Subgroups — C₇₃×#59833 #32969237

Order 18688.

2096 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2720	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2677	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2580	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#2556	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2556	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2492	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2473	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2465	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2454	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2452	C₂	1	1	yes	maximal, characteristic
17	C₇₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2367	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2367	C₂	1	1	yes	maximal, characteristic
20	C₇₃×#2360	C₂	1	2	yes	maximal, complemented
21	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic
24	#557×C₇₃	—	2	8	no	—
25	#554×C₇₃	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#125×C₇₃	C₂²	1	2	yes	—
33	C₂×#125×C₇₃	C₂²	1	2	yes	—
34	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
50	#400×C₇₃	C₂²	1	2	yes	—
51	#400×C₇₃	C₂²	1	2	yes	—
52	#399×C₇₃	C₂²	1	2	yes	—
53	#399×C₇₃	C₂²	1	2	yes	—
54	#398×C₇₃	C₂²	1	2	yes	—
55	#398×C₇₃	C₂²	1	2	yes	—
56	#398×C₇₃	C₂²	1	2	yes	—
57	#398×C₇₃	C₂²	1	2	yes	—
58	#396×C₇₃	C₂²	1	2	yes	—
59	#396×C₇₃	C₂²	1	2	yes	—
60	#395×C₇₃	C₂²	1	2	yes	—
61	#395×C₇₃	C₂²	1	2	yes	—
62	#395×C₇₃	C₂²	1	2	yes	—
63	#395×C₇₃	C₂²	1	2	yes	—
64	#393×C₇₃	C₂²	1	2	yes	—
65	#393×C₇₃	C₂²	1	2	yes	—
66	#391×C₇₃	C₂²	1	1	yes	characteristic
67	#391×C₇₃	C₂²	1	2	yes	—
68	#391×C₇₃	C₂²	1	1	yes	characteristic
69	#391×C₇₃	C₂²	1	1	yes	characteristic
70	#391×C₇₃	C₂²	1	1	yes	characteristic
71	#391×C₇₃	C₂²	1	2	yes	—
72	#391×C₇₃	C₂²	1	2	yes	—
73	#391×C₇₃	C₂²	1	1	yes	characteristic
74	#390×C₇₃	C₂²	1	1	yes	characteristic
75	#390×C₇₃	C₂²	1	1	yes	characteristic
76	#390×C₇₃	C₂²	1	1	yes	characteristic
77	#389×C₇₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
83	#389×C₇₃	C₂²	1	1	yes	characteristic
84	#389×C₇₃	C₂²	1	1	yes	characteristic
85	#389×C₇₃	C₂²	1	1	yes	characteristic
86	#389×C₇₃	C₂²	1	2	yes	—
87	#389×C₇₃	C₂²	1	2	yes	—
88	#389×C₇₃	C₂²	1	1	yes	characteristic
89	#389×C₇₃	C₂²	1	1	yes	characteristic
90	#388×C₇₃	C₂²	1	2	yes	—
91	#388×C₇₃	C₂²	1	2	yes	—
92	#388×C₇₃	C₂²	1	2	yes	—
93	#388×C₇₃	C₂²	1	2	yes	—
94	#388×C₇₃	C₂²	1	2	yes	—
95	#388×C₇₃	C₂²	1	2	yes	—
96	#387×C₇₃	C₂²	1	2	yes	—
97	#387×C₇₃	C₂²	1	2	yes	—
98	#387×C₇₃	C₂²	1	2	yes	—
99	#387×C₇₃	C₂²	1	2	yes	—
100	#387×C₇₃	C₂²	1	2	yes	—
101	#387×C₇₃	C₂²	1	2	yes	—
102	#385×C₇₃	C₂²	1	2	yes	—
103	#385×C₇₃	C₂²	1	2	yes	—
104	#385×C₇₃	C₂²	1	2	yes	—
105	#385×C₇₃	C₂²	1	2	yes	—
106	#385×C₇₃	C₂²	1	2	yes	—
107	#385×C₇₃	C₂²	1	2	yes	—
108	#384×C₇₃	C₂²	1	1	yes	characteristic
109	#382×C₇₃	C₂²	1	1	yes	characteristic
110	#382×C₇₃	C₂²	1	1	yes	characteristic
111	#380×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	1	yes	characteristic
117	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
124	C₄³×C₇₃	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
127	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
130	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₇₃	—	2	4	no	—
135	C₄⋊Q₈×C₇₃	—	2	8	no	—
136	C₄⋊Q₈×C₇₃	—	2	4	no	—
137	C₄⋊Q₈×C₇₃	—	2	4	no	—
138	#125×C₇₃	—	2	4	no	—
139	#125×C₇₃	—	2	8	no	—
140	#125×C₇₃	—	2	8	no	—
141	#125×C₇₃	—	2	4	no	—
142	#125×C₇₃	D₄	1	8	yes	—
143	#124×C₇₃	Q₈	1	8	yes	complemented
144	C₂²⋊Q₈×C₇₃	—	2	8	no	—
145	C₂²⋊Q₈×C₇₃	—	2	8	no	—
146	C₂²⋊Q₈×C₇₃	—	2	8	no	—
147	C₂²⋊Q₈×C₇₃	—	2	8	no	—
148	C₄×Q₈×C₇₃	—	2	4	no	—
149	C₄×Q₈×C₇₃	—	2	8	no	—
150	C₄×Q₈×C₇₃	—	2	4	no	—
151	C₄×Q₈×C₇₃	—	2	4	no	—
152	C₄×Q₈×C₇₃	—	2	4	no	—
153	C₄×Q₈×C₇₃	—	2	4	no	—
154	C₄×D₄×C₇₃	—	2	4	no	—
155	C₄×D₄×C₇₃	—	2	4	no	—
156	C₄×D₄×C₇₃	—	2	4	no	—
157	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
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	1	yes	characteristic
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
222	#95×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
228	#95×C₇₃	C₂³	1	2	yes	—
229	#95×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
234	#95×C₇₃	C₂³	1	2	yes	—
235	#95×C₇₃	C₂³	1	2	yes	—
236	#95×C₇₃	C₂³	1	2	yes	—
237	#95×C₇₃	C₂³	1	2	yes	—
238	#95×C₇₃	C₂³	1	1	yes	characteristic
239	#95×C₇₃	C₂³	1	1	yes	characteristic
240	#95×C₇₃	C₂³	1	1	yes	characteristic
241	#95×C₇₃	C₂³	1	1	yes	characteristic
242	#95×C₇₃	C₂³	1	2	yes	—
243	#95×C₇₃	C₂³	1	2	yes	—
244	#95×C₇₃	C₂³	1	2	yes	—
245	#95×C₇₃	C₂³	1	2	yes	—
246	#95×C₇₃	C₂³	1	2	yes	—
247	#95×C₇₃	C₂³	1	2	yes	—
248	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₇₃	—	2	2	no	—
250	C₂×Q₈×C₇₃	—	2	2	no	—
251	C₂×Q₈×C₇₃	—	2	4	no	—
252	C₂×Q₈×C₇₃	—	2	2	no	—
253	C₂×Q₈×C₇₃	—	2	4	no	—
254	C₂×Q₈×C₇₃	—	2	4	no	—
255	C₂×Q₈×C₇₃	—	2	2	no	—
256	C₂×Q₈×C₇₃	—	2	2	no	—
257	C₂×Q₈×C₇₃	—	2	2	no	—
258	C₂×Q₈×C₇₃	—	4	2	no	—
259	C₂×Q₈×C₇₃	—	4	1	no	—
260	C₂×Q₈×C₇₃	—	4	1	no	—
261	C₂×Q₈×C₇₃	—	4	2	no	—
262	C₂×Q₈×C₇₃	—	4	2	no	—
263	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	—
264	C₂×D₄×C₇₃	—	2	2	no	—
265	C₂×D₄×C₇₃	—	2	2	no	—
266	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
267	C₂²×C₄×C₇₃	—	2	4	no	—
268	C₂²×C₄×C₇₃	—	2	4	no	—
269	C₂²×C₄×C₇₃	—	2	4	no	—
270	C₂²×C₄×C₇₃	—	2	4	no	—
271	C₂²×C₄×C₇₃	—	4	2	no	—
272	C₂²×C₄×C₇₃	—	4	2	no	—
273	C₂²×C₄×C₇₃	—	4	2	no	—
274	C₂²×C₄×C₇₃	—	4	2	no	—
275	C₂²×C₄×C₇₃	—	4	2	no	—
276	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₇₃	—	2	2	no	—
299	C₄⋊C₄×C₇₃	—	2	4	no	—
300	C₄⋊C₄×C₇₃	—	2	4	no	—
301	C₄⋊C₄×C₇₃	—	2	2	no	—
302	C₄⋊C₄×C₇₃	—	2	2	no	—
303	C₄⋊C₄×C₇₃	—	2	2	no	—
304	C₄⋊C₄×C₇₃	—	2	2	no	—
305	C₄⋊C₄×C₇₃	—	2	4	no	—
306	C₄⋊C₄×C₇₃	—	2	2	no	—
307	C₄⋊C₄×C₇₃	—	2	4	no	—
308	C₄⋊C₄×C₇₃	—	2	2	no	—
309	C₄⋊C₄×C₇₃	—	2	4	no	—
310	C₄⋊C₄×C₇₃	—	2	4	no	—
311	C₄⋊C₄×C₇₃	—	2	2	no	—
312	C₄⋊C₄×C₇₃	—	2	4	no	—
313	C₄⋊C₄×C₇₃	—	2	4	no	—
314	C₄⋊C₄×C₇₃	—	2	4	no	—
315	C₄⋊C₄×C₇₃	—	2	4	no	—
316	C₄⋊C₄×C₇₃	—	2	4	no	—
317	C₄⋊C₄×C₇₃	—	2	2	no	—
318	C₄⋊C₄×C₇₃	—	2	2	no	—
319	C₄⋊C₄×C₇₃	—	2	2	no	—
320	C₄⋊C₄×C₇₃	—	2	2	no	—
321	C₄⋊C₄×C₇₃	—	2	2	no	—
322	C₄⋊C₄×C₇₃	—	4	1	no	—
323	C₄⋊C₄×C₇₃	—	4	1	no	—
324	C₄⋊C₄×C₇₃	—	4	1	no	—
325	C₄⋊C₄×C₇₃	—	4	1	no	—
326	C₄⋊C₄×C₇₃	—	4	2	no	—
327	C₄⋊C₄×C₇₃	—	4	2	no	—
328	C₄⋊C₄×C₇₃	—	4	2	no	—
329	C₄⋊C₄×C₇₃	—	4	2	no	—
330	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
331	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
332	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
333	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
334	C₄⋊C₄×C₇₃	#41	1	4	yes	—
335	C₂²⋊C₄×C₇₃	—	2	4	no	—
336	C₂²⋊C₄×C₇₃	—	2	4	no	—
337	C₂²⋊C₄×C₇₃	—	2	4	no	—
338	C₂²⋊C₄×C₇₃	—	2	4	no	—
339	C₂²⋊C₄×C₇₃	—	2	4	no	—
340	C₂²⋊C₄×C₇₃	—	4	2	no	—
341	C₂²⋊C₄×C₇₃	—	4	2	no	—
342	C₂²⋊C₄×C₇₃	—	4	2	no	—
343	C₂²⋊C₄×C₇₃	—	4	2	no	—
344	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
345	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
346	C₄²×C₇₃	—	2	2	no	—
347	C₄²×C₇₃	—	2	2	no	—
348	C₄²×C₇₃	—	2	4	no	—
349	C₄²×C₇₃	—	2	4	no	—
350	C₄²×C₇₃	—	2	2	no	—
351	C₄²×C₇₃	—	2	4	no	—
352	C₄²×C₇₃	—	2	2	no	—
353	C₄²×C₇₃	—	2	2	no	—
354	C₄²×C₇₃	—	2	2	no	—
355	C₄²×C₇₃	—	4	1	no	—
356	C₄²×C₇₃	—	4	2	no	—
357	C₄²×C₇₃	—	4	2	no	—
358	C₄²×C₇₃	—	4	1	no	—
359	C₄²×C₇₃	—	4	1	no	—
360	C₄²×C₇₃	C₂×D₄	1	4	yes	—
361	C₄²×C₇₃	C₂×Q₈	1	4	yes	—
362	C₂³×C₇₃	—	2	2	no	—
363	C₂³×C₇₃	—	2	2	no	—
364	C₂³×C₇₃	—	2	2	no	—
365	C₂³×C₇₃	—	2	2	no	—
366	C₂³×C₇₃	—	2	2	no	—
367	C₂³×C₇₃	—	2	2	no	—
368	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
369	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
370	Q₈×C₇₃	—	2	8	no	—
371	Q₈×C₇₃	—	4	4	no	—
372	Q₈×C₇₃	—	4	8	no	—
373	Q₈×C₇₃	—	4	4	no	—
374	Q₈×C₇₃	—	8	4	no	—
375	D₄×C₇₃	—	2	8	no	—
376	C₂×C₄×C₇₃	—	2	2	no	—
377	C₂×C₄×C₇₃	—	2	1	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	2	1	no	—
383	C₂×C₄×C₇₃	—	2	2	no	—
384	C₂×C₄×C₇₃	—	2	1	no	—
385	C₂×C₄×C₇₃	—	2	1	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	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	1	no	—
402	C₂×C₄×C₇₃	—	2	1	no	—
403	C₂×C₄×C₇₃	—	2	2	no	—
404	C₂×C₄×C₇₃	—	2	2	no	—
405	C₂×C₄×C₇₃	—	2	2	no	—
406	C₂×C₄×C₇₃	—	2	1	no	—
407	C₂×C₄×C₇₃	—	2	1	no	—
408	C₂×C₄×C₇₃	—	2	1	no	—
409	C₂×C₄×C₇₃	—	2	2	no	—
410	C₂×C₄×C₇₃	—	2	2	no	—
411	C₂×C₄×C₇₃	—	2	1	no	—
412	C₂×C₄×C₇₃	—	2	2	no	—
413	C₂×C₄×C₇₃	—	2	2	no	—
414	C₂×C₄×C₇₃	—	2	1	no	—
415	C₂×C₄×C₇₃	—	2	1	no	—
416	C₂×C₄×C₇₃	—	2	1	no	—
417	C₂×C₄×C₇₃	—	2	1	no	—
418	C₂×C₄×C₇₃	—	2	2	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	—	2	1	no	—
425	C₂×C₄×C₇₃	—	2	2	no	—
426	C₂×C₄×C₇₃	—	2	2	no	—
427	C₂×C₄×C₇₃	—	2	1	no	—
428	C₂×C₄×C₇₃	—	2	1	no	—
429	C₂×C₄×C₇₃	—	4	8	no	—
430	C₂×C₄×C₇₃	—	8	4	no	—
431	C₂×C₄×C₇₃	—	8	4	no	—
432	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
434	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
435	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
438	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
439	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
440	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
441	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
443	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
445	C₂²×C₇₃	—	2	4	no	—
446	C₂²×C₇₃	—	2	4	no	—
447	C₂²×C₇₃	—	2	4	no	—
448	C₂²×C₇₃	—	4	2	no	—
449	C₂²×C₇₃	—	4	2	no	—
450	C₂²×C₇₃	—	4	2	no	—
451	C₂²×C₇₃	—	4	2	no	—
452	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
453	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
454	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
455	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂²×C₇₃	#585	1	1	yes	characteristic
457	C₂²×C₇₃	#585	1	1	yes	characteristic
458	C₂²×C₇₃	#585	1	1	yes	characteristic
459	C₄×C₇₃	—	2	4	no	—
460	C₄×C₇₃	—	2	2	no	—
461	C₄×C₇₃	—	2	4	no	—
462	C₄×C₇₃	—	2	2	no	—
463	C₄×C₇₃	—	2	2	no	—
464	C₄×C₇₃	—	2	2	no	—
465	C₄×C₇₃	—	2	2	no	—
466	C₄×C₇₃	—	2	4	no	—
467	C₄×C₇₃	—	2	2	no	—
468	C₄×C₇₃	—	2	2	no	—
469	C₄×C₇₃	—	4	1	no	—
470	C₄×C₇₃	—	4	2	no	—
471	C₄×C₇₃	—	4	1	no	—
472	C₄×C₇₃	—	4	1	no	—
473	C₄×C₇₃	—	4	1	no	—
474	C₄×C₇₃	—	4	1	no	—
475	C₄×C₇₃	—	4	2	no	—
476	C₄×C₇₃	—	4	1	no	—
477	C₄×C₇₃	—	4	2	no	—
478	C₄×C₇₃	—	4	1	no	—
479	C₄×C₇₃	—	4	2	no	—
480	C₄×C₇₃	D₄×Q₈	1	4	yes	—
481	#59833	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₂×C₇₃	—	4	4	no	—
483	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
484	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
485	C₂×C₇₃	Q₈×#41	1	1	yes	characteristic
486	C₂×C₇₃	#3500	1	1	yes	characteristic
487	C₂×C₇₃	#3504	1	1	yes	characteristic
488	C₂×C₇₃	#3507	1	1	yes	characteristic
489	C₂×C₇₃	#3557	1	1	yes	characteristic
490	C₂×#557	C₂×C₇₃	1	1	yes	characteristic, complemented
491	C₂×#554	C₂×C₇₃	1	1	yes	characteristic
492	#2720	C₂×C₇₃	1	2	yes	complemented
493	#2677	C₂×C₇₃	1	2	yes	complemented
494	#2581	C₂×C₇₃	1	1	yes	characteristic, complemented
495	#2580	C₂×C₇₃	1	1	yes	characteristic
496	#2556	C₂×C₇₃	1	2	yes	complemented
497	#2556	C₂×C₇₃	1	2	yes	complemented
498	#2550	C₂×C₇₃	1	1	yes	characteristic, complemented
499	#2550	C₂×C₇₃	1	1	yes	characteristic, complemented
500	#2492	C₂×C₇₃	1	2	yes	complemented
501	#2473	C₂×C₇₃	1	2	yes	complemented
502	#2465	C₂×C₇₃	1	2	yes	complemented
503	#2454	C₂×C₇₃	1	1	yes	characteristic
504	#2453	C₂×C₇₃	1	1	yes	characteristic, complemented
505	#2452	C₂×C₇₃	1	1	yes	characteristic
506	#2451	C₂×C₇₃	1	1	yes	characteristic, complemented
507	#2367	C₂×C₇₃	1	1	yes	characteristic
508	#2367	C₂×C₇₃	1	1	yes	characteristic
509	#2360	C₂×C₇₃	1	2	yes	complemented
510	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
511	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
512	C₄×#124	C₂×C₇₃	1	1	yes	characteristic
513	C₇₃	#59833	1	1	yes	characteristic, direct product factor, Sylow
514	#557	—	2	8	no	—
515	#554	—	2	8	no	—
516	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
517	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
518	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
519	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
520	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
521	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
522	C₂×#125	C₂²×C₇₃	1	2	yes	—
523	C₂×#125	C₂²×C₇₃	1	2	yes	—
524	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
525	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
526	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
527	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
528	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
529	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
530	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
531	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
532	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
533	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
534	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
535	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
536	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
537	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
538	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
539	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
540	#400	C₂²×C₇₃	1	2	yes	—
541	#400	C₂²×C₇₃	1	2	yes	—
542	#399	C₂²×C₇₃	1	2	yes	—
543	#399	C₂²×C₇₃	1	2	yes	—
544	#398	C₂²×C₇₃	1	2	yes	—
545	#398	C₂²×C₇₃	1	2	yes	—
546	#398	C₂²×C₇₃	1	2	yes	—
547	#398	C₂²×C₇₃	1	2	yes	—
548	#396	C₂²×C₇₃	1	2	yes	—
549	#396	C₂²×C₇₃	1	2	yes	—
550	#395	C₂²×C₇₃	1	2	yes	—
551	#395	C₂²×C₇₃	1	2	yes	—
552	#395	C₂²×C₇₃	1	2	yes	—
553	#395	C₂²×C₇₃	1	2	yes	—
554	#393	C₂²×C₇₃	1	2	yes	—
555	#393	C₂²×C₇₃	1	2	yes	—
556	#391	C₂²×C₇₃	1	1	yes	characteristic
557	#391	C₂²×C₇₃	1	1	yes	characteristic
558	#391	C₂²×C₇₃	1	1	yes	characteristic
559	#391	C₂²×C₇₃	1	1	yes	characteristic
560	#391	C₂²×C₇₃	1	2	yes	—
561	#391	C₂²×C₇₃	1	1	yes	characteristic
562	#391	C₂²×C₇₃	1	2	yes	—
563	#391	C₂²×C₇₃	1	2	yes	—
564	#390	C₂²×C₇₃	1	1	yes	characteristic
565	#390	C₂²×C₇₃	1	1	yes	characteristic
566	#390	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	#389	C₂²×C₇₃	1	1	yes	characteristic
571	#389	C₂²×C₇₃	1	1	yes	characteristic
572	#389	C₂²×C₇₃	1	1	yes	characteristic
573	#389	C₂²×C₇₃	1	1	yes	characteristic
574	#389	C₂²×C₇₃	1	1	yes	characteristic
575	#389	C₂²×C₇₃	1	1	yes	characteristic
576	#389	C₂²×C₇₃	1	1	yes	characteristic
577	#389	C₂²×C₇₃	1	2	yes	—
578	#389	C₂²×C₇₃	1	2	yes	—
579	#389	C₂²×C₇₃	1	2	yes	—
580	#388	C₂²×C₇₃	1	2	yes	—
581	#388	C₂²×C₇₃	1	2	yes	—
582	#388	C₂²×C₇₃	1	2	yes	—
583	#388	C₂²×C₇₃	1	2	yes	—
584	#388	C₂²×C₇₃	1	2	yes	—
585	#388	C₂²×C₇₃	1	2	yes	—
586	#387	C₂²×C₇₃	1	2	yes	—
587	#387	C₂²×C₇₃	1	2	yes	—
588	#387	C₂²×C₇₃	1	2	yes	—
589	#387	C₂²×C₇₃	1	2	yes	—
590	#387	C₂²×C₇₃	1	2	yes	—
591	#387	C₂²×C₇₃	1	2	yes	—
592	#385	C₂²×C₇₃	1	2	yes	—
593	#385	C₂²×C₇₃	1	2	yes	—
594	#385	C₂²×C₇₃	1	2	yes	—
595	#385	C₂²×C₇₃	1	2	yes	—
596	#385	C₂²×C₇₃	1	2	yes	—
597	#385	C₂²×C₇₃	1	2	yes	—
598	#384	C₂²×C₇₃	1	1	yes	characteristic
599	#382	C₂²×C₇₃	1	1	yes	characteristic
600	#382	C₂²×C₇₃	1	1	yes	characteristic
601	#380	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	2	yes	—
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	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
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	2	yes	—
613	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
614	C₄³	C₂²×C₇₃	1	1	yes	characteristic
615	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
617	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
618	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
619	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
620	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
622	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
623	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
624	C₄⋊Q₈	—	2	4	no	—
625	C₄⋊Q₈	—	2	8	no	—
626	C₄⋊Q₈	—	2	4	no	—
627	C₄⋊Q₈	—	2	4	no	—
628	#125	—	2	4	no	—
629	#125	—	2	8	no	—
630	#125	—	2	8	no	—
631	#125	—	2	4	no	—
632	#125	D₄×C₇₃	1	8	yes	—
633	#124	Q₈×C₇₃	1	8	yes	complemented
634	C₂²⋊Q₈	—	2	8	no	—
635	C₂²⋊Q₈	—	2	8	no	—
636	C₂²⋊Q₈	—	2	8	no	—
637	C₂²⋊Q₈	—	2	8	no	—
638	C₄×Q₈	—	2	4	no	—
639	C₄×Q₈	—	2	8	no	—
640	C₄×Q₈	—	2	4	no	—
641	C₄×Q₈	—	2	4	no	—
642	C₄×Q₈	—	2	4	no	—
643	C₄×Q₈	—	2	4	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	2	4	no	—
646	C₄×D₄	—	2	4	no	—
647	C₂×C₄⋊C₄	—	2	8	no	—
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
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	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
709	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
710	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
712	#95	C₂³×C₇₃	1	1	yes	characteristic
713	#95	C₂³×C₇₃	1	1	yes	characteristic
714	#95	C₂³×C₇₃	1	2	yes	—
715	#95	C₂³×C₇₃	1	2	yes	—
716	#95	C₂³×C₇₃	1	2	yes	—
717	#95	C₂³×C₇₃	1	2	yes	—
718	#95	C₂³×C₇₃	1	2	yes	—
719	#95	C₂³×C₇₃	1	2	yes	—
720	#95	C₂³×C₇₃	1	1	yes	characteristic
721	#95	C₂³×C₇₃	1	2	yes	—
722	#95	C₂³×C₇₃	1	2	yes	—
723	#95	C₂³×C₇₃	1	1	yes	characteristic
724	#95	C₂³×C₇₃	1	2	yes	—
725	#95	C₂³×C₇₃	1	2	yes	—
726	#95	C₂³×C₇₃	1	2	yes	—
727	#95	C₂³×C₇₃	1	2	yes	—
728	#95	C₂³×C₇₃	1	1	yes	characteristic
729	#95	C₂³×C₇₃	1	1	yes	characteristic
730	#95	C₂³×C₇₃	1	1	yes	characteristic
731	#95	C₂³×C₇₃	1	1	yes	characteristic
732	#95	C₂³×C₇₃	1	2	yes	—
733	#95	C₂³×C₇₃	1	2	yes	—
734	#95	C₂³×C₇₃	1	2	yes	—
735	#95	C₂³×C₇₃	1	2	yes	—
736	#95	C₂³×C₇₃	1	2	yes	—
737	#95	C₂³×C₇₃	1	2	yes	—
738	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	2	4	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	2	4	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	—	4	1	no	—
750	C₂×Q₈	—	4	1	no	—
751	C₂×Q₈	—	4	2	no	—
752	C₂×Q₈	—	4	2	no	—
753	C₂×Q₈	C₂×Q₈×C₇₃	1	4	yes	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
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	2	yes	—
774	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
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	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	1	no	—
814	C₄⋊C₄	—	4	1	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
821	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
822	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
823	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
824	C₄⋊C₄	#41×C₇₃	1	4	yes	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
835	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	4	no	—
839	C₄²	—	2	4	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	4	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	4	1	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₄²	—	4	1	no	—
849	C₄²	—	4	1	no	—
850	C₄²	C₂×D₄×C₇₃	1	4	yes	—
851	C₄²	C₂×Q₈×C₇₃	1	4	yes	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	C₂²×Q₈×C₇₃	1	4	yes	—
859	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
860	Q₈	—	2	8	no	—
861	Q₈	—	4	4	no	—
862	Q₈	—	4	8	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	8	4	no	—
865	D₄	—	2	8	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	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	2	no	—
884	C₂×C₄	—	2	1	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	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	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	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	4	8	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	—	8	4	no	—
922	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
923	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
924	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
925	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
927	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
928	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
929	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
930	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
931	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
932	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
933	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
934	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
943	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
944	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
945	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
946	C₂²	#585×C₇₃	1	1	yes	characteristic
947	C₂²	#585×C₇₃	1	1	yes	characteristic
948	C₂²	#585×C₇₃	1	1	yes	characteristic
949	C₄	—	2	4	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	4	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	4	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	D₄×Q₈×C₇₃	1	4	yes	—
971	C₂	—	4	4	no	—
972	C₂	C₂×D₄×Q₈×C₇₃	1	1	yes	characteristic
973	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
974	C₂	Q₈×#41×C₇₃	1	1	yes	characteristic
975	C₂	C₇₃×#3500	1	1	yes	characteristic
976	C₂	C₇₃×#3504	1	1	yes	characteristic
977	C₂	C₇₃×#3507	1	1	yes	characteristic
978	C₂	C₇₃×#3557	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂²×D₄×C₇₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#557×C₇₃	C₂	semidirect
3. C₇₃×#2720	C₂	semidirect
4. C₇₃×#2677	C₂	semidirect
5. C₇₃×#2581	C₂	semidirect
7. C₇₃×#2556	C₂	semidirect
8. C₇₃×#2556	C₂	semidirect
9. C₇₃×#2550	C₂	semidirect
10. C₇₃×#2550	C₂	semidirect
11. C₇₃×#2492	C₂	semidirect
12. C₇₃×#2473	C₂	semidirect
13. C₇₃×#2465	C₂	semidirect
15. C₇₃×#2453	C₂	semidirect
17. C₇₃×#2451	C₂	semidirect
20. C₇₃×#2360	C₂	semidirect
21. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
22. C₄×#125×C₇₃	C₂	semidirect
143. #124×C₇₃	Q₈	semidirect
481. #59833	C₇₃	direct (N × H)
490. C₂×#557	C₂×C₇₃	semidirect
492. #2720	C₂×C₇₃	semidirect
493. #2677	C₂×C₇₃	semidirect
494. #2581	C₂×C₇₃	semidirect
496. #2556	C₂×C₇₃	semidirect
497. #2556	C₂×C₇₃	semidirect
498. #2550	C₂×C₇₃	semidirect
499. #2550	C₂×C₇₃	semidirect
500. #2492	C₂×C₇₃	semidirect
501. #2473	C₂×C₇₃	semidirect
502. #2465	C₂×C₇₃	semidirect
504. #2453	C₂×C₇₃	semidirect
506. #2451	C₂×C₇₃	semidirect
509. #2360	C₂×C₇₃	semidirect
510. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
511. C₄×#125	C₂×C₇₃	semidirect
513. C₇₃	#59833	direct (N × H)
633. #124	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₇₃	2
C₂×#554×C₇₃	2
C₇₃×#2720	2
C₇₃×#2677	2
C₇₃×#2581	2
C₇₃×#2580	2
C₇₃×#2556	2
C₇₃×#2550	2
C₇₃×#2492	2
C₇₃×#2473	2
C₇₃×#2465	2
C₇₃×#2454	2
C₇₃×#2453	2
C₇₃×#2452	2
C₇₃×#2451	2
C₇₃×#2367	2
C₇₃×#2360	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#125×C₇₃	2
C₄×#124×C₇₃	2
#59833	73

Subgroups — C73×#59833 #32969237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59833 #32969237