Subgroups — C₇₃×#59868 #32969272

Order 18688.

1674 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2802	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2774	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2585	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2583	C₂	1	2	yes	maximal
6	C₇₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2509	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2505	C₂	1	2	yes	maximal
11	C₇₃×#2505	C₂	1	2	yes	maximal
12	C₇₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2442	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2442	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic
18	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₃×#2345	C₂	1	2	yes	maximal
21	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
22	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
23	C₂×#389×C₇₃	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×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
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	#400×C₇₃	C₂²	1	2	yes	—
41	#400×C₇₃	C₂²	1	2	yes	—
42	#400×C₇₃	C₂²	1	2	yes	—
43	#400×C₇₃	C₂²	1	2	yes	—
44	#398×C₇₃	C₂²	1	2	yes	—
45	#398×C₇₃	C₂²	1	2	yes	—
46	#398×C₇₃	C₂²	1	2	yes	—
47	#398×C₇₃	C₂²	1	2	yes	—
48	#398×C₇₃	C₂²	1	2	yes	—
49	#398×C₇₃	C₂²	1	2	yes	—
50	#395×C₇₃	C₂²	1	2	yes	—
51	#395×C₇₃	C₂²	1	2	yes	—
52	#391×C₇₃	C₂²	1	1	yes	characteristic
53	#391×C₇₃	C₂²	1	1	yes	characteristic
54	#391×C₇₃	C₂²	1	1	yes	characteristic
55	#391×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	1	yes	characteristic
59	#389×C₇₃	C₂²	1	1	yes	characteristic
60	#389×C₇₃	C₂²	1	1	yes	characteristic
61	#389×C₇₃	C₂²	1	2	yes	—
62	#389×C₇₃	C₂²	1	1	yes	characteristic
63	#389×C₇₃	C₂²	1	2	yes	—
64	#389×C₇₃	C₂²	1	2	yes	—
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	#389×C₇₃	C₂²	1	2	yes	—
70	#389×C₇₃	C₂²	1	2	yes	—
71	#389×C₇₃	C₂²	1	2	yes	—
72	#389×C₇₃	C₂²	1	2	yes	—
73	#389×C₇₃	C₂²	1	2	yes	—
74	#389×C₇₃	C₂²	1	1	yes	characteristic
75	#389×C₇₃	C₂²	1	2	yes	—
76	#389×C₇₃	C₂²	1	1	yes	characteristic
77	#389×C₇₃	C₂²	1	2	yes	—
78	#389×C₇₃	C₂²	1	1	yes	characteristic
79	#389×C₇₃	C₂²	1	2	yes	—
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	2	yes	—
85	#387×C₇₃	C₂²	1	2	yes	—
86	#387×C₇₃	C₂²	1	1	yes	characteristic
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	#387×C₇₃	C₂²	1	1	yes	characteristic
93	#385×C₇₃	C₂²	1	2	yes	—
94	#385×C₇₃	C₂²	1	2	yes	—
95	#385×C₇₃	C₂²	1	1	yes	characteristic
96	#385×C₇₃	C₂²	1	1	yes	characteristic
97	#385×C₇₃	C₂²	1	2	yes	—
98	#385×C₇₃	C₂²	1	2	yes	—
99	#385×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	2	yes	—
103	#382×C₇₃	C₂²	1	2	yes	—
104	#380×C₇₃	C₂²	1	1	yes	characteristic
105	#380×C₇₃	C₂²	1	2	yes	—
106	#380×C₇₃	C₂²	1	2	yes	—
107	#380×C₇₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊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	C₂×#95×C₇₃	C₂²	1	2	yes	—
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
130	#125×C₇₃	—	2	4	no	—
131	#125×C₇₃	—	4	2	no	—
132	C₂²⋊Q₈×C₇₃	—	2	4	no	—
133	C₂²⋊Q₈×C₇₃	Q₈	1	8	yes	complemented
134	C₄×Q₈×C₇₃	—	2	4	no	—
135	C₄×Q₈×C₇₃	—	4	2	no	—
136	C₄×Q₈×C₇₃	—	4	2	no	—
137	C₄×Q₈×C₇₃	—	4	2	no	—
138	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
139	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
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	2	yes	—
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	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	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	2	yes	—
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
167	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₇₃	—	4	2	no	—
185	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
199	#95×C₇₃	C₂³	1	1	yes	characteristic
200	#95×C₇₃	C₂³	1	2	yes	—
201	#95×C₇₃	C₂³	1	1	yes	characteristic
202	#95×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
209	#95×C₇₃	C₂³	1	1	yes	characteristic
210	#95×C₇₃	C₂³	1	1	yes	characteristic
211	#95×C₇₃	C₂³	1	2	yes	—
212	#95×C₇₃	C₂³	1	2	yes	—
213	#95×C₇₃	C₂³	1	2	yes	—
214	#95×C₇₃	C₂³	1	1	yes	characteristic
215	#95×C₇₃	C₂³	1	1	yes	characteristic
216	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	#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	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
235	C₂×Q₈×C₇₃	—	2	2	no	—
236	C₂×Q₈×C₇₃	—	2	2	no	—
237	C₂×Q₈×C₇₃	—	2	2	no	—
238	C₂×Q₈×C₇₃	—	4	1	no	—
239	C₂×Q₈×C₇₃	—	4	1	no	—
240	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	—
241	C₂²×C₄×C₇₃	—	2	2	no	—
242	C₂²×C₄×C₇₃	—	2	2	no	—
243	C₂²×C₄×C₇₃	—	2	4	no	—
244	C₂²×C₄×C₇₃	—	2	2	no	—
245	C₂²×C₄×C₇₃	—	2	4	no	—
246	C₂²×C₄×C₇₃	—	2	4	no	—
247	C₂²×C₄×C₇₃	—	4	1	no	—
248	C₂²×C₄×C₇₃	—	4	1	no	—
249	C₂²×C₄×C₇₃	—	4	1	no	—
250	C₂²×C₄×C₇₃	—	4	2	no	—
251	C₂²×C₄×C₇₃	—	4	1	no	—
252	C₂²×C₄×C₇₃	—	4	2	no	—
253	C₂²×C₄×C₇₃	—	4	2	no	—
254	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
255	C₂²×C₄×C₇₃	#41	1	4	yes	—
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	2	yes	—
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	2	yes	—
265	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₇₃	—	2	4	no	—
279	C₄⋊C₄×C₇₃	—	2	4	no	—
280	C₄⋊C₄×C₇₃	—	2	4	no	—
281	C₄⋊C₄×C₇₃	—	2	4	no	—
282	C₄⋊C₄×C₇₃	—	2	4	no	—
283	C₄⋊C₄×C₇₃	—	2	2	no	—
284	C₄⋊C₄×C₇₃	—	2	4	no	—
285	C₄⋊C₄×C₇₃	—	2	2	no	—
286	C₄⋊C₄×C₇₃	—	2	2	no	—
287	C₄⋊C₄×C₇₃	—	2	2	no	—
288	C₄⋊C₄×C₇₃	—	2	4	no	—
289	C₄⋊C₄×C₇₃	—	2	4	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	2	no	—
294	C₄⋊C₄×C₇₃	—	4	2	no	—
295	C₄⋊C₄×C₇₃	—	4	2	no	—
296	C₄⋊C₄×C₇₃	—	4	2	no	—
297	C₄⋊C₄×C₇₃	—	4	2	no	—
298	C₄⋊C₄×C₇₃	—	4	2	no	—
299	C₄⋊C₄×C₇₃	—	4	1	no	—
300	C₄⋊C₄×C₇₃	—	4	1	no	—
301	C₄⋊C₄×C₇₃	—	4	2	no	—
302	C₄⋊C₄×C₇₃	—	4	2	no	—
303	C₄⋊C₄×C₇₃	—	4	1	no	—
304	C₄⋊C₄×C₇₃	—	4	2	no	—
305	C₄⋊C₄×C₇₃	—	4	1	no	—
306	C₄⋊C₄×C₇₃	—	4	2	no	—
307	C₄⋊C₄×C₇₃	—	4	2	no	—
308	C₄⋊C₄×C₇₃	—	4	1	no	—
309	C₄⋊C₄×C₇₃	—	4	1	no	—
310	C₄⋊C₄×C₇₃	—	4	2	no	—
311	C₄⋊C₄×C₇₃	—	4	2	no	—
312	C₄⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
313	C₄⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
314	C₄⋊C₄×C₇₃	#41	1	4	yes	—
315	C₂²⋊C₄×C₇₃	—	2	2	no	—
316	C₂²⋊C₄×C₇₃	—	2	2	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	2	no	—
319	C₂²⋊C₄×C₇₃	—	2	4	no	—
320	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
321	C₄²×C₇₃	—	2	4	no	—
322	C₄²×C₇₃	—	2	2	no	—
323	C₄²×C₇₃	—	2	2	no	—
324	C₄²×C₇₃	—	2	2	no	—
325	C₄²×C₇₃	—	2	2	no	—
326	C₄²×C₇₃	—	2	2	no	—
327	C₄²×C₇₃	—	2	2	no	—
328	C₄²×C₇₃	—	4	1	no	—
329	C₄²×C₇₃	—	4	1	no	—
330	C₄²×C₇₃	—	4	2	no	—
331	C₄²×C₇₃	—	4	2	no	—
332	C₄²×C₇₃	—	4	2	no	—
333	C₄²×C₇₃	—	4	2	no	—
334	C₄²×C₇₃	—	4	2	no	—
335	C₂³×C₇₃	—	2	1	no	—
336	C₂³×C₇₃	—	2	1	no	—
337	C₂³×C₇₃	—	2	1	no	—
338	C₂³×C₇₃	—	2	1	no	—
339	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
340	C₂³×C₇₃	C₂×#41	1	2	yes	—
341	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
342	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
343	Q₈×C₇₃	—	2	8	no	—
344	Q₈×C₇₃	—	4	4	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	1	no	—
347	C₂×C₄×C₇₃	—	2	2	no	—
348	C₂×C₄×C₇₃	—	2	1	no	—
349	C₂×C₄×C₇₃	—	2	1	no	—
350	C₂×C₄×C₇₃	—	2	1	no	—
351	C₂×C₄×C₇₃	—	2	2	no	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	1	no	—
354	C₂×C₄×C₇₃	—	2	2	no	—
355	C₂×C₄×C₇₃	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	1	no	—
357	C₂×C₄×C₇₃	—	2	8	no	—
358	C₂×C₄×C₇₃	—	2	1	no	—
359	C₂×C₄×C₇₃	—	2	1	no	—
360	C₂×C₄×C₇₃	—	2	1	no	—
361	C₂×C₄×C₇₃	—	2	1	no	—
362	C₂×C₄×C₇₃	—	2	1	no	—
363	C₂×C₄×C₇₃	—	2	1	no	—
364	C₂×C₄×C₇₃	—	2	1	no	—
365	C₂×C₄×C₇₃	—	2	1	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	2	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	1	no	—
373	C₂×C₄×C₇₃	—	2	1	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	2	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	1	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	2	no	—
391	C₂×C₄×C₇₃	—	2	2	no	—
392	C₂×C₄×C₇₃	—	2	1	no	—
393	C₂×C₄×C₇₃	—	2	1	no	—
394	C₂×C₄×C₇₃	—	2	1	no	—
395	C₂×C₄×C₇₃	—	2	1	no	—
396	C₂×C₄×C₇₃	—	2	2	no	—
397	C₂×C₄×C₇₃	—	2	2	no	—
398	C₂×C₄×C₇₃	—	2	2	no	—
399	C₂×C₄×C₇₃	—	2	1	no	—
400	C₂×C₄×C₇₃	—	2	1	no	—
401	C₂×C₄×C₇₃	—	2	1	no	—
402	C₂×C₄×C₇₃	—	2	1	no	—
403	C₂×C₄×C₇₃	—	4	4	no	—
404	C₂×C₄×C₇₃	—	4	8	no	—
405	C₂×C₄×C₇₃	—	4	4	no	—
406	C₂×C₄×C₇₃	—	8	4	no	—
407	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
408	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
409	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
410	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
411	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
412	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
413	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
415	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
416	C₂²×C₇₃	—	2	2	no	—
417	C₂²×C₇₃	—	2	2	no	—
418	C₂²×C₇₃	—	2	2	no	—
419	C₂²×C₇₃	—	2	2	no	—
420	C₂²×C₇₃	—	2	2	no	—
421	C₂²×C₇₃	—	2	2	no	—
422	C₂²×C₇₃	#557	1	4	yes	—
423	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
424	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂²×C₇₃	#585	1	1	yes	characteristic
429	C₂²×C₇₃	#585	1	1	yes	characteristic
430	C₄×C₇₃	—	2	2	no	—
431	C₄×C₇₃	—	2	4	no	—
432	C₄×C₇₃	—	2	4	no	—
433	C₄×C₇₃	—	2	4	no	—
434	C₄×C₇₃	—	2	2	no	—
435	C₄×C₇₃	—	2	2	no	—
436	C₄×C₇₃	—	4	1	no	—
437	C₄×C₇₃	—	4	1	no	—
438	C₄×C₇₃	—	4	2	no	—
439	C₄×C₇₃	—	4	2	no	—
440	C₄×C₇₃	—	4	2	no	—
441	C₄×C₇₃	—	4	1	no	—
442	C₄×C₇₃	—	4	1	no	—
443	C₄×C₇₃	—	4	1	no	—
444	C₄×C₇₃	—	4	1	no	—
445	C₄×C₇₃	—	4	2	no	—
446	C₄×C₇₃	—	4	1	no	—
447	C₄×C₇₃	—	4	1	no	—
448	C₄×C₇₃	—	4	2	no	—
449	C₄×C₇₃	—	4	1	no	—
450	C₄×C₇₃	—	4	1	no	—
451	C₄×C₇₃	#554	1	4	yes	—
452	#59868	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂×C₇₃	—	2	4	no	—
454	C₂×C₇₃	C₂×#554	1	1	yes	characteristic
455	C₂×C₇₃	#3475	1	1	yes	characteristic
456	C₂×C₇₃	C₂×#557	1	1	yes	characteristic
457	C₂×C₇₃	#3504	1	1	yes	characteristic
458	C₂×C₇₃	#3505	1	1	yes	characteristic
459	C₂×C₇₃	#3516	1	1	yes	characteristic
460	C₂×C₇₃	#3541	1	1	yes	characteristic
461	#2802	C₂×C₇₃	1	2	yes	complemented
462	#2774	C₂×C₇₃	1	2	yes	complemented
463	#2585	C₂×C₇₃	1	2	yes	complemented
464	#2584	C₂×C₇₃	1	1	yes	characteristic, complemented
465	#2583	C₂×C₇₃	1	2	yes	—
466	#2581	C₂×C₇₃	1	1	yes	characteristic, complemented
467	#2509	C₂×C₇₃	1	2	yes	complemented
468	#2509	C₂×C₇₃	1	1	yes	characteristic, complemented
469	#2508	C₂×C₇₃	1	1	yes	characteristic, complemented
470	#2505	C₂×C₇₃	1	2	yes	—
471	#2505	C₂×C₇₃	1	2	yes	—
472	#2453	C₂×C₇₃	1	1	yes	characteristic, complemented
473	#2453	C₂×C₇₃	1	1	yes	characteristic, complemented
474	#2442	C₂×C₇₃	1	1	yes	characteristic
475	#2442	C₂×C₇₃	1	1	yes	characteristic
476	#2370	C₂×C₇₃	1	1	yes	characteristic, complemented
477	#2360	C₂×C₇₃	1	1	yes	characteristic
478	#2360	C₂×C₇₃	1	1	yes	characteristic
479	#2351	C₂×C₇₃	1	1	yes	characteristic, complemented
480	#2345	C₂×C₇₃	1	2	yes	—
481	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
482	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
483	C₂×#389	C₂×C₇₃	1	1	yes	characteristic
484	C₇₃	#59868	1	1	yes	characteristic, direct product factor, Sylow
485	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
486	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
487	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
488	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
489	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
490	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
491	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
493	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
494	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
495	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
496	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
497	#400	C₂²×C₇₃	1	2	yes	—
498	#400	C₂²×C₇₃	1	2	yes	—
499	#400	C₂²×C₇₃	1	2	yes	—
500	#400	C₂²×C₇₃	1	2	yes	—
501	#400	C₂²×C₇₃	1	2	yes	—
502	#400	C₂²×C₇₃	1	2	yes	—
503	#400	C₂²×C₇₃	1	2	yes	—
504	#400	C₂²×C₇₃	1	2	yes	—
505	#398	C₂²×C₇₃	1	2	yes	—
506	#398	C₂²×C₇₃	1	2	yes	—
507	#398	C₂²×C₇₃	1	2	yes	—
508	#398	C₂²×C₇₃	1	2	yes	—
509	#398	C₂²×C₇₃	1	2	yes	—
510	#398	C₂²×C₇₃	1	2	yes	—
511	#395	C₂²×C₇₃	1	2	yes	—
512	#395	C₂²×C₇₃	1	2	yes	—
513	#391	C₂²×C₇₃	1	1	yes	characteristic
514	#391	C₂²×C₇₃	1	1	yes	characteristic
515	#391	C₂²×C₇₃	1	1	yes	characteristic
516	#391	C₂²×C₇₃	1	1	yes	characteristic
517	#389	C₂²×C₇₃	1	1	yes	characteristic
518	#389	C₂²×C₇₃	1	1	yes	characteristic
519	#389	C₂²×C₇₃	1	2	yes	—
520	#389	C₂²×C₇₃	1	2	yes	—
521	#389	C₂²×C₇₃	1	2	yes	—
522	#389	C₂²×C₇₃	1	2	yes	—
523	#389	C₂²×C₇₃	1	2	yes	—
524	#389	C₂²×C₇₃	1	1	yes	characteristic
525	#389	C₂²×C₇₃	1	1	yes	characteristic
526	#389	C₂²×C₇₃	1	1	yes	characteristic
527	#389	C₂²×C₇₃	1	2	yes	—
528	#389	C₂²×C₇₃	1	1	yes	characteristic
529	#389	C₂²×C₇₃	1	2	yes	—
530	#389	C₂²×C₇₃	1	2	yes	—
531	#389	C₂²×C₇₃	1	1	yes	characteristic
532	#389	C₂²×C₇₃	1	2	yes	—
533	#389	C₂²×C₇₃	1	1	yes	characteristic
534	#389	C₂²×C₇₃	1	2	yes	—
535	#389	C₂²×C₇₃	1	2	yes	—
536	#389	C₂²×C₇₃	1	1	yes	characteristic
537	#389	C₂²×C₇₃	1	1	yes	characteristic
538	#389	C₂²×C₇₃	1	1	yes	characteristic
539	#389	C₂²×C₇₃	1	2	yes	—
540	#389	C₂²×C₇₃	1	1	yes	characteristic
541	#387	C₂²×C₇₃	1	2	yes	—
542	#387	C₂²×C₇₃	1	2	yes	—
543	#387	C₂²×C₇₃	1	1	yes	characteristic
544	#387	C₂²×C₇₃	1	2	yes	—
545	#387	C₂²×C₇₃	1	2	yes	—
546	#387	C₂²×C₇₃	1	2	yes	—
547	#387	C₂²×C₇₃	1	2	yes	—
548	#387	C₂²×C₇₃	1	2	yes	—
549	#387	C₂²×C₇₃	1	2	yes	—
550	#387	C₂²×C₇₃	1	2	yes	—
551	#387	C₂²×C₇₃	1	2	yes	—
552	#387	C₂²×C₇₃	1	1	yes	characteristic
553	#387	C₂²×C₇₃	1	2	yes	—
554	#385	C₂²×C₇₃	1	2	yes	—
555	#385	C₂²×C₇₃	1	2	yes	—
556	#385	C₂²×C₇₃	1	2	yes	—
557	#385	C₂²×C₇₃	1	2	yes	—
558	#385	C₂²×C₇₃	1	1	yes	characteristic
559	#385	C₂²×C₇₃	1	1	yes	characteristic
560	#385	C₂²×C₇₃	1	2	yes	—
561	#382	C₂²×C₇₃	1	1	yes	characteristic
562	#382	C₂²×C₇₃	1	1	yes	characteristic
563	#382	C₂²×C₇₃	1	2	yes	—
564	#382	C₂²×C₇₃	1	2	yes	—
565	#380	C₂²×C₇₃	1	1	yes	characteristic
566	#380	C₂²×C₇₃	1	2	yes	—
567	#380	C₂²×C₇₃	1	2	yes	—
568	#380	C₂²×C₇₃	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
571	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
573	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
582	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
583	C₂×#95	C₂²×C₇₃	1	2	yes	—
584	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
587	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
589	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
591	#125	—	2	4	no	—
592	#125	—	4	2	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	Q₈×C₇₃	1	8	yes	complemented
595	C₄×Q₈	—	2	4	no	—
596	C₄×Q₈	—	4	2	no	—
597	C₄×Q₈	—	4	2	no	—
598	C₄×Q₈	—	4	2	no	—
599	C₂×C₄⋊C₄	—	2	8	no	—
600	C₂×C₄⋊C₄	—	2	4	no	—
601	C₂×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
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	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
645	C₂×C₄²	—	4	2	no	—
646	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
658	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
660	#95	C₂³×C₇₃	1	2	yes	—
661	#95	C₂³×C₇₃	1	2	yes	—
662	#95	C₂³×C₇₃	1	2	yes	—
663	#95	C₂³×C₇₃	1	2	yes	—
664	#95	C₂³×C₇₃	1	1	yes	characteristic
665	#95	C₂³×C₇₃	1	2	yes	—
666	#95	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
672	#95	C₂³×C₇₃	1	1	yes	characteristic
673	#95	C₂³×C₇₃	1	2	yes	—
674	#95	C₂³×C₇₃	1	1	yes	characteristic
675	#95	C₂³×C₇₃	1	1	yes	characteristic
676	#95	C₂³×C₇₃	1	2	yes	—
677	#95	C₂³×C₇₃	1	2	yes	—
678	#95	C₂³×C₇₃	1	2	yes	—
679	#95	C₂³×C₇₃	1	1	yes	characteristic
680	#95	C₂³×C₇₃	1	1	yes	characteristic
681	#95	C₂³×C₇₃	1	1	yes	characteristic
682	#95	C₂³×C₇₃	1	2	yes	—
683	#95	C₂³×C₇₃	1	2	yes	—
684	#95	C₂³×C₇₃	1	2	yes	—
685	#95	C₂³×C₇₃	1	1	yes	characteristic
686	#95	C₂³×C₇₃	1	2	yes	—
687	#95	C₂³×C₇₃	1	2	yes	—
688	#95	C₂³×C₇₃	1	2	yes	—
689	#95	C₂³×C₇₃	1	2	yes	—
690	#95	C₂³×C₇₃	1	2	yes	—
691	#95	C₂³×C₇₃	1	2	yes	—
692	#95	C₂³×C₇₃	1	2	yes	—
693	#95	C₂³×C₇₃	1	2	yes	—
694	#95	C₂³×C₇₃	1	2	yes	—
695	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	4	1	no	—
700	C₂×Q₈	—	4	1	no	—
701	C₂×Q₈	C₂×Q₈×C₇₃	1	4	yes	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
716	C₂²×C₄	#41×C₇₃	1	4	yes	—
717	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	1	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	1	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
774	C₄⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
775	C₄⋊C₄	#41×C₇₃	1	4	yes	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	4	1	no	—
790	C₄²	—	4	1	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
801	C₂³	C₂×#41×C₇₃	1	2	yes	—
802	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
803	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
804	Q₈	—	2	8	no	—
805	Q₈	—	4	4	no	—
806	C₂×C₄	—	2	2	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	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	8	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	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	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	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	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	8	4	no	—
868	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
869	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
870	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
871	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
872	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
873	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
874	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
875	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
876	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	#557×C₇₃	1	4	yes	—
884	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
885	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
886	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
887	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
888	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
889	C₂²	#585×C₇₃	1	1	yes	characteristic
890	C₂²	#585×C₇₃	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	#554×C₇₃	1	4	yes	—
913	C₂	—	2	4	no	—
914	C₂	C₂×#554×C₇₃	1	1	yes	characteristic
915	C₂	C₇₃×#3475	1	1	yes	characteristic
916	C₂	C₂×#557×C₇₃	1	1	yes	characteristic
917	C₂	C₇₃×#3504	1	1	yes	characteristic
918	C₂	C₇₃×#3505	1	1	yes	characteristic
919	C₂	C₇₃×#3516	1	1	yes	characteristic
920	C₂	C₇₃×#3541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂⁴×C₇₃	C₂⁴
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×#2802	C₂	semidirect
2. C₇₃×#2774	C₂	semidirect
3. C₇₃×#2585	C₂	semidirect
4. C₇₃×#2584	C₂	semidirect
6. C₇₃×#2581	C₂	semidirect
7. C₇₃×#2509	C₂	semidirect
8. C₇₃×#2509	C₂	semidirect
9. C₇₃×#2508	C₂	semidirect
12. C₇₃×#2453	C₂	semidirect
13. C₇₃×#2453	C₂	semidirect
16. C₇₃×#2370	C₂	semidirect
19. C₇₃×#2351	C₂	semidirect
133. C₂²⋊Q₈×C₇₃	Q₈	semidirect
452. #59868	C₇₃	direct (N × H)
461. #2802	C₂×C₇₃	semidirect
462. #2774	C₂×C₇₃	semidirect
463. #2585	C₂×C₇₃	semidirect
464. #2584	C₂×C₇₃	semidirect
466. #2581	C₂×C₇₃	semidirect
467. #2509	C₂×C₇₃	semidirect
468. #2509	C₂×C₇₃	semidirect
469. #2508	C₂×C₇₃	semidirect
472. #2453	C₂×C₇₃	semidirect
473. #2453	C₂×C₇₃	semidirect
476. #2370	C₂×C₇₃	semidirect
479. #2351	C₂×C₇₃	semidirect
484. C₇₃	#59868	direct (N × H)
594. C₂²⋊Q₈	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2802	2
C₇₃×#2774	2
C₇₃×#2585	2
C₇₃×#2584	2
C₇₃×#2583	2
C₇₃×#2581	2
C₇₃×#2509	2
C₇₃×#2508	2
C₇₃×#2505	2
C₇₃×#2453	2
C₇₃×#2442	2
C₇₃×#2370	2
C₇₃×#2360	2
C₇₃×#2351	2
C₇₃×#2345	2
C₄×C₂²⋊Q₈×C₇₃	2
C₂×#389×C₇₃	2
#59868	73

Subgroups — C73×#59868 #32969272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59868 #32969272