Subgroups — C₇₃×#62569 #32971973

Order 18688.

1712 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3329	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3322	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3321	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3320	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3319	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3308	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3221	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#3179	C₂	1	2	yes	maximal, complemented
17	C₇₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#3137	C₂	1	2	yes	maximal, complemented
19	C₇₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₇₃	—	2	1	no	—
21	#562×C₇₃	—	2	1	no	—
22	#562×C₇₃	—	2	2	no	—
23	#556×C₇₃	C₂²	1	2	yes	—
24	#555×C₇₃	C₂²	1	2	yes	—
25	#555×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
27	#553×C₇₃	C₂²	1	2	yes	—
28	#552×C₇₃	—	2	1	no	—
29	#551×C₇₃	—	2	2	no	—
30	D₄×Q₈×C₇₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	#548×C₇₃	—	2	1	no	—
33	#548×C₇₃	C₂²	1	2	yes	—
34	#547×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	#546×C₇₃	C₂²	1	2	yes	—
36	#544×C₇₃	C₂²	1	2	yes	complemented
37	#543×C₇₃	—	2	1	no	—
38	#542×C₇₃	—	2	2	no	—
39	#542×C₇₃	—	2	2	no	—
40	#542×C₇₃	C₂²	1	2	yes	—
41	#540×C₇₃	C₂²	1	2	yes	complemented
42	#538×C₇₃	—	2	1	no	—
43	#537×C₇₃	—	2	1	no	—
44	#536×C₇₃	—	2	1	no	—
45	#536×C₇₃	C₂²	1	2	yes	—
46	#533×C₇₃	C₂²	1	1	yes	characteristic
47	#533×C₇₃	C₂²	1	1	yes	characteristic
48	#532×C₇₃	C₂²	1	1	yes	characteristic
49	#529×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
51	#501×C₇₃	C₂²	1	2	yes	complemented
52	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	#496×C₇₃	C₂²	1	2	yes	—
54	#492×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	#491×C₇₃	C₂²	1	2	yes	complemented
56	#491×C₇₃	C₂²	1	2	yes	complemented
57	#489×C₇₃	C₂²	1	2	yes	—
58	#489×C₇₃	C₂²	1	2	yes	—
59	#489×C₇₃	C₂²	1	2	yes	—
60	#489×C₇₃	C₂²	1	2	yes	—
61	#488×C₇₃	C₂²	1	2	yes	—
62	#488×C₇₃	C₂²	1	2	yes	—
63	#488×C₇₃	C₂²	1	2	yes	—
64	#487×C₇₃	C₂²	1	2	yes	complemented
65	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	#486×C₇₃	C₂²	1	1	yes	characteristic, complemented
67	#485×C₇₃	C₂²	1	2	yes	—
68	#485×C₇₃	C₂²	1	2	yes	—
69	#485×C₇₃	C₂²	1	2	yes	complemented
70	#484×C₇₃	C₂²	1	2	yes	complemented
71	#482×C₇₃	C₂²	1	2	yes	—
72	#480×C₇₃	C₂²	1	2	yes	—
73	#479×C₇₃	C₂²	1	2	yes	complemented
74	#478×C₇₃	C₂²	1	2	yes	—
75	#477×C₇₃	C₂²	1	2	yes	complemented
76	#477×C₇₃	C₂²	1	2	yes	complemented
77	#475×C₇₃	C₂²	1	2	yes	complemented
78	#474×C₇₃	C₂²	1	2	yes	—
79	#469×C₇₃	C₂²	1	2	yes	—
80	#468×C₇₃	C₂²	1	2	yes	—
81	#468×C₇₃	C₂²	1	2	yes	—
82	#468×C₇₃	C₂²	1	2	yes	complemented
83	#466×C₇₃	C₂²	1	2	yes	—
84	#465×C₇₃	C₂²	1	2	yes	complemented
85	#463×C₇₃	C₂²	1	2	yes	—
86	#463×C₇₃	C₂²	1	2	yes	—
87	#463×C₇₃	C₂²	1	2	yes	—
88	#463×C₇₃	C₂²	1	2	yes	—
89	#461×C₇₃	C₂²	1	2	yes	complemented
90	#461×C₇₃	C₂²	1	2	yes	complemented
91	#449×C₇₃	C₂²	1	2	yes	—
92	#449×C₇₃	C₂²	1	2	yes	—
93	#448×C₇₃	C₂²	1	1	yes	characteristic
94	#448×C₇₃	C₂²	1	1	yes	characteristic
95	#448×C₇₃	C₂²	1	2	yes	complemented
96	#448×C₇₃	C₂²	1	2	yes	complemented
97	#447×C₇₃	C₂²	1	1	yes	characteristic
98	#447×C₇₃	C₂²	1	1	yes	characteristic
99	#446×C₇₃	C₂²	1	2	yes	complemented
100	#442×C₇₃	C₂²	1	2	yes	—
101	#440×C₇₃	C₂²	1	2	yes	complemented
102	#440×C₇₃	C₂²	1	2	yes	complemented
103	#440×C₇₃	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₇₃	C₂²	1	2	yes	—
106	#436×C₇₃	C₂²	1	2	yes	—
107	#435×C₇₃	C₂²	1	2	yes	—
108	#435×C₇₃	C₂²	1	2	yes	complemented
109	#433×C₇₃	C₂²	1	2	yes	complemented
110	#432×C₇₃	C₂²	1	1	yes	characteristic
111	#419×C₇₃	C₂²	1	2	yes	—
112	#419×C₇₃	C₂²	1	2	yes	complemented
113	#418×C₇₃	C₂²	1	2	yes	—
114	#417×C₇₃	C₂²	1	2	yes	—
115	#416×C₇₃	C₂²	1	2	yes	—
116	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
117	#405×C₇₃	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₃	—	2	1	no	—
120	C₂×#41×C₇₃	—	2	1	no	—
121	C₂×#41×C₇₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₇₃	—	2	1	no	—
123	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
124	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
130	C₂×D₈×C₇₃	C₂³	1	2	yes	—
131	C₂×D₈×C₇₃	C₂³	1	2	yes	—
132	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₇₃	—	2	2	no	—
136	C₄⋊Q₈×C₇₃	—	2	2	no	—
137	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
141	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
144	#127×C₇₃	C₂³	1	1	yes	characteristic
145	#126×C₇₃	—	2	2	no	—
146	#126×C₇₃	—	2	2	no	—
147	#126×C₇₃	—	2	2	no	—
148	#126×C₇₃	—	2	2	no	—
149	#126×C₇₃	D₄	1	2	yes	—
150	#125×C₇₃	—	2	2	no	—
151	#125×C₇₃	—	2	1	no	—
152	#125×C₇₃	D₄	1	1	yes	characteristic
153	#125×C₇₃	C₂³	1	2	yes	—
154	#125×C₇₃	C₂³	1	2	yes	—
155	#124×C₇₃	—	2	2	no	—
156	#124×C₇₃	—	2	2	no	—
157	#124×C₇₃	—	2	2	no	—
158	#124×C₇₃	—	2	2	no	—
159	#124×C₇₃	—	2	2	no	—
160	#124×C₇₃	—	2	1	no	—
161	#124×C₇₃	—	2	1	no	—
162	#124×C₇₃	—	2	1	no	—
163	#124×C₇₃	D₄	1	1	yes	characteristic
164	#124×C₇₃	C₂³	1	2	yes	—
165	#124×C₇₃	C₂³	1	2	yes	—
166	#124×C₇₃	C₂³	1	2	yes	—
167	#123×C₇₃	—	2	2	no	—
168	#123×C₇₃	—	2	2	no	—
169	#123×C₇₃	—	2	2	no	—
170	#123×C₇₃	—	2	2	no	—
171	#123×C₇₃	—	2	2	no	—
172	#123×C₇₃	—	2	2	no	—
173	#123×C₇₃	—	2	2	no	—
174	#123×C₇₃	—	2	2	no	—
175	#123×C₇₃	D₄	1	2	yes	—
176	C₂²⋊Q₈×C₇₃	—	2	1	no	—
177	C₂²⋊Q₈×C₇₃	—	2	2	no	—
178	C₂²⋊Q₈×C₇₃	—	2	1	no	—
179	C₂²⋊Q₈×C₇₃	—	2	1	no	—
180	C₂²⋊Q₈×C₇₃	—	2	1	no	—
181	C₂²⋊Q₈×C₇₃	—	2	1	no	—
182	C₂²⋊Q₈×C₇₃	—	2	2	no	—
183	C₂²⋊Q₈×C₇₃	—	2	2	no	—
184	C₂²⋊Q₈×C₇₃	—	2	1	no	—
185	C₂²⋊Q₈×C₇₃	—	2	2	no	—
186	C₂²⋊Q₈×C₇₃	—	2	2	no	—
187	C₂²⋊Q₈×C₇₃	—	2	2	no	—
188	C₂²⋊Q₈×C₇₃	—	2	2	no	—
189	C₂²⋊Q₈×C₇₃	—	2	2	no	—
190	C₂²⋊Q₈×C₇₃	—	2	2	no	—
191	C₂²⋊Q₈×C₇₃	—	2	2	no	—
192	C₂²⋊Q₈×C₇₃	—	2	2	no	—
193	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
196	#121×C₇₃	—	2	1	no	—
197	#121×C₇₃	—	2	2	no	—
198	#121×C₇₃	—	2	2	no	—
199	#121×C₇₃	—	2	2	no	—
200	#121×C₇₃	—	2	1	no	—
201	#121×C₇₃	—	2	2	no	—
202	#121×C₇₃	—	2	2	no	—
203	#121×C₇₃	—	2	2	no	—
204	#121×C₇₃	D₄	1	1	yes	characteristic
205	#121×C₇₃	C₂³	1	1	yes	characteristic
206	#121×C₇₃	C₂³	1	1	yes	characteristic
207	#121×C₇₃	C₂³	1	2	yes	—
208	#121×C₇₃	C₂³	1	2	yes	—
209	#121×C₇₃	C₂³	1	2	yes	—
210	#120×C₇₃	—	2	2	no	—
211	C₄×Q₈×C₇₃	—	2	1	no	—
212	C₄×Q₈×C₇₃	—	2	1	no	—
213	C₄×Q₈×C₇₃	—	2	1	no	—
214	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₇₃	—	2	2	no	—
218	C₄×D₄×C₇₃	—	2	2	no	—
219	C₄×D₄×C₇₃	—	2	2	no	—
220	C₄×D₄×C₇₃	—	2	1	no	—
221	C₄×D₄×C₇₃	C₂³	1	2	yes	—
222	C₄×D₄×C₇₃	C₂³	1	2	yes	—
223	C₄×D₄×C₇₃	C₂³	1	2	yes	—
224	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₇₃	C₂³	1	2	yes	—
227	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
228	#117×C₇₃	—	2	1	no	—
229	#117×C₇₃	—	2	1	no	—
230	#117×C₇₃	—	2	2	no	—
231	#117×C₇₃	—	2	2	no	—
232	#117×C₇₃	C₂³	1	2	yes	—
233	#117×C₇₃	C₂³	1	2	yes	—
234	#117×C₇₃	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
236	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
240	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
241	#107×C₇₃	C₂³	1	2	yes	—
242	#107×C₇₃	C₂³	1	2	yes	—
243	#107×C₇₃	C₂³	1	2	yes	—
244	#107×C₇₃	C₂³	1	2	yes	—
245	#106×C₇₃	C₂³	1	2	yes	—
246	#106×C₇₃	C₂³	1	2	yes	—
247	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
248	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
249	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
250	#103×C₇₃	C₂³	1	2	yes	—
251	#103×C₇₃	C₂³	1	2	yes	—
252	#103×C₇₃	C₂³	1	2	yes	—
253	#103×C₇₃	C₂³	1	2	yes	—
254	#103×C₇₃	C₂³	1	2	yes	—
255	#103×C₇₃	C₂³	1	2	yes	—
256	#103×C₇₃	C₂³	1	2	yes	—
257	#103×C₇₃	C₂³	1	2	yes	—
258	#103×C₇₃	C₂³	1	2	yes	—
259	#103×C₇₃	C₂³	1	2	yes	—
260	#103×C₇₃	C₂³	1	2	yes	—
261	#103×C₇₃	C₂³	1	2	yes	—
262	#102×C₇₃	C₂³	1	2	yes	—
263	#102×C₇₃	C₂³	1	2	yes	—
264	#102×C₇₃	C₂³	1	2	yes	—
265	#102×C₇₃	C₂³	1	2	yes	—
266	#102×C₇₃	C₂³	1	2	yes	—
267	#102×C₇₃	C₂³	1	2	yes	—
268	#102×C₇₃	C₂³	1	2	yes	—
269	#102×C₇₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
274	#97×C₇₃	C₂³	1	2	yes	—
275	#97×C₇₃	C₂³	1	2	yes	—
276	#97×C₇₃	C₂³	1	2	yes	—
277	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₇₃	C₂³	1	2	yes	—
280	C₂⁴×C₇₃	—	2	1	no	—
281	#41×C₇₃	—	4	2	no	—
282	#41×C₇₃	—	4	2	no	—
283	#41×C₇₃	—	8	2	no	—
284	#41×C₇₃	—	8	2	no	—
285	C₂×Q₈×C₇₃	—	2	1	no	—
286	C₂×Q₈×C₇₃	—	2	1	no	—
287	C₂×Q₈×C₇₃	—	2	1	no	—
288	C₂×Q₈×C₇₃	—	2	2	no	—
289	C₂×Q₈×C₇₃	—	2	1	no	—
290	C₂×Q₈×C₇₃	—	2	2	no	—
291	C₂×Q₈×C₇₃	—	2	1	no	—
292	C₂×Q₈×C₇₃	—	4	2	no	—
293	C₂×Q₈×C₇₃	—	4	2	no	—
294	C₂×Q₈×C₇₃	—	4	2	no	—
295	C₂×Q₈×C₇₃	—	8	2	no	—
296	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
299	C₂×D₄×C₇₃	—	2	2	no	—
300	C₂×D₄×C₇₃	—	2	2	no	—
301	C₂×D₄×C₇₃	—	2	2	no	—
302	C₂×D₄×C₇₃	—	2	1	no	—
303	C₂×D₄×C₇₃	—	2	2	no	—
304	C₂×D₄×C₇₃	—	2	1	no	—
305	C₂×D₄×C₇₃	—	2	1	no	—
306	C₂×D₄×C₇₃	—	2	1	no	—
307	C₂×D₄×C₇₃	—	2	1	no	—
308	C₂×D₄×C₇₃	—	4	2	no	—
309	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
312	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
313	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₇₃	—	2	1	no	—
315	C₂²×C₄×C₇₃	—	2	2	no	—
316	C₂²×C₄×C₇₃	—	2	2	no	—
317	C₂²×C₄×C₇₃	—	2	1	no	—
318	C₂²×C₄×C₇₃	—	2	1	no	—
319	C₂²×C₄×C₇₃	—	2	2	no	—
320	C₂²×C₄×C₇₃	—	2	2	no	—
321	C₂²×C₄×C₇₃	—	2	2	no	—
322	C₂²×C₄×C₇₃	—	2	2	no	—
323	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
327	SD₁₆×C₇₃	—	4	2	no	—
328	SD₁₆×C₇₃	—	4	2	no	—
329	SD₁₆×C₇₃	—	4	2	no	—
330	SD₁₆×C₇₃	—	4	2	no	—
331	D₈×C₇₃	—	4	2	no	—
332	D₈×C₇₃	—	4	2	no	—
333	M₁₆×C₇₃	—	4	2	no	—
334	M₁₆×C₇₃	—	4	2	no	—
335	C₂×C₈×C₇₃	—	4	2	no	—
336	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₇₃	—	2	1	no	—
341	C₄⋊C₄×C₇₃	—	2	2	no	—
342	C₄⋊C₄×C₇₃	—	2	2	no	—
343	C₄⋊C₄×C₇₃	—	2	2	no	—
344	C₄⋊C₄×C₇₃	—	2	2	no	—
345	C₄⋊C₄×C₇₃	—	2	1	no	—
346	C₄⋊C₄×C₇₃	—	2	1	no	—
347	C₄⋊C₄×C₇₃	—	2	1	no	—
348	C₄⋊C₄×C₇₃	—	2	2	no	—
349	C₄⋊C₄×C₇₃	—	2	2	no	—
350	C₄⋊C₄×C₇₃	—	2	2	no	—
351	C₄⋊C₄×C₇₃	—	2	2	no	—
352	C₄⋊C₄×C₇₃	—	2	2	no	—
353	C₄⋊C₄×C₇₃	—	2	2	no	—
354	C₄⋊C₄×C₇₃	—	2	1	no	—
355	C₄⋊C₄×C₇₃	—	2	1	no	—
356	C₄⋊C₄×C₇₃	—	2	2	no	—
357	C₄⋊C₄×C₇₃	—	2	2	no	—
358	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₇₃	—	2	2	no	—
370	C₂²⋊C₄×C₇₃	—	2	2	no	—
371	C₂²⋊C₄×C₇₃	—	2	2	no	—
372	C₂²⋊C₄×C₇₃	—	2	2	no	—
373	C₂²⋊C₄×C₇₃	—	2	2	no	—
374	C₂²⋊C₄×C₇₃	—	2	2	no	—
375	C₂²⋊C₄×C₇₃	—	2	2	no	—
376	C₂²⋊C₄×C₇₃	—	2	2	no	—
377	C₂²⋊C₄×C₇₃	—	2	2	no	—
378	C₂²⋊C₄×C₇₃	—	2	2	no	—
379	C₂²⋊C₄×C₇₃	—	2	1	no	—
380	C₂²⋊C₄×C₇₃	—	2	2	no	—
381	C₂²⋊C₄×C₇₃	—	2	2	no	—
382	C₂²⋊C₄×C₇₃	—	2	2	no	—
383	C₂²⋊C₄×C₇₃	—	2	1	no	—
384	C₂²⋊C₄×C₇₃	—	2	2	no	—
385	C₂²⋊C₄×C₇₃	—	2	2	no	—
386	C₂²⋊C₄×C₇₃	—	2	1	no	—
387	C₂²⋊C₄×C₇₃	—	2	2	no	—
388	C₂²⋊C₄×C₇₃	—	2	1	no	—
389	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
394	C₄²×C₇₃	—	2	2	no	—
395	C₄²×C₇₃	—	2	2	no	—
396	C₄²×C₇₃	—	2	2	no	—
397	C₄²×C₇₃	—	2	2	no	—
398	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₇₃	C₂⁴	1	2	yes	—
402	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₂³×C₇₃	—	2	2	no	—
404	C₂³×C₇₃	—	2	1	no	—
405	C₂³×C₇₃	—	2	1	no	—
406	C₂³×C₇₃	—	4	2	no	—
407	C₂³×C₇₃	—	8	1	no	—
408	C₂³×C₇₃	—	8	1	no	—
409	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
410	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
411	Q₈×C₇₃	—	2	2	no	—
412	Q₈×C₇₃	—	2	2	no	—
413	Q₈×C₇₃	—	2	2	no	—
414	Q₈×C₇₃	—	2	2	no	—
415	Q₈×C₇₃	—	4	1	no	—
416	Q₈×C₇₃	—	4	2	no	—
417	Q₈×C₇₃	—	8	1	no	—
418	Q₈×C₇₃	—	8	1	no	—
419	Q₈×C₇₃	—	8	2	no	—
420	Q₈×C₇₃	—	8	1	no	—
421	Q₈×C₇₃	—	8	2	no	—
422	Q₈×C₇₃	—	8	1	no	—
423	D₄×C₇₃	—	2	2	no	—
424	D₄×C₇₃	—	2	2	no	—
425	D₄×C₇₃	—	2	2	no	—
426	D₄×C₇₃	—	2	2	no	—
427	D₄×C₇₃	—	4	2	no	—
428	D₄×C₇₃	—	4	1	no	—
429	D₄×C₇₃	—	8	1	no	—
430	D₄×C₇₃	—	8	1	no	—
431	D₄×C₇₃	—	8	1	no	—
432	D₄×C₇₃	—	8	2	no	—
433	D₄×C₇₃	—	8	2	no	—
434	D₄×C₇₃	—	8	2	no	—
435	D₄×C₇₃	—	8	1	no	—
436	D₄×C₇₃	—	8	1	no	—
437	D₄×C₇₃	—	8	2	no	—
438	C₂×C₄×C₇₃	—	2	2	no	—
439	C₂×C₄×C₇₃	—	2	2	no	—
440	C₂×C₄×C₇₃	—	2	2	no	—
441	C₂×C₄×C₇₃	—	2	2	no	—
442	C₂×C₄×C₇₃	—	2	2	no	—
443	C₂×C₄×C₇₃	—	2	1	no	—
444	C₂×C₄×C₇₃	—	2	2	no	—
445	C₂×C₄×C₇₃	—	2	2	no	—
446	C₂×C₄×C₇₃	—	2	2	no	—
447	C₂×C₄×C₇₃	—	2	1	no	—
448	C₂×C₄×C₇₃	—	4	1	no	—
449	C₂×C₄×C₇₃	—	4	1	no	—
450	C₂×C₄×C₇₃	—	4	2	no	—
451	C₂×C₄×C₇₃	—	4	2	no	—
452	C₂×C₄×C₇₃	—	8	2	no	—
453	C₂×C₄×C₇₃	—	8	2	no	—
454	C₂×C₄×C₇₃	—	8	2	no	—
455	C₂×C₄×C₇₃	—	8	2	no	—
456	C₂×C₄×C₇₃	—	8	2	no	—
457	C₂×C₄×C₇₃	—	8	1	no	—
458	C₂×C₄×C₇₃	—	8	2	no	—
459	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
468	C₈×C₇₃	—	2	2	no	—
469	C₈×C₇₃	—	2	2	no	—
470	C₈×C₇₃	—	2	2	no	—
471	C₈×C₇₃	—	2	2	no	—
472	C₂²×C₇₃	—	2	1	no	—
473	C₂²×C₇₃	—	2	2	no	—
474	C₂²×C₇₃	—	2	1	no	—
475	C₂²×C₇₃	—	2	2	no	—
476	C₂²×C₇₃	—	2	2	no	—
477	C₂²×C₇₃	—	2	1	no	—
478	C₂²×C₇₃	—	4	1	no	—
479	C₂²×C₇₃	—	4	1	no	—
480	C₂²×C₇₃	—	4	2	no	—
481	C₂²×C₇₃	—	4	1	no	—
482	C₂²×C₇₃	—	4	1	no	—
483	C₂²×C₇₃	—	4	2	no	—
484	C₂²×C₇₃	—	4	2	no	—
485	C₂²×C₇₃	—	4	1	no	—
486	C₂²×C₇₃	—	4	1	no	—
487	C₂²×C₇₃	—	16	2	no	—
488	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₇₃	—	2	1	no	—
490	C₄×C₇₃	—	2	1	no	—
491	C₄×C₇₃	—	2	2	no	—
492	C₄×C₇₃	—	2	1	no	—
493	C₄×C₇₃	—	2	1	no	—
494	C₄×C₇₃	—	2	2	no	—
495	C₄×C₇₃	—	2	2	no	—
496	C₄×C₇₃	—	2	1	no	—
497	C₄×C₇₃	—	4	1	no	—
498	C₄×C₇₃	—	4	1	no	—
499	C₄×C₇₃	—	4	2	no	—
500	C₄×C₇₃	—	4	2	no	—
501	C₄×C₇₃	—	4	2	no	—
502	C₄×C₇₃	—	4	2	no	—
503	C₄×C₇₃	—	4	2	no	—
504	C₄×C₇₃	#585	1	2	yes	—
505	#62569	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
506	C₂×C₇₃	—	4	2	no	—
507	C₂×C₇₃	—	4	1	no	—
508	C₂×C₇₃	—	8	1	no	—
509	C₂×C₇₃	—	8	1	no	—
510	C₂×C₇₃	—	8	2	no	—
511	C₂×C₇₃	#3500	1	1	yes	characteristic
512	C₂×C₇₃	#3585	1	1	yes	characteristic
513	C₂×C₇₃	#3586	1	1	yes	characteristic
514	#3561	C₂×C₇₃	1	1	yes	characteristic, complemented
515	#3547	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#3376	C₂×C₇₃	1	2	yes	complemented
517	#3367	C₂×C₇₃	1	2	yes	complemented
518	#3329	C₂×C₇₃	1	2	yes	complemented
519	#3322	C₂×C₇₃	1	2	yes	complemented
520	#3321	C₂×C₇₃	1	2	yes	complemented
521	#3320	C₂×C₇₃	1	2	yes	complemented
522	#3319	C₂×C₇₃	1	2	yes	complemented
523	#3308	C₂×C₇₃	1	2	yes	complemented
524	#3243	C₂×C₇₃	1	2	yes	complemented
525	#3237	C₂×C₇₃	1	1	yes	characteristic, complemented
526	#3221	C₂×C₇₃	1	2	yes	complemented
527	#3213	C₂×C₇₃	1	1	yes	characteristic, complemented
528	#3182	C₂×C₇₃	1	1	yes	characteristic, complemented
529	#3179	C₂×C₇₃	1	2	yes	complemented
530	#3140	C₂×C₇₃	1	1	yes	characteristic, complemented
531	#3137	C₂×C₇₃	1	2	yes	complemented
532	#2967	C₂×C₇₃	1	1	yes	characteristic, complemented
533	C₇₃	#62569	1	1	yes	characteristic, direct product factor, Sylow
534	#563	—	2	1	no	—
535	#562	—	2	1	no	—
536	#562	—	2	2	no	—
537	#556	C₂²×C₇₃	1	2	yes	—
538	#555	C₂²×C₇₃	1	2	yes	—
539	#555	C₂²×C₇₃	1	1	yes	characteristic, complemented
540	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
541	#553	C₂²×C₇₃	1	2	yes	—
542	#552	—	2	1	no	—
543	#551	—	2	2	no	—
544	D₄×Q₈	C₂²×C₇₃	1	2	yes	—
545	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
546	#548	—	2	1	no	—
547	#548	C₂²×C₇₃	1	2	yes	—
548	#547	C₂²×C₇₃	1	1	yes	characteristic, complemented
549	#546	C₂²×C₇₃	1	2	yes	—
550	#544	C₂²×C₇₃	1	2	yes	complemented
551	#543	—	2	1	no	—
552	#542	—	2	2	no	—
553	#542	—	2	2	no	—
554	#542	C₂²×C₇₃	1	2	yes	—
555	#540	C₂²×C₇₃	1	2	yes	complemented
556	#538	—	2	1	no	—
557	#537	—	2	1	no	—
558	#536	—	2	1	no	—
559	#536	C₂²×C₇₃	1	2	yes	—
560	#533	C₂²×C₇₃	1	1	yes	characteristic
561	#533	C₂²×C₇₃	1	1	yes	characteristic
562	#532	C₂²×C₇₃	1	1	yes	characteristic
563	#529	C₂²×C₇₃	1	1	yes	characteristic
564	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
565	#501	C₂²×C₇₃	1	2	yes	complemented
566	#500	C₂²×C₇₃	1	1	yes	characteristic, complemented
567	#496	C₂²×C₇₃	1	2	yes	—
568	#492	C₂²×C₇₃	1	1	yes	characteristic, complemented
569	#491	C₂²×C₇₃	1	2	yes	complemented
570	#491	C₂²×C₇₃	1	2	yes	complemented
571	#489	C₂²×C₇₃	1	2	yes	—
572	#489	C₂²×C₇₃	1	2	yes	—
573	#489	C₂²×C₇₃	1	2	yes	—
574	#489	C₂²×C₇₃	1	2	yes	—
575	#488	C₂²×C₇₃	1	2	yes	—
576	#488	C₂²×C₇₃	1	2	yes	—
577	#488	C₂²×C₇₃	1	2	yes	—
578	#487	C₂²×C₇₃	1	2	yes	complemented
579	#487	C₂²×C₇₃	1	1	yes	characteristic, complemented
580	#486	C₂²×C₇₃	1	1	yes	characteristic, complemented
581	#485	C₂²×C₇₃	1	2	yes	—
582	#485	C₂²×C₇₃	1	2	yes	—
583	#485	C₂²×C₇₃	1	2	yes	complemented
584	#484	C₂²×C₇₃	1	2	yes	complemented
585	#482	C₂²×C₇₃	1	2	yes	—
586	#480	C₂²×C₇₃	1	2	yes	—
587	#479	C₂²×C₇₃	1	2	yes	complemented
588	#478	C₂²×C₇₃	1	2	yes	—
589	#477	C₂²×C₇₃	1	2	yes	complemented
590	#477	C₂²×C₇₃	1	2	yes	complemented
591	#475	C₂²×C₇₃	1	2	yes	complemented
592	#474	C₂²×C₇₃	1	2	yes	—
593	#469	C₂²×C₇₃	1	2	yes	—
594	#468	C₂²×C₇₃	1	2	yes	—
595	#468	C₂²×C₇₃	1	2	yes	—
596	#468	C₂²×C₇₃	1	2	yes	complemented
597	#466	C₂²×C₇₃	1	2	yes	—
598	#465	C₂²×C₇₃	1	2	yes	complemented
599	#463	C₂²×C₇₃	1	2	yes	—
600	#463	C₂²×C₇₃	1	2	yes	—
601	#463	C₂²×C₇₃	1	2	yes	—
602	#463	C₂²×C₇₃	1	2	yes	—
603	#461	C₂²×C₇₃	1	2	yes	complemented
604	#461	C₂²×C₇₃	1	2	yes	complemented
605	#449	C₂²×C₇₃	1	2	yes	—
606	#449	C₂²×C₇₃	1	2	yes	—
607	#448	C₂²×C₇₃	1	1	yes	characteristic
608	#448	C₂²×C₇₃	1	1	yes	characteristic
609	#448	C₂²×C₇₃	1	2	yes	complemented
610	#448	C₂²×C₇₃	1	2	yes	complemented
611	#447	C₂²×C₇₃	1	1	yes	characteristic
612	#447	C₂²×C₇₃	1	1	yes	characteristic
613	#446	C₂²×C₇₃	1	2	yes	complemented
614	#442	C₂²×C₇₃	1	2	yes	—
615	#440	C₂²×C₇₃	1	2	yes	complemented
616	#440	C₂²×C₇₃	1	2	yes	complemented
617	#440	C₂²×C₇₃	1	2	yes	complemented
618	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
619	C₄×D₈	C₂²×C₇₃	1	2	yes	—
620	#436	C₂²×C₇₃	1	2	yes	—
621	#435	C₂²×C₇₃	1	2	yes	—
622	#435	C₂²×C₇₃	1	2	yes	complemented
623	#433	C₂²×C₇₃	1	2	yes	complemented
624	#432	C₂²×C₇₃	1	1	yes	characteristic
625	#419	C₂²×C₇₃	1	2	yes	—
626	#419	C₂²×C₇₃	1	2	yes	complemented
627	#418	C₂²×C₇₃	1	2	yes	—
628	#417	C₂²×C₇₃	1	2	yes	—
629	#416	C₂²×C₇₃	1	2	yes	—
630	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
631	#405	C₂²×C₇₃	1	2	yes	complemented
632	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
633	C₂×#41	—	2	1	no	—
634	C₂×#41	—	2	1	no	—
635	C₂×#41	C₂³×C₇₃	1	2	yes	—
636	C₂²×Q₈	—	2	1	no	—
637	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
638	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
639	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
640	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
644	C₂×D₈	C₂³×C₇₃	1	2	yes	—
645	C₂×D₈	C₂³×C₇₃	1	2	yes	—
646	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
647	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
648	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
653	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
655	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
656	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
657	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
658	#127	C₂³×C₇₃	1	1	yes	characteristic
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	D₄×C₇₃	1	2	yes	—
664	#125	—	2	2	no	—
665	#125	—	2	1	no	—
666	#125	D₄×C₇₃	1	1	yes	characteristic
667	#125	C₂³×C₇₃	1	2	yes	—
668	#125	C₂³×C₇₃	1	2	yes	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#124	—	2	1	no	—
675	#124	—	2	1	no	—
676	#124	—	2	1	no	—
677	#124	D₄×C₇₃	1	1	yes	characteristic
678	#124	C₂³×C₇₃	1	2	yes	—
679	#124	C₂³×C₇₃	1	2	yes	—
680	#124	C₂³×C₇₃	1	2	yes	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	D₄×C₇₃	1	2	yes	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	—	2	1	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
708	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
709	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
710	#121	—	2	1	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	—	2	1	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	D₄×C₇₃	1	1	yes	characteristic
719	#121	C₂³×C₇₃	1	1	yes	characteristic
720	#121	C₂³×C₇₃	1	1	yes	characteristic
721	#121	C₂³×C₇₃	1	2	yes	—
722	#121	C₂³×C₇₃	1	2	yes	—
723	#121	C₂³×C₇₃	1	2	yes	—
724	#120	—	2	2	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	—	2	1	no	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
729	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
730	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
737	C₄×D₄	C₂³×C₇₃	1	2	yes	—
738	C₄×D₄	C₂³×C₇₃	1	2	yes	—
739	C₄×D₄	C₂³×C₇₃	1	2	yes	—
740	C₄×D₄	C₂³×C₇₃	1	2	yes	—
741	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
742	#117	—	2	1	no	—
743	#117	—	2	1	no	—
744	#117	—	2	2	no	—
745	#117	—	2	2	no	—
746	#117	C₂³×C₇₃	1	2	yes	—
747	#117	C₂³×C₇₃	1	2	yes	—
748	#117	C₂³×C₇₃	1	2	yes	—
749	C₂×C₄⋊C₄	—	2	1	no	—
750	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₂²⋊C₄	—	2	1	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
755	#107	C₂³×C₇₃	1	2	yes	—
756	#107	C₂³×C₇₃	1	2	yes	—
757	#107	C₂³×C₇₃	1	2	yes	—
758	#107	C₂³×C₇₃	1	2	yes	—
759	#106	C₂³×C₇₃	1	2	yes	—
760	#106	C₂³×C₇₃	1	2	yes	—
761	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
762	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
763	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
764	#103	C₂³×C₇₃	1	2	yes	—
765	#103	C₂³×C₇₃	1	2	yes	—
766	#103	C₂³×C₇₃	1	2	yes	—
767	#103	C₂³×C₇₃	1	2	yes	—
768	#103	C₂³×C₇₃	1	2	yes	—
769	#103	C₂³×C₇₃	1	2	yes	—
770	#103	C₂³×C₇₃	1	2	yes	—
771	#103	C₂³×C₇₃	1	2	yes	—
772	#103	C₂³×C₇₃	1	2	yes	—
773	#103	C₂³×C₇₃	1	2	yes	—
774	#103	C₂³×C₇₃	1	2	yes	—
775	#103	C₂³×C₇₃	1	2	yes	—
776	#102	C₂³×C₇₃	1	2	yes	—
777	#102	C₂³×C₇₃	1	2	yes	—
778	#102	C₂³×C₇₃	1	2	yes	—
779	#102	C₂³×C₇₃	1	2	yes	—
780	#102	C₂³×C₇₃	1	2	yes	—
781	#102	C₂³×C₇₃	1	2	yes	—
782	#102	C₂³×C₇₃	1	2	yes	—
783	#102	C₂³×C₇₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
786	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
788	#97	C₂³×C₇₃	1	2	yes	—
789	#97	C₂³×C₇₃	1	2	yes	—
790	#97	C₂³×C₇₃	1	2	yes	—
791	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
792	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
793	C₄×C₈	C₂³×C₇₃	1	2	yes	—
794	C₂⁴	—	2	1	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	8	2	no	—
798	#41	—	8	2	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	8	2	no	—
810	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
811	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
812	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
824	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
825	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
826	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
841	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	2	no	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	D₈	—	4	2	no	—
846	D₈	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	M₁₆	—	4	2	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
853	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
873	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
874	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
875	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
880	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
882	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	1	no	—
903	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
913	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
914	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
915	C₄²	C₂⁴×C₇₃	1	2	yes	—
916	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
917	C₂³	—	2	2	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	4	2	no	—
921	C₂³	—	8	1	no	—
922	C₂³	—	8	1	no	—
923	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	8	2	no	—
932	Q₈	—	8	1	no	—
933	Q₈	—	8	2	no	—
934	Q₈	—	8	1	no	—
935	Q₈	—	8	1	no	—
936	Q₈	—	8	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	4	1	no	—
942	D₄	—	4	2	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	1	no	—
948	D₄	—	8	1	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	D₄	—	8	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
981	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₈	—	2	2	no	—
985	C₈	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	16	2	no	—
1002	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	#585×C₇₃	1	2	yes	—
1019	C₂	—	4	1	no	—
1020	C₂	—	4	2	no	—
1021	C₂	—	8	2	no	—
1022	C₂	—	8	1	no	—
1023	C₂	—	8	1	no	—
1024	C₂	C₇₃×#3500	1	1	yes	characteristic
1025	C₂	C₇₃×#3585	1	1	yes	characteristic
1026	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #529×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3561	C₂	semidirect
2. C₇₃×#3547	C₂	semidirect
3. C₇₃×#3376	C₂	semidirect
4. C₇₃×#3367	C₂	semidirect
5. C₇₃×#3329	C₂	semidirect
6. C₇₃×#3322	C₂	semidirect
7. C₇₃×#3321	C₂	semidirect
8. C₇₃×#3320	C₂	semidirect
9. C₇₃×#3319	C₂	semidirect
10. C₇₃×#3308	C₂	semidirect
11. C₇₃×#3243	C₂	semidirect
12. C₇₃×#3237	C₂	semidirect
13. C₇₃×#3221	C₂	semidirect
14. C₇₃×#3213	C₂	semidirect
15. C₇₃×#3182	C₂	semidirect
16. C₇₃×#3179	C₂	semidirect
17. C₇₃×#3140	C₂	semidirect
18. C₇₃×#3137	C₂	semidirect
19. C₇₃×#2967	C₂	semidirect
25. #555×C₇₃	C₂²	semidirect
26. #554×C₇₃	C₂²	semidirect
31. D₄×Q₈×C₇₃	C₂²	semidirect
34. #547×C₇₃	C₂²	semidirect
36. #544×C₇₃	C₂²	semidirect
41. #540×C₇₃	C₂²	semidirect
51. #501×C₇₃	C₂²	semidirect
52. #500×C₇₃	C₂²	semidirect
54. #492×C₇₃	C₂²	semidirect
55. #491×C₇₃	C₂²	semidirect
56. #491×C₇₃	C₂²	semidirect
64. #487×C₇₃	C₂²	semidirect
65. #487×C₇₃	C₂²	semidirect
66. #486×C₇₃	C₂²	semidirect
69. #485×C₇₃	C₂²	semidirect
70. #484×C₇₃	C₂²	semidirect
73. #479×C₇₃	C₂²	semidirect
75. #477×C₇₃	C₂²	semidirect
76. #477×C₇₃	C₂²	semidirect
77. #475×C₇₃	C₂²	semidirect
82. #468×C₇₃	C₂²	semidirect
84. #465×C₇₃	C₂²	semidirect
89. #461×C₇₃	C₂²	semidirect
90. #461×C₇₃	C₂²	semidirect
95. #448×C₇₃	C₂²	semidirect
96. #448×C₇₃	C₂²	semidirect
99. #446×C₇₃	C₂²	semidirect
101. #440×C₇₃	C₂²	semidirect
102. #440×C₇₃	C₂²	semidirect
103. #440×C₇₃	C₂²	semidirect
104. C₄×SD₁₆×C₇₃	C₂²	semidirect
108. #435×C₇₃	C₂²	semidirect
109. #433×C₇₃	C₂²	semidirect
112. #419×C₇₃	C₂²	semidirect
116. C₂×#103×C₇₃	C₂²	semidirect
117. #405×C₇₃	C₂²	semidirect
505. #62569	C₇₃	direct (N × H)
514. #3561	C₂×C₇₃	semidirect
515. #3547	C₂×C₇₃	semidirect
516. #3376	C₂×C₇₃	semidirect
517. #3367	C₂×C₇₃	semidirect
518. #3329	C₂×C₇₃	semidirect
519. #3322	C₂×C₇₃	semidirect
520. #3321	C₂×C₇₃	semidirect
521. #3320	C₂×C₇₃	semidirect
522. #3319	C₂×C₇₃	semidirect
523. #3308	C₂×C₇₃	semidirect
524. #3243	C₂×C₇₃	semidirect
525. #3237	C₂×C₇₃	semidirect
526. #3221	C₂×C₇₃	semidirect
527. #3213	C₂×C₇₃	semidirect
528. #3182	C₂×C₇₃	semidirect
529. #3179	C₂×C₇₃	semidirect
530. #3140	C₂×C₇₃	semidirect
531. #3137	C₂×C₇₃	semidirect
532. #2967	C₂×C₇₃	semidirect
533. C₇₃	#62569	direct (N × H)
539. #555	C₂²×C₇₃	semidirect
540. #554	C₂²×C₇₃	semidirect
545. D₄×Q₈	C₂²×C₇₃	semidirect
548. #547	C₂²×C₇₃	semidirect
550. #544	C₂²×C₇₃	semidirect
555. #540	C₂²×C₇₃	semidirect
565. #501	C₂²×C₇₃	semidirect
566. #500	C₂²×C₇₃	semidirect
568. #492	C₂²×C₇₃	semidirect
569. #491	C₂²×C₇₃	semidirect
570. #491	C₂²×C₇₃	semidirect
578. #487	C₂²×C₇₃	semidirect
579. #487	C₂²×C₇₃	semidirect
580. #486	C₂²×C₇₃	semidirect
583. #485	C₂²×C₇₃	semidirect
584. #484	C₂²×C₇₃	semidirect
587. #479	C₂²×C₇₃	semidirect
589. #477	C₂²×C₇₃	semidirect
590. #477	C₂²×C₇₃	semidirect
591. #475	C₂²×C₇₃	semidirect
596. #468	C₂²×C₇₃	semidirect
598. #465	C₂²×C₇₃	semidirect
603. #461	C₂²×C₇₃	semidirect
604. #461	C₂²×C₇₃	semidirect
609. #448	C₂²×C₇₃	semidirect
610. #448	C₂²×C₇₃	semidirect
613. #446	C₂²×C₇₃	semidirect
615. #440	C₂²×C₇₃	semidirect
616. #440	C₂²×C₇₃	semidirect
617. #440	C₂²×C₇₃	semidirect
618. C₄×SD₁₆	C₂²×C₇₃	semidirect
622. #435	C₂²×C₇₃	semidirect
623. #433	C₂²×C₇₃	semidirect
626. #419	C₂²×C₇₃	semidirect
630. C₂×#103	C₂²×C₇₃	semidirect
631. #405	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3561	2
C₇₃×#3547	2
C₇₃×#3376	2
C₇₃×#3367	2
C₇₃×#3329	2
C₇₃×#3322	2
C₇₃×#3321	2
C₇₃×#3320	2
C₇₃×#3319	2
C₇₃×#3308	2
C₇₃×#3243	2
C₇₃×#3237	2
C₇₃×#3221	2
C₇₃×#3213	2
C₇₃×#3182	2
C₇₃×#3179	2
C₇₃×#3140	2
C₇₃×#3137	2
C₇₃×#2967	2
#62569	73

Subgroups — C73×#62569 #32971973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62569 #32971973