Subgroups — C₇₃×#59918 #32969322

Order 18688.

1762 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2806	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2792	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2586	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2583	C₂	1	2	yes	maximal
5	C₇₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2549	C₂	1	2	yes	maximal
8	C₇₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2507	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2502	C₂	1	2	yes	maximal
12	C₇₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2440	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2440	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2368	C₂	1	2	yes	maximal
18	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic
20	Q₈×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
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×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×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×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×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	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
37	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
38	#398×C₇₃	C₂²	1	2	yes	—
39	#398×C₇₃	C₂²	1	2	yes	—
40	#398×C₇₃	C₂²	1	2	yes	—
41	#398×C₇₃	C₂²	1	2	yes	—
42	#398×C₇₃	C₂²	1	2	yes	—
43	#398×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	#395×C₇₃	C₂²	1	2	yes	—
49	#395×C₇₃	C₂²	1	2	yes	—
50	#395×C₇₃	C₂²	1	2	yes	—
51	#395×C₇₃	C₂²	1	2	yes	—
52	#395×C₇₃	C₂²	1	2	yes	—
53	#395×C₇₃	C₂²	1	2	yes	—
54	#391×C₇₃	C₂²	1	1	yes	characteristic
55	#391×C₇₃	C₂²	1	2	yes	—
56	#391×C₇₃	C₂²	1	2	yes	—
57	#391×C₇₃	C₂²	1	1	yes	characteristic
58	#391×C₇₃	C₂²	1	1	yes	characteristic
59	#391×C₇₃	C₂²	1	2	yes	—
60	#391×C₇₃	C₂²	1	2	yes	—
61	#391×C₇₃	C₂²	1	1	yes	characteristic
62	#391×C₇₃	C₂²	1	2	yes	—
63	#391×C₇₃	C₂²	1	2	yes	—
64	#389×C₇₃	C₂²	1	1	yes	characteristic
65	#389×C₇₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
70	#389×C₇₃	C₂²	1	2	yes	—
71	#389×C₇₃	C₂²	1	2	yes	—
72	#389×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
77	#389×C₇₃	C₂²	1	2	yes	—
78	#389×C₇₃	C₂²	1	1	yes	characteristic
79	#389×C₇₃	C₂²	1	1	yes	characteristic
80	#389×C₇₃	C₂²	1	1	yes	characteristic
81	#389×C₇₃	C₂²	1	2	yes	—
82	#389×C₇₃	C₂²	1	2	yes	—
83	#389×C₇₃	C₂²	1	1	yes	characteristic
84	#389×C₇₃	C₂²	1	2	yes	—
85	#389×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	2	yes	—
90	#387×C₇₃	C₂²	1	2	yes	—
91	#387×C₇₃	C₂²	1	2	yes	—
92	#387×C₇₃	C₂²	1	2	yes	—
93	#387×C₇₃	C₂²	1	2	yes	—
94	#387×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
100	#385×C₇₃	C₂²	1	2	yes	—
101	#385×C₇₃	C₂²	1	1	yes	characteristic
102	#384×C₇₃	C₂²	1	1	yes	characteristic
103	#384×C₇₃	C₂²	1	1	yes	characteristic
104	#384×C₇₃	C₂²	1	2	yes	—
105	#384×C₇₃	C₂²	1	2	yes	—
106	#380×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
111	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₇₃	C₂²	1	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	2	yes	—
125	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
126	C₂²×Q₈×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	2	yes	—
130	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₇₃	—	2	4	no	—
133	C₄⋊Q₈×C₇₃	—	4	2	no	—
134	C₂²⋊Q₈×C₇₃	—	4	4	no	—
135	C₂²⋊Q₈×C₇₃	—	4	4	no	—
136	C₂²⋊Q₈×C₇₃	Q₈	1	8	yes	complemented
137	C₂²⋊Q₈×C₇₃	Q₈	1	8	yes	complemented
138	C₄×Q₈×C₇₃	—	2	4	no	—
139	C₄×Q₈×C₇₃	—	4	2	no	—
140	C₄×Q₈×C₇₃	—	4	2	no	—
141	C₄×Q₈×C₇₃	—	4	2	no	—
142	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
143	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
144	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	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	1	yes	characteristic
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	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	1	yes	characteristic
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	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	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	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×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
183	C₂×C₄⋊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	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₇₃	—	4	2	no	—
191	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
204	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
205	#95×C₇₃	C₂³	1	1	yes	characteristic
206	#95×C₇₃	C₂³	1	2	yes	—
207	#95×C₇₃	C₂³	1	1	yes	characteristic
208	#95×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
216	#95×C₇₃	C₂³	1	1	yes	characteristic
217	#95×C₇₃	C₂³	1	1	yes	characteristic
218	#95×C₇₃	C₂³	1	2	yes	—
219	#95×C₇₃	C₂³	1	1	yes	characteristic
220	#95×C₇₃	C₂³	1	2	yes	—
221	#95×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
226	#95×C₇₃	C₂³	1	2	yes	—
227	#95×C₇₃	C₂³	1	2	yes	—
228	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
237	C₂×Q₈×C₇₃	—	2	2	no	—
238	C₂×Q₈×C₇₃	—	2	4	no	—
239	C₂×Q₈×C₇₃	—	2	2	no	—
240	C₂×Q₈×C₇₃	—	4	1	no	—
241	C₂×Q₈×C₇₃	—	4	1	no	—
242	C₂×Q₈×C₇₃	—	4	2	no	—
243	C₂×Q₈×C₇₃	—	4	2	no	—
244	C₂×Q₈×C₇₃	—	4	2	no	—
245	C₂×Q₈×C₇₃	—	4	2	no	—
246	C₂×Q₈×C₇₃	—	4	2	no	—
247	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	—
248	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	—
249	C₂²×C₄×C₇₃	—	2	2	no	—
250	C₂²×C₄×C₇₃	—	2	2	no	—
251	C₂²×C₄×C₇₃	—	2	2	no	—
252	C₂²×C₄×C₇₃	—	2	4	no	—
253	C₂²×C₄×C₇₃	—	2	4	no	—
254	C₂²×C₄×C₇₃	—	2	4	no	—
255	C₂²×C₄×C₇₃	—	4	1	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	2	no	—
261	C₂²×C₄×C₇₃	—	4	2	no	—
262	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
263	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
285	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₇₃	—	2	4	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	2	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	2	no	—
304	C₄⋊C₄×C₇₃	—	4	1	no	—
305	C₄⋊C₄×C₇₃	—	4	2	no	—
306	C₄⋊C₄×C₇₃	—	4	1	no	—
307	C₄⋊C₄×C₇₃	—	4	1	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	—	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	C₂×Q₈	1	4	yes	—
321	C₄⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
322	C₄⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
323	C₄⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
324	C₄⋊C₄×C₇₃	#41	1	4	yes	—
325	C₂²⋊C₄×C₇₃	—	2	2	no	—
326	C₂²⋊C₄×C₇₃	—	2	2	no	—
327	C₂²⋊C₄×C₇₃	—	2	4	no	—
328	C₂²⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
329	C₂²⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
330	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
331	C₄²×C₇₃	—	2	4	no	—
332	C₄²×C₇₃	—	2	2	no	—
333	C₄²×C₇₃	—	2	2	no	—
334	C₄²×C₇₃	—	2	2	no	—
335	C₄²×C₇₃	—	2	2	no	—
336	C₄²×C₇₃	—	2	2	no	—
337	C₄²×C₇₃	—	2	2	no	—
338	C₄²×C₇₃	—	4	1	no	—
339	C₄²×C₇₃	—	4	1	no	—
340	C₄²×C₇₃	—	4	2	no	—
341	C₄²×C₇₃	—	4	2	no	—
342	C₄²×C₇₃	—	4	2	no	—
343	C₄²×C₇₃	—	4	2	no	—
344	C₄²×C₇₃	—	4	2	no	—
345	C₂³×C₇₃	—	2	1	no	—
346	C₂³×C₇₃	—	2	1	no	—
347	C₂³×C₇₃	—	2	1	no	—
348	C₂³×C₇₃	—	2	1	no	—
349	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
350	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
351	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
352	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
353	Q₈×C₇₃	—	2	8	no	—
354	Q₈×C₇₃	—	4	4	no	—
355	Q₈×C₇₃	—	8	4	no	—
356	Q₈×C₇₃	—	8	4	no	—
357	C₂×C₄×C₇₃	—	2	1	no	—
358	C₂×C₄×C₇₃	—	2	1	no	—
359	C₂×C₄×C₇₃	—	2	2	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	1	no	—
369	C₂×C₄×C₇₃	—	2	2	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	2	no	—
374	C₂×C₄×C₇₃	—	2	1	no	—
375	C₂×C₄×C₇₃	—	2	1	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	8	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	2	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	2	1	no	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	1	no	—
385	C₂×C₄×C₇₃	—	2	1	no	—
386	C₂×C₄×C₇₃	—	2	2	no	—
387	C₂×C₄×C₇₃	—	2	2	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	2	no	—
395	C₂×C₄×C₇₃	—	2	2	no	—
396	C₂×C₄×C₇₃	—	2	1	no	—
397	C₂×C₄×C₇₃	—	2	1	no	—
398	C₂×C₄×C₇₃	—	2	2	no	—
399	C₂×C₄×C₇₃	—	2	2	no	—
400	C₂×C₄×C₇₃	—	2	2	no	—
401	C₂×C₄×C₇₃	—	2	2	no	—
402	C₂×C₄×C₇₃	—	2	1	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	1	no	—
410	C₂×C₄×C₇₃	—	2	1	no	—
411	C₂×C₄×C₇₃	—	4	4	no	—
412	C₂×C₄×C₇₃	—	4	8	no	—
413	C₂×C₄×C₇₃	—	4	4	no	—
414	C₂×C₄×C₇₃	—	8	4	no	—
415	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
416	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
417	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
418	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
419	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
420	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
421	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
422	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
423	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
424	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
425	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
426	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
427	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
428	C₂²×C₇₃	—	2	2	no	—
429	C₂²×C₇₃	—	2	2	no	—
430	C₂²×C₇₃	—	2	2	no	—
431	C₂²×C₇₃	—	2	2	no	—
432	C₂²×C₇₃	—	2	2	no	—
433	C₂²×C₇₃	—	2	2	no	—
434	C₂²×C₇₃	Q₈²	1	4	yes	—
435	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
436	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
437	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₇₃	#585	1	1	yes	characteristic
441	C₂²×C₇₃	#585	1	1	yes	characteristic
442	C₄×C₇₃	—	2	2	no	—
443	C₄×C₇₃	—	2	4	no	—
444	C₄×C₇₃	—	2	2	no	—
445	C₄×C₇₃	—	2	2	no	—
446	C₄×C₇₃	—	2	2	no	—
447	C₄×C₇₃	—	2	2	no	—
448	C₄×C₇₃	—	2	2	no	—
449	C₄×C₇₃	—	2	2	no	—
450	C₄×C₇₃	—	2	4	no	—
451	C₄×C₇₃	—	2	4	no	—
452	C₄×C₇₃	—	4	1	no	—
453	C₄×C₇₃	—	4	2	no	—
454	C₄×C₇₃	—	4	2	no	—
455	C₄×C₇₃	—	4	1	no	—
456	C₄×C₇₃	—	4	1	no	—
457	C₄×C₇₃	—	4	1	no	—
458	C₄×C₇₃	—	4	1	no	—
459	C₄×C₇₃	—	4	2	no	—
460	C₄×C₇₃	—	4	2	no	—
461	C₄×C₇₃	—	4	2	no	—
462	C₄×C₇₃	—	4	1	no	—
463	C₄×C₇₃	#554	1	4	yes	—
464	#59918	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂×C₇₃	—	2	4	no	—
466	C₂×C₇₃	C₂×#554	1	1	yes	characteristic
467	C₂×C₇₃	C₂×Q₈²	1	1	yes	characteristic
468	C₂×C₇₃	Q₈×#41	1	1	yes	characteristic
469	C₂×C₇₃	#3501	1	1	yes	characteristic
470	C₂×C₇₃	#3504	1	1	yes	characteristic
471	C₂×C₇₃	#3513	1	1	yes	characteristic
472	C₂×C₇₃	#3542	1	1	yes	characteristic
473	#2806	C₂×C₇₃	1	2	yes	complemented
474	#2792	C₂×C₇₃	1	2	yes	complemented
475	#2586	C₂×C₇₃	1	2	yes	complemented
476	#2583	C₂×C₇₃	1	2	yes	—
477	#2582	C₂×C₇₃	1	1	yes	characteristic, complemented
478	#2567	C₂×C₇₃	1	1	yes	characteristic, complemented
479	#2549	C₂×C₇₃	1	2	yes	—
480	#2507	C₂×C₇₃	1	2	yes	complemented
481	#2507	C₂×C₇₃	1	1	yes	characteristic, complemented
482	#2507	C₂×C₇₃	1	1	yes	characteristic, complemented
483	#2502	C₂×C₇₃	1	2	yes	—
484	#2451	C₂×C₇₃	1	1	yes	characteristic, complemented
485	#2451	C₂×C₇₃	1	1	yes	characteristic, complemented
486	#2440	C₂×C₇₃	1	1	yes	characteristic
487	#2440	C₂×C₇₃	1	1	yes	characteristic
488	#2369	C₂×C₇₃	1	1	yes	characteristic, complemented
489	#2368	C₂×C₇₃	1	2	yes	—
490	#2360	C₂×C₇₃	1	1	yes	characteristic
491	#2360	C₂×C₇₃	1	1	yes	characteristic
492	Q₈×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
493	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
494	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
495	C₂×#389	C₂×C₇₃	1	1	yes	characteristic
496	C₇₃	#59918	1	1	yes	characteristic, direct product factor, Sylow
497	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
498	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
499	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
501	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
502	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
503	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
504	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
505	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
506	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
507	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
508	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
509	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
510	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
511	#398	C₂²×C₇₃	1	2	yes	—
512	#398	C₂²×C₇₃	1	2	yes	—
513	#398	C₂²×C₇₃	1	2	yes	—
514	#398	C₂²×C₇₃	1	2	yes	—
515	#398	C₂²×C₇₃	1	2	yes	—
516	#398	C₂²×C₇₃	1	2	yes	—
517	#398	C₂²×C₇₃	1	2	yes	—
518	#398	C₂²×C₇₃	1	2	yes	—
519	#398	C₂²×C₇₃	1	2	yes	—
520	#398	C₂²×C₇₃	1	2	yes	—
521	#395	C₂²×C₇₃	1	2	yes	—
522	#395	C₂²×C₇₃	1	2	yes	—
523	#395	C₂²×C₇₃	1	2	yes	—
524	#395	C₂²×C₇₃	1	2	yes	—
525	#395	C₂²×C₇₃	1	2	yes	—
526	#395	C₂²×C₇₃	1	2	yes	—
527	#391	C₂²×C₇₃	1	2	yes	—
528	#391	C₂²×C₇₃	1	1	yes	characteristic
529	#391	C₂²×C₇₃	1	2	yes	—
530	#391	C₂²×C₇₃	1	1	yes	characteristic
531	#391	C₂²×C₇₃	1	2	yes	—
532	#391	C₂²×C₇₃	1	2	yes	—
533	#391	C₂²×C₇₃	1	2	yes	—
534	#391	C₂²×C₇₃	1	1	yes	characteristic
535	#391	C₂²×C₇₃	1	2	yes	—
536	#391	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	1	yes	characteristic
540	#389	C₂²×C₇₃	1	1	yes	characteristic
541	#389	C₂²×C₇₃	1	2	yes	—
542	#389	C₂²×C₇₃	1	1	yes	characteristic
543	#389	C₂²×C₇₃	1	1	yes	characteristic
544	#389	C₂²×C₇₃	1	2	yes	—
545	#389	C₂²×C₇₃	1	2	yes	—
546	#389	C₂²×C₇₃	1	2	yes	—
547	#389	C₂²×C₇₃	1	2	yes	—
548	#389	C₂²×C₇₃	1	1	yes	characteristic
549	#389	C₂²×C₇₃	1	2	yes	—
550	#389	C₂²×C₇₃	1	1	yes	characteristic
551	#389	C₂²×C₇₃	1	2	yes	—
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	1	yes	characteristic
556	#389	C₂²×C₇₃	1	2	yes	—
557	#389	C₂²×C₇₃	1	1	yes	characteristic
558	#389	C₂²×C₇₃	1	2	yes	—
559	#387	C₂²×C₇₃	1	1	yes	characteristic
560	#387	C₂²×C₇₃	1	2	yes	—
561	#387	C₂²×C₇₃	1	2	yes	—
562	#387	C₂²×C₇₃	1	2	yes	—
563	#387	C₂²×C₇₃	1	2	yes	—
564	#387	C₂²×C₇₃	1	2	yes	—
565	#387	C₂²×C₇₃	1	2	yes	—
566	#387	C₂²×C₇₃	1	1	yes	characteristic
567	#387	C₂²×C₇₃	1	2	yes	—
568	#385	C₂²×C₇₃	1	1	yes	characteristic
569	#385	C₂²×C₇₃	1	2	yes	—
570	#385	C₂²×C₇₃	1	2	yes	—
571	#385	C₂²×C₇₃	1	2	yes	—
572	#385	C₂²×C₇₃	1	2	yes	—
573	#385	C₂²×C₇₃	1	2	yes	—
574	#385	C₂²×C₇₃	1	1	yes	characteristic
575	#384	C₂²×C₇₃	1	2	yes	—
576	#384	C₂²×C₇₃	1	1	yes	characteristic
577	#384	C₂²×C₇₃	1	1	yes	characteristic
578	#384	C₂²×C₇₃	1	2	yes	—
579	#380	C₂²×C₇₃	1	1	yes	characteristic
580	#380	C₂²×C₇₃	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
591	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
593	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
594	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
595	C₂×#95	C₂²×C₇₃	1	2	yes	—
596	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
598	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
599	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
601	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
603	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
605	C₄⋊Q₈	—	2	4	no	—
606	C₄⋊Q₈	—	4	2	no	—
607	C₂²⋊Q₈	—	4	4	no	—
608	C₂²⋊Q₈	—	4	4	no	—
609	C₂²⋊Q₈	Q₈×C₇₃	1	8	yes	complemented
610	C₂²⋊Q₈	Q₈×C₇₃	1	8	yes	complemented
611	C₄×Q₈	—	2	4	no	—
612	C₄×Q₈	—	4	2	no	—
613	C₄×Q₈	—	4	2	no	—
614	C₄×Q₈	—	4	2	no	—
615	C₂×C₄⋊C₄	—	2	4	no	—
616	C₂×C₄⋊C₄	—	4	2	no	—
617	C₂×C₄⋊C₄	—	4	4	no	—
618	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
663	C₂×C₄²	—	4	2	no	—
664	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
668	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
676	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
678	#95	C₂³×C₇₃	1	2	yes	—
679	#95	C₂³×C₇₃	1	2	yes	—
680	#95	C₂³×C₇₃	1	2	yes	—
681	#95	C₂³×C₇₃	1	2	yes	—
682	#95	C₂³×C₇₃	1	1	yes	characteristic
683	#95	C₂³×C₇₃	1	2	yes	—
684	#95	C₂³×C₇₃	1	1	yes	characteristic
685	#95	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
690	#95	C₂³×C₇₃	1	1	yes	characteristic
691	#95	C₂³×C₇₃	1	2	yes	—
692	#95	C₂³×C₇₃	1	1	yes	characteristic
693	#95	C₂³×C₇₃	1	1	yes	characteristic
694	#95	C₂³×C₇₃	1	2	yes	—
695	#95	C₂³×C₇₃	1	1	yes	characteristic
696	#95	C₂³×C₇₃	1	2	yes	—
697	#95	C₂³×C₇₃	1	2	yes	—
698	#95	C₂³×C₇₃	1	2	yes	—
699	#95	C₂³×C₇₃	1	1	yes	characteristic
700	#95	C₂³×C₇₃	1	2	yes	—
701	#95	C₂³×C₇₃	1	1	yes	characteristic
702	#95	C₂³×C₇₃	1	2	yes	—
703	#95	C₂³×C₇₃	1	2	yes	—
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	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	4	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	4	1	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	—	4	2	no	—
716	C₂×Q₈	—	4	2	no	—
717	C₂×Q₈	—	4	2	no	—
718	C₂×Q₈	—	4	2	no	—
719	C₂×Q₈	—	4	2	no	—
720	C₂×Q₈	C₂×Q₈×C₇₃	1	4	yes	—
721	C₂×Q₈	C₂×Q₈×C₇₃	1	4	yes	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
736	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	1	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	1	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	1	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
793	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
794	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
795	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
796	C₄⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
797	C₄⋊C₄	#41×C₇₃	1	4	yes	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
802	C₂²⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
803	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
804	C₄²	—	2	4	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	4	1	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
823	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
824	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
825	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
826	Q₈	—	2	8	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	8	4	no	—
829	Q₈	—	8	4	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	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	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	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	8	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	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	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	4	no	—
887	C₂×C₄	—	8	4	no	—
888	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
889	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
890	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
891	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
892	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
893	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
894	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
895	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
896	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
897	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
898	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
899	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
900	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	Q₈²×C₇₃	1	4	yes	—
908	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
909	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
910	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
911	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
912	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
913	C₂²	#585×C₇₃	1	1	yes	characteristic
914	C₂²	#585×C₇₃	1	1	yes	characteristic
915	C₄	—	2	2	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	4	no	—
924	C₄	—	2	4	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	1	no	—
936	C₄	#554×C₇₃	1	4	yes	—
937	C₂	—	2	4	no	—
938	C₂	C₂×#554×C₇₃	1	1	yes	characteristic
939	C₂	C₂×Q₈²×C₇₃	1	1	yes	characteristic
940	C₂	Q₈×#41×C₇₃	1	1	yes	characteristic
941	C₂	C₇₃×#3501	1	1	yes	characteristic
942	C₂	C₇₃×#3504	1	1	yes	characteristic
943	C₂	C₇₃×#3513	1	1	yes	characteristic
944	C₂	C₇₃×#3542	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×#2806	C₂	semidirect
2. C₇₃×#2792	C₂	semidirect
3. C₇₃×#2586	C₂	semidirect
5. C₇₃×#2582	C₂	semidirect
6. C₇₃×#2567	C₂	semidirect
8. C₇₃×#2507	C₂	semidirect
9. C₇₃×#2507	C₂	semidirect
10. C₇₃×#2507	C₂	semidirect
12. C₇₃×#2451	C₂	semidirect
13. C₇₃×#2451	C₂	semidirect
16. C₇₃×#2369	C₂	semidirect
20. Q₈×C₄⋊C₄×C₇₃	C₂	semidirect
136. C₂²⋊Q₈×C₇₃	Q₈	semidirect
137. C₂²⋊Q₈×C₇₃	Q₈	semidirect
464. #59918	C₇₃	direct (N × H)
473. #2806	C₂×C₇₃	semidirect
474. #2792	C₂×C₇₃	semidirect
475. #2586	C₂×C₇₃	semidirect
477. #2582	C₂×C₇₃	semidirect
478. #2567	C₂×C₇₃	semidirect
480. #2507	C₂×C₇₃	semidirect
481. #2507	C₂×C₇₃	semidirect
482. #2507	C₂×C₇₃	semidirect
484. #2451	C₂×C₇₃	semidirect
485. #2451	C₂×C₇₃	semidirect
488. #2369	C₂×C₇₃	semidirect
492. Q₈×C₄⋊C₄	C₂×C₇₃	semidirect
496. C₇₃	#59918	direct (N × H)
609. C₂²⋊Q₈	Q₈×C₇₃	semidirect
610. 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×#2806	2
C₇₃×#2792	2
C₇₃×#2586	2
C₇₃×#2583	2
C₇₃×#2582	2
C₇₃×#2567	2
C₇₃×#2549	2
C₇₃×#2507	2
C₇₃×#2502	2
C₇₃×#2451	2
C₇₃×#2440	2
C₇₃×#2369	2
C₇₃×#2368	2
C₇₃×#2360	2
Q₈×C₄⋊C₄×C₇₃	2
C₄×C₂²⋊Q₈×C₇₃	2
C₂×#389×C₇₃	2
#59918	73

Subgroups — C73×#59918 #32969322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59918 #32969322