Subgroups — C₇₃×#59645 #32969049

Order 18688.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2798	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2797	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2597	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2595	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2557	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2540	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#2517	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2513	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2504	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2499	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2489	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2374	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#123×C₇₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
38	#400×C₇₃	C₂²	1	2	yes	—
39	#400×C₇₃	C₂²	1	2	yes	—
40	#399×C₇₃	C₂²	1	2	yes	—
41	#397×C₇₃	C₂²	1	2	yes	—
42	#397×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	#397×C₇₃	C₂²	1	2	yes	—
48	#397×C₇₃	C₂²	1	2	yes	—
49	#397×C₇₃	C₂²	1	2	yes	—
50	#394×C₇₃	C₂²	1	2	yes	—
51	#394×C₇₃	C₂²	1	2	yes	—
52	#393×C₇₃	C₂²	1	2	yes	—
53	#392×C₇₃	C₂²	1	2	yes	—
54	#391×C₇₃	C₂²	1	1	yes	characteristic
55	#391×C₇₃	C₂²	1	1	yes	characteristic
56	#391×C₇₃	C₂²	1	1	yes	characteristic
57	#391×C₇₃	C₂²	1	1	yes	characteristic
58	#391×C₇₃	C₂²	1	2	yes	—
59	#390×C₇₃	C₂²	1	1	yes	characteristic
60	#390×C₇₃	C₂²	1	2	yes	—
61	#390×C₇₃	C₂²	1	1	yes	characteristic
62	#390×C₇₃	C₂²	1	1	yes	characteristic
63	#390×C₇₃	C₂²	1	2	yes	—
64	#390×C₇₃	C₂²	1	2	yes	—
65	#390×C₇₃	C₂²	1	2	yes	—
66	#390×C₇₃	C₂²	1	1	yes	characteristic
67	#389×C₇₃	C₂²	1	2	yes	—
68	#389×C₇₃	C₂²	1	1	yes	characteristic
69	#389×C₇₃	C₂²	1	1	yes	characteristic
70	#388×C₇₃	C₂²	1	2	yes	—
71	#388×C₇₃	C₂²	1	2	yes	—
72	#388×C₇₃	C₂²	1	1	yes	characteristic
73	#388×C₇₃	C₂²	1	2	yes	—
74	#388×C₇₃	C₂²	1	2	yes	—
75	#388×C₇₃	C₂²	1	2	yes	—
76	#388×C₇₃	C₂²	1	2	yes	—
77	#388×C₇₃	C₂²	1	2	yes	—
78	#388×C₇₃	C₂²	1	2	yes	—
79	#388×C₇₃	C₂²	1	1	yes	characteristic
80	#388×C₇₃	C₂²	1	1	yes	characteristic
81	#388×C₇₃	C₂²	1	1	yes	characteristic
82	#388×C₇₃	C₂²	1	2	yes	—
83	#387×C₇₃	C₂²	1	2	yes	—
84	#387×C₇₃	C₂²	1	2	yes	—
85	#387×C₇₃	C₂²	1	2	yes	—
86	#387×C₇₃	C₂²	1	2	yes	—
87	#387×C₇₃	C₂²	1	2	yes	—
88	#387×C₇₃	C₂²	1	2	yes	—
89	#387×C₇₃	C₂²	1	2	yes	—
90	#387×C₇₃	C₂²	1	2	yes	—
91	#387×C₇₃	C₂²	1	2	yes	—
92	#386×C₇₃	C₂²	1	2	yes	—
93	#386×C₇₃	C₂²	1	2	yes	—
94	#386×C₇₃	C₂²	1	2	yes	—
95	#386×C₇₃	C₂²	1	2	yes	—
96	#385×C₇₃	C₂²	1	2	yes	—
97	#385×C₇₃	C₂²	1	2	yes	—
98	#384×C₇₃	C₂²	1	1	yes	characteristic
99	#382×C₇₃	C₂²	1	2	yes	—
100	#382×C₇₃	C₂²	1	1	yes	characteristic
101	#382×C₇₃	C₂²	1	1	yes	characteristic
102	#382×C₇₃	C₂²	1	1	yes	characteristic
103	#382×C₇₃	C₂²	1	1	yes	characteristic
104	#380×C₇₃	C₂²	1	1	yes	characteristic
105	#380×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	2	yes	—
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	2	yes	—
113	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊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	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
122	C₄³×C₇₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
133	#125×C₇₃	—	2	4	no	—
134	#124×C₇₃	—	2	4	no	—
135	#124×C₇₃	—	2	4	no	—
136	#123×C₇₃	—	2	8	no	—
137	C₂²⋊Q₈×C₇₃	—	2	4	no	—
138	C₂²⋊Q₈×C₇₃	—	4	2	no	—
139	#121×C₇₃	—	2	4	no	—
140	#121×C₇₃	—	4	2	no	—
141	C₄×Q₈×C₇₃	—	2	4	no	—
142	C₄×Q₈×C₇₃	—	4	2	no	—
143	C₄×D₄×C₇₃	—	2	4	no	—
144	C₄×D₄×C₇₃	—	4	2	no	—
145	#117×C₇₃	—	4	2	no	—
146	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
165	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×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	2	yes	—
212	#95×C₇₃	C₂³	1	1	yes	characteristic
213	#95×C₇₃	C₂³	1	1	yes	characteristic
214	#95×C₇₃	C₂³	1	2	yes	—
215	#95×C₇₃	C₂³	1	1	yes	characteristic
216	#95×C₇₃	C₂³	1	2	yes	—
217	#95×C₇₃	C₂³	1	1	yes	characteristic
218	#95×C₇₃	C₂³	1	2	yes	—
219	#95×C₇₃	C₂³	1	2	yes	—
220	#95×C₇₃	C₂³	1	1	yes	characteristic
221	#95×C₇₃	C₂³	1	1	yes	characteristic
222	#95×C₇₃	C₂³	1	1	yes	characteristic
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	#95×C₇₃	C₂³	1	2	yes	—
231	#95×C₇₃	C₂³	1	2	yes	—
232	#95×C₇₃	C₂³	1	2	yes	—
233	#95×C₇₃	C₂³	1	2	yes	—
234	#95×C₇₃	C₂³	1	2	yes	—
235	#95×C₇₃	C₂³	1	2	yes	—
236	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
237	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₇₃	—	2	2	no	—
240	C₂×Q₈×C₇₃	—	2	2	no	—
241	C₂×Q₈×C₇₃	—	2	2	no	—
242	C₂×Q₈×C₇₃	—	2	2	no	—
243	C₂×Q₈×C₇₃	—	2	2	no	—
244	C₂×Q₈×C₇₃	—	4	1	no	—
245	C₂×D₄×C₇₃	—	2	2	no	—
246	C₂×D₄×C₇₃	—	2	4	no	—
247	C₂×D₄×C₇₃	—	2	2	no	—
248	C₂×D₄×C₇₃	—	2	2	no	—
249	C₂×D₄×C₇₃	—	2	2	no	—
250	C₂×D₄×C₇₃	—	2	4	no	—
251	C₂×D₄×C₇₃	—	2	2	no	—
252	C₂×D₄×C₇₃	—	4	1	no	—
253	C₂×D₄×C₇₃	—	4	2	no	—
254	C₂×D₄×C₇₃	—	4	2	no	—
255	C₂×D₄×C₇₃	—	4	2	no	—
256	C₂×D₄×C₇₃	—	4	2	no	—
257	C₂²×C₄×C₇₃	—	2	2	no	—
258	C₂²×C₄×C₇₃	—	2	2	no	—
259	C₂²×C₄×C₇₃	—	2	2	no	—
260	C₂²×C₄×C₇₃	—	2	2	no	—
261	C₂²×C₄×C₇₃	—	2	2	no	—
262	C₂²×C₄×C₇₃	—	2	2	no	—
263	C₂²×C₄×C₇₃	—	2	4	no	—
264	C₂²×C₄×C₇₃	—	4	2	no	—
265	C₂²×C₄×C₇₃	—	4	2	no	—
266	C₂²×C₄×C₇₃	—	4	2	no	—
267	C₂²×C₄×C₇₃	—	4	2	no	—
268	C₂²×C₄×C₇₃	—	4	2	no	—
269	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₇₃	—	2	2	no	—
290	C₄⋊C₄×C₇₃	—	2	2	no	—
291	C₄⋊C₄×C₇₃	—	2	2	no	—
292	C₄⋊C₄×C₇₃	—	2	2	no	—
293	C₄⋊C₄×C₇₃	—	2	4	no	—
294	C₄⋊C₄×C₇₃	—	2	4	no	—
295	C₄⋊C₄×C₇₃	—	2	4	no	—
296	C₄⋊C₄×C₇₃	—	2	4	no	—
297	C₄⋊C₄×C₇₃	—	2	4	no	—
298	C₄⋊C₄×C₇₃	—	2	2	no	—
299	C₄⋊C₄×C₇₃	—	2	2	no	—
300	C₄⋊C₄×C₇₃	—	2	2	no	—
301	C₄⋊C₄×C₇₃	—	2	2	no	—
302	C₄⋊C₄×C₇₃	—	2	2	no	—
303	C₄⋊C₄×C₇₃	—	4	2	no	—
304	C₄⋊C₄×C₇₃	—	4	2	no	—
305	C₄⋊C₄×C₇₃	—	4	2	no	—
306	C₄⋊C₄×C₇₃	—	4	2	no	—
307	C₄⋊C₄×C₇₃	—	4	2	no	—
308	C₄⋊C₄×C₇₃	#41	1	4	yes	—
309	C₂²⋊C₄×C₇₃	—	2	4	no	—
310	C₂²⋊C₄×C₇₃	—	2	2	no	—
311	C₂²⋊C₄×C₇₃	—	2	2	no	—
312	C₂²⋊C₄×C₇₃	—	2	2	no	—
313	C₂²⋊C₄×C₇₃	—	2	4	no	—
314	C₂²⋊C₄×C₇₃	—	2	4	no	—
315	C₂²⋊C₄×C₇₃	—	2	4	no	—
316	C₂²⋊C₄×C₇₃	—	2	2	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	4	no	—
319	C₂²⋊C₄×C₇₃	—	2	4	no	—
320	C₂²⋊C₄×C₇₃	—	4	1	no	—
321	C₂²⋊C₄×C₇₃	—	4	2	no	—
322	C₂²⋊C₄×C₇₃	—	4	1	no	—
323	C₂²⋊C₄×C₇₃	—	4	1	no	—
324	C₂²⋊C₄×C₇₃	—	4	2	no	—
325	C₂²⋊C₄×C₇₃	—	4	2	no	—
326	C₂²⋊C₄×C₇₃	—	4	2	no	—
327	C₂²⋊C₄×C₇₃	—	4	1	no	—
328	C₂²⋊C₄×C₇₃	—	4	2	no	—
329	C₂²⋊C₄×C₇₃	—	4	2	no	—
330	C₂²⋊C₄×C₇₃	—	4	2	no	—
331	C₂²⋊C₄×C₇₃	—	4	2	no	—
332	C₂²⋊C₄×C₇₃	—	4	2	no	—
333	C₂²⋊C₄×C₇₃	—	4	2	no	—
334	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
335	C₄²×C₇₃	—	2	2	no	—
336	C₄²×C₇₃	—	2	2	no	—
337	C₄²×C₇₃	—	2	2	no	—
338	C₄²×C₇₃	—	2	2	no	—
339	C₄²×C₇₃	—	2	2	no	—
340	C₄²×C₇₃	—	4	2	no	—
341	C₄²×C₇₃	—	4	1	no	—
342	C₄²×C₇₃	—	4	1	no	—
343	C₄²×C₇₃	—	4	2	no	—
344	C₄²×C₇₃	—	4	2	no	—
345	C₄²×C₇₃	—	4	2	no	—
346	C₄²×C₇₃	—	4	1	no	—
347	C₄²×C₇₃	—	4	2	no	—
348	C₄²×C₇₃	—	4	2	no	—
349	C₄²×C₇₃	#41	1	4	yes	—
350	C₂³×C₇₃	—	2	1	no	—
351	C₂³×C₇₃	—	2	1	no	—
352	C₂³×C₇₃	—	2	1	no	—
353	C₂³×C₇₃	—	2	1	no	—
354	C₂³×C₇₃	—	2	1	no	—
355	C₂³×C₇₃	—	2	1	no	—
356	C₂³×C₇₃	—	2	1	no	—
357	C₂³×C₇₃	—	2	2	no	—
358	C₂³×C₇₃	—	2	1	no	—
359	C₂³×C₇₃	—	2	2	no	—
360	C₂³×C₇₃	—	2	2	no	—
361	C₂³×C₇₃	—	2	1	no	—
362	C₂³×C₇₃	—	2	1	no	—
363	C₂³×C₇₃	—	2	2	no	—
364	C₂³×C₇₃	—	2	1	no	—
365	C₂³×C₇₃	—	2	2	no	—
366	C₂³×C₇₃	—	2	2	no	—
367	C₂³×C₇₃	—	2	1	no	—
368	C₂³×C₇₃	—	2	2	no	—
369	C₂³×C₇₃	—	2	1	no	—
370	C₂³×C₇₃	C₂×#41	1	2	yes	—
371	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
372	Q₈×C₇₃	—	4	4	no	—
373	Q₈×C₇₃	—	4	4	no	—
374	D₄×C₇₃	—	4	4	no	—
375	D₄×C₇₃	—	4	4	no	—
376	D₄×C₇₃	—	8	4	no	—
377	D₄×C₇₃	—	8	4	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	1	no	—
382	C₂×C₄×C₇₃	—	2	1	no	—
383	C₂×C₄×C₇₃	—	2	2	no	—
384	C₂×C₄×C₇₃	—	2	1	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	1	no	—
387	C₂×C₄×C₇₃	—	2	1	no	—
388	C₂×C₄×C₇₃	—	2	1	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	—	2	1	no	—
394	C₂×C₄×C₇₃	—	2	2	no	—
395	C₂×C₄×C₇₃	—	2	1	no	—
396	C₂×C₄×C₇₃	—	2	1	no	—
397	C₂×C₄×C₇₃	—	2	2	no	—
398	C₂×C₄×C₇₃	—	2	1	no	—
399	C₂×C₄×C₇₃	—	2	1	no	—
400	C₂×C₄×C₇₃	—	2	2	no	—
401	C₂×C₄×C₇₃	—	2	2	no	—
402	C₂×C₄×C₇₃	—	2	2	no	—
403	C₂×C₄×C₇₃	—	2	1	no	—
404	C₂×C₄×C₇₃	—	2	2	no	—
405	C₂×C₄×C₇₃	—	2	1	no	—
406	C₂×C₄×C₇₃	—	2	1	no	—
407	C₂×C₄×C₇₃	—	2	2	no	—
408	C₂×C₄×C₇₃	—	2	2	no	—
409	C₂×C₄×C₇₃	—	2	2	no	—
410	C₂×C₄×C₇₃	—	2	2	no	—
411	C₂×C₄×C₇₃	—	2	2	no	—
412	C₂×C₄×C₇₃	—	2	1	no	—
413	C₂×C₄×C₇₃	—	2	1	no	—
414	C₂×C₄×C₇₃	—	2	1	no	—
415	C₂×C₄×C₇₃	—	2	2	no	—
416	C₂×C₄×C₇₃	—	2	1	no	—
417	C₂×C₄×C₇₃	—	2	1	no	—
418	C₂×C₄×C₇₃	—	2	1	no	—
419	C₂×C₄×C₇₃	—	2	2	no	—
420	C₂×C₄×C₇₃	—	2	2	no	—
421	C₂×C₄×C₇₃	—	2	1	no	—
422	C₂×C₄×C₇₃	—	2	2	no	—
423	C₂×C₄×C₇₃	—	2	2	no	—
424	C₂×C₄×C₇₃	—	2	1	no	—
425	C₂×C₄×C₇₃	—	2	1	no	—
426	C₂×C₄×C₇₃	—	2	2	no	—
427	C₂×C₄×C₇₃	—	2	1	no	—
428	C₂×C₄×C₇₃	—	2	1	no	—
429	C₂×C₄×C₇₃	—	2	2	no	—
430	C₂×C₄×C₇₃	—	4	4	no	—
431	C₂×C₄×C₇₃	—	4	4	no	—
432	C₂×C₄×C₇₃	—	8	4	no	—
433	C₂×C₄×C₇₃	—	8	4	no	—
434	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
435	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
437	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
439	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
442	C₂²×C₇₃	—	2	2	no	—
443	C₂²×C₇₃	—	2	2	no	—
444	C₂²×C₇₃	—	2	2	no	—
445	C₂²×C₇₃	—	4	1	no	—
446	C₂²×C₇₃	—	4	1	no	—
447	C₂²×C₇₃	—	4	1	no	—
448	C₂²×C₇₃	—	4	1	no	—
449	C₂²×C₇₃	—	4	1	no	—
450	C₂²×C₇₃	—	4	2	no	—
451	C₂²×C₇₃	—	4	1	no	—
452	C₂²×C₇₃	—	4	2	no	—
453	C₂²×C₇₃	—	4	1	no	—
454	C₂²×C₇₃	—	4	2	no	—
455	C₂²×C₇₃	—	4	2	no	—
456	C₂²×C₇₃	—	4	1	no	—
457	C₂²×C₇₃	—	4	2	no	—
458	C₂²×C₇₃	—	4	1	no	—
459	C₂²×C₇₃	—	4	1	no	—
460	C₂²×C₇₃	—	4	2	no	—
461	C₂²×C₇₃	—	4	1	no	—
462	C₂²×C₇₃	—	4	2	no	—
463	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
464	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
466	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²×C₇₃	#585	1	1	yes	characteristic
468	C₂²×C₇₃	#585	1	1	yes	characteristic
469	C₂²×C₇₃	#585	1	1	yes	characteristic
470	C₄×C₇₃	—	2	2	no	—
471	C₄×C₇₃	—	2	2	no	—
472	C₄×C₇₃	—	2	2	no	—
473	C₄×C₇₃	—	2	2	no	—
474	C₄×C₇₃	—	2	4	no	—
475	C₄×C₇₃	—	4	1	no	—
476	C₄×C₇₃	—	4	1	no	—
477	C₄×C₇₃	—	4	1	no	—
478	C₄×C₇₃	—	4	2	no	—
479	C₄×C₇₃	—	4	1	no	—
480	C₄×C₇₃	—	4	2	no	—
481	C₄×C₇₃	—	4	1	no	—
482	C₄×C₇₃	—	4	1	no	—
483	C₄×C₇₃	—	4	2	no	—
484	C₄×C₇₃	—	4	2	no	—
485	C₄×C₇₃	—	4	1	no	—
486	C₄×C₇₃	—	4	1	no	—
487	C₄×C₇₃	—	4	2	no	—
488	C₄×C₇₃	—	4	2	no	—
489	C₄×C₇₃	#559	1	4	yes	—
490	#59645	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂×C₇₃	—	4	2	no	—
492	C₂×C₇₃	—	8	1	no	—
493	C₂×C₇₃	—	8	2	no	—
494	C₂×C₇₃	#3475	1	1	yes	characteristic
495	C₂×C₇₃	C₂×#559	1	1	yes	characteristic
496	C₂×C₇₃	#3480	1	1	yes	characteristic
497	C₂×C₇₃	#3512	1	1	yes	characteristic
498	C₂×C₇₃	#3514	1	1	yes	characteristic
499	C₂×C₇₃	#3521	1	1	yes	characteristic
500	C₂×C₇₃	#3562	1	1	yes	characteristic
501	#2798	C₂×C₇₃	1	2	yes	complemented
502	#2797	C₂×C₇₃	1	2	yes	complemented
503	#2597	C₂×C₇₃	1	2	yes	complemented
504	#2595	C₂×C₇₃	1	2	yes	complemented
505	#2592	C₂×C₇₃	1	1	yes	characteristic, complemented
506	#2557	C₂×C₇₃	1	2	yes	complemented
507	#2540	C₂×C₇₃	1	1	yes	characteristic
508	#2517	C₂×C₇₃	1	2	yes	complemented
509	#2513	C₂×C₇₃	1	2	yes	complemented
510	#2504	C₂×C₇₃	1	1	yes	characteristic, complemented
511	#2499	C₂×C₇₃	1	1	yes	characteristic, complemented
512	#2490	C₂×C₇₃	1	1	yes	characteristic, complemented
513	#2489	C₂×C₇₃	1	1	yes	characteristic, complemented
514	#2422	C₂×C₇₃	1	1	yes	characteristic, complemented
515	#2421	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#2374	C₂×C₇₃	1	2	yes	complemented
517	#2363	C₂×C₇₃	1	1	yes	characteristic, complemented
518	#2360	C₂×C₇₃	1	1	yes	characteristic, complemented
519	#2355	C₂×C₇₃	1	1	yes	characteristic, complemented
520	#2352	C₂×C₇₃	1	1	yes	characteristic, complemented
521	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
522	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
523	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
524	C₇₃	#59645	1	1	yes	characteristic, direct product factor, Sylow
525	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
526	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
527	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
528	C₂×#123	C₂²×C₇₃	1	2	yes	—
529	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
530	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
531	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
532	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
533	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
534	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
535	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
536	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
537	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
538	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
539	#400	C₂²×C₇₃	1	2	yes	—
540	#400	C₂²×C₇₃	1	2	yes	—
541	#399	C₂²×C₇₃	1	2	yes	—
542	#397	C₂²×C₇₃	1	2	yes	—
543	#397	C₂²×C₇₃	1	2	yes	—
544	#397	C₂²×C₇₃	1	2	yes	—
545	#397	C₂²×C₇₃	1	2	yes	—
546	#397	C₂²×C₇₃	1	2	yes	—
547	#397	C₂²×C₇₃	1	2	yes	—
548	#397	C₂²×C₇₃	1	2	yes	—
549	#397	C₂²×C₇₃	1	2	yes	—
550	#397	C₂²×C₇₃	1	2	yes	—
551	#394	C₂²×C₇₃	1	2	yes	—
552	#394	C₂²×C₇₃	1	2	yes	—
553	#393	C₂²×C₇₃	1	2	yes	—
554	#392	C₂²×C₇₃	1	2	yes	—
555	#391	C₂²×C₇₃	1	1	yes	characteristic
556	#391	C₂²×C₇₃	1	1	yes	characteristic
557	#391	C₂²×C₇₃	1	2	yes	—
558	#391	C₂²×C₇₃	1	1	yes	characteristic
559	#391	C₂²×C₇₃	1	1	yes	characteristic
560	#390	C₂²×C₇₃	1	1	yes	characteristic
561	#390	C₂²×C₇₃	1	1	yes	characteristic
562	#390	C₂²×C₇₃	1	2	yes	—
563	#390	C₂²×C₇₃	1	2	yes	—
564	#390	C₂²×C₇₃	1	2	yes	—
565	#390	C₂²×C₇₃	1	1	yes	characteristic
566	#390	C₂²×C₇₃	1	2	yes	—
567	#390	C₂²×C₇₃	1	1	yes	characteristic
568	#389	C₂²×C₇₃	1	1	yes	characteristic
569	#389	C₂²×C₇₃	1	1	yes	characteristic
570	#389	C₂²×C₇₃	1	2	yes	—
571	#388	C₂²×C₇₃	1	2	yes	—
572	#388	C₂²×C₇₃	1	2	yes	—
573	#388	C₂²×C₇₃	1	1	yes	characteristic
574	#388	C₂²×C₇₃	1	2	yes	—
575	#388	C₂²×C₇₃	1	2	yes	—
576	#388	C₂²×C₇₃	1	1	yes	characteristic
577	#388	C₂²×C₇₃	1	2	yes	—
578	#388	C₂²×C₇₃	1	2	yes	—
579	#388	C₂²×C₇₃	1	1	yes	characteristic
580	#388	C₂²×C₇₃	1	2	yes	—
581	#388	C₂²×C₇₃	1	2	yes	—
582	#388	C₂²×C₇₃	1	1	yes	characteristic
583	#388	C₂²×C₇₃	1	2	yes	—
584	#387	C₂²×C₇₃	1	2	yes	—
585	#387	C₂²×C₇₃	1	2	yes	—
586	#387	C₂²×C₇₃	1	2	yes	—
587	#387	C₂²×C₇₃	1	2	yes	—
588	#387	C₂²×C₇₃	1	2	yes	—
589	#387	C₂²×C₇₃	1	2	yes	—
590	#387	C₂²×C₇₃	1	2	yes	—
591	#387	C₂²×C₇₃	1	2	yes	—
592	#387	C₂²×C₇₃	1	2	yes	—
593	#386	C₂²×C₇₃	1	2	yes	—
594	#386	C₂²×C₇₃	1	2	yes	—
595	#386	C₂²×C₇₃	1	2	yes	—
596	#386	C₂²×C₇₃	1	2	yes	—
597	#385	C₂²×C₇₃	1	2	yes	—
598	#385	C₂²×C₇₃	1	2	yes	—
599	#384	C₂²×C₇₃	1	1	yes	characteristic
600	#382	C₂²×C₇₃	1	1	yes	characteristic
601	#382	C₂²×C₇₃	1	1	yes	characteristic
602	#382	C₂²×C₇₃	1	1	yes	characteristic
603	#382	C₂²×C₇₃	1	2	yes	—
604	#382	C₂²×C₇₃	1	1	yes	characteristic
605	#380	C₂²×C₇₃	1	1	yes	characteristic
606	#380	C₂²×C₇₃	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
609	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
610	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
611	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
612	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
614	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
615	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
616	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
617	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
618	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
619	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
620	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
621	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
622	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
623	C₄³	C₂²×C₇₃	1	1	yes	characteristic
624	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
625	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
626	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
629	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
630	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
633	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
634	#125	—	2	4	no	—
635	#124	—	2	4	no	—
636	#124	—	2	4	no	—
637	#123	—	2	8	no	—
638	C₂²⋊Q₈	—	2	4	no	—
639	C₂²⋊Q₈	—	4	2	no	—
640	#121	—	2	4	no	—
641	#121	—	4	2	no	—
642	C₄×Q₈	—	2	4	no	—
643	C₄×Q₈	—	4	2	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	4	2	no	—
646	#117	—	4	2	no	—
647	C₂×C₄⋊C₄	—	4	2	no	—
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
700	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
701	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
706	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
707	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
708	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
709	#95	C₂³×C₇₃	1	1	yes	characteristic
710	#95	C₂³×C₇₃	1	2	yes	—
711	#95	C₂³×C₇₃	1	2	yes	—
712	#95	C₂³×C₇₃	1	2	yes	—
713	#95	C₂³×C₇₃	1	1	yes	characteristic
714	#95	C₂³×C₇₃	1	1	yes	characteristic
715	#95	C₂³×C₇₃	1	2	yes	—
716	#95	C₂³×C₇₃	1	1	yes	characteristic
717	#95	C₂³×C₇₃	1	2	yes	—
718	#95	C₂³×C₇₃	1	1	yes	characteristic
719	#95	C₂³×C₇₃	1	2	yes	—
720	#95	C₂³×C₇₃	1	2	yes	—
721	#95	C₂³×C₇₃	1	1	yes	characteristic
722	#95	C₂³×C₇₃	1	1	yes	characteristic
723	#95	C₂³×C₇₃	1	1	yes	characteristic
724	#95	C₂³×C₇₃	1	2	yes	—
725	#95	C₂³×C₇₃	1	2	yes	—
726	#95	C₂³×C₇₃	1	2	yes	—
727	#95	C₂³×C₇₃	1	2	yes	—
728	#95	C₂³×C₇₃	1	2	yes	—
729	#95	C₂³×C₇₃	1	2	yes	—
730	#95	C₂³×C₇₃	1	2	yes	—
731	#95	C₂³×C₇₃	1	2	yes	—
732	#95	C₂³×C₇₃	1	2	yes	—
733	#95	C₂³×C₇₃	1	2	yes	—
734	#95	C₂³×C₇₃	1	2	yes	—
735	#95	C₂³×C₇₃	1	2	yes	—
736	#95	C₂³×C₇₃	1	2	yes	—
737	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
738	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
739	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	4	1	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	#41×C₇₃	1	4	yes	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	4	1	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	1	no	—
824	C₂²⋊C₄	—	4	1	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	1	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	#41×C₇₃	1	4	yes	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	2	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	1	no	—
848	C₄²	—	4	2	no	—
849	C₄²	—	4	2	no	—
850	C₄²	#41×C₇₃	1	4	yes	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	1	no	—
871	C₂³	C₂×#41×C₇₃	1	2	yes	—
872	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
873	Q₈	—	4	4	no	—
874	Q₈	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	8	4	no	—
878	D₄	—	8	4	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	8	4	no	—
934	C₂×C₄	—	8	4	no	—
935	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
936	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
937	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
938	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
939	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
940	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
941	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
942	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	2	no	—
964	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
965	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
966	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
967	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
968	C₂²	#585×C₇₃	1	1	yes	characteristic
969	C₂²	#585×C₇₃	1	1	yes	characteristic
970	C₂²	#585×C₇₃	1	1	yes	characteristic
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	4	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	#559×C₇₃	1	4	yes	—
991	C₂	—	4	2	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₇₃×#3475	1	1	yes	characteristic
995	C₂	C₂×#559×C₇₃	1	1	yes	characteristic
996	C₂	C₇₃×#3480	1	1	yes	characteristic
997	C₂	C₇₃×#3512	1	1	yes	characteristic
998	C₂	C₇₃×#3514	1	1	yes	characteristic
999	C₂	C₇₃×#3521	1	1	yes	characteristic
1000	C₂	C₇₃×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2540	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. C₇₃×#2798	C₂	semidirect
2. C₇₃×#2797	C₂	semidirect
3. C₇₃×#2597	C₂	semidirect
4. C₇₃×#2595	C₂	semidirect
5. C₇₃×#2592	C₂	semidirect
6. C₇₃×#2557	C₂	semidirect
8. C₇₃×#2517	C₂	semidirect
9. C₇₃×#2513	C₂	semidirect
10. C₇₃×#2504	C₂	semidirect
11. C₇₃×#2499	C₂	semidirect
12. C₇₃×#2490	C₂	semidirect
13. C₇₃×#2489	C₂	semidirect
14. C₇₃×#2422	C₂	semidirect
15. C₇₃×#2421	C₂	semidirect
16. C₇₃×#2374	C₂	semidirect
17. C₇₃×#2363	C₂	semidirect
18. C₇₃×#2360	C₂	semidirect
19. C₇₃×#2355	C₂	semidirect
20. C₇₃×#2352	C₂	semidirect
21. C₄×#125×C₇₃	C₂	semidirect
22. C₄×#124×C₇₃	C₂	semidirect
23. C₄×#124×C₇₃	C₂	semidirect
490. #59645	C₇₃	direct (N × H)
501. #2798	C₂×C₇₃	semidirect
502. #2797	C₂×C₇₃	semidirect
503. #2597	C₂×C₇₃	semidirect
504. #2595	C₂×C₇₃	semidirect
505. #2592	C₂×C₇₃	semidirect
506. #2557	C₂×C₇₃	semidirect
508. #2517	C₂×C₇₃	semidirect
509. #2513	C₂×C₇₃	semidirect
510. #2504	C₂×C₇₃	semidirect
511. #2499	C₂×C₇₃	semidirect
512. #2490	C₂×C₇₃	semidirect
513. #2489	C₂×C₇₃	semidirect
514. #2422	C₂×C₇₃	semidirect
515. #2421	C₂×C₇₃	semidirect
516. #2374	C₂×C₇₃	semidirect
517. #2363	C₂×C₇₃	semidirect
518. #2360	C₂×C₇₃	semidirect
519. #2355	C₂×C₇₃	semidirect
520. #2352	C₂×C₇₃	semidirect
521. C₄×#125	C₂×C₇₃	semidirect
522. C₄×#124	C₂×C₇₃	semidirect
523. C₄×#124	C₂×C₇₃	semidirect
524. C₇₃	#59645	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×#2798	2
C₇₃×#2797	2
C₇₃×#2597	2
C₇₃×#2595	2
C₇₃×#2592	2
C₇₃×#2557	2
C₇₃×#2540	2
C₇₃×#2517	2
C₇₃×#2513	2
C₇₃×#2504	2
C₇₃×#2499	2
C₇₃×#2490	2
C₇₃×#2489	2
C₇₃×#2422	2
C₇₃×#2421	2
C₇₃×#2374	2
C₇₃×#2363	2
C₇₃×#2360	2
C₇₃×#2355	2
C₇₃×#2352	2
C₄×#125×C₇₃	2
C₄×#124×C₇₃	2
#59645	73

Subgroups — C73×#59645 #32969049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59645 #32969049