Subgroups — C₇₃×#59895 #32969299

Order 18688.

1600 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2787	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2771	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2611	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2573	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2515	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2494	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2493	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2454	C₂	1	1	yes	maximal, characteristic
13	C₇₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2447	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2447	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2367	C₂	1	1	yes	maximal, characteristic
18	C₇₃×#2357	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2349	C₂	1	1	yes	maximal, characteristic
20	C₇₃×#2343	C₂	1	2	yes	maximal, complemented
21	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2293	C₂	1	1	yes	maximal, characteristic
24	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₃	C₂²	1	2	yes	—
32	#401×C₇₃	C₂²	1	2	yes	—
33	#401×C₇₃	C₂²	1	2	yes	—
34	#400×C₇₃	C₂²	1	2	yes	—
35	#400×C₇₃	C₂²	1	2	yes	—
36	#400×C₇₃	C₂²	1	2	yes	—
37	#400×C₇₃	C₂²	1	2	yes	—
38	#400×C₇₃	C₂²	1	2	yes	—
39	#400×C₇₃	C₂²	1	2	yes	—
40	#399×C₇₃	C₂²	1	2	yes	—
41	#398×C₇₃	C₂²	1	2	yes	—
42	#398×C₇₃	C₂²	1	2	yes	—
43	#397×C₇₃	C₂²	1	2	yes	—
44	#397×C₇₃	C₂²	1	2	yes	—
45	#397×C₇₃	C₂²	1	2	yes	—
46	#397×C₇₃	C₂²	1	2	yes	—
47	#396×C₇₃	C₂²	1	2	yes	—
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	1	yes	characteristic
50	#391×C₇₃	C₂²	1	1	yes	characteristic
51	#391×C₇₃	C₂²	1	1	yes	characteristic
52	#391×C₇₃	C₂²	1	1	yes	characteristic
53	#390×C₇₃	C₂²	1	1	yes	characteristic
54	#390×C₇₃	C₂²	1	1	yes	characteristic
55	#390×C₇₃	C₂²	1	1	yes	characteristic
56	#389×C₇₃	C₂²	1	1	yes	characteristic
57	#389×C₇₃	C₂²	1	1	yes	characteristic
58	#389×C₇₃	C₂²	1	2	yes	—
59	#389×C₇₃	C₂²	1	1	yes	characteristic
60	#389×C₇₃	C₂²	1	1	yes	characteristic
61	#389×C₇₃	C₂²	1	1	yes	characteristic
62	#389×C₇₃	C₂²	1	1	yes	characteristic
63	#389×C₇₃	C₂²	1	2	yes	—
64	#389×C₇₃	C₂²	1	1	yes	characteristic
65	#389×C₇₃	C₂²	1	2	yes	—
66	#389×C₇₃	C₂²	1	1	yes	characteristic
67	#389×C₇₃	C₂²	1	1	yes	characteristic
68	#389×C₇₃	C₂²	1	1	yes	characteristic
69	#388×C₇₃	C₂²	1	2	yes	—
70	#388×C₇₃	C₂²	1	2	yes	—
71	#388×C₇₃	C₂²	1	2	yes	—
72	#388×C₇₃	C₂²	1	2	yes	—
73	#388×C₇₃	C₂²	1	2	yes	—
74	#388×C₇₃	C₂²	1	2	yes	—
75	#387×C₇₃	C₂²	1	2	yes	—
76	#387×C₇₃	C₂²	1	1	yes	characteristic
77	#387×C₇₃	C₂²	1	2	yes	—
78	#387×C₇₃	C₂²	1	2	yes	—
79	#387×C₇₃	C₂²	1	1	yes	characteristic
80	#387×C₇₃	C₂²	1	2	yes	—
81	#387×C₇₃	C₂²	1	2	yes	—
82	#387×C₇₃	C₂²	1	2	yes	—
83	#387×C₇₃	C₂²	1	2	yes	—
84	#387×C₇₃	C₂²	1	1	yes	characteristic
85	#387×C₇₃	C₂²	1	2	yes	—
86	#387×C₇₃	C₂²	1	2	yes	—
87	#387×C₇₃	C₂²	1	1	yes	characteristic
88	#385×C₇₃	C₂²	1	2	yes	—
89	#385×C₇₃	C₂²	1	2	yes	—
90	#385×C₇₃	C₂²	1	2	yes	—
91	#385×C₇₃	C₂²	1	2	yes	—
92	#385×C₇₃	C₂²	1	2	yes	—
93	#385×C₇₃	C₂²	1	2	yes	—
94	#383×C₇₃	C₂²	1	2	yes	—
95	#383×C₇₃	C₂²	1	2	yes	—
96	#382×C₇₃	C₂²	1	2	yes	—
97	#382×C₇₃	C₂²	1	1	yes	characteristic
98	#382×C₇₃	C₂²	1	1	yes	characteristic
99	#382×C₇₃	C₂²	1	1	yes	characteristic
100	#381×C₇₃	C₂²	1	2	yes	—
101	#381×C₇₃	C₂²	1	2	yes	—
102	#381×C₇₃	C₂²	1	2	yes	—
103	#380×C₇₃	C₂²	1	2	yes	—
104	#380×C₇₃	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
120	#376×C₇₃	C₂²	1	2	yes	—
121	C₂×#95×C₇₃	C₂²	1	2	yes	—
122	C₄³×C₇₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
128	#125×C₇₃	—	2	4	no	—
129	#125×C₇₃	—	2	4	no	—
130	#124×C₇₃	—	2	4	no	—
131	C₄×Q₈×C₇₃	—	2	4	no	—
132	C₄×D₄×C₇₃	—	2	4	no	—
133	C₄×D₄×C₇₃	—	2	4	no	—
134	C₄×D₄×C₇₃	—	2	4	no	—
135	#117×C₇₃	—	2	8	no	—
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
192	#95×C₇₃	C₂³	1	1	yes	characteristic
193	#95×C₇₃	C₂³	1	1	yes	characteristic
194	#95×C₇₃	C₂³	1	2	yes	—
195	#95×C₇₃	C₂³	1	2	yes	—
196	#95×C₇₃	C₂³	1	2	yes	—
197	#95×C₇₃	C₂³	1	2	yes	—
198	#95×C₇₃	C₂³	1	1	yes	characteristic
199	#95×C₇₃	C₂³	1	1	yes	characteristic
200	#95×C₇₃	C₂³	1	1	yes	characteristic
201	#95×C₇₃	C₂³	1	1	yes	characteristic
202	#95×C₇₃	C₂³	1	1	yes	characteristic
203	#95×C₇₃	C₂³	1	2	yes	—
204	#95×C₇₃	C₂³	1	2	yes	—
205	#95×C₇₃	C₂³	1	2	yes	—
206	#95×C₇₃	C₂³	1	1	yes	characteristic
207	#95×C₇₃	C₂³	1	1	yes	characteristic
208	#95×C₇₃	C₂³	1	1	yes	characteristic
209	#95×C₇₃	C₂³	1	2	yes	—
210	#95×C₇₃	C₂³	1	2	yes	—
211	#95×C₇₃	C₂³	1	1	yes	characteristic
212	#95×C₇₃	C₂³	1	1	yes	characteristic
213	#95×C₇₃	C₂³	1	2	yes	—
214	#95×C₇₃	C₂³	1	2	yes	—
215	#95×C₇₃	C₂³	1	2	yes	—
216	#95×C₇₃	C₂³	1	2	yes	—
217	#95×C₇₃	C₂³	1	2	yes	—
218	#95×C₇₃	C₂³	1	2	yes	—
219	#95×C₇₃	C₂³	1	2	yes	—
220	#95×C₇₃	C₂³	1	2	yes	—
221	#95×C₇₃	C₂³	1	2	yes	—
222	#95×C₇₃	C₂³	1	2	yes	—
223	#95×C₇₃	C₂³	1	2	yes	—
224	#95×C₇₃	C₂³	1	2	yes	—
225	#95×C₇₃	C₂³	1	2	yes	—
226	#95×C₇₃	C₂³	1	2	yes	—
227	#95×C₇₃	C₂³	1	2	yes	—
228	#95×C₇₃	C₂³	1	2	yes	—
229	#95×C₇₃	C₂³	1	2	yes	—
230	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₇₃	—	2	2	no	—
232	C₂×Q₈×C₇₃	—	2	2	no	—
233	C₂×Q₈×C₇₃	—	2	2	no	—
234	C₂×D₄×C₇₃	—	2	2	no	—
235	C₂×D₄×C₇₃	—	2	2	no	—
236	C₂×D₄×C₇₃	#41	1	4	yes	—
237	C₂²×C₄×C₇₃	—	2	4	no	—
238	C₂²×C₄×C₇₃	—	2	4	no	—
239	C₂²×C₄×C₇₃	—	2	4	no	—
240	C₂²×C₄×C₇₃	—	2	4	no	—
241	C₂²×C₄×C₇₃	—	4	2	no	—
242	C₂²×C₄×C₇₃	—	4	2	no	—
243	C₂²×C₄×C₇₃	—	4	2	no	—
244	C₂²×C₄×C₇₃	—	4	2	no	—
245	C₂²×C₄×C₇₃	—	4	2	no	—
246	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
268	C₄⋊C₄×C₇₃	—	2	4	no	—
269	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	2	no	—
271	C₄⋊C₄×C₇₃	—	2	2	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	—	2	4	no	—
275	C₄⋊C₄×C₇₃	—	2	2	no	—
276	C₄⋊C₄×C₇₃	—	2	2	no	—
277	C₄⋊C₄×C₇₃	—	2	2	no	—
278	C₄⋊C₄×C₇₃	—	2	2	no	—
279	C₄⋊C₄×C₇₃	—	2	2	no	—
280	C₄⋊C₄×C₇₃	—	2	2	no	—
281	C₄⋊C₄×C₇₃	—	2	2	no	—
282	C₄⋊C₄×C₇₃	—	2	2	no	—
283	C₄⋊C₄×C₇₃	—	2	2	no	—
284	C₄⋊C₄×C₇₃	—	4	1	no	—
285	C₄⋊C₄×C₇₃	—	4	1	no	—
286	C₄⋊C₄×C₇₃	—	4	2	no	—
287	C₄⋊C₄×C₇₃	—	4	2	no	—
288	C₄⋊C₄×C₇₃	—	4	2	no	—
289	C₄⋊C₄×C₇₃	—	4	2	no	—
290	C₄⋊C₄×C₇₃	—	4	1	no	—
291	C₄⋊C₄×C₇₃	—	4	1	no	—
292	C₄⋊C₄×C₇₃	—	4	1	no	—
293	C₄⋊C₄×C₇₃	—	4	1	no	—
294	C₄⋊C₄×C₇₃	—	4	2	no	—
295	C₄⋊C₄×C₇₃	—	4	2	no	—
296	C₄⋊C₄×C₇₃	#41	1	4	yes	—
297	C₂²⋊C₄×C₇₃	—	2	4	no	—
298	C₂²⋊C₄×C₇₃	—	2	4	no	—
299	C₂²⋊C₄×C₇₃	—	2	4	no	—
300	C₂²⋊C₄×C₇₃	—	2	4	no	—
301	C₂²⋊C₄×C₇₃	—	2	4	no	—
302	C₂²⋊C₄×C₇₃	—	2	4	no	—
303	C₂²⋊C₄×C₇₃	—	2	4	no	—
304	C₂²⋊C₄×C₇₃	—	4	2	no	—
305	C₂²⋊C₄×C₇₃	—	4	2	no	—
306	C₂²⋊C₄×C₇₃	—	4	2	no	—
307	C₂²⋊C₄×C₇₃	—	4	2	no	—
308	C₄²×C₇₃	—	2	4	no	—
309	C₄²×C₇₃	—	2	2	no	—
310	C₄²×C₇₃	—	2	2	no	—
311	C₄²×C₇₃	—	2	2	no	—
312	C₄²×C₇₃	—	2	2	no	—
313	C₄²×C₇₃	—	2	4	no	—
314	C₄²×C₇₃	—	2	2	no	—
315	C₄²×C₇₃	—	2	2	no	—
316	C₄²×C₇₃	—	2	2	no	—
317	C₄²×C₇₃	—	4	1	no	—
318	C₄²×C₇₃	—	4	2	no	—
319	C₄²×C₇₃	—	4	1	no	—
320	C₄²×C₇₃	—	4	2	no	—
321	C₄²×C₇₃	—	4	1	no	—
322	C₄²×C₇₃	—	4	2	no	—
323	C₄²×C₇₃	#41	1	4	yes	—
324	C₂³×C₇₃	—	2	2	no	—
325	C₂³×C₇₃	—	2	2	no	—
326	C₂³×C₇₃	—	2	2	no	—
327	C₂³×C₇₃	—	2	2	no	—
328	C₂³×C₇₃	—	2	2	no	—
329	C₂³×C₇₃	—	2	2	no	—
330	C₂³×C₇₃	C₂×#41	1	4	yes	—
331	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
332	Q₈×C₇₃	—	4	4	no	—
333	D₄×C₇₃	—	2	8	no	—
334	C₂×C₄×C₇₃	—	2	1	no	—
335	C₂×C₄×C₇₃	—	2	1	no	—
336	C₂×C₄×C₇₃	—	2	1	no	—
337	C₂×C₄×C₇₃	—	2	1	no	—
338	C₂×C₄×C₇₃	—	2	1	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	2	1	no	—
341	C₂×C₄×C₇₃	—	2	2	no	—
342	C₂×C₄×C₇₃	—	2	1	no	—
343	C₂×C₄×C₇₃	—	2	1	no	—
344	C₂×C₄×C₇₃	—	2	1	no	—
345	C₂×C₄×C₇₃	—	2	1	no	—
346	C₂×C₄×C₇₃	—	2	1	no	—
347	C₂×C₄×C₇₃	—	2	2	no	—
348	C₂×C₄×C₇₃	—	2	2	no	—
349	C₂×C₄×C₇₃	—	2	1	no	—
350	C₂×C₄×C₇₃	—	2	1	no	—
351	C₂×C₄×C₇₃	—	2	1	no	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	1	no	—
354	C₂×C₄×C₇₃	—	2	1	no	—
355	C₂×C₄×C₇₃	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	2	no	—
357	C₂×C₄×C₇₃	—	2	2	no	—
358	C₂×C₄×C₇₃	—	2	1	no	—
359	C₂×C₄×C₇₃	—	2	1	no	—
360	C₂×C₄×C₇₃	—	2	2	no	—
361	C₂×C₄×C₇₃	—	2	1	no	—
362	C₂×C₄×C₇₃	—	2	1	no	—
363	C₂×C₄×C₇₃	—	2	2	no	—
364	C₂×C₄×C₇₃	—	2	1	no	—
365	C₂×C₄×C₇₃	—	2	2	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	2	no	—
368	C₂×C₄×C₇₃	—	2	2	no	—
369	C₂×C₄×C₇₃	—	2	1	no	—
370	C₂×C₄×C₇₃	—	2	1	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	1	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	1	no	—
375	C₂×C₄×C₇₃	—	2	1	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	1	no	—
378	C₂×C₄×C₇₃	—	2	2	no	—
379	C₂×C₄×C₇₃	—	2	2	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	1	no	—
382	C₂×C₄×C₇₃	—	2	2	no	—
383	C₂×C₄×C₇₃	—	2	2	no	—
384	C₂×C₄×C₇₃	—	2	1	no	—
385	C₂×C₄×C₇₃	—	2	1	no	—
386	C₂×C₄×C₇₃	—	2	1	no	—
387	C₂×C₄×C₇₃	—	2	1	no	—
388	C₂×C₄×C₇₃	—	2	2	no	—
389	C₂×C₄×C₇₃	—	2	1	no	—
390	C₂×C₄×C₇₃	—	2	1	no	—
391	C₂×C₄×C₇₃	—	2	1	no	—
392	C₂×C₄×C₇₃	—	2	1	no	—
393	C₂×C₄×C₇₃	—	4	8	no	—
394	C₂×C₄×C₇₃	—	8	4	no	—
395	C₂×C₄×C₇₃	—	8	4	no	—
396	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
397	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
398	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
399	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
400	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
401	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
402	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
403	C₂²×C₇₃	—	2	4	no	—
404	C₂²×C₇₃	—	2	4	no	—
405	C₂²×C₇₃	—	2	4	no	—
406	C₂²×C₇₃	—	4	2	no	—
407	C₂²×C₇₃	—	4	2	no	—
408	C₂²×C₇₃	—	4	2	no	—
409	C₂²×C₇₃	—	4	2	no	—
410	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
414	C₂²×C₇₃	#585	1	1	yes	characteristic
415	C₂²×C₇₃	#585	1	1	yes	characteristic
416	C₂²×C₇₃	#585	1	1	yes	characteristic
417	C₄×C₇₃	—	2	2	no	—
418	C₄×C₇₃	—	2	2	no	—
419	C₄×C₇₃	—	2	2	no	—
420	C₄×C₇₃	—	2	4	no	—
421	C₄×C₇₃	—	4	2	no	—
422	C₄×C₇₃	—	4	1	no	—
423	C₄×C₇₃	—	4	1	no	—
424	C₄×C₇₃	—	4	2	no	—
425	C₄×C₇₃	—	4	1	no	—
426	C₄×C₇₃	—	4	2	no	—
427	C₄×C₇₃	—	4	1	no	—
428	C₄×C₇₃	—	4	2	no	—
429	C₄×C₇₃	—	4	1	no	—
430	C₄×C₇₃	—	4	1	no	—
431	C₄×C₇₃	—	4	1	no	—
432	C₄×C₇₃	—	4	1	no	—
433	C₄×C₇₃	—	4	2	no	—
434	C₄×C₇₃	—	4	1	no	—
435	C₄×C₇₃	—	4	1	no	—
436	C₄×C₇₃	—	4	1	no	—
437	C₄×C₇₃	—	4	2	no	—
438	C₄×C₇₃	#552	1	4	yes	—
439	#59895	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂×C₇₃	—	4	4	no	—
441	C₂×C₇₃	C₂×#552	1	1	yes	characteristic
442	C₂×C₇₃	#3475	1	1	yes	characteristic
443	C₂×C₇₃	#3480	1	1	yes	characteristic
444	C₂×C₇₃	#3507	1	1	yes	characteristic
445	C₂×C₇₃	#3521	1	1	yes	characteristic
446	C₂×C₇₃	#3521	1	1	yes	characteristic
447	C₂×C₇₃	#3557	1	1	yes	characteristic
448	#2787	C₂×C₇₃	1	2	yes	complemented
449	#2771	C₂×C₇₃	1	2	yes	complemented
450	#2611	C₂×C₇₃	1	2	yes	complemented
451	#2573	C₂×C₇₃	1	2	yes	complemented
452	#2515	C₂×C₇₃	1	2	yes	complemented
453	#2514	C₂×C₇₃	1	1	yes	characteristic, complemented
454	#2514	C₂×C₇₃	1	1	yes	characteristic, complemented
455	#2509	C₂×C₇₃	1	1	yes	characteristic, complemented
456	#2508	C₂×C₇₃	1	1	yes	characteristic, complemented
457	#2494	C₂×C₇₃	1	2	yes	complemented
458	#2493	C₂×C₇₃	1	2	yes	complemented
459	#2454	C₂×C₇₃	1	1	yes	characteristic
460	#2453	C₂×C₇₃	1	1	yes	characteristic, complemented
461	#2447	C₂×C₇₃	1	1	yes	characteristic
462	#2447	C₂×C₇₃	1	1	yes	characteristic
463	#2370	C₂×C₇₃	1	1	yes	characteristic, complemented
464	#2367	C₂×C₇₃	1	1	yes	characteristic
465	#2357	C₂×C₇₃	1	1	yes	characteristic
466	#2349	C₂×C₇₃	1	1	yes	characteristic
467	#2343	C₂×C₇₃	1	2	yes	complemented
468	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
469	#2295	C₂×C₇₃	1	1	yes	characteristic, complemented
470	#2293	C₂×C₇₃	1	1	yes	characteristic
471	C₇₃	#59895	1	1	yes	characteristic, direct product factor, Sylow
472	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
473	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
474	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
475	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
476	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
477	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
478	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
479	C₂×#117	C₂²×C₇₃	1	2	yes	—
480	#401	C₂²×C₇₃	1	2	yes	—
481	#401	C₂²×C₇₃	1	2	yes	—
482	#400	C₂²×C₇₃	1	2	yes	—
483	#400	C₂²×C₇₃	1	2	yes	—
484	#400	C₂²×C₇₃	1	2	yes	—
485	#400	C₂²×C₇₃	1	2	yes	—
486	#400	C₂²×C₇₃	1	2	yes	—
487	#400	C₂²×C₇₃	1	2	yes	—
488	#399	C₂²×C₇₃	1	2	yes	—
489	#398	C₂²×C₇₃	1	2	yes	—
490	#398	C₂²×C₇₃	1	2	yes	—
491	#397	C₂²×C₇₃	1	2	yes	—
492	#397	C₂²×C₇₃	1	2	yes	—
493	#397	C₂²×C₇₃	1	2	yes	—
494	#397	C₂²×C₇₃	1	2	yes	—
495	#396	C₂²×C₇₃	1	2	yes	—
496	#391	C₂²×C₇₃	1	1	yes	characteristic
497	#391	C₂²×C₇₃	1	1	yes	characteristic
498	#391	C₂²×C₇₃	1	1	yes	characteristic
499	#391	C₂²×C₇₃	1	1	yes	characteristic
500	#391	C₂²×C₇₃	1	1	yes	characteristic
501	#390	C₂²×C₇₃	1	1	yes	characteristic
502	#390	C₂²×C₇₃	1	1	yes	characteristic
503	#390	C₂²×C₇₃	1	1	yes	characteristic
504	#389	C₂²×C₇₃	1	1	yes	characteristic
505	#389	C₂²×C₇₃	1	1	yes	characteristic
506	#389	C₂²×C₇₃	1	2	yes	—
507	#389	C₂²×C₇₃	1	1	yes	characteristic
508	#389	C₂²×C₇₃	1	1	yes	characteristic
509	#389	C₂²×C₇₃	1	2	yes	—
510	#389	C₂²×C₇₃	1	1	yes	characteristic
511	#389	C₂²×C₇₃	1	2	yes	—
512	#389	C₂²×C₇₃	1	1	yes	characteristic
513	#389	C₂²×C₇₃	1	1	yes	characteristic
514	#389	C₂²×C₇₃	1	1	yes	characteristic
515	#389	C₂²×C₇₃	1	1	yes	characteristic
516	#389	C₂²×C₇₃	1	1	yes	characteristic
517	#388	C₂²×C₇₃	1	2	yes	—
518	#388	C₂²×C₇₃	1	2	yes	—
519	#388	C₂²×C₇₃	1	2	yes	—
520	#388	C₂²×C₇₃	1	2	yes	—
521	#388	C₂²×C₇₃	1	2	yes	—
522	#388	C₂²×C₇₃	1	2	yes	—
523	#387	C₂²×C₇₃	1	1	yes	characteristic
524	#387	C₂²×C₇₃	1	1	yes	characteristic
525	#387	C₂²×C₇₃	1	1	yes	characteristic
526	#387	C₂²×C₇₃	1	1	yes	characteristic
527	#387	C₂²×C₇₃	1	2	yes	—
528	#387	C₂²×C₇₃	1	2	yes	—
529	#387	C₂²×C₇₃	1	2	yes	—
530	#387	C₂²×C₇₃	1	2	yes	—
531	#387	C₂²×C₇₃	1	2	yes	—
532	#387	C₂²×C₇₃	1	2	yes	—
533	#387	C₂²×C₇₃	1	2	yes	—
534	#387	C₂²×C₇₃	1	2	yes	—
535	#387	C₂²×C₇₃	1	2	yes	—
536	#385	C₂²×C₇₃	1	2	yes	—
537	#385	C₂²×C₇₃	1	2	yes	—
538	#385	C₂²×C₇₃	1	2	yes	—
539	#385	C₂²×C₇₃	1	2	yes	—
540	#385	C₂²×C₇₃	1	2	yes	—
541	#385	C₂²×C₇₃	1	2	yes	—
542	#383	C₂²×C₇₃	1	2	yes	—
543	#383	C₂²×C₇₃	1	2	yes	—
544	#382	C₂²×C₇₃	1	1	yes	characteristic
545	#382	C₂²×C₇₃	1	1	yes	characteristic
546	#382	C₂²×C₇₃	1	1	yes	characteristic
547	#382	C₂²×C₇₃	1	2	yes	—
548	#381	C₂²×C₇₃	1	2	yes	—
549	#381	C₂²×C₇₃	1	2	yes	—
550	#381	C₂²×C₇₃	1	2	yes	—
551	#380	C₂²×C₇₃	1	2	yes	—
552	#380	C₂²×C₇₃	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
561	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
565	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
568	#376	C₂²×C₇₃	1	2	yes	—
569	C₂×#95	C₂²×C₇₃	1	2	yes	—
570	C₄³	C₂²×C₇₃	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
574	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
575	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
576	#125	—	2	4	no	—
577	#125	—	2	4	no	—
578	#124	—	2	4	no	—
579	C₄×Q₈	—	2	4	no	—
580	C₄×D₄	—	2	4	no	—
581	C₄×D₄	—	2	4	no	—
582	C₄×D₄	—	2	4	no	—
583	#117	—	2	8	no	—
584	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
624	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
625	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
639	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
640	#95	C₂³×C₇₃	1	1	yes	characteristic
641	#95	C₂³×C₇₃	1	2	yes	—
642	#95	C₂³×C₇₃	1	2	yes	—
643	#95	C₂³×C₇₃	1	2	yes	—
644	#95	C₂³×C₇₃	1	2	yes	—
645	#95	C₂³×C₇₃	1	2	yes	—
646	#95	C₂³×C₇₃	1	2	yes	—
647	#95	C₂³×C₇₃	1	1	yes	characteristic
648	#95	C₂³×C₇₃	1	1	yes	characteristic
649	#95	C₂³×C₇₃	1	2	yes	—
650	#95	C₂³×C₇₃	1	2	yes	—
651	#95	C₂³×C₇₃	1	2	yes	—
652	#95	C₂³×C₇₃	1	2	yes	—
653	#95	C₂³×C₇₃	1	1	yes	characteristic
654	#95	C₂³×C₇₃	1	1	yes	characteristic
655	#95	C₂³×C₇₃	1	1	yes	characteristic
656	#95	C₂³×C₇₃	1	1	yes	characteristic
657	#95	C₂³×C₇₃	1	1	yes	characteristic
658	#95	C₂³×C₇₃	1	2	yes	—
659	#95	C₂³×C₇₃	1	2	yes	—
660	#95	C₂³×C₇₃	1	2	yes	—
661	#95	C₂³×C₇₃	1	1	yes	characteristic
662	#95	C₂³×C₇₃	1	1	yes	characteristic
663	#95	C₂³×C₇₃	1	2	yes	—
664	#95	C₂³×C₇₃	1	1	yes	characteristic
665	#95	C₂³×C₇₃	1	1	yes	characteristic
666	#95	C₂³×C₇₃	1	2	yes	—
667	#95	C₂³×C₇₃	1	2	yes	—
668	#95	C₂³×C₇₃	1	2	yes	—
669	#95	C₂³×C₇₃	1	2	yes	—
670	#95	C₂³×C₇₃	1	2	yes	—
671	#95	C₂³×C₇₃	1	2	yes	—
672	#95	C₂³×C₇₃	1	2	yes	—
673	#95	C₂³×C₇₃	1	2	yes	—
674	#95	C₂³×C₇₃	1	2	yes	—
675	#95	C₂³×C₇₃	1	2	yes	—
676	#95	C₂³×C₇₃	1	2	yes	—
677	#95	C₂³×C₇₃	1	2	yes	—
678	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	#41×C₇₃	1	4	yes	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	#41×C₇₃	1	4	yes	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	4	1	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	2	no	—
771	C₄²	#41×C₇₃	1	4	yes	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	C₂×#41×C₇₃	1	4	yes	—
779	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
780	Q₈	—	4	4	no	—
781	D₄	—	2	8	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	8	4	no	—
843	C₂×C₄	—	8	4	no	—
844	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
845	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
846	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
847	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
848	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
849	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
850	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
859	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
860	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
861	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
862	C₂²	#585×C₇₃	1	1	yes	characteristic
863	C₂²	#585×C₇₃	1	1	yes	characteristic
864	C₂²	#585×C₇₃	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	4	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	#552×C₇₃	1	4	yes	—
887	C₂	—	4	4	no	—
888	C₂	C₂×#552×C₇₃	1	1	yes	characteristic
889	C₂	C₇₃×#3475	1	1	yes	characteristic
890	C₂	C₇₃×#3480	1	1	yes	characteristic
891	C₂	C₇₃×#3507	1	1	yes	characteristic
892	C₂	C₇₃×#3521	1	1	yes	characteristic
893	C₂	C₇₃×#3521	1	1	yes	characteristic
894	C₂	C₇₃×#3557	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂²×D₄×C₇₃	C₂³
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. C₇₃×#2787	C₂	semidirect
2. C₇₃×#2771	C₂	semidirect
3. C₇₃×#2611	C₂	semidirect
4. C₇₃×#2573	C₂	semidirect
5. C₇₃×#2515	C₂	semidirect
6. C₇₃×#2514	C₂	semidirect
7. C₇₃×#2514	C₂	semidirect
8. C₇₃×#2509	C₂	semidirect
9. C₇₃×#2508	C₂	semidirect
10. C₇₃×#2494	C₂	semidirect
11. C₇₃×#2493	C₂	semidirect
13. C₇₃×#2453	C₂	semidirect
16. C₇₃×#2370	C₂	semidirect
20. C₇₃×#2343	C₂	semidirect
21. C₄×#125×C₇₃	C₂	semidirect
22. C₇₃×#2295	C₂	semidirect
439. #59895	C₇₃	direct (N × H)
448. #2787	C₂×C₇₃	semidirect
449. #2771	C₂×C₇₃	semidirect
450. #2611	C₂×C₇₃	semidirect
451. #2573	C₂×C₇₃	semidirect
452. #2515	C₂×C₇₃	semidirect
453. #2514	C₂×C₇₃	semidirect
454. #2514	C₂×C₇₃	semidirect
455. #2509	C₂×C₇₃	semidirect
456. #2508	C₂×C₇₃	semidirect
457. #2494	C₂×C₇₃	semidirect
458. #2493	C₂×C₇₃	semidirect
460. #2453	C₂×C₇₃	semidirect
463. #2370	C₂×C₇₃	semidirect
467. #2343	C₂×C₇₃	semidirect
468. C₄×#125	C₂×C₇₃	semidirect
469. #2295	C₂×C₇₃	semidirect
471. C₇₃	#59895	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2787	2
C₇₃×#2771	2
C₇₃×#2611	2
C₇₃×#2573	2
C₇₃×#2515	2
C₇₃×#2514	2
C₇₃×#2509	2
C₇₃×#2508	2
C₇₃×#2494	2
C₇₃×#2493	2
C₇₃×#2454	2
C₇₃×#2453	2
C₇₃×#2447	2
C₇₃×#2370	2
C₇₃×#2367	2
C₇₃×#2357	2
C₇₃×#2349	2
C₇₃×#2343	2
C₄×#125×C₇₃	2
C₇₃×#2295	2
C₇₃×#2293	2
#59895	73

Subgroups — C73×#59895 #32969299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59895 #32969299