C₂×#41×C₇₃	1	2	yes	—
1021	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
1022	Q₈	—	4	4	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	8	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	4	no	—
1027	D₄	—	4	4	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	8	4	no	—
1032	D₄	—	8	4	no	—
1033	D₄	—	8	4	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	4	8	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	4	no	—
1083	C₂×C₄	—	8	4	no	—
1084	C₂×C₄	—	8	4	no	—
1085	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
1087	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
1088	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1090	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1091	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1092	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1093	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1094	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1131	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1132	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1133	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1134	C₂²	#585×C₇₃	1	1	yes	characteristic
1135	C₂²	#585×C₇₃	1	1	yes	characteristic
1136	C₂²	#585×C₇₃	1	1	yes	characteristic
1137	C₄	—	2	4	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	4	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	#550×C₇₃	1	4	yes	—
1155	C₂	—	4	2	no	—
1156	C₂	—	4	2	no	—
1157	C₂	—	8	1	no	—
1158	C₂	—	8	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
1161	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
1162	C₂	C₇₃×#3475	1	1	yes	characteristic
1163	C₂	C₇₃×#3500	1	1	yes	characteristic
1164	C₂	C₇₃×#3505	1	1	yes	characteristic
1165	C₂	C₇₃×#3512	1	1	yes	characteristic
1166	C₂	C₇₃×#3551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#553×C₇₃	C₂	semidirect
2. C₂×#552×C₇₃	C₂	semidirect
3. C₇₃×#2721	C₂	semidirect
4. C₇₃×#2673	C₂	semidirect
5. C₇₃×#2554	C₂	semidirect
6. C₇₃×#2554	C₂	semidirect
7. C₇₃×#2540	C₂	semidirect
8. C₇₃×#2540	C₂	semidirect
9. C₇₃×#2536	C₂	semidirect
10. C₇₃×#2535	C₂	semidirect
11. C₇₃×#2490	C₂	semidirect
12. C₇₃×#2471	C₂	semidirect
13. C₇₃×#2467	C₂	semidirect
14. C₇₃×#2417	C₂	semidirect
15. C₇₃×#2416	C₂	semidirect
16. C₇₃×#2415	C₂	semidirect
17. C₇₃×#2414	C₂	semidirect
18. C₇₃×#2363	C₂	semidirect
19. C₇₃×#2352	C₂	semidirect
20. C₇₃×#2352	C₂	semidirect
21. C₄×#127×C₇₃	C₂	semidirect
22. C₄×#125×C₇₃	C₂	semidirect
23. C₄×#124×C₇₃	C₂	semidirect
148. #125×C₇₃	D₄	semidirect
571. #59824	C₇₃	direct (N × H)
584. C₂×#553	C₂×C₇₃	semidirect
585. C₂×#552	C₂×C₇₃	semidirect
586. #2721	C₂×C₇₃	semidirect
587. #2673	C₂×C₇₃	semidirect
588. #2554	C₂×C₇₃	semidirect
589. #2554	C₂×C₇₃	semidirect
590. #2540	C₂×C₇₃	semidirect
591. #2540	C₂×C₇₃	semidirect
592. #2536	C₂×C₇₃	semidirect
593. #2535	C₂×C₇₃	semidirect
594. #2490	C₂×C₇₃	semidirect
595. #2471	C₂×C₇₃	semidirect
596. #2467	C₂×C₇₃	semidirect
597. #2417	C₂×C₇₃	semidirect
598. #2416	C₂×C₇₃	semidirect
599. #2415	C₂×C₇₃	semidirect
600. #2414	C₂×C₇₃	semidirect
601. #2363	C₂×C₇₃	semidirect
602. #2352	C₂×C₇₃	semidirect
603. #2352	C₂×C₇₃	semidirect
604. C₄×#127	C₂×C₇₃	semidirect
605. C₄×#125	C₂×C₇₃	semidirect
606. C₄×#124	C₂×C₇₃	semidirect
607. C₇₃	#59824	direct (N × H)
732. #125	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₇₃	2
C₂×#552×C₇₃	2
C₇₃×#2721	2
C₇₃×#2673	2
C₇₃×#2554	2
C₇₃×#2540	2
C₇₃×#2536	2
C₇₃×#2535	2
C₇₃×#2490	2
C₇₃×#2471	2
C₇₃×#2467	2
C₇₃×#2417	2
C₇₃×#2416	2
C₇₃×#2415	2
C₇₃×#2414	2
C₇₃×#2363	2
C₇₃×#2352	2
C₄×#127×C₇₃	2
C₄×#125×C₇₃	2
C₄×#124×C₇₃	2
#59824	73

Subgroups — C73×#59824 #32969228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59824 #32969228