Subgroups — C₇₃×#59641 #32969045

Order 18688.

2452 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2710	C₂	1	4	yes	maximal, complemented
3	C₇₃×#2580	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2541	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2501	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2491	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2455	C₂	1	4	yes	maximal, complemented
9	C₇₃×#2448	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2445	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2422	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2361	C₂	1	2	yes	maximal, complemented
13	Q₈×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₇₃	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#127×C₇₃	C₂²	1	2	yes	—
21	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#124×C₇₃	C₂²	1	2	yes	—
23	C₂×#124×C₇₃	C₂²	1	4	yes	—
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₃	C₂²	1	4	yes	—
26	C₂×#123×C₇₃	C₂²	1	4	yes	—
27	C₂×#123×C₇₃	C₂²	1	4	yes	—
28	C₂×#121×C₇₃	C₂²	1	2	yes	—
29	C₂×#121×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
40	#399×C₇₃	C₂²	1	4	yes	—
41	#399×C₇₃	C₂²	1	4	yes	—
42	#397×C₇₃	C₂²	1	4	yes	—
43	#394×C₇₃	C₂²	1	4	yes	—
44	#394×C₇₃	C₂²	1	4	yes	—
45	#394×C₇₃	C₂²	1	4	yes	—
46	#393×C₇₃	C₂²	1	4	yes	—
47	#392×C₇₃	C₂²	1	4	yes	—
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	2	yes	—
50	#390×C₇₃	C₂²	1	1	yes	characteristic
51	#390×C₇₃	C₂²	1	2	yes	—
52	#390×C₇₃	C₂²	1	2	yes	—
53	#390×C₇₃	C₂²	1	2	yes	—
54	#390×C₇₃	C₂²	1	2	yes	—
55	#390×C₇₃	C₂²	1	2	yes	—
56	#390×C₇₃	C₂²	1	2	yes	—
57	#390×C₇₃	C₂²	1	2	yes	—
58	#389×C₇₃	C₂²	1	2	yes	—
59	#389×C₇₃	C₂²	1	2	yes	—
60	#389×C₇₃	C₂²	1	4	yes	—
61	#389×C₇₃	C₂²	1	2	yes	—
62	#389×C₇₃	C₂²	1	1	yes	characteristic
63	#389×C₇₃	C₂²	1	1	yes	characteristic
64	#388×C₇₃	C₂²	1	4	yes	—
65	#388×C₇₃	C₂²	1	4	yes	—
66	#388×C₇₃	C₂²	1	2	yes	—
67	#388×C₇₃	C₂²	1	2	yes	—
68	#386×C₇₃	C₂²	1	4	yes	—
69	#385×C₇₃	C₂²	1	4	yes	—
70	#385×C₇₃	C₂²	1	4	yes	—
71	#385×C₇₃	C₂²	1	4	yes	—
72	#384×C₇₃	C₂²	1	1	yes	characteristic
73	#384×C₇₃	C₂²	1	2	yes	—
74	#384×C₇₃	C₂²	1	1	yes	characteristic
75	#382×C₇₃	C₂²	1	1	yes	characteristic
76	#380×C₇₃	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
83	C₄³×C₇₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
92	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₇₃	—	2	4	no	—
96	#127×C₇₃	—	2	8	no	—
97	#127×C₇₃	—	2	4	no	—
98	#124×C₇₃	—	2	8	no	—
99	#124×C₇₃	—	2	16	no	—
100	#124×C₇₃	D₄	1	8	yes	complemented
101	#123×C₇₃	—	2	16	no	—
102	#123×C₇₃	—	2	16	no	—
103	#123×C₇₃	—	4	8	no	—
104	#121×C₇₃	—	2	8	no	—
105	#121×C₇₃	—	4	4	no	—
106	C₄×Q₈×C₇₃	—	2	8	no	—
107	C₄×Q₈×C₇₃	—	2	8	no	—
108	C₄×Q₈×C₇₃	—	2	4	no	—
109	C₄×D₄×C₇₃	—	2	8	no	—
110	C₄×D₄×C₇₃	—	2	16	no	—
111	C₄×D₄×C₇₃	—	2	8	no	—
112	C₄×D₄×C₇₃	—	2	4	no	—
113	C₄×D₄×C₇₃	—	4	4	no	—
114	C₄×D₄×C₇₃	—	4	4	no	—
115	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
116	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
156	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
160	#95×C₇₃	C₂³	1	2	yes	—
161	#95×C₇₃	C₂³	1	2	yes	—
162	#95×C₇₃	C₂³	1	2	yes	—
163	#95×C₇₃	C₂³	1	2	yes	—
164	#95×C₇₃	C₂³	1	2	yes	—
165	#95×C₇₃	C₂³	1	4	yes	—
166	#95×C₇₃	C₂³	1	2	yes	—
167	#95×C₇₃	C₂³	1	2	yes	—
168	#95×C₇₃	C₂³	1	2	yes	—
169	#95×C₇₃	C₂³	1	4	yes	—
170	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
171	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
172	C₂×Q₈×C₇₃	—	2	4	no	—
173	C₂×Q₈×C₇₃	—	2	2	no	—
174	C₂×Q₈×C₇₃	—	2	4	no	—
175	C₂×Q₈×C₇₃	—	2	2	no	—
176	C₂×Q₈×C₇₃	—	4	2	no	—
177	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
178	C₂×D₄×C₇₃	—	2	8	no	—
179	C₂×D₄×C₇₃	—	2	8	no	—
180	C₂×D₄×C₇₃	—	2	4	no	—
181	C₂×D₄×C₇₃	—	2	2	no	—
182	C₂×D₄×C₇₃	—	2	8	no	—
183	C₂×D₄×C₇₃	—	2	4	no	—
184	C₂×D₄×C₇₃	—	2	4	no	—
185	C₂×D₄×C₇₃	—	2	4	no	—
186	C₂×D₄×C₇₃	—	2	4	no	—
187	C₂×D₄×C₇₃	—	2	4	no	—
188	C₂×D₄×C₇₃	—	2	2	no	—
189	C₂×D₄×C₇₃	—	2	4	no	—
190	C₂×D₄×C₇₃	—	4	2	no	—
191	C₂×D₄×C₇₃	—	4	2	no	—
192	C₂×D₄×C₇₃	—	4	4	no	—
193	C₂×D₄×C₇₃	—	4	4	no	—
194	C₂×D₄×C₇₃	—	4	4	no	—
195	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₇₃	—	2	8	no	—
197	C₂²×C₄×C₇₃	—	2	4	no	—
198	C₂²×C₄×C₇₃	—	2	4	no	—
199	C₂²×C₄×C₇₃	—	2	4	no	—
200	C₂²×C₄×C₇₃	—	2	8	no	—
201	C₂²×C₄×C₇₃	—	4	4	no	—
202	C₂²×C₄×C₇₃	—	4	4	no	—
203	C₂²×C₄×C₇₃	—	4	4	no	—
204	C₂²×C₄×C₇₃	—	4	4	no	—
205	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₇₃	—	2	4	no	—
221	C₄⋊C₄×C₇₃	—	2	4	no	—
222	C₄⋊C₄×C₇₃	—	2	4	no	—
223	C₄⋊C₄×C₇₃	—	2	8	no	—
224	C₄⋊C₄×C₇₃	—	2	4	no	—
225	C₄⋊C₄×C₇₃	—	2	2	no	—
226	C₄⋊C₄×C₇₃	—	2	4	no	—
227	C₄⋊C₄×C₇₃	—	2	2	no	—
228	C₄⋊C₄×C₇₃	—	2	4	no	—
229	C₄⋊C₄×C₇₃	—	2	2	no	—
230	C₄⋊C₄×C₇₃	—	2	2	no	—
231	C₄⋊C₄×C₇₃	—	2	4	no	—
232	C₄⋊C₄×C₇₃	—	2	2	no	—
233	C₄⋊C₄×C₇₃	—	2	4	no	—
234	C₄⋊C₄×C₇₃	—	4	4	no	—
235	C₄⋊C₄×C₇₃	—	4	2	no	—
236	C₄⋊C₄×C₇₃	—	4	4	no	—
237	C₄⋊C₄×C₇₃	#41	1	4	yes	—
238	C₂²⋊C₄×C₇₃	—	2	8	no	—
239	C₂²⋊C₄×C₇₃	—	2	8	no	—
240	C₂²⋊C₄×C₇₃	—	2	8	no	—
241	C₂²⋊C₄×C₇₃	—	2	8	no	—
242	C₂²⋊C₄×C₇₃	—	2	4	no	—
243	C₂²⋊C₄×C₇₃	—	2	8	no	—
244	C₂²⋊C₄×C₇₃	—	2	8	no	—
245	C₂²⋊C₄×C₇₃	—	2	4	no	—
246	C₂²⋊C₄×C₇₃	—	4	2	no	—
247	C₂²⋊C₄×C₇₃	—	4	4	no	—
248	C₂²⋊C₄×C₇₃	—	4	4	no	—
249	C₂²⋊C₄×C₇₃	—	4	4	no	—
250	C₂²⋊C₄×C₇₃	—	4	4	no	—
251	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
252	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
253	C₄²×C₇₃	—	2	8	no	—
254	C₄²×C₇₃	—	2	4	no	—
255	C₄²×C₇₃	—	2	4	no	—
256	C₄²×C₇₃	—	2	4	no	—
257	C₄²×C₇₃	—	2	2	no	—
258	C₄²×C₇₃	—	2	2	no	—
259	C₄²×C₇₃	—	2	2	no	—
260	C₄²×C₇₃	—	2	2	no	—
261	C₄²×C₇₃	—	4	1	no	—
262	C₄²×C₇₃	C₂×D₄	1	4	yes	—
263	C₄²×C₇₃	#41	1	4	yes	—
264	C₂³×C₇₃	—	2	2	no	—
265	C₂³×C₇₃	—	2	2	no	—
266	C₂³×C₇₃	—	2	2	no	—
267	C₂³×C₇₃	—	2	2	no	—
268	C₂³×C₇₃	—	2	2	no	—
269	C₂³×C₇₃	—	2	2	no	—
270	C₂³×C₇₃	—	2	4	no	—
271	C₂³×C₇₃	—	2	4	no	—
272	C₂³×C₇₃	—	2	4	no	—
273	C₂³×C₇₃	—	2	4	no	—
274	C₂³×C₇₃	—	2	4	no	—
275	C₂³×C₇₃	—	2	4	no	—
276	C₂³×C₇₃	—	2	4	no	—
277	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
278	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
279	Q₈×C₇₃	—	2	8	no	—
280	Q₈×C₇₃	—	4	8	no	—
281	D₄×C₇₃	—	2	8	no	—
282	D₄×C₇₃	—	4	16	no	—
283	D₄×C₇₃	—	4	8	no	—
284	D₄×C₇₃	—	4	8	no	—
285	D₄×C₇₃	—	4	8	no	—
286	D₄×C₇₃	—	8	8	no	—
287	C₂×C₄×C₇₃	—	2	2	no	—
288	C₂×C₄×C₇₃	—	2	1	no	—
289	C₂×C₄×C₇₃	—	2	2	no	—
290	C₂×C₄×C₇₃	—	2	1	no	—
291	C₂×C₄×C₇₃	—	2	1	no	—
292	C₂×C₄×C₇₃	—	2	1	no	—
293	C₂×C₄×C₇₃	—	2	1	no	—
294	C₂×C₄×C₇₃	—	2	1	no	—
295	C₂×C₄×C₇₃	—	2	2	no	—
296	C₂×C₄×C₇₃	—	2	1	no	—
297	C₂×C₄×C₇₃	—	2	1	no	—
298	C₂×C₄×C₇₃	—	2	2	no	—
299	C₂×C₄×C₇₃	—	2	2	no	—
300	C₂×C₄×C₇₃	—	2	4	no	—
301	C₂×C₄×C₇₃	—	2	2	no	—
302	C₂×C₄×C₇₃	—	2	2	no	—
303	C₂×C₄×C₇₃	—	2	2	no	—
304	C₂×C₄×C₇₃	—	2	2	no	—
305	C₂×C₄×C₇₃	—	2	2	no	—
306	C₂×C₄×C₇₃	—	2	2	no	—
307	C₂×C₄×C₇₃	—	2	1	no	—
308	C₂×C₄×C₇₃	—	2	2	no	—
309	C₂×C₄×C₇₃	—	2	4	no	—
310	C₂×C₄×C₇₃	—	2	2	no	—
311	C₂×C₄×C₇₃	—	2	2	no	—
312	C₂×C₄×C₇₃	—	2	2	no	—
313	C₂×C₄×C₇₃	—	2	4	no	—
314	C₂×C₄×C₇₃	—	2	2	no	—
315	C₂×C₄×C₇₃	—	2	2	no	—
316	C₂×C₄×C₇₃	—	2	1	no	—
317	C₂×C₄×C₇₃	—	2	1	no	—
318	C₂×C₄×C₇₃	—	2	2	no	—
319	C₂×C₄×C₇₃	—	2	2	no	—
320	C₂×C₄×C₇₃	—	4	8	no	—
321	C₂×C₄×C₇₃	—	8	8	no	—
322	C₂×C₄×C₇₃	—	8	8	no	—
323	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
328	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
329	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
330	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
332	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
333	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
334	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
335	C₂²×C₇₃	—	2	4	no	—
336	C₂²×C₇₃	—	2	4	no	—
337	C₂²×C₇₃	—	2	4	no	—
338	C₂²×C₇₃	—	4	2	no	—
339	C₂²×C₇₃	—	4	2	no	—
340	C₂²×C₇₃	—	4	2	no	—
341	C₂²×C₇₃	—	4	2	no	—
342	C₂²×C₇₃	—	4	4	no	—
343	C₂²×C₇₃	—	4	4	no	—
344	C₂²×C₇₃	—	4	4	no	—
345	C₂²×C₇₃	—	4	4	no	—
346	C₂²×C₇₃	—	4	4	no	—
347	C₂²×C₇₃	—	4	4	no	—
348	C₂²×C₇₃	—	4	4	no	—
349	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
350	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
352	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂²×C₇₃	#585	1	1	yes	characteristic
356	C₄×C₇₃	—	2	4	no	—
357	C₄×C₇₃	—	2	2	no	—
358	C₄×C₇₃	—	2	4	no	—
359	C₄×C₇₃	—	2	2	no	—
360	C₄×C₇₃	—	2	2	no	—
361	C₄×C₇₃	—	2	2	no	—
362	C₄×C₇₃	—	4	2	no	—
363	C₄×C₇₃	—	4	2	no	—
364	C₄×C₇₃	—	4	4	no	—
365	C₄×C₇₃	—	4	2	no	—
366	C₄×C₇₃	—	4	2	no	—
367	C₄×C₇₃	—	4	2	no	—
368	C₄×C₇₃	—	4	1	no	—
369	C₄×C₇₃	#547	1	4	yes	—
370	C₄×C₇₃	#559	1	4	yes	complemented
371	#59641	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₇₃	—	4	4	no	—
373	C₂×C₇₃	—	8	4	no	—
374	C₂×C₇₃	C₂×#547	1	1	yes	characteristic
375	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
376	C₂×C₇₃	C₂×#559	1	1	yes	characteristic
377	C₂×C₇₃	#3498	1	1	yes	characteristic
378	C₂×C₇₃	#3506	1	1	yes	characteristic
379	C₂×C₇₃	#3522	1	1	yes	characteristic
380	C₂×C₇₃	#3554	1	1	yes	characteristic
381	C₂×#559	C₂×C₇₃	1	2	yes	complemented
382	#2710	C₂×C₇₃	1	4	yes	complemented
383	#2580	C₂×C₇₃	1	2	yes	complemented
384	#2548	C₂×C₇₃	1	1	yes	characteristic, complemented
385	#2541	C₂×C₇₃	1	1	yes	characteristic
386	#2501	C₂×C₇₃	1	2	yes	complemented
387	#2491	C₂×C₇₃	1	2	yes	complemented
388	#2455	C₂×C₇₃	1	4	yes	complemented
389	#2448	C₂×C₇₃	1	2	yes	complemented
390	#2445	C₂×C₇₃	1	2	yes	complemented
391	#2422	C₂×C₇₃	1	2	yes	complemented
392	#2361	C₂×C₇₃	1	2	yes	complemented
393	Q₈×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
394	D₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
395	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
396	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
397	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
398	C₇₃	#59641	1	1	yes	characteristic, direct product factor, Sylow
399	#559	—	2	16	no	—
400	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
401	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
402	C₂×#127	C₂²×C₇₃	1	2	yes	—
403	C₂×#124	C₂²×C₇₃	1	2	yes	—
404	C₂×#124	C₂²×C₇₃	1	4	yes	—
405	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
406	C₂×#123	C₂²×C₇₃	1	4	yes	—
407	C₂×#123	C₂²×C₇₃	1	4	yes	—
408	C₂×#123	C₂²×C₇₃	1	4	yes	—
409	C₂×#121	C₂²×C₇₃	1	2	yes	—
410	C₂×#121	C₂²×C₇₃	1	2	yes	—
411	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
412	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
413	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
415	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
418	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
420	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
421	#399	C₂²×C₇₃	1	4	yes	—
422	#399	C₂²×C₇₃	1	4	yes	—
423	#397	C₂²×C₇₃	1	4	yes	—
424	#394	C₂²×C₇₃	1	4	yes	—
425	#394	C₂²×C₇₃	1	4	yes	—
426	#394	C₂²×C₇₃	1	4	yes	—
427	#393	C₂²×C₇₃	1	4	yes	—
428	#392	C₂²×C₇₃	1	4	yes	—
429	#391	C₂²×C₇₃	1	2	yes	—
430	#391	C₂²×C₇₃	1	1	yes	characteristic
431	#390	C₂²×C₇₃	1	2	yes	—
432	#390	C₂²×C₇₃	1	2	yes	—
433	#390	C₂²×C₇₃	1	2	yes	—
434	#390	C₂²×C₇₃	1	2	yes	—
435	#390	C₂²×C₇₃	1	2	yes	—
436	#390	C₂²×C₇₃	1	2	yes	—
437	#390	C₂²×C₇₃	1	2	yes	—
438	#390	C₂²×C₇₃	1	1	yes	characteristic
439	#389	C₂²×C₇₃	1	1	yes	characteristic
440	#389	C₂²×C₇₃	1	1	yes	characteristic
441	#389	C₂²×C₇₃	1	2	yes	—
442	#389	C₂²×C₇₃	1	2	yes	—
443	#389	C₂²×C₇₃	1	2	yes	—
444	#389	C₂²×C₇₃	1	4	yes	—
445	#388	C₂²×C₇₃	1	4	yes	—
446	#388	C₂²×C₇₃	1	4	yes	—
447	#388	C₂²×C₇₃	1	2	yes	—
448	#388	C₂²×C₇₃	1	2	yes	—
449	#386	C₂²×C₇₃	1	4	yes	—
450	#385	C₂²×C₇₃	1	4	yes	—
451	#385	C₂²×C₇₃	1	4	yes	—
452	#385	C₂²×C₇₃	1	4	yes	—
453	#384	C₂²×C₇₃	1	1	yes	characteristic
454	#384	C₂²×C₇₃	1	1	yes	characteristic
455	#384	C₂²×C₇₃	1	2	yes	—
456	#382	C₂²×C₇₃	1	1	yes	characteristic
457	#380	C₂²×C₇₃	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
464	C₄³	C₂²×C₇₃	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
466	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
469	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
470	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
472	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
473	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
475	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
476	C₄⋊Q₈	—	2	4	no	—
477	#127	—	2	8	no	—
478	#127	—	2	4	no	—
479	#124	—	2	8	no	—
480	#124	—	2	16	no	—
481	#124	D₄×C₇₃	1	8	yes	complemented
482	#123	—	2	16	no	—
483	#123	—	2	16	no	—
484	#123	—	4	8	no	—
485	#121	—	2	8	no	—
486	#121	—	4	4	no	—
487	C₄×Q₈	—	2	8	no	—
488	C₄×Q₈	—	2	8	no	—
489	C₄×Q₈	—	2	4	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	16	no	—
492	C₄×D₄	—	2	8	no	—
493	C₄×D₄	—	2	4	no	—
494	C₄×D₄	—	4	4	no	—
495	C₄×D₄	—	4	4	no	—
496	C₂×C₄⋊C₄	—	4	4	no	—
497	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
534	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
541	#95	C₂³×C₇₃	1	2	yes	—
542	#95	C₂³×C₇₃	1	2	yes	—
543	#95	C₂³×C₇₃	1	2	yes	—
544	#95	C₂³×C₇₃	1	2	yes	—
545	#95	C₂³×C₇₃	1	2	yes	—
546	#95	C₂³×C₇₃	1	4	yes	—
547	#95	C₂³×C₇₃	1	2	yes	—
548	#95	C₂³×C₇₃	1	2	yes	—
549	#95	C₂³×C₇₃	1	2	yes	—
550	#95	C₂³×C₇₃	1	4	yes	—
551	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
552	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	2	no	—
558	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
591	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	4	no	—
618	C₄⋊C₄	#41×C₇₃	1	4	yes	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	—	4	4	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
633	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
634	C₄²	—	2	8	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	4	1	no	—
643	C₄²	C₂×D₄×C₇₃	1	4	yes	—
644	C₄²	#41×C₇₃	1	4	yes	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	4	no	—
658	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
659	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
660	Q₈	—	2	8	no	—
661	Q₈	—	4	8	no	—
662	D₄	—	2	8	no	—
663	D₄	—	4	16	no	—
664	D₄	—	4	8	no	—
665	D₄	—	4	8	no	—
666	D₄	—	4	8	no	—
667	D₄	—	8	8	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	8	8	no	—
703	C₂×C₄	—	8	8	no	—
704	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
705	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
708	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
709	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
710	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
711	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
712	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
713	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
714	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
715	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	4	no	—
730	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
731	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
732	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
733	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
734	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
735	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
736	C₂²	#585×C₇₃	1	1	yes	characteristic
737	C₄	—	2	4	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	1	no	—
750	C₄	#547×C₇₃	1	4	yes	—
751	C₄	#559×C₇₃	1	4	yes	complemented
752	C₂	—	4	4	no	—
753	C₂	—	8	4	no	—
754	C₂	C₂×#547×C₇₃	1	1	yes	characteristic
755	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
756	C₂	C₂×#559×C₇₃	1	1	yes	characteristic
757	C₂	C₇₃×#3498	1	1	yes	characteristic
758	C₂	C₇₃×#3506	1	1	yes	characteristic
759	C₂	C₇₃×#3522	1	1	yes	characteristic
760	C₂	C₇₃×#3554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2541	C₂
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×#559×C₇₃	C₂	semidirect
2. C₇₃×#2710	C₂	semidirect
3. C₇₃×#2580	C₂	semidirect
4. C₇₃×#2548	C₂	semidirect
6. C₇₃×#2501	C₂	semidirect
7. C₇₃×#2491	C₂	semidirect
8. C₇₃×#2455	C₂	semidirect
9. C₇₃×#2448	C₂	semidirect
10. C₇₃×#2445	C₂	semidirect
11. C₇₃×#2422	C₂	semidirect
12. C₇₃×#2361	C₂	semidirect
13. Q₈×C₄⋊C₄×C₇₃	C₂	semidirect
14. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
15. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
16. C₄×#127×C₇₃	C₂	semidirect
17. C₄×#124×C₇₃	C₂	semidirect
100. #124×C₇₃	D₄	semidirect
370. C₄×C₇₃	#559	semidirect
371. #59641	C₇₃	direct (N × H)
381. C₂×#559	C₂×C₇₃	semidirect
382. #2710	C₂×C₇₃	semidirect
383. #2580	C₂×C₇₃	semidirect
384. #2548	C₂×C₇₃	semidirect
386. #2501	C₂×C₇₃	semidirect
387. #2491	C₂×C₇₃	semidirect
388. #2455	C₂×C₇₃	semidirect
389. #2448	C₂×C₇₃	semidirect
390. #2445	C₂×C₇₃	semidirect
391. #2422	C₂×C₇₃	semidirect
392. #2361	C₂×C₇₃	semidirect
393. Q₈×C₄⋊C₄	C₂×C₇₃	semidirect
394. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
395. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
396. C₄×#127	C₂×C₇₃	semidirect
397. C₄×#124	C₂×C₇₃	semidirect
398. C₇₃	#59641	direct (N × H)
481. #124	D₄×C₇₃	semidirect
751. C₄	#559×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₇₃	2
C₇₃×#2710	2
C₇₃×#2580	2
C₇₃×#2548	2
C₇₃×#2541	2
C₇₃×#2501	2
C₇₃×#2491	2
C₇₃×#2455	2
C₇₃×#2448	2
C₇₃×#2445	2
C₇₃×#2422	2
C₇₃×#2361	2
Q₈×C₄⋊C₄×C₇₃	2
D₄×C₄⋊C₄×C₇₃	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
#59641	73

Subgroups — C73×#59641 #32969045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59641 #32969045