Subgroups — C₇₃×#59569 #32968973

Order 18688.

1830 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2780	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2748	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2587	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2556	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2522	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2454	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2449	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2363	C₂	1	1	yes	maximal, characteristic
18	C₇₃×#2363	C₂	1	1	yes	maximal, characteristic
19	D₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₃×#2345	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
29	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
38	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
39	#400×C₇₃	C₂²	1	2	yes	—
40	#399×C₇₃	C₂²	1	2	yes	—
41	#399×C₇₃	C₂²	1	2	yes	—
42	#399×C₇₃	C₂²	1	2	yes	—
43	#399×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	#396×C₇₃	C₂²	1	2	yes	—
49	#396×C₇₃	C₂²	1	2	yes	—
50	#396×C₇₃	C₂²	1	2	yes	—
51	#396×C₇₃	C₂²	1	2	yes	—
52	#396×C₇₃	C₂²	1	2	yes	—
53	#396×C₇₃	C₂²	1	2	yes	—
54	#395×C₇₃	C₂²	1	2	yes	—
55	#391×C₇₃	C₂²	1	1	yes	characteristic
56	#390×C₇₃	C₂²	1	1	yes	characteristic
57	#390×C₇₃	C₂²	1	2	yes	—
58	#390×C₇₃	C₂²	1	2	yes	—
59	#390×C₇₃	C₂²	1	1	yes	characteristic
60	#390×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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
72	#389×C₇₃	C₂²	1	1	yes	characteristic
73	#389×C₇₃	C₂²	1	1	yes	characteristic
74	#389×C₇₃	C₂²	1	1	yes	characteristic
75	#389×C₇₃	C₂²	1	1	yes	characteristic
76	#389×C₇₃	C₂²	1	1	yes	characteristic
77	#389×C₇₃	C₂²	1	2	yes	—
78	#389×C₇₃	C₂²	1	1	yes	characteristic
79	#388×C₇₃	C₂²	1	2	yes	—
80	#388×C₇₃	C₂²	1	2	yes	—
81	#388×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	2	yes	—
87	#387×C₇₃	C₂²	1	2	yes	—
88	#387×C₇₃	C₂²	1	1	yes	characteristic
89	#387×C₇₃	C₂²	1	1	yes	characteristic
90	#386×C₇₃	C₂²	1	2	yes	—
91	#386×C₇₃	C₂²	1	2	yes	—
92	#386×C₇₃	C₂²	1	2	yes	—
93	#385×C₇₃	C₂²	1	2	yes	—
94	#385×C₇₃	C₂²	1	2	yes	—
95	#385×C₇₃	C₂²	1	2	yes	—
96	#385×C₇₃	C₂²	1	2	yes	—
97	#385×C₇₃	C₂²	1	1	yes	characteristic
98	#385×C₇₃	C₂²	1	2	yes	—
99	#385×C₇₃	C₂²	1	1	yes	characteristic
100	#385×C₇₃	C₂²	1	2	yes	—
101	#384×C₇₃	C₂²	1	1	yes	characteristic
102	#384×C₇₃	C₂²	1	1	yes	characteristic
103	#380×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
108	#380×C₇₃	C₂²	1	2	yes	—
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	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
132	#125×C₇₃	—	2	4	no	—
133	#125×C₇₃	—	4	2	no	—
134	#125×C₇₃	—	4	4	no	—
135	C₂²⋊Q₈×C₇₃	—	2	4	no	—
136	C₂²⋊Q₈×C₇₃	—	4	4	no	—
137	#121×C₇₃	Q₈	1	8	yes	complemented
138	C₄×Q₈×C₇₃	—	4	2	no	—
139	C₄×D₄×C₇₃	—	2	4	no	—
140	C₄×D₄×C₇₃	—	4	2	no	—
141	C₄×D₄×C₇₃	—	4	2	no	—
142	C₄×D₄×C₇₃	—	4	4	no	—
143	#117×C₇₃	—	2	4	no	—
144	#117×C₇₃	—	4	2	no	—
145	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
163	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
176	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₇₃	—	4	2	no	—
199	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
216	#95×C₇₃	C₂³	1	2	yes	—
217	#95×C₇₃	C₂³	1	2	yes	—
218	#95×C₇₃	C₂³	1	1	yes	characteristic
219	#95×C₇₃	C₂³	1	1	yes	characteristic
220	#95×C₇₃	C₂³	1	1	yes	characteristic
221	#95×C₇₃	C₂³	1	1	yes	characteristic
222	#95×C₇₃	C₂³	1	2	yes	—
223	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
228	#95×C₇₃	C₂³	1	2	yes	—
229	#95×C₇₃	C₂³	1	1	yes	characteristic
230	#95×C₇₃	C₂³	1	1	yes	characteristic
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	#95×C₇₃	C₂³	1	2	yes	—
237	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₇₃	—	2	2	no	—
240	C₂×Q₈×C₇₃	—	2	2	no	—
241	C₂×Q₈×C₇₃	—	4	1	no	—
242	C₂×D₄×C₇₃	—	2	2	no	—
243	C₂×D₄×C₇₃	—	2	2	no	—
244	C₂×D₄×C₇₃	—	4	2	no	—
245	C₂×D₄×C₇₃	—	4	2	no	—
246	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
247	C₂×D₄×C₇₃	C₂×Q₈	1	8	yes	—
248	C₂²×C₄×C₇₃	—	2	2	no	—
249	C₂²×C₄×C₇₃	—	2	2	no	—
250	C₂²×C₄×C₇₃	—	2	4	no	—
251	C₂²×C₄×C₇₃	—	2	4	no	—
252	C₂²×C₄×C₇₃	—	2	2	no	—
253	C₂²×C₄×C₇₃	—	2	2	no	—
254	C₂²×C₄×C₇₃	—	2	4	no	—
255	C₂²×C₄×C₇₃	—	2	4	no	—
256	C₂²×C₄×C₇₃	—	4	1	no	—
257	C₂²×C₄×C₇₃	—	4	1	no	—
258	C₂²×C₄×C₇₃	—	4	2	no	—
259	C₂²×C₄×C₇₃	—	4	1	no	—
260	C₂²×C₄×C₇₃	—	4	1	no	—
261	C₂²×C₄×C₇₃	—	4	2	no	—
262	C₂²×C₄×C₇₃	—	4	2	no	—
263	C₂²×C₄×C₇₃	—	4	2	no	—
264	C₂²×C₄×C₇₃	—	4	2	no	—
265	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
266	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
284	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
287	C₄⋊C₄×C₇₃	—	2	4	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	4	no	—
294	C₄⋊C₄×C₇₃	—	2	4	no	—
295	C₄⋊C₄×C₇₃	—	2	2	no	—
296	C₄⋊C₄×C₇₃	—	2	2	no	—
297	C₄⋊C₄×C₇₃	—	2	2	no	—
298	C₄⋊C₄×C₇₃	—	2	4	no	—
299	C₄⋊C₄×C₇₃	—	2	2	no	—
300	C₄⋊C₄×C₇₃	—	2	4	no	—
301	C₄⋊C₄×C₇₃	—	2	2	no	—
302	C₄⋊C₄×C₇₃	—	4	2	no	—
303	C₄⋊C₄×C₇₃	—	4	2	no	—
304	C₄⋊C₄×C₇₃	—	4	1	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	2	no	—
309	C₄⋊C₄×C₇₃	—	4	1	no	—
310	C₄⋊C₄×C₇₃	—	4	1	no	—
311	C₄⋊C₄×C₇₃	—	4	1	no	—
312	C₄⋊C₄×C₇₃	—	4	2	no	—
313	C₄⋊C₄×C₇₃	—	4	2	no	—
314	C₄⋊C₄×C₇₃	—	4	2	no	—
315	C₄⋊C₄×C₇₃	—	4	2	no	—
316	C₄⋊C₄×C₇₃	—	4	2	no	—
317	C₄⋊C₄×C₇₃	—	4	2	no	—
318	C₄⋊C₄×C₇₃	—	4	2	no	—
319	C₄⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
320	C₄⋊C₄×C₇₃	#41	1	4	yes	—
321	C₄⋊C₄×C₇₃	#41	1	4	yes	—
322	C₂²⋊C₄×C₇₃	—	2	4	no	—
323	C₂²⋊C₄×C₇₃	—	2	4	no	—
324	C₂²⋊C₄×C₇₃	—	2	2	no	—
325	C₂²⋊C₄×C₇₃	—	2	2	no	—
326	C₂²⋊C₄×C₇₃	—	2	4	no	—
327	C₂²⋊C₄×C₇₃	—	4	2	no	—
328	C₂²⋊C₄×C₇₃	—	4	2	no	—
329	C₂²⋊C₄×C₇₃	—	4	1	no	—
330	C₂²⋊C₄×C₇₃	—	4	1	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	—	4	2	no	—
335	C₂²⋊C₄×C₇₃	—	4	2	no	—
336	C₂²⋊C₄×C₇₃	—	4	2	no	—
337	C₂²⋊C₄×C₇₃	—	4	2	no	—
338	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
339	C₄²×C₇₃	—	2	4	no	—
340	C₄²×C₇₃	—	2	2	no	—
341	C₄²×C₇₃	—	2	2	no	—
342	C₄²×C₇₃	—	2	2	no	—
343	C₄²×C₇₃	—	2	2	no	—
344	C₄²×C₇₃	—	2	2	no	—
345	C₄²×C₇₃	—	2	2	no	—
346	C₄²×C₇₃	—	4	1	no	—
347	C₄²×C₇₃	—	4	1	no	—
348	C₄²×C₇₃	—	4	2	no	—
349	C₄²×C₇₃	—	4	2	no	—
350	C₄²×C₇₃	—	4	2	no	—
351	C₄²×C₇₃	—	4	2	no	—
352	C₂³×C₇₃	—	2	1	no	—
353	C₂³×C₇₃	—	2	1	no	—
354	C₂³×C₇₃	—	2	2	no	—
355	C₂³×C₇₃	—	2	2	no	—
356	C₂³×C₇₃	—	2	2	no	—
357	C₂³×C₇₃	—	2	1	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	2	no	—
363	C₂³×C₇₃	—	2	1	no	—
364	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
365	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
366	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
367	Q₈×C₇₃	—	4	4	no	—
368	D₄×C₇₃	—	2	8	no	—
369	D₄×C₇₃	—	4	8	no	—
370	C₂×C₄×C₇₃	—	2	1	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	2	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	1	no	—
378	C₂×C₄×C₇₃	—	2	2	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	2	2	no	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	8	no	—
385	C₂×C₄×C₇₃	—	2	1	no	—
386	C₂×C₄×C₇₃	—	2	2	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	2	no	—
392	C₂×C₄×C₇₃	—	2	2	no	—
393	C₂×C₄×C₇₃	—	2	2	no	—
394	C₂×C₄×C₇₃	—	2	1	no	—
395	C₂×C₄×C₇₃	—	2	1	no	—
396	C₂×C₄×C₇₃	—	2	1	no	—
397	C₂×C₄×C₇₃	—	2	1	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	2	no	—
404	C₂×C₄×C₇₃	—	2	1	no	—
405	C₂×C₄×C₇₃	—	2	2	no	—
406	C₂×C₄×C₇₃	—	2	2	no	—
407	C₂×C₄×C₇₃	—	2	2	no	—
408	C₂×C₄×C₇₃	—	2	1	no	—
409	C₂×C₄×C₇₃	—	2	1	no	—
410	C₂×C₄×C₇₃	—	2	1	no	—
411	C₂×C₄×C₇₃	—	2	1	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	2	no	—
417	C₂×C₄×C₇₃	—	2	2	no	—
418	C₂×C₄×C₇₃	—	2	1	no	—
419	C₂×C₄×C₇₃	—	2	2	no	—
420	C₂×C₄×C₇₃	—	2	1	no	—
421	C₂×C₄×C₇₃	—	2	1	no	—
422	C₂×C₄×C₇₃	—	2	1	no	—
423	C₂×C₄×C₇₃	—	2	1	no	—
424	C₂×C₄×C₇₃	—	4	8	no	—
425	C₂×C₄×C₇₃	—	4	4	no	—
426	C₂×C₄×C₇₃	—	4	4	no	—
427	C₂×C₄×C₇₃	—	8	4	no	—
428	C₂×C₄×C₇₃	—	8	4	no	—
429	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
430	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
431	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
432	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
433	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
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	H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
439	C₂²×C₇₃	—	2	2	no	—
440	C₂²×C₇₃	—	2	4	no	—
441	C₂²×C₇₃	—	2	2	no	—
442	C₂²×C₇₃	—	2	4	no	—
443	C₂²×C₇₃	—	2	2	no	—
444	C₂²×C₇₃	—	2	4	no	—
445	C₂²×C₇₃	—	4	2	no	—
446	C₂²×C₇₃	—	4	1	no	—
447	C₂²×C₇₃	—	4	1	no	—
448	C₂²×C₇₃	—	4	2	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	C₂³×Q₈	1	1	yes	characteristic
454	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
455	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
456	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₇₃	#585	1	1	yes	characteristic
459	C₂²×C₇₃	#585	1	1	yes	characteristic
460	C₄×C₇₃	—	2	2	no	—
461	C₄×C₇₃	—	2	2	no	—
462	C₄×C₇₃	—	2	4	no	—
463	C₄×C₇₃	—	2	4	no	—
464	C₄×C₇₃	—	2	2	no	—
465	C₄×C₇₃	—	2	2	no	—
466	C₄×C₇₃	—	2	2	no	—
467	C₄×C₇₃	—	4	1	no	—
468	C₄×C₇₃	—	4	1	no	—
469	C₄×C₇₃	—	4	2	no	—
470	C₄×C₇₃	—	4	1	no	—
471	C₄×C₇₃	—	4	2	no	—
472	C₄×C₇₃	—	4	2	no	—
473	C₄×C₇₃	—	4	2	no	—
474	C₄×C₇₃	—	4	1	no	—
475	C₄×C₇₃	—	4	1	no	—
476	C₄×C₇₃	—	4	1	no	—
477	C₄×C₇₃	—	4	2	no	—
478	C₄×C₇₃	—	4	1	no	—
479	C₄×C₇₃	—	4	1	no	—
480	C₄×C₇₃	#554	1	4	yes	—
481	#59569	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₂×C₇₃	—	4	2	no	—
483	C₂×C₇₃	—	4	4	no	—
484	C₂×C₇₃	C₂×#554	1	1	yes	characteristic
485	C₂×C₇₃	#3475	1	1	yes	characteristic
486	C₂×C₇₃	Q₈×#41	1	1	yes	characteristic
487	C₂×C₇₃	#3501	1	1	yes	characteristic
488	C₂×C₇₃	#3517	1	1	yes	characteristic
489	C₂×C₇₃	#3519	1	1	yes	characteristic
490	C₂×C₇₃	#3539	1	1	yes	characteristic
491	#2780	C₂×C₇₃	1	2	yes	complemented
492	#2748	C₂×C₇₃	1	2	yes	complemented
493	#2587	C₂×C₇₃	1	2	yes	complemented
494	#2584	C₂×C₇₃	1	1	yes	characteristic, complemented
495	#2556	C₂×C₇₃	1	2	yes	complemented
496	#2538	C₂×C₇₃	1	1	yes	characteristic, complemented
497	#2522	C₂×C₇₃	1	2	yes	complemented
498	#2507	C₂×C₇₃	1	1	yes	characteristic, complemented
499	#2506	C₂×C₇₃	1	1	yes	characteristic, complemented
500	#2454	C₂×C₇₃	1	1	yes	characteristic, complemented
501	#2454	C₂×C₇₃	1	1	yes	characteristic, complemented
502	#2454	C₂×C₇₃	1	2	yes	complemented
503	#2449	C₂×C₇₃	1	2	yes	complemented
504	#2441	C₂×C₇₃	1	1	yes	characteristic, complemented
505	#2441	C₂×C₇₃	1	1	yes	characteristic, complemented
506	#2370	C₂×C₇₃	1	1	yes	characteristic, complemented
507	#2363	C₂×C₇₃	1	1	yes	characteristic
508	#2363	C₂×C₇₃	1	1	yes	characteristic
509	D₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
510	#2345	C₂×C₇₃	1	2	yes	complemented
511	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
512	C₄×#121	C₂×C₇₃	1	1	yes	characteristic
513	#2296	C₂×C₇₃	1	1	yes	characteristic, complemented
514	C₇₃	#59569	1	1	yes	characteristic, direct product factor, Sylow
515	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
516	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
517	C₂×#125	C₂²×C₇₃	1	2	yes	—
518	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
519	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
520	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
521	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
522	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
526	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
527	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
528	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
529	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
530	#400	C₂²×C₇₃	1	2	yes	—
531	#399	C₂²×C₇₃	1	2	yes	—
532	#399	C₂²×C₇₃	1	2	yes	—
533	#399	C₂²×C₇₃	1	2	yes	—
534	#399	C₂²×C₇₃	1	2	yes	—
535	#398	C₂²×C₇₃	1	2	yes	—
536	#398	C₂²×C₇₃	1	2	yes	—
537	#398	C₂²×C₇₃	1	2	yes	—
538	#398	C₂²×C₇₃	1	2	yes	—
539	#396	C₂²×C₇₃	1	2	yes	—
540	#396	C₂²×C₇₃	1	2	yes	—
541	#396	C₂²×C₇₃	1	2	yes	—
542	#396	C₂²×C₇₃	1	2	yes	—
543	#396	C₂²×C₇₃	1	2	yes	—
544	#396	C₂²×C₇₃	1	2	yes	—
545	#395	C₂²×C₇₃	1	2	yes	—
546	#391	C₂²×C₇₃	1	1	yes	characteristic
547	#390	C₂²×C₇₃	1	1	yes	characteristic
548	#390	C₂²×C₇₃	1	2	yes	—
549	#390	C₂²×C₇₃	1	2	yes	—
550	#390	C₂²×C₇₃	1	1	yes	characteristic
551	#390	C₂²×C₇₃	1	1	yes	characteristic
552	#389	C₂²×C₇₃	1	2	yes	—
553	#389	C₂²×C₇₃	1	1	yes	characteristic
554	#389	C₂²×C₇₃	1	1	yes	characteristic
555	#389	C₂²×C₇₃	1	2	yes	—
556	#389	C₂²×C₇₃	1	1	yes	characteristic
557	#389	C₂²×C₇₃	1	1	yes	characteristic
558	#389	C₂²×C₇₃	1	2	yes	—
559	#389	C₂²×C₇₃	1	2	yes	—
560	#389	C₂²×C₇₃	1	2	yes	—
561	#389	C₂²×C₇₃	1	2	yes	—
562	#389	C₂²×C₇₃	1	1	yes	characteristic
563	#389	C₂²×C₇₃	1	1	yes	characteristic
564	#389	C₂²×C₇₃	1	1	yes	characteristic
565	#389	C₂²×C₇₃	1	1	yes	characteristic
566	#389	C₂²×C₇₃	1	1	yes	characteristic
567	#389	C₂²×C₇₃	1	1	yes	characteristic
568	#389	C₂²×C₇₃	1	1	yes	characteristic
569	#389	C₂²×C₇₃	1	1	yes	characteristic
570	#388	C₂²×C₇₃	1	2	yes	—
571	#388	C₂²×C₇₃	1	2	yes	—
572	#388	C₂²×C₇₃	1	2	yes	—
573	#387	C₂²×C₇₃	1	1	yes	characteristic
574	#387	C₂²×C₇₃	1	2	yes	—
575	#387	C₂²×C₇₃	1	1	yes	characteristic
576	#387	C₂²×C₇₃	1	2	yes	—
577	#387	C₂²×C₇₃	1	2	yes	—
578	#387	C₂²×C₇₃	1	2	yes	—
579	#387	C₂²×C₇₃	1	2	yes	—
580	#387	C₂²×C₇₃	1	2	yes	—
581	#386	C₂²×C₇₃	1	2	yes	—
582	#386	C₂²×C₇₃	1	2	yes	—
583	#386	C₂²×C₇₃	1	2	yes	—
584	#385	C₂²×C₇₃	1	2	yes	—
585	#385	C₂²×C₇₃	1	2	yes	—
586	#385	C₂²×C₇₃	1	2	yes	—
587	#385	C₂²×C₇₃	1	2	yes	—
588	#385	C₂²×C₇₃	1	2	yes	—
589	#385	C₂²×C₇₃	1	1	yes	characteristic
590	#385	C₂²×C₇₃	1	2	yes	—
591	#385	C₂²×C₇₃	1	1	yes	characteristic
592	#384	C₂²×C₇₃	1	1	yes	characteristic
593	#384	C₂²×C₇₃	1	1	yes	characteristic
594	#380	C₂²×C₇₃	1	2	yes	—
595	#380	C₂²×C₇₃	1	2	yes	—
596	#380	C₂²×C₇₃	1	2	yes	—
597	#380	C₂²×C₇₃	1	2	yes	—
598	#380	C₂²×C₇₃	1	1	yes	characteristic
599	#380	C₂²×C₇₃	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
602	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
603	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
605	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
606	C₄×C₄⋊C₄	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×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
615	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
617	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
618	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
621	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
622	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
623	#125	—	2	4	no	—
624	#125	—	4	2	no	—
625	#125	—	4	4	no	—
626	C₂²⋊Q₈	—	2	4	no	—
627	C₂²⋊Q₈	—	4	4	no	—
628	#121	Q₈×C₇₃	1	8	yes	complemented
629	C₄×Q₈	—	4	2	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	4	2	no	—
632	C₄×D₄	—	4	2	no	—
633	C₄×D₄	—	4	4	no	—
634	#117	—	2	4	no	—
635	#117	—	4	2	no	—
636	C₂×C₄⋊C₄	—	2	8	no	—
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
689	C₂×C₄²	—	4	2	no	—
690	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
693	C₂×C₄²	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	2	yes	—
698	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
699	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
700	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
702	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
703	#95	C₂³×C₇₃	1	1	yes	characteristic
704	#95	C₂³×C₇₃	1	1	yes	characteristic
705	#95	C₂³×C₇₃	1	2	yes	—
706	#95	C₂³×C₇₃	1	2	yes	—
707	#95	C₂³×C₇₃	1	2	yes	—
708	#95	C₂³×C₇₃	1	2	yes	—
709	#95	C₂³×C₇₃	1	1	yes	characteristic
710	#95	C₂³×C₇₃	1	1	yes	characteristic
711	#95	C₂³×C₇₃	1	1	yes	characteristic
712	#95	C₂³×C₇₃	1	1	yes	characteristic
713	#95	C₂³×C₇₃	1	2	yes	—
714	#95	C₂³×C₇₃	1	2	yes	—
715	#95	C₂³×C₇₃	1	1	yes	characteristic
716	#95	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
721	#95	C₂³×C₇₃	1	1	yes	characteristic
722	#95	C₂³×C₇₃	1	2	yes	—
723	#95	C₂³×C₇₃	1	2	yes	—
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	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
729	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	4	1	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	—
738	C₂×D₄	C₂×Q₈×C₇₃	1	8	yes	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	1	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	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	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
757	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	1	no	—
796	C₄⋊C₄	—	4	1	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	1	no	—
801	C₄⋊C₄	—	4	1	no	—
802	C₄⋊C₄	—	4	1	no	—
803	C₄⋊C₄	—	4	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	—	4	2	no	—
810	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
811	C₄⋊C₄	#41×C₇₃	1	4	yes	—
812	C₄⋊C₄	#41×C₇₃	1	4	yes	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	1	no	—
821	C₂²⋊C₄	—	4	1	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
830	C₄²	—	2	4	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	1	no	—
839	C₄²	—	4	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	2	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	1	no	—
855	C₂³	C₂²×Q₈×C₇₃	1	4	yes	—
856	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
857	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
858	Q₈	—	4	4	no	—
859	D₄	—	2	8	no	—
860	D₄	—	4	8	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	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	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	4	no	—
919	C₂×C₄	—	8	4	no	—
920	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
921	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
922	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
923	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
924	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
925	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
926	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
927	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
928	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
929	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
945	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
946	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
947	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
948	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
949	C₂²	#585×C₇₃	1	1	yes	characteristic
950	C₂²	#585×C₇₃	1	1	yes	characteristic
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	4	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	2	no	—
971	C₄	#554×C₇₃	1	4	yes	—
972	C₂	—	4	2	no	—
973	C₂	—	4	4	no	—
974	C₂	C₂×#554×C₇₃	1	1	yes	characteristic
975	C₂	C₇₃×#3475	1	1	yes	characteristic
976	C₂	Q₈×#41×C₇₃	1	1	yes	characteristic
977	C₂	C₇₃×#3501	1	1	yes	characteristic
978	C₂	C₇₃×#3517	1	1	yes	characteristic
979	C₂	C₇₃×#3519	1	1	yes	characteristic
980	C₂	C₇₃×#3539	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
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×#2780	C₂	semidirect
2. C₇₃×#2748	C₂	semidirect
3. C₇₃×#2587	C₂	semidirect
4. C₇₃×#2584	C₂	semidirect
5. C₇₃×#2556	C₂	semidirect
6. C₇₃×#2538	C₂	semidirect
7. C₇₃×#2522	C₂	semidirect
8. C₇₃×#2507	C₂	semidirect
9. C₇₃×#2506	C₂	semidirect
10. C₇₃×#2454	C₂	semidirect
11. C₇₃×#2454	C₂	semidirect
12. C₇₃×#2454	C₂	semidirect
13. C₇₃×#2449	C₂	semidirect
14. C₇₃×#2441	C₂	semidirect
15. C₇₃×#2441	C₂	semidirect
16. C₇₃×#2370	C₂	semidirect
19. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
20. C₇₃×#2345	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₇₃	C₂	semidirect
23. C₇₃×#2296	C₂	semidirect
137. #121×C₇₃	Q₈	semidirect
481. #59569	C₇₃	direct (N × H)
491. #2780	C₂×C₇₃	semidirect
492. #2748	C₂×C₇₃	semidirect
493. #2587	C₂×C₇₃	semidirect
494. #2584	C₂×C₇₃	semidirect
495. #2556	C₂×C₇₃	semidirect
496. #2538	C₂×C₇₃	semidirect
497. #2522	C₂×C₇₃	semidirect
498. #2507	C₂×C₇₃	semidirect
499. #2506	C₂×C₇₃	semidirect
500. #2454	C₂×C₇₃	semidirect
501. #2454	C₂×C₇₃	semidirect
502. #2454	C₂×C₇₃	semidirect
503. #2449	C₂×C₇₃	semidirect
504. #2441	C₂×C₇₃	semidirect
505. #2441	C₂×C₇₃	semidirect
506. #2370	C₂×C₇₃	semidirect
509. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
510. #2345	C₂×C₇₃	semidirect
511. C₄×C₂²⋊Q₈	C₂×C₇₃	semidirect
513. #2296	C₂×C₇₃	semidirect
514. C₇₃	#59569	direct (N × H)
628. #121	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×#2780	2
C₇₃×#2748	2
C₇₃×#2587	2
C₇₃×#2584	2
C₇₃×#2556	2
C₇₃×#2538	2
C₇₃×#2522	2
C₇₃×#2507	2
C₇₃×#2506	2
C₇₃×#2454	2
C₇₃×#2449	2
C₇₃×#2441	2
C₇₃×#2370	2
C₇₃×#2363	2
D₄×C₄⋊C₄×C₇₃	2
C₇₃×#2345	2
C₄×C₂²⋊Q₈×C₇₃	2
C₄×#121×C₇₃	2
C₇₃×#2296	2
#59569	73

Subgroups — C73×#59569 #32968973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59569 #32968973