Subgroups — C₇₃×#59809 #32969213

Order 18688.

2394 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2713	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2692	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2556	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2549	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2492	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2487	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2450	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2450	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2409	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2409	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2364	C₂	1	2	yes	maximal
19	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic
23	C₂×#391×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	#554×C₇₃	—	2	8	no	—
27	D₄×Q₈×C₇₃	—	2	8	no	—
28	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#125×C₇₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
53	#400×C₇₃	C₂²	1	2	yes	—
54	#400×C₇₃	C₂²	1	2	yes	—
55	#400×C₇₃	C₂²	1	2	yes	—
56	#399×C₇₃	C₂²	1	2	yes	—
57	#398×C₇₃	C₂²	1	2	yes	—
58	#398×C₇₃	C₂²	1	2	yes	—
59	#398×C₇₃	C₂²	1	2	yes	—
60	#398×C₇₃	C₂²	1	2	yes	—
61	#396×C₇₃	C₂²	1	2	yes	—
62	#396×C₇₃	C₂²	1	2	yes	—
63	#395×C₇₃	C₂²	1	2	yes	—
64	#395×C₇₃	C₂²	1	2	yes	—
65	#395×C₇₃	C₂²	1	2	yes	—
66	#393×C₇₃	C₂²	1	2	yes	—
67	#393×C₇₃	C₂²	1	2	yes	—
68	#393×C₇₃	C₂²	1	2	yes	—
69	#391×C₇₃	C₂²	1	1	yes	characteristic
70	#391×C₇₃	C₂²	1	1	yes	characteristic
71	#391×C₇₃	C₂²	1	1	yes	characteristic
72	#391×C₇₃	C₂²	1	2	yes	—
73	#391×C₇₃	C₂²	1	2	yes	—
74	#391×C₇₃	C₂²	1	1	yes	characteristic
75	#391×C₇₃	C₂²	1	1	yes	characteristic
76	#391×C₇₃	C₂²	1	2	yes	—
77	#391×C₇₃	C₂²	1	2	yes	—
78	#391×C₇₃	C₂²	1	2	yes	—
79	#391×C₇₃	C₂²	1	2	yes	—
80	#391×C₇₃	C₂²	1	1	yes	characteristic
81	#391×C₇₃	C₂²	1	1	yes	characteristic
82	#390×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	1	yes	characteristic
87	#389×C₇₃	C₂²	1	2	yes	—
88	#389×C₇₃	C₂²	1	2	yes	—
89	#388×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	1	yes	characteristic
93	#387×C₇₃	C₂²	1	2	yes	—
94	#387×C₇₃	C₂²	1	2	yes	—
95	#387×C₇₃	C₂²	1	2	yes	—
96	#387×C₇₃	C₂²	1	2	yes	—
97	#387×C₇₃	C₂²	1	2	yes	—
98	#386×C₇₃	C₂²	1	1	yes	characteristic
99	#386×C₇₃	C₂²	1	1	yes	characteristic
100	#386×C₇₃	C₂²	1	2	yes	—
101	#386×C₇₃	C₂²	1	2	yes	—
102	#386×C₇₃	C₂²	1	2	yes	—
103	#386×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	#385×C₇₃	C₂²	1	2	yes	—
109	#380×C₇₃	C₂²	1	2	yes	—
110	#380×C₇₃	C₂²	1	2	yes	—
111	#380×C₇₃	C₂²	1	1	yes	characteristic
112	#380×C₇₃	C₂²	1	1	yes	characteristic
113	#380×C₇₃	C₂²	1	1	yes	characteristic
114	#380×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
123	C₂×#95×C₇₃	C₂²	1	2	yes	—
124	C₂×#95×C₇₃	C₂²	1	2	yes	—
125	C₂²×Q₈×C₇₃	—	2	4	no	—
126	C₂²×Q₈×C₇₃	—	2	4	no	—
127	C₂²×Q₈×C₇₃	—	2	4	no	—
128	C₂²×Q₈×C₇₃	—	2	4	no	—
129	C₂²×Q₈×C₇₃	—	4	2	no	—
130	C₂²×Q₈×C₇₃	—	4	2	no	—
131	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
134	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₄⋊Q₈×C₇₃	—	2	4	no	—
150	C₄⋊Q₈×C₇₃	—	2	8	no	—
151	C₄⋊Q₈×C₇₃	—	2	4	no	—
152	#125×C₇₃	—	2	8	no	—
153	C₂²⋊Q₈×C₇₃	—	2	4	no	—
154	C₂²⋊Q₈×C₇₃	—	2	4	no	—
155	C₂²⋊Q₈×C₇₃	—	2	8	no	—
156	C₂²⋊Q₈×C₇₃	—	2	4	no	—
157	C₂²⋊Q₈×C₇₃	—	2	8	no	—
158	C₂²⋊Q₈×C₇₃	—	2	8	no	—
159	C₂²⋊Q₈×C₇₃	—	2	8	no	—
160	C₂²⋊Q₈×C₇₃	—	4	2	no	—
161	C₂²⋊Q₈×C₇₃	D₄	1	8	yes	complemented
162	#121×C₇₃	Q₈	1	8	yes	complemented
163	C₄×Q₈×C₇₃	—	2	4	no	—
164	C₄×Q₈×C₇₃	—	2	4	no	—
165	C₄×Q₈×C₇₃	—	4	2	no	—
166	C₄×D₄×C₇₃	—	2	4	no	—
167	C₄×D₄×C₇₃	—	2	4	no	—
168	C₄×D₄×C₇₃	—	2	8	no	—
169	C₄×D₄×C₇₃	—	2	8	no	—
170	C₄×D₄×C₇₃	—	4	2	no	—
171	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
172	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
173	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
184	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
194	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇₃	—	4	2	no	—
218	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
225	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×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	1	yes	characteristic
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	1	yes	characteristic
237	#95×C₇₃	C₂³	1	2	yes	—
238	#95×C₇₃	C₂³	1	2	yes	—
239	#95×C₇₃	C₂³	1	2	yes	—
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	#95×C₇₃	C₂³	1	2	yes	—
249	#95×C₇₃	C₂³	1	2	yes	—
250	#95×C₇₃	C₂³	1	2	yes	—
251	#95×C₇₃	C₂³	1	2	yes	—
252	#95×C₇₃	C₂³	1	2	yes	—
253	#95×C₇₃	C₂³	1	2	yes	—
254	#95×C₇₃	C₂³	1	2	yes	—
255	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₇₃	—	2	2	no	—
259	C₂×Q₈×C₇₃	—	2	4	no	—
260	C₂×Q₈×C₇₃	—	2	4	no	—
261	C₂×Q₈×C₇₃	—	2	2	no	—
262	C₂×Q₈×C₇₃	—	2	4	no	—
263	C₂×Q₈×C₇₃	—	2	2	no	—
264	C₂×Q₈×C₇₃	—	2	4	no	—
265	C₂×Q₈×C₇₃	—	2	4	no	—
266	C₂×Q₈×C₇₃	—	2	2	no	—
267	C₂×Q₈×C₇₃	—	2	2	no	—
268	C₂×Q₈×C₇₃	—	2	2	no	—
269	C₂×Q₈×C₇₃	—	2	2	no	—
270	C₂×Q₈×C₇₃	—	4	2	no	—
271	C₂×Q₈×C₇₃	—	4	2	no	—
272	C₂×Q₈×C₇₃	—	4	2	no	—
273	C₂×Q₈×C₇₃	—	4	2	no	—
274	C₂×Q₈×C₇₃	—	4	16	no	—
275	C₂×Q₈×C₇₃	—	4	16	no	—
276	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
277	C₂×Q₈×C₇₃	#41	1	4	yes	—
278	C₂×D₄×C₇₃	—	2	2	no	—
279	C₂×D₄×C₇₃	—	2	2	no	—
280	C₂×D₄×C₇₃	—	2	2	no	—
281	C₂×D₄×C₇₃	—	2	2	no	—
282	C₂×D₄×C₇₃	—	4	1	no	—
283	C₂×D₄×C₇₃	—	4	1	no	—
284	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
285	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	complemented
286	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	complemented
287	C₂²×C₄×C₇₃	—	2	2	no	—
288	C₂²×C₄×C₇₃	—	2	2	no	—
289	C₂²×C₄×C₇₃	—	2	4	no	—
290	C₂²×C₄×C₇₃	—	2	2	no	—
291	C₂²×C₄×C₇₃	—	2	4	no	—
292	C₂²×C₄×C₇₃	—	2	2	no	—
293	C₂²×C₄×C₇₃	—	2	4	no	—
294	C₂²×C₄×C₇₃	—	2	2	no	—
295	C₂²×C₄×C₇₃	—	2	2	no	—
296	C₂²×C₄×C₇₃	—	2	4	no	—
297	C₂²×C₄×C₇₃	—	2	4	no	—
298	C₂²×C₄×C₇₃	—	2	2	no	—
299	C₂²×C₄×C₇₃	—	2	2	no	—
300	C₂²×C₄×C₇₃	—	2	2	no	—
301	C₂²×C₄×C₇₃	—	2	4	no	—
302	C₂²×C₄×C₇₃	—	4	1	no	—
303	C₂²×C₄×C₇₃	—	4	1	no	—
304	C₂²×C₄×C₇₃	—	4	1	no	—
305	C₂²×C₄×C₇₃	—	4	1	no	—
306	C₂²×C₄×C₇₃	—	4	2	no	—
307	C₂²×C₄×C₇₃	—	4	2	no	—
308	C₂²×C₄×C₇₃	—	4	2	no	—
309	C₂²×C₄×C₇₃	—	4	2	no	—
310	C₂²×C₄×C₇₃	—	4	2	no	—
311	C₂²×C₄×C₇₃	—	4	2	no	—
312	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
313	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	complemented
314	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄×C₇₃	—	2	2	no	—
335	C₄⋊C₄×C₇₃	—	2	4	no	—
336	C₄⋊C₄×C₇₃	—	2	4	no	—
337	C₄⋊C₄×C₇₃	—	2	2	no	—
338	C₄⋊C₄×C₇₃	—	2	2	no	—
339	C₄⋊C₄×C₇₃	—	2	4	no	—
340	C₄⋊C₄×C₇₃	—	2	4	no	—
341	C₄⋊C₄×C₇₃	—	2	2	no	—
342	C₄⋊C₄×C₇₃	—	2	4	no	—
343	C₄⋊C₄×C₇₃	—	2	4	no	—
344	C₄⋊C₄×C₇₃	—	2	4	no	—
345	C₄⋊C₄×C₇₃	—	2	4	no	—
346	C₄⋊C₄×C₇₃	—	2	4	no	—
347	C₄⋊C₄×C₇₃	—	2	2	no	—
348	C₄⋊C₄×C₇₃	—	2	4	no	—
349	C₄⋊C₄×C₇₃	—	2	2	no	—
350	C₄⋊C₄×C₇₃	—	4	1	no	—
351	C₄⋊C₄×C₇₃	—	4	2	no	—
352	C₄⋊C₄×C₇₃	—	4	2	no	—
353	C₄⋊C₄×C₇₃	—	4	2	no	—
354	C₄⋊C₄×C₇₃	—	4	1	no	—
355	C₄⋊C₄×C₇₃	—	4	2	no	—
356	C₄⋊C₄×C₇₃	—	4	2	no	—
357	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
358	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
359	C₄⋊C₄×C₇₃	C₂×Q₈	1	4	yes	complemented
360	C₂²⋊C₄×C₇₃	—	2	2	no	—
361	C₂²⋊C₄×C₇₃	—	2	2	no	—
362	C₂²⋊C₄×C₇₃	—	2	4	no	—
363	C₂²⋊C₄×C₇₃	—	2	2	no	—
364	C₂²⋊C₄×C₇₃	—	2	2	no	—
365	C₂²⋊C₄×C₇₃	—	2	4	no	—
366	C₂²⋊C₄×C₇₃	—	2	4	no	—
367	C₂²⋊C₄×C₇₃	—	2	4	no	—
368	C₂²⋊C₄×C₇₃	—	4	2	no	—
369	C₂²⋊C₄×C₇₃	—	4	1	no	—
370	C₂²⋊C₄×C₇₃	—	4	1	no	—
371	C₂²⋊C₄×C₇₃	—	4	2	no	—
372	C₂²⋊C₄×C₇₃	—	4	1	no	—
373	C₂²⋊C₄×C₇₃	—	4	1	no	—
374	C₂²⋊C₄×C₇₃	—	4	2	no	—
375	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
376	C₂²⋊C₄×C₇₃	C₂×Q₈	1	4	yes	complemented
377	C₂²⋊C₄×C₇₃	C₂×Q₈	1	4	yes	complemented
378	C₄²×C₇₃	—	2	4	no	—
379	C₄²×C₇₃	—	2	4	no	—
380	C₄²×C₇₃	—	2	2	no	—
381	C₄²×C₇₃	—	2	2	no	—
382	C₄²×C₇₃	—	2	2	no	—
383	C₄²×C₇₃	—	2	2	no	—
384	C₄²×C₇₃	—	4	1	no	—
385	C₄²×C₇₃	—	4	1	no	—
386	C₄²×C₇₃	—	4	2	no	—
387	C₄²×C₇₃	—	4	2	no	—
388	C₂³×C₇₃	—	2	1	no	—
389	C₂³×C₇₃	—	2	1	no	—
390	C₂³×C₇₃	—	2	1	no	—
391	C₂³×C₇₃	—	2	1	no	—
392	C₂³×C₇₃	—	2	1	no	—
393	C₂³×C₇₃	—	2	1	no	—
394	C₂³×C₇₃	—	2	1	no	—
395	C₂³×C₇₃	—	2	1	no	—
396	C₂³×C₇₃	—	2	1	no	—
397	C₂³×C₇₃	—	2	1	no	—
398	C₂³×C₇₃	—	2	1	no	—
399	C₂³×C₇₃	—	2	1	no	—
400	C₂³×C₇₃	—	2	1	no	—
401	C₂³×C₇₃	—	2	1	no	—
402	C₂³×C₇₃	—	2	1	no	—
403	C₂³×C₇₃	—	2	1	no	—
404	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
405	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
406	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
407	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
408	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
409	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
410	Q₈×C₇₃	—	2	8	no	—
411	Q₈×C₇₃	—	2	8	no	—
412	Q₈×C₇₃	—	4	8	no	—
413	Q₈×C₇₃	—	4	8	no	—
414	Q₈×C₇₃	—	4	4	no	—
415	Q₈×C₇₃	—	8	4	no	—
416	D₄×C₇₃	—	2	8	no	—
417	D₄×C₇₃	—	2	8	no	—
418	D₄×C₇₃	—	4	4	no	—
419	C₂×C₄×C₇₃	—	2	1	no	—
420	C₂×C₄×C₇₃	—	2	1	no	—
421	C₂×C₄×C₇₃	—	2	2	no	—
422	C₂×C₄×C₇₃	—	2	1	no	—
423	C₂×C₄×C₇₃	—	2	2	no	—
424	C₂×C₄×C₇₃	—	2	1	no	—
425	C₂×C₄×C₇₃	—	2	1	no	—
426	C₂×C₄×C₇₃	—	2	1	no	—
427	C₂×C₄×C₇₃	—	2	2	no	—
428	C₂×C₄×C₇₃	—	2	2	no	—
429	C₂×C₄×C₇₃	—	2	1	no	—
430	C₂×C₄×C₇₃	—	2	1	no	—
431	C₂×C₄×C₇₃	—	2	1	no	—
432	C₂×C₄×C₇₃	—	2	2	no	—
433	C₂×C₄×C₇₃	—	2	1	no	—
434	C₂×C₄×C₇₃	—	2	2	no	—
435	C₂×C₄×C₇₃	—	2	8	no	—
436	C₂×C₄×C₇₃	—	2	1	no	—
437	C₂×C₄×C₇₃	—	2	1	no	—
438	C₂×C₄×C₇₃	—	2	2	no	—
439	C₂×C₄×C₇₃	—	2	1	no	—
440	C₂×C₄×C₇₃	—	2	2	no	—
441	C₂×C₄×C₇₃	—	2	1	no	—
442	C₂×C₄×C₇₃	—	2	2	no	—
443	C₂×C₄×C₇₃	—	2	2	no	—
444	C₂×C₄×C₇₃	—	2	1	no	—
445	C₂×C₄×C₇₃	—	2	1	no	—
446	C₂×C₄×C₇₃	—	2	2	no	—
447	C₂×C₄×C₇₃	—	2	1	no	—
448	C₂×C₄×C₇₃	—	2	1	no	—
449	C₂×C₄×C₇₃	—	2	2	no	—
450	C₂×C₄×C₇₃	—	2	1	no	—
451	C₂×C₄×C₇₃	—	2	1	no	—
452	C₂×C₄×C₇₃	—	2	2	no	—
453	C₂×C₄×C₇₃	—	2	2	no	—
454	C₂×C₄×C₇₃	—	2	2	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	—	2	1	no	—
457	C₂×C₄×C₇₃	—	2	2	no	—
458	C₂×C₄×C₇₃	—	2	1	no	—
459	C₂×C₄×C₇₃	—	2	1	no	—
460	C₂×C₄×C₇₃	—	2	2	no	—
461	C₂×C₄×C₇₃	—	2	2	no	—
462	C₂×C₄×C₇₃	—	2	2	no	—
463	C₂×C₄×C₇₃	—	2	1	no	—
464	C₂×C₄×C₇₃	—	2	1	no	—
465	C₂×C₄×C₇₃	—	2	1	no	—
466	C₂×C₄×C₇₃	—	2	2	no	—
467	C₂×C₄×C₇₃	—	2	2	no	—
468	C₂×C₄×C₇₃	—	2	1	no	—
469	C₂×C₄×C₇₃	—	4	4	no	—
470	C₂×C₄×C₇₃	—	4	8	no	—
471	C₂×C₄×C₇₃	—	4	8	no	—
472	C₂×C₄×C₇₃	—	4	4	no	—
473	C₂×C₄×C₇₃	—	4	4	no	—
474	C₂×C₄×C₇₃	—	4	4	no	—
475	C₂×C₄×C₇₃	—	8	4	no	—
476	C₂×C₄×C₇₃	—	8	4	no	—
477	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
478	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
479	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
482	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
483	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
484	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
485	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
486	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
487	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
488	C₂²×C₇₃	—	2	2	no	—
489	C₂²×C₇₃	—	2	2	no	—
490	C₂²×C₇₃	—	2	2	no	—
491	C₂²×C₇₃	—	2	2	no	—
492	C₂²×C₇₃	—	2	2	no	—
493	C₂²×C₇₃	—	2	2	no	—
494	C₂²×C₇₃	—	2	2	no	—
495	C₂²×C₇₃	—	2	2	no	—
496	C₂²×C₇₃	—	2	2	no	—
497	C₂²×C₇₃	—	2	2	no	—
498	C₂²×C₇₃	—	2	2	no	—
499	C₂²×C₇₃	—	2	2	no	—
500	C₂²×C₇₃	—	4	1	no	—
501	C₂²×C₇₃	—	4	1	no	—
502	C₂²×C₇₃	—	4	1	no	—
503	C₂²×C₇₃	—	4	1	no	—
504	C₂²×C₇₃	—	4	1	no	—
505	C₂²×C₇₃	—	4	1	no	—
506	C₂²×C₇₃	—	4	1	no	—
507	C₂²×C₇₃	—	4	1	no	—
508	C₂²×C₇₃	D₄×Q₈	1	4	yes	—
509	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
510	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
511	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
512	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂²×C₇₃	#585	1	1	yes	characteristic
515	C₂²×C₇₃	#585	1	1	yes	characteristic
516	C₄×C₇₃	—	2	2	no	—
517	C₄×C₇₃	—	2	4	no	—
518	C₄×C₇₃	—	2	4	no	—
519	C₄×C₇₃	—	2	2	no	—
520	C₄×C₇₃	—	2	2	no	—
521	C₄×C₇₃	—	2	4	no	—
522	C₄×C₇₃	—	2	2	no	—
523	C₄×C₇₃	—	2	2	no	—
524	C₄×C₇₃	—	4	1	no	—
525	C₄×C₇₃	—	4	1	no	—
526	C₄×C₇₃	—	4	2	no	—
527	C₄×C₇₃	—	4	1	no	—
528	C₄×C₇₃	—	4	2	no	—
529	C₄×C₇₃	—	4	2	no	—
530	C₄×C₇₃	—	4	1	no	—
531	C₄×C₇₃	—	4	2	no	—
532	C₄×C₇₃	—	4	2	no	—
533	C₄×C₇₃	—	4	1	no	—
534	C₄×C₇₃	—	4	1	no	—
535	C₄×C₇₃	#546	1	4	yes	—
536	#59809	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
537	C₂×C₇₃	—	2	4	no	—
538	C₂×C₇₃	—	4	2	no	—
539	C₂×C₇₃	—	4	2	no	—
540	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
541	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
542	C₂×C₇₃	Q₈×#41	1	1	yes	characteristic
543	C₂×C₇₃	#3500	1	1	yes	characteristic
544	C₂×C₇₃	#3501	1	1	yes	characteristic
545	C₂×C₇₃	#3516	1	1	yes	characteristic
546	C₂×C₇₃	#3541	1	1	yes	characteristic
547	C₂×#554	C₂×C₇₃	1	1	yes	characteristic, complemented
548	C₂×D₄×Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
549	#2713	C₂×C₇₃	1	2	yes	complemented
550	#2692	C₂×C₇₃	1	2	yes	complemented
551	#2556	C₂×C₇₃	1	2	yes	complemented
552	#2549	C₂×C₇₃	1	2	yes	complemented
553	#2492	C₂×C₇₃	1	1	yes	characteristic, complemented
554	#2492	C₂×C₇₃	1	2	yes	complemented
555	#2487	C₂×C₇₃	1	1	yes	characteristic, complemented
556	#2451	C₂×C₇₃	1	1	yes	characteristic, complemented
557	#2450	C₂×C₇₃	1	2	yes	complemented
558	#2450	C₂×C₇₃	1	2	yes	complemented
559	#2446	C₂×C₇₃	1	1	yes	characteristic, complemented
560	#2429	C₂×C₇₃	1	1	yes	characteristic, complemented
561	#2417	C₂×C₇₃	1	1	yes	characteristic, complemented
562	#2409	C₂×C₇₃	1	1	yes	characteristic, complemented
563	#2409	C₂×C₇₃	1	1	yes	characteristic, complemented
564	#2364	C₂×C₇₃	1	2	yes	—
565	#2360	C₂×C₇₃	1	1	yes	characteristic, complemented
566	Q₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
567	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
568	C₄×#121	C₂×C₇₃	1	1	yes	characteristic
569	C₂×#391	C₂×C₇₃	1	1	yes	characteristic, complemented
570	C₇₃	#59809	1	1	yes	characteristic, direct product factor, Sylow
571	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
572	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
573	#554	—	2	8	no	—
574	D₄×Q₈	—	2	8	no	—
575	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
576	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
577	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
578	C₂×#125	C₂²×C₇₃	1	2	yes	—
579	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
580	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
581	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
582	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
583	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
584	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
585	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
586	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
587	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
588	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
589	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
590	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
591	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
593	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
594	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
595	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
596	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
597	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
598	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
599	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
600	#400	C₂²×C₇₃	1	2	yes	—
601	#400	C₂²×C₇₃	1	2	yes	—
602	#400	C₂²×C₇₃	1	2	yes	—
603	#399	C₂²×C₇₃	1	2	yes	—
604	#398	C₂²×C₇₃	1	2	yes	—
605	#398	C₂²×C₇₃	1	2	yes	—
606	#398	C₂²×C₇₃	1	2	yes	—
607	#398	C₂²×C₇₃	1	2	yes	—
608	#396	C₂²×C₇₃	1	2	yes	—
609	#396	C₂²×C₇₃	1	2	yes	—
610	#395	C₂²×C₇₃	1	2	yes	—
611	#395	C₂²×C₇₃	1	2	yes	—
612	#395	C₂²×C₇₃	1	2	yes	—
613	#393	C₂²×C₇₃	1	2	yes	—
614	#393	C₂²×C₇₃	1	2	yes	—
615	#393	C₂²×C₇₃	1	2	yes	—
616	#391	C₂²×C₇₃	1	1	yes	characteristic
617	#391	C₂²×C₇₃	1	1	yes	characteristic
618	#391	C₂²×C₇₃	1	2	yes	—
619	#391	C₂²×C₇₃	1	2	yes	—
620	#391	C₂²×C₇₃	1	1	yes	characteristic
621	#391	C₂²×C₇₃	1	1	yes	characteristic
622	#391	C₂²×C₇₃	1	1	yes	characteristic
623	#391	C₂²×C₇₃	1	1	yes	characteristic
624	#391	C₂²×C₇₃	1	1	yes	characteristic
625	#391	C₂²×C₇₃	1	2	yes	—
626	#391	C₂²×C₇₃	1	2	yes	—
627	#391	C₂²×C₇₃	1	2	yes	—
628	#391	C₂²×C₇₃	1	2	yes	—
629	#390	C₂²×C₇₃	1	1	yes	characteristic
630	#389	C₂²×C₇₃	1	1	yes	characteristic
631	#389	C₂²×C₇₃	1	2	yes	—
632	#389	C₂²×C₇₃	1	1	yes	characteristic
633	#389	C₂²×C₇₃	1	1	yes	characteristic
634	#389	C₂²×C₇₃	1	2	yes	—
635	#389	C₂²×C₇₃	1	1	yes	characteristic
636	#388	C₂²×C₇₃	1	2	yes	—
637	#388	C₂²×C₇₃	1	2	yes	—
638	#388	C₂²×C₇₃	1	1	yes	characteristic
639	#388	C₂²×C₇₃	1	1	yes	characteristic
640	#387	C₂²×C₇₃	1	2	yes	—
641	#387	C₂²×C₇₃	1	2	yes	—
642	#387	C₂²×C₇₃	1	2	yes	—
643	#387	C₂²×C₇₃	1	2	yes	—
644	#387	C₂²×C₇₃	1	2	yes	—
645	#386	C₂²×C₇₃	1	2	yes	—
646	#386	C₂²×C₇₃	1	2	yes	—
647	#386	C₂²×C₇₃	1	2	yes	—
648	#386	C₂²×C₇₃	1	2	yes	—
649	#386	C₂²×C₇₃	1	1	yes	characteristic
650	#386	C₂²×C₇₃	1	1	yes	characteristic
651	#385	C₂²×C₇₃	1	2	yes	—
652	#385	C₂²×C₇₃	1	2	yes	—
653	#385	C₂²×C₇₃	1	2	yes	—
654	#385	C₂²×C₇₃	1	2	yes	—
655	#385	C₂²×C₇₃	1	2	yes	—
656	#380	C₂²×C₇₃	1	1	yes	characteristic
657	#380	C₂²×C₇₃	1	2	yes	—
658	#380	C₂²×C₇₃	1	1	yes	characteristic
659	#380	C₂²×C₇₃	1	1	yes	characteristic
660	#380	C₂²×C₇₃	1	2	yes	—
661	#380	C₂²×C₇₃	1	1	yes	characteristic
662	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
663	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
664	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
665	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
666	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
668	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
669	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
670	C₂×#95	C₂²×C₇₃	1	2	yes	—
671	C₂×#95	C₂²×C₇₃	1	2	yes	—
672	C₂²×Q₈	—	2	4	no	—
673	C₂²×Q₈	—	2	4	no	—
674	C₂²×Q₈	—	2	4	no	—
675	C₂²×Q₈	—	2	4	no	—
676	C₂²×Q₈	—	4	2	no	—
677	C₂²×Q₈	—	4	2	no	—
678	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
679	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
680	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
681	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
683	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
684	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
685	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
690	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
691	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
693	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
694	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
696	C₄⋊Q₈	—	2	4	no	—
697	C₄⋊Q₈	—	2	8	no	—
698	C₄⋊Q₈	—	2	4	no	—
699	#125	—	2	8	no	—
700	C₂²⋊Q₈	—	2	4	no	—
701	C₂²⋊Q₈	—	2	4	no	—
702	C₂²⋊Q₈	—	2	8	no	—
703	C₂²⋊Q₈	—	2	4	no	—
704	C₂²⋊Q₈	—	2	8	no	—
705	C₂²⋊Q₈	—	2	8	no	—
706	C₂²⋊Q₈	—	2	8	no	—
707	C₂²⋊Q₈	—	4	2	no	—
708	C₂²⋊Q₈	D₄×C₇₃	1	8	yes	complemented
709	#121	Q₈×C₇₃	1	8	yes	complemented
710	C₄×Q₈	—	2	4	no	—
711	C₄×Q₈	—	2	4	no	—
712	C₄×Q₈	—	4	2	no	—
713	C₄×D₄	—	2	4	no	—
714	C₄×D₄	—	2	4	no	—
715	C₄×D₄	—	2	8	no	—
716	C₄×D₄	—	2	8	no	—
717	C₄×D₄	—	4	2	no	—
718	C₂×C₄⋊C₄	—	2	4	no	—
719	C₂×C₄⋊C₄	—	2	4	no	—
720	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
764	C₂×C₄²	—	4	2	no	—
765	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
766	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
769	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
772	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
773	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
775	#95	C₂³×C₇₃	1	2	yes	—
776	#95	C₂³×C₇₃	1	2	yes	—
777	#95	C₂³×C₇₃	1	2	yes	—
778	#95	C₂³×C₇₃	1	2	yes	—
779	#95	C₂³×C₇₃	1	2	yes	—
780	#95	C₂³×C₇₃	1	2	yes	—
781	#95	C₂³×C₇₃	1	2	yes	—
782	#95	C₂³×C₇₃	1	2	yes	—
783	#95	C₂³×C₇₃	1	1	yes	characteristic
784	#95	C₂³×C₇₃	1	1	yes	characteristic
785	#95	C₂³×C₇₃	1	2	yes	—
786	#95	C₂³×C₇₃	1	1	yes	characteristic
787	#95	C₂³×C₇₃	1	2	yes	—
788	#95	C₂³×C₇₃	1	2	yes	—
789	#95	C₂³×C₇₃	1	2	yes	—
790	#95	C₂³×C₇₃	1	1	yes	characteristic
791	#95	C₂³×C₇₃	1	2	yes	—
792	#95	C₂³×C₇₃	1	2	yes	—
793	#95	C₂³×C₇₃	1	2	yes	—
794	#95	C₂³×C₇₃	1	1	yes	characteristic
795	#95	C₂³×C₇₃	1	1	yes	characteristic
796	#95	C₂³×C₇₃	1	2	yes	—
797	#95	C₂³×C₇₃	1	2	yes	—
798	#95	C₂³×C₇₃	1	2	yes	—
799	#95	C₂³×C₇₃	1	2	yes	—
800	#95	C₂³×C₇₃	1	2	yes	—
801	#95	C₂³×C₇₃	1	2	yes	—
802	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
803	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
804	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	4	no	—
807	C₂×Q₈	—	2	4	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	4	no	—
810	C₂×Q₈	—	2	2	no	—
811	C₂×Q₈	—	2	4	no	—
812	C₂×Q₈	—	2	4	no	—
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×Q₈	—	4	2	no	—
820	C₂×Q₈	—	4	2	no	—
821	C₂×Q₈	—	4	16	no	—
822	C₂×Q₈	—	4	16	no	—
823	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
824	C₂×Q₈	#41×C₇₃	1	4	yes	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	—
832	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	complemented
833	C₂×D₄	C₂×Q₈×C₇₃	1	4	yes	complemented
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
860	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	complemented
861	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
867	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	4	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	4	1	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	1	no	—
902	C₄⋊C₄	—	4	2	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
905	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
906	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	complemented
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	1	no	—
917	C₂²⋊C₄	—	4	1	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	1	no	—
920	C₂²⋊C₄	—	4	1	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
923	C₂²⋊C₄	C₂×Q₈×C₇₃	1	4	yes	complemented
924	C₂²⋊C₄	C₂×Q₈×C₇₃	1	4	yes	complemented
925	C₄²	—	2	4	no	—
926	C₄²	—	2	4	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	4	1	no	—
932	C₄²	—	4	1	no	—
933	C₄²	—	4	2	no	—
934	C₄²	—	4	2	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
952	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
953	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
954	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
955	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
956	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
957	Q₈	—	2	8	no	—
958	Q₈	—	2	8	no	—
959	Q₈	—	4	8	no	—
960	Q₈	—	4	8	no	—
961	Q₈	—	4	4	no	—
962	Q₈	—	8	4	no	—
963	D₄	—	2	8	no	—
964	D₄	—	2	8	no	—
965	D₄	—	4	4	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	8	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	4	4	no	—
1017	C₂×C₄	—	4	8	no	—
1018	C₂×C₄	—	4	8	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	8	4	no	—
1023	C₂×C₄	—	8	4	no	—
1024	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
1025	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
1026	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1028	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
1029	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
1030	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
1031	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
1032	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
1033	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1034	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	D₄×Q₈×C₇₃	1	4	yes	—
1056	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1057	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
1058	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1059	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1060	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
1061	C₂²	#585×C₇₃	1	1	yes	characteristic
1062	C₂²	#585×C₇₃	1	1	yes	characteristic
1063	C₄	—	2	2	no	—
1064	C₄	—	2	4	no	—
1065	C₄	—	2	4	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	4	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	#546×C₇₃	1	4	yes	—
1083	C₂	—	2	4	no	—
1084	C₂	—	4	2	no	—
1085	C₂	—	4	2	no	—
1086	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
1087	C₂	C₂×D₄×Q₈×C₇₃	1	1	yes	characteristic
1088	C₂	Q₈×#41×C₇₃	1	1	yes	characteristic
1089	C₂	C₇₃×#3500	1	1	yes	characteristic
1090	C₂	C₇₃×#3501	1	1	yes	characteristic
1091	C₂	C₇₃×#3516	1	1	yes	characteristic
1092	C₂	C₇₃×#3541	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. C₂×#554×C₇₃	C₂	semidirect
2. C₂×D₄×Q₈×C₇₃	C₂	semidirect
3. C₇₃×#2713	C₂	semidirect
4. C₇₃×#2692	C₂	semidirect
5. C₇₃×#2556	C₂	semidirect
6. C₇₃×#2549	C₂	semidirect
7. C₇₃×#2492	C₂	semidirect
8. C₇₃×#2492	C₂	semidirect
9. C₇₃×#2487	C₂	semidirect
10. C₇₃×#2451	C₂	semidirect
11. C₇₃×#2450	C₂	semidirect
12. C₇₃×#2450	C₂	semidirect
13. C₇₃×#2446	C₂	semidirect
14. C₇₃×#2429	C₂	semidirect
15. C₇₃×#2417	C₂	semidirect
16. C₇₃×#2409	C₂	semidirect
17. C₇₃×#2409	C₂	semidirect
19. C₇₃×#2360	C₂	semidirect
20. Q₈×C₂²⋊C₄×C₇₃	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₇₃	C₂	semidirect
23. C₂×#391×C₇₃	C₂	semidirect
161. C₂²⋊Q₈×C₇₃	D₄	semidirect
162. #121×C₇₃	Q₈	semidirect
285. C₂×D₄×C₇₃	C₂×Q₈	semidirect
286. C₂×D₄×C₇₃	C₂×Q₈	semidirect
313. C₂²×C₄×C₇₃	C₂×Q₈	semidirect
359. C₄⋊C₄×C₇₃	C₂×Q₈	semidirect
376. C₂²⋊C₄×C₇₃	C₂×Q₈	semidirect
377. C₂²⋊C₄×C₇₃	C₂×Q₈	semidirect
536. #59809	C₇₃	direct (N × H)
547. C₂×#554	C₂×C₇₃	semidirect
548. C₂×D₄×Q₈	C₂×C₇₃	semidirect
549. #2713	C₂×C₇₃	semidirect
550. #2692	C₂×C₇₃	semidirect
551. #2556	C₂×C₇₃	semidirect
552. #2549	C₂×C₇₃	semidirect
553. #2492	C₂×C₇₃	semidirect
554. #2492	C₂×C₇₃	semidirect
555. #2487	C₂×C₇₃	semidirect
556. #2451	C₂×C₇₃	semidirect
557. #2450	C₂×C₇₃	semidirect
558. #2450	C₂×C₇₃	semidirect
559. #2446	C₂×C₇₃	semidirect
560. #2429	C₂×C₇₃	semidirect
561. #2417	C₂×C₇₃	semidirect
562. #2409	C₂×C₇₃	semidirect
563. #2409	C₂×C₇₃	semidirect
565. #2360	C₂×C₇₃	semidirect
566. Q₈×C₂²⋊C₄	C₂×C₇₃	semidirect
567. C₄×C₂²⋊Q₈	C₂×C₇₃	semidirect
569. C₂×#391	C₂×C₇₃	semidirect
570. C₇₃	#59809	direct (N × H)
708. C₂²⋊Q₈	D₄×C₇₃	semidirect
709. #121	Q₈×C₇₃	semidirect
832. C₂×D₄	C₂×Q₈×C₇₃	semidirect
833. C₂×D₄	C₂×Q₈×C₇₃	semidirect
860. C₂²×C₄	C₂×Q₈×C₇₃	semidirect
906. C₄⋊C₄	C₂×Q₈×C₇₃	semidirect
923. C₂²⋊C₄	C₂×Q₈×C₇₃	semidirect
924. C₂²⋊C₄	C₂×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×#554×C₇₃	2
C₂×D₄×Q₈×C₇₃	2
C₇₃×#2713	2
C₇₃×#2692	2
C₇₃×#2556	2
C₇₃×#2549	2
C₇₃×#2492	2
C₇₃×#2487	2
C₇₃×#2451	2
C₇₃×#2450	2
C₇₃×#2446	2
C₇₃×#2429	2
C₇₃×#2417	2
C₇₃×#2409	2
C₇₃×#2364	2
C₇₃×#2360	2
Q₈×C₂²⋊C₄×C₇₃	2
C₄×C₂²⋊Q₈×C₇₃	2
C₄×#121×C₇₃	2
C₂×#391×C₇₃	2
#59809	73

Subgroups — C73×#59809 #32969213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59809 #32969213