Subgroups — #3183×D₇₃ #33955930

Order 18688.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#529×D₇₃	C₂	1	2	yes	maximal, complemented
2	#22620663	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620662	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620661	C₂	1	1	yes	maximal, characteristic, complemented
5	#22620660	C₂	1	1	yes	maximal, characteristic, complemented
6	#22620659	C₂	1	2	yes	maximal, complemented
7	#22620658	C₂	1	1	yes	maximal, characteristic, complemented
8	#22620657	C₂	1	1	yes	maximal, characteristic, complemented
9	#22620656	C₂	1	2	yes	maximal, complemented
10	#22620655	C₂	1	1	yes	maximal, characteristic, complemented
11	#22620654	C₂	1	2	yes	maximal, complemented
12	#22620653	C₂	1	2	yes	maximal, complemented
13	#499×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#488×D₇₃	C₂	1	2	yes	maximal, complemented
16	#470×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#469×D₇₃	C₂	1	1	yes	maximal, characteristic
18	#468×D₇₃	C₂	1	2	yes	maximal, complemented
19	#442×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#441×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#440×D₇₃	C₂	1	2	yes	maximal, complemented
22	C₄×M₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3183	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
26	C₂×D₈×D₇₃	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
28	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
29	#17989124	C₂²	1	2	yes	complemented
30	#17989123	C₂²	1	2	yes	complemented
31	#17989122	C₂²	1	2	yes	complemented
32	#17989121	C₂²	1	2	yes	complemented
33	#17989120	—	2	2	no	—
34	#17989119	C₂²	1	2	yes	complemented
35	#17989118	C₂²	1	2	yes	complemented
36	#17989117	—	2	2	no	—
37	#17989116	C₂²	1	2	yes	complemented
38	#17989115	—	2	2	no	—
39	#17989114	—	2	2	no	—
40	#126×D₇₃	—	2	2	no	—
41	#125×D₇₃	C₂²	1	2	yes	—
42	#124×D₇₃	C₂²	1	2	yes	—
43	#123×D₇₃	—	2	2	no	—
44	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
45	#121×D₇₃	C₂²	1	2	yes	—
46	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
47	C₄×D₄×D₇₃	—	2	2	no	—
48	C₄×D₄×D₇₃	C₂²	1	2	yes	—
49	#117×D₇₃	—	2	2	no	—
50	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
51	#17988989	C₂²	1	1	yes	characteristic, complemented
52	#17988988	C₂²	1	2	yes	complemented
53	#17988987	C₂²	1	1	yes	characteristic, complemented
54	#17988987	C₂²	1	1	yes	characteristic, complemented
55	#17988986	C₂²	1	2	yes	complemented
56	#17988972	C₂²	1	1	yes	characteristic, complemented
57	#17988971	C₂²	1	1	yes	characteristic, complemented
58	#17988970	C₂²	1	1	yes	characteristic, complemented
59	#17988969	C₂²	1	2	yes	complemented
60	#17988968	C₂²	1	2	yes	complemented
61	#17988944	C₂²	1	2	yes	complemented
62	#17988943	C₂²	1	2	yes	complemented
63	#17988943	C₂²	1	2	yes	complemented
64	#17988942	C₂²	1	2	yes	complemented
65	#17988941	C₂²	1	2	yes	complemented
66	#17988940	C₂²	1	2	yes	complemented
67	#17988940	C₂²	1	2	yes	complemented
68	#17988846	C₂²	1	1	yes	characteristic, complemented
69	#17988845	C₂²	1	1	yes	characteristic, complemented
70	#17988844	C₂²	1	2	yes	complemented
71	#17988843	C₂²	1	2	yes	complemented
72	#17988842	C₂²	1	1	yes	characteristic, complemented
73	#17988841	C₂²	1	1	yes	characteristic
74	#17988840	C₂²	1	1	yes	characteristic
75	#17988839	C₂²	1	2	yes	—
76	#17988838	C₂²	1	2	yes	—
77	#17988837	C₂²	1	1	yes	characteristic
78	#17988836	C₂²	1	2	yes	complemented
79	#17988835	C₂²	1	2	yes	complemented
80	#17988834	C₂²	1	2	yes	complemented
81	#17988833	C₂²	1	2	yes	complemented
82	#17988832	C₂²	1	2	yes	complemented
83	#17988831	C₂²	1	2	yes	complemented
84	#17988830	C₂²	1	2	yes	complemented
85	#17988700	C₂²	1	1	yes	characteristic, complemented
86	#17988699	C₂²	1	1	yes	characteristic, complemented
87	#17988698	C₂²	1	1	yes	characteristic, complemented
88	#17988697	C₂²	1	2	yes	complemented
89	#17988696	C₂²	1	2	yes	complemented
90	#17988695	C₂²	1	1	yes	characteristic, complemented
91	#17988694	C₂²	1	1	yes	characteristic, complemented
92	#17988693	C₂²	1	1	yes	characteristic, complemented
93	#17988692	C₂²	1	2	yes	complemented
94	#17988691	C₂²	1	2	yes	complemented
95	#17988690	C₂²	1	2	yes	complemented
96	#17988689	C₂²	1	2	yes	complemented
97	#17988688	C₂²	1	2	yes	complemented
98	#17988687	C₂²	1	2	yes	complemented
99	#17988686	C₂²	1	2	yes	complemented
100	#17988685	C₂²	1	2	yes	complemented
101	#17988684	C₂²	1	2	yes	complemented
102	#107×D₇₃	C₂²	1	2	yes	—
103	#106×D₇₃	C₂²	1	1	yes	characteristic
104	#106×D₇₃	C₂²	1	1	yes	characteristic
105	#103×D₇₃	C₂²	1	2	yes	—
106	#103×D₇₃	C₂²	1	2	yes	—
107	#102×D₇₃	C₂²	1	2	yes	—
108	#102×D₇₃	C₂²	1	2	yes	—
109	C₄×#11924012	C₂²	1	1	yes	characteristic, complemented
110	#17988539	C₂²	1	1	yes	characteristic, complemented
111	#17988539	C₂²	1	1	yes	characteristic, complemented
112	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
113	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×#11924011	C₂²	1	1	yes	characteristic, complemented
115	C₄×#11924011	C₂²	1	1	yes	characteristic, complemented
116	#97×D₇₃	C₂²	1	1	yes	characteristic
117	#97×D₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
120	#529×C₇₃	C₂²	1	2	yes	complemented
121	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#495×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#488×C₇₃	C₂²	1	2	yes	complemented
124	#470×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#469×C₇₃	C₂²	1	1	yes	characteristic
126	#468×C₇₃	C₂²	1	2	yes	complemented
127	#442×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#440×C₇₃	C₂²	1	2	yes	complemented
130	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
132	C₂×D₄×D₇₃	—	2	2	no	—
133	C₂×D₄×D₇₃	C₂³	1	2	yes	—
134	C₂²×C₄×D₇₃	—	2	2	no	—
135	C₂²×C₄×D₇₃	D₄	1	2	yes	—
136	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
138	C₂×#11924018	C₂³	1	2	yes	—
139	Q₁₆×D₇₃	—	2	4	no	—
140	C₂×#11924017	C₂³	1	2	yes	—
141	C₂×#11924016	C₂³	1	2	yes	—
142	C₂×#11924015	C₂³	1	2	yes	—
143	SD₁₆×D₇₃	—	2	8	no	—
144	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
145	C₂×#11924013	C₂³	1	2	yes	—
146	D₈×D₇₃	—	2	4	no	—
147	C₂×#11924012	C₂³	1	1	yes	characteristic
148	C₂×#11924012	C₂³	1	1	yes	characteristic
149	C₂×#11924011	C₂³	1	1	yes	characteristic
150	C₂×#11924011	C₂³	1	1	yes	characteristic
151	C₂×#11924011	C₂³	1	1	yes	characteristic
152	C₂×#11924011	C₂³	1	1	yes	characteristic
153	M₁₆×D₇₃	—	2	4	no	—
154	M₁₆×D₇₃	—	2	4	no	—
155	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
159	#14556586	—	2	2	no	—
160	#14556586	—	2	2	no	—
161	#14556586	—	2	2	no	—
162	#14556585	—	2	2	no	—
163	#14556584	—	2	2	no	—
164	#14556584	—	2	2	no	—
165	#14556584	—	2	2	no	—
166	#14556583	C₂³	1	2	yes	—
167	#14556582	C₂³	1	2	yes	—
168	#14556582	C₂³	1	2	yes	—
169	#14556581	—	2	2	no	—
170	#14556581	—	2	2	no	—
171	#14556580	C₂³	1	2	yes	—
172	#14556579	C₂³	1	2	yes	—
173	#14556578	C₂³	1	2	yes	—
174	#14556577	—	2	2	no	—
175	#14556577	—	2	2	no	—
176	#14556576	—	2	2	no	—
177	#14556576	—	2	2	no	—
178	#14556575	—	2	2	no	—
179	#14556574	—	2	2	no	—
180	#14556573	—	2	2	no	—
181	#14556573	—	2	2	no	—
182	#14556572	—	2	2	no	—
183	#14556571	C₂³	1	2	yes	—
184	#14556570	C₂³	1	2	yes	—
185	#14556569	—	2	2	no	—
186	#14556568	—	2	2	no	—
187	#14556567	C₂³	1	2	yes	—
188	#14556566	C₂³	1	2	yes	—
189	#14556565	C₂³	1	2	yes	—
190	#14556564	—	2	2	no	—
191	#14556563	—	2	2	no	—
192	#14556562	C₂³	1	2	yes	—
193	Q₈×Dic₇₃	C₂³	1	2	yes	—
194	C₄×Dic₁₄₆	—	2	2	no	—
195	C₄×Dic₁₄₆	C₂³	1	2	yes	—
196	#14556556	—	2	2	no	—
197	#14556556	C₂³	1	2	yes	—
198	C₄×D₂₉₂	—	2	2	no	—
199	C₄×D₂₉₂	C₂³	1	2	yes	—
200	D₄×Dic₇₃	—	2	2	no	—
201	D₄×Dic₇₃	C₂³	1	2	yes	—
202	#14556553	—	2	2	no	—
203	#14556553	C₂³	1	2	yes	—
204	C₄×C₂²⋊D₇₃	—	2	2	no	—
205	C₄×C₂²⋊D₇₃	—	2	2	no	—
206	C₄×C₂²⋊D₇₃	—	2	2	no	—
207	#14556551	—	2	2	no	—
208	#14556551	—	2	2	no	—
209	#14556551	—	2	2	no	—
210	#14556550	—	2	2	no	—
211	#14556549	—	2	2	no	—
212	#14556549	—	2	2	no	—
213	#14556548	—	2	2	no	—
214	#14556548	—	2	2	no	—
215	#14556547	—	2	2	no	—
216	#14556547	—	2	2	no	—
217	C₄⋊C₄×D₇₃	—	2	2	no	—
218	C₄⋊C₄×D₇₃	—	2	2	no	—
219	C₄⋊C₄×D₇₃	—	2	2	no	—
220	C₄⋊C₄×D₇₃	—	2	2	no	—
221	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
222	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×D₇₃	—	2	2	no	—
224	C₂²⋊C₄×D₇₃	—	2	2	no	—
225	C₂²⋊C₄×D₇₃	—	2	2	no	—
226	C₂²⋊C₄×D₇₃	—	2	2	no	—
227	C₂²⋊C₄×D₇₃	—	2	2	no	—
228	C₂×C₄×Dic₇₃	D₄	1	2	yes	—
229	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
230	C₄²×D₇₃	—	2	2	no	—
231	C₄²×D₇₃	D₄	1	2	yes	—
232	C₄²×D₇₃	D₄	1	2	yes	—
233	C₄²×D₇₃	C₂³	1	1	yes	characteristic
234	C₄²×D₇₃	C₂³	1	1	yes	characteristic
235	C₄²×D₇₃	C₂³	1	1	yes	characteristic
236	C₄²×D₇₃	C₂³	1	1	yes	characteristic
237	#14556525	C₂³	1	2	yes	—
238	#14556524	C₂³	1	2	yes	—
239	#14556524	C₂³	1	2	yes	—
240	#14556523	C₂³	1	1	yes	characteristic
241	#14556523	C₂³	1	1	yes	characteristic
242	#14556522	C₂³	1	2	yes	—
243	#14556522	C₂³	1	2	yes	—
244	#14556516	C₂³	1	2	yes	—
245	#14556516	C₂³	1	2	yes	—
246	#14556515	C₂³	1	2	yes	—
247	#14556515	C₂³	1	2	yes	—
248	#14556514	C₂³	1	2	yes	—
249	#14556514	C₂³	1	2	yes	—
250	#14556513	C₂³	1	2	yes	—
251	#14556513	C₂³	1	2	yes	—
252	#14556512	C₂³	1	2	yes	—
253	#14556512	C₂³	1	2	yes	—
254	#14556511	C₂³	1	2	yes	—
255	#14556511	C₂³	1	2	yes	—
256	#14556502	C₂³	1	1	yes	characteristic
257	#14556502	C₂³	1	1	yes	characteristic
258	#14556501	C₂³	1	1	yes	characteristic
259	#14556501	C₂³	1	1	yes	characteristic
260	#14556501	C₂³	1	1	yes	characteristic
261	#14556501	C₂³	1	1	yes	characteristic
262	C₄×#10596831	C₂³	1	1	yes	characteristic
263	C₄×#10596831	C₂³	1	1	yes	characteristic
264	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
268	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
269	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
270	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
272	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
273	#126×C₇₃	—	2	2	no	—
274	#125×C₇₃	C₂³	1	2	yes	—
275	#124×C₇₃	C₂³	1	2	yes	—
276	#123×C₇₃	—	2	2	no	—
277	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
278	#121×C₇₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
280	C₄×D₄×C₇₃	—	2	2	no	—
281	C₄×D₄×C₇₃	C₂³	1	2	yes	—
282	#117×C₇₃	—	2	2	no	—
283	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
284	#107×C₇₃	C₂³	1	2	yes	—
285	#106×C₇₃	C₂³	1	1	yes	characteristic
286	#106×C₇₃	C₂³	1	1	yes	characteristic
287	#103×C₇₃	C₂³	1	2	yes	—
288	#103×C₇₃	C₂³	1	2	yes	—
289	#102×C₇₃	C₂³	1	2	yes	—
290	#102×C₇₃	C₂³	1	2	yes	—
291	#97×C₇₃	C₂³	1	1	yes	characteristic
292	#97×C₇₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₂³×D₇₃	—	2	2	no	—
296	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Dic₁₄₆	—	2	2	no	—
298	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
299	Q₈×D₇₃	—	2	4	no	—
300	Q₈×D₇₃	—	2	4	no	—
301	C₂×D₂₉₂	—	2	2	no	—
302	C₂×D₂₉₂	C₂⁴	1	2	yes	—
303	C₂×C₂²⋊D₇₃	—	2	2	no	—
304	C₂×C₂²⋊D₇₃	—	2	2	no	—
305	C₂×C₂²⋊D₇₃	—	2	2	no	—
306	D₄×D₇₃	—	2	4	no	—
307	D₄×D₇₃	—	2	4	no	—
308	D₄×D₇₃	—	4	8	no	—
309	C₂²×Dic₇₃	—	2	2	no	—
310	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
312	C₂×C₄×D₇₃	—	2	2	no	—
313	C₂×C₄×D₇₃	—	2	2	no	—
314	C₂×C₄×D₇₃	—	2	2	no	—
315	C₂×C₄×D₇₃	—	2	2	no	—
316	C₂×C₄×D₇₃	—	2	2	no	—
317	C₂×C₄×D₇₃	—	2	2	no	—
318	C₂×C₄×D₇₃	—	2	2	no	—
319	C₂×C₄×D₇₃	—	4	4	no	—
320	C₂×C₄×D₇₃	—	4	8	no	—
321	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
322	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
323	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
324	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
325	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
326	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
327	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
329	Dic₂₉₂	—	2	2	no	—
330	#11924018	—	2	4	no	—
331	#11924017	—	2	4	no	—
332	#11924016	—	2	4	no	—
333	#11924015	—	2	4	no	—
334	D₅₈₄	—	2	2	no	—
335	#11924013	—	2	4	no	—
336	#11924012	—	2	2	no	—
337	#11924012	—	2	2	no	—
338	#11924011	—	2	2	no	—
339	#11924011	—	2	2	no	—
340	#11924011	—	2	2	no	—
341	#11924011	—	2	2	no	—
342	C₂×#10596831	C₂⁴	1	1	yes	characteristic
343	C₂×#10596831	C₂⁴	1	1	yes	characteristic
344	C₂×#10596831	C₂⁴	1	1	yes	characteristic
345	C₂×#10596831	C₂⁴	1	1	yes	characteristic
346	C₈×D₇₃	—	2	2	no	—
347	C₈×D₇₃	—	2	2	no	—
348	C₈×D₇₃	#41	1	4	yes	—
349	C₈×D₇₃	#41	1	4	yes	—
350	C₄⋊Dic₇₃	—	2	2	no	—
351	C₄⋊Dic₇₃	—	2	2	no	—
352	C₄⋊Dic₇₃	—	2	2	no	—
353	C₄⋊Dic₇₃	—	2	2	no	—
354	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
355	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
356	#11924007	—	2	2	no	—
357	#11924007	—	2	2	no	—
358	#11924007	—	2	2	no	—
359	#11924007	—	2	2	no	—
360	#11924007	—	2	2	no	—
361	#11924007	—	2	2	no	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
365	#11924007	—	2	2	no	—
366	C₂²⋊Dic₇₃	—	2	2	no	—
367	C₂²⋊Dic₇₃	—	2	2	no	—
368	C₂²⋊Dic₇₃	—	2	2	no	—
369	C₂²⋊Dic₇₃	—	2	2	no	—
370	C₂²⋊Dic₇₃	—	2	2	no	—
371	#11924005	—	2	2	no	—
372	#11924005	—	2	2	no	—
373	#11924005	—	2	2	no	—
374	#11924005	—	2	2	no	—
375	#11924005	—	2	2	no	—
376	#11924005	—	2	2	no	—
377	#11924005	—	2	2	no	—
378	#11924005	—	2	2	no	—
379	#11924005	—	2	2	no	—
380	#11924005	—	2	2	no	—
381	C₄×Dic₇₃	—	2	2	no	—
382	C₄×Dic₇₃	—	2	2	no	—
383	C₄×Dic₇₃	—	2	2	no	—
384	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
385	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
386	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
387	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
388	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
389	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
390	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
391	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
392	C₂×D₄×C₇₃	—	2	2	no	—
393	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₇₃	—	2	2	no	—
395	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
396	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
397	Q₁₆×C₇₃	—	2	2	no	—
398	SD₁₆×C₇₃	—	2	4	no	—
399	D₈×C₇₃	—	2	2	no	—
400	M₁₆×C₇₃	—	2	2	no	—
401	M₁₆×C₇₃	—	2	2	no	—
402	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₇₃	—	2	2	no	—
407	C₄⋊C₄×C₇₃	—	2	2	no	—
408	C₄⋊C₄×C₇₃	—	2	2	no	—
409	C₄⋊C₄×C₇₃	—	2	2	no	—
410	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
412	C₂²⋊C₄×C₇₃	—	2	2	no	—
413	C₂²⋊C₄×C₇₃	—	2	2	no	—
414	C₂²⋊C₄×C₇₃	—	2	2	no	—
415	C₂²⋊C₄×C₇₃	—	2	2	no	—
416	C₂²⋊C₄×C₇₃	—	2	2	no	—
417	C₄²×C₇₃	—	2	2	no	—
418	C₄²×C₇₃	C₂×D₄	1	2	yes	—
419	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂³×C₇₃	—	2	2	no	—
422	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
423	C₂²×D₇₃	—	2	2	no	—
424	C₂²×D₇₃	—	2	4	no	—
425	C₂²×D₇₃	—	2	2	no	—
426	C₂²×D₇₃	—	4	4	no	—
427	C₂²×D₇₃	—	4	4	no	—
428	C₂²×D₇₃	—	4	4	no	—
429	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
430	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
431	Q₈×C₇₃	—	2	2	no	—
432	Q₈×C₇₃	—	2	2	no	—
433	D₄×C₇₃	—	2	2	no	—
434	D₄×C₇₃	—	2	2	no	—
435	D₄×C₇₃	—	4	4	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	2	no	—
440	C₂×C₄×C₇₃	—	2	2	no	—
441	C₂×C₄×C₇₃	—	4	2	no	—
442	C₂×C₄×C₇₃	—	4	4	no	—
443	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
447	C₂²⋊D₇₃	—	4	4	no	—
448	C₂²⋊D₇₃	—	4	4	no	—
449	C₂²⋊D₇₃	—	4	4	no	—
450	C₂×Dic₇₃	—	2	2	no	—
451	C₂×Dic₇₃	—	2	2	no	—
452	C₂×Dic₇₃	—	2	2	no	—
453	C₂×Dic₇₃	—	2	2	no	—
454	C₂×Dic₇₃	—	4	2	no	—
455	C₂×Dic₇₃	—	4	4	no	—
456	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
457	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
459	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
460	D₂₉₂	—	2	2	no	—
461	D₂₉₂	—	2	2	no	—
462	D₂₉₂	—	4	4	no	—
463	C₄×D₇₃	—	2	2	no	—
464	C₄×D₇₃	—	2	4	no	—
465	C₄×D₇₃	—	2	4	no	—
466	C₄×D₇₃	—	2	1	no	—
467	C₄×D₇₃	—	2	1	no	—
468	C₄×D₇₃	—	2	2	no	—
469	C₄×D₇₃	—	4	2	no	—
470	C₄×D₇₃	—	4	2	no	—
471	C₄×D₇₃	—	4	4	no	—
472	C₄×D₇₃	—	4	4	no	—
473	C₄×D₇₃	—	4	4	no	—
474	C₄×D₇₃	—	4	4	no	—
475	C₄×D₇₃	—	4	4	no	—
476	C₄×D₇₃	C₂×#41	1	2	yes	—
477	C₄×D₇₃	C₂×#41	1	2	yes	—
478	Dic₁₄₆	—	2	2	no	—
479	Dic₁₄₆	—	2	2	no	—
480	Dic₁₄₆	—	4	4	no	—
481	C₈×C₇₃	—	2	1	no	—
482	C₈×C₇₃	—	2	1	no	—
483	C₈×C₇₃	C₂×#41	1	2	yes	—
484	C₈×C₇₃	C₂×#41	1	2	yes	—
485	#10596831	—	2	1	no	—
486	#10596831	—	2	1	no	—
487	#10596831	C₂×#41	1	2	yes	—
488	#10596831	C₂×#41	1	2	yes	—
489	C₂²×C₇₃	—	2	1	no	—
490	C₂²×C₇₃	—	2	2	no	—
491	C₂²×C₇₃	—	4	2	no	—
492	C₂²×C₇₃	—	4	2	no	—
493	C₂²×C₇₃	—	4	2	no	—
494	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
495	C₂×D₇₃	—	2	1	no	—
496	C₂×D₇₃	—	2	2	no	—
497	C₂×D₇₃	—	4	4	no	—
498	C₂×D₇₃	—	4	2	no	—
499	C₂×D₇₃	—	4	2	no	—
500	C₂×D₇₃	—	4	2	no	—
501	C₂×D₇₃	—	8	8	no	—
502	C₂×D₇₃	#532	1	2	yes	—
503	C₂×D₇₃	#575	1	4	yes	—
504	C₄×C₇₃	—	2	1	no	—
505	C₄×C₇₃	—	2	2	no	—
506	C₄×C₇₃	—	2	2	no	—
507	C₄×C₇₃	—	4	2	no	—
508	C₄×C₇₃	—	4	2	no	—
509	C₄×C₇₃	—	4	2	no	—
510	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
511	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
512	Dic₇₃	—	2	1	no	—
513	Dic₇₃	—	2	2	no	—
514	Dic₇₃	—	2	2	no	—
515	Dic₇₃	—	4	2	no	—
516	Dic₇₃	—	4	2	no	—
517	Dic₇₃	—	4	2	no	—
518	Dic₇₃	#532	1	2	yes	—
519	C₂×#3183	—	73	1	no	maximal, Sylow
520	C₂×C₇₃	—	4	1	no	—
521	C₂×C₇₃	—	8	2	no	—
522	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
523	C₂×C₇₃	C₂×#575	1	2	yes	—
524	D₇₃	—	4	1	no	—
525	D₇₃	—	8	2	no	—
526	D₇₃	#3183	1	4	yes	direct product factor
527	C₂×#529	—	73	2	no	—
528	#3183	—	73	1	no	—
529	#3183	—	73	1	no	—
530	#3183	—	73	2	no	—
531	#3183	—	73	1	no	—
532	#3183	—	73	1	no	—
533	#3183	—	73	2	no	—
534	#3183	—	73	1	no	—
535	#3183	—	73	1	no	—
536	#3183	—	73	2	no	—
537	#3183	—	73	1	no	—
538	#3183	—	73	2	no	—
539	#3183	D₇₃	1	1	yes	characteristic, direct product factor
540	C₂×#499	—	73	1	no	—
541	C₂×#495	—	73	1	no	—
542	C₂×#488	—	73	2	no	—
543	C₂×#470	—	73	1	no	—
544	C₂×#469	—	73	1	no	—
545	C₂×#468	—	73	2	no	—
546	C₂×#442	—	73	1	no	—
547	C₂×#441	—	73	1	no	—
548	C₂×#440	—	73	2	no	—
549	C₂×C₄×M₁₆	—	73	1	no	—
550	C₇₃	C₂×#3183	1	1	yes	characteristic, complemented, Sylow
551	C₂²×Q₁₆	—	73	1	no	—
552	C₂²×SD₁₆	—	73	2	no	—
553	C₂²×D₈	—	73	1	no	—
554	C₂²×M₁₆	—	73	1	no	—
555	C₂²×M₁₆	—	73	1	no	—
556	#529	—	73	2	no	—
557	#529	—	73	2	no	—
558	#529	—	73	2	no	—
559	#529	—	73	2	no	—
560	#529	—	73	2	no	—
561	#529	—	73	2	no	—
562	#529	—	73	2	no	—
563	#529	—	146	2	no	—
564	#529	—	146	2	no	—
565	#529	—	146	2	no	—
566	#529	—	146	2	no	—
567	#529	C₂×D₇₃	1	2	yes	complemented
568	C₂×#126	—	146	2	no	—
569	C₂×#125	—	73	2	no	—
570	C₂×#124	—	73	2	no	—
571	C₂×#123	—	146	2	no	—
572	C₂×C₂²⋊Q₈	—	73	2	no	—
573	C₂×#121	—	73	2	no	—
574	C₂×C₄×Q₈	—	73	2	no	—
575	C₂×C₄×D₄	—	73	2	no	—
576	C₂×C₄×D₄	—	146	2	no	—
577	C₂×#117	—	146	2	no	—
578	C₂²×C₄²	—	73	1	no	—
579	#499	—	73	2	no	—
580	#499	—	73	2	no	—
581	#499	—	73	1	no	—
582	#499	—	73	1	no	—
583	#499	—	73	1	no	—
584	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
585	#495	—	73	1	no	—
586	#495	—	73	2	no	—
587	#495	—	73	1	no	—
588	#495	—	73	2	no	—
589	#495	—	73	1	no	—
590	#495	C₂×D₇₃	1	1	yes	characteristic, complemented
591	#488	—	73	2	no	—
592	#488	—	73	2	no	—
593	#488	—	73	2	no	—
594	#488	—	73	2	no	—
595	#488	—	73	2	no	—
596	#488	—	73	2	no	—
597	#488	—	73	2	no	—
598	#488	C₂×D₇₃	1	2	yes	complemented
599	#470	—	73	1	no	—
600	#470	—	73	1	no	—
601	#470	—	73	2	no	—
602	#470	—	73	1	no	—
603	#470	—	73	2	no	—
604	#470	C₂×D₇₃	1	1	yes	characteristic, complemented
605	#469	—	73	1	no	—
606	#469	—	73	1	no	—
607	#469	—	73	2	no	—
608	#469	—	73	1	no	—
609	#469	—	73	2	no	—
610	#469	C₂×D₇₃	1	1	yes	characteristic
611	#468	—	73	2	no	—
612	#468	—	73	2	no	—
613	#468	—	73	2	no	—
614	#468	—	73	2	no	—
615	#468	—	73	2	no	—
616	#468	—	73	2	no	—
617	#468	—	73	2	no	—
618	#468	C₂×D₇₃	1	2	yes	complemented
619	#442	—	73	1	no	—
620	#442	—	73	2	no	—
621	#442	—	73	1	no	—
622	#442	—	73	2	no	—
623	#442	—	73	1	no	—
624	#442	C₂×D₇₃	1	1	yes	characteristic, complemented
625	#441	—	73	1	no	—
626	#441	—	73	2	no	—
627	#441	—	73	1	no	—
628	#441	—	73	2	no	—
629	#441	—	73	1	no	—
630	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
631	#440	—	73	2	no	—
632	#440	—	73	2	no	—
633	#440	—	73	2	no	—
634	#440	—	73	2	no	—
635	#440	—	73	2	no	—
636	#440	—	73	2	no	—
637	#440	—	73	2	no	—
638	#440	C₂×D₇₃	1	2	yes	complemented
639	C₂×#107	—	73	2	no	—
640	C₂×#106	—	73	1	no	—
641	C₂×#106	—	73	1	no	—
642	C₂×#103	—	73	2	no	—
643	C₂×#103	—	73	2	no	—
644	C₂×#102	—	73	2	no	—
645	C₂×#102	—	73	2	no	—
646	C₄×M₁₆	—	73	1	no	—
647	C₄×M₁₆	—	73	1	no	—
648	C₄×M₁₆	—	73	1	no	—
649	C₄×M₁₆	—	73	1	no	—
650	C₄×M₁₆	—	73	1	no	—
651	C₄×M₁₆	—	73	1	no	—
652	C₄×M₁₆	—	73	1	no	—
653	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
654	C₂×#97	—	73	1	no	—
655	C₂×#97	—	73	1	no	—
656	C₂×C₄×C₈	—	73	1	no	—
657	C₂×C₄×C₈	—	73	1	no	—
658	C₂²×Q₈	—	73	2	no	—
659	C₂²×D₄	—	73	2	no	—
660	C₂²×D₄	—	146	2	no	—
661	C₂³×C₄	—	73	2	no	—
662	C₂³×C₄	—	73	1	no	—
663	C₂³×C₄	—	146	2	no	—
664	C₂×Q₁₆	—	73	2	no	—
665	C₂×Q₁₆	—	73	1	no	—
666	C₂×Q₁₆	—	146	4	no	—
667	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
668	C₂×SD₁₆	—	73	2	no	—
669	C₂×SD₁₆	—	73	2	no	—
670	C₂×SD₁₆	—	73	2	no	—
671	C₂×SD₁₆	—	146	8	no	—
672	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
673	C₂×D₈	—	73	2	no	—
674	C₂×D₈	—	73	1	no	—
675	C₂×D₈	—	146	4	no	—
676	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
677	C₂×M₁₆	—	73	1	no	—
678	C₂×M₁₆	—	73	1	no	—
679	C₂×M₁₆	—	73	1	no	—
680	C₂×M₁₆	—	73	1	no	—
681	C₂×M₁₆	—	73	1	no	—
682	C₂×M₁₆	—	73	1	no	—
683	C₂×M₁₆	—	146	4	no	—
684	C₂×M₁₆	—	146	4	no	—
685	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
686	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
687	C₂²×C₈	—	73	1	no	—
688	C₂²×C₈	—	73	1	no	—
689	C₂²×C₈	—	73	1	no	—
690	C₂²×C₈	—	73	1	no	—
691	#126	—	2	2	no	—
692	#126	—	146	2	no	—
693	#126	—	146	2	no	—
694	#126	—	146	2	no	—
695	#126	—	146	2	no	—
696	#126	—	146	2	no	—
697	#126	—	146	2	no	—
698	#126	—	146	2	no	—
699	#125	—	73	2	no	—
700	#125	—	73	2	no	—
701	#125	—	73	2	no	—
702	#125	—	146	2	no	—
703	#125	—	146	2	no	—
704	#125	C₂²×D₇₃	1	2	yes	—
705	#124	—	73	2	no	—
706	#124	—	73	2	no	—
707	#124	—	73	2	no	—
708	#124	—	146	2	no	—
709	#124	—	146	2	no	—
710	#124	C₂²×D₇₃	1	2	yes	—
711	#123	—	2	2	no	—
712	#123	—	146	2	no	—
713	#123	—	146	2	no	—
714	#123	—	146	2	no	—
715	#123	—	146	2	no	—
716	#123	—	146	2	no	—
717	#123	—	146	2	no	—
718	#123	—	146	2	no	—
719	C₂²⋊Q₈	—	73	2	no	—
720	C₂²⋊Q₈	—	73	2	no	—
721	C₂²⋊Q₈	—	73	2	no	—
722	C₂²⋊Q₈	—	146	2	no	—
723	C₂²⋊Q₈	—	146	2	no	—
724	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
725	#121	—	73	2	no	—
726	#121	—	73	2	no	—
727	#121	—	73	2	no	—
728	#121	—	146	2	no	—
729	#121	—	146	2	no	—
730	#121	C₂²×D₇₃	1	2	yes	—
731	C₄×Q₈	—	73	2	no	—
732	C₄×Q₈	—	73	2	no	—
733	C₄×Q₈	—	73	2	no	—
734	C₄×Q₈	—	146	2	no	—
735	C₄×Q₈	—	146	2	no	—
736	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	73	2	no	—
739	C₄×D₄	—	73	2	no	—
740	C₄×D₄	—	73	2	no	—
741	C₄×D₄	—	146	2	no	—
742	C₄×D₄	—	146	2	no	—
743	C₄×D₄	—	146	2	no	—
744	C₄×D₄	—	146	2	no	—
745	C₄×D₄	—	146	2	no	—
746	C₄×D₄	—	146	2	no	—
747	C₄×D₄	—	146	2	no	—
748	C₄×D₄	—	146	2	no	—
749	C₄×D₄	—	146	2	no	—
750	C₄×D₄	C₂²×D₇₃	1	2	yes	—
751	#117	—	2	2	no	—
752	#117	—	146	2	no	—
753	#117	—	146	2	no	—
754	#117	—	146	2	no	—
755	#117	—	146	2	no	—
756	#117	—	146	2	no	—
757	#117	—	146	2	no	—
758	#117	—	146	2	no	—
759	C₂×C₄⋊C₄	—	73	2	no	—
760	C₂×C₄⋊C₄	—	73	2	no	—
761	C₂×C₄⋊C₄	—	146	2	no	—
762	C₂×C₄⋊C₄	—	146	2	no	—
763	C₂×C₄⋊C₄	—	146	2	no	—
764	C₂×C₄⋊C₄	—	146	2	no	—
765	C₂×C₂²⋊C₄	—	146	2	no	—
766	C₂×C₂²⋊C₄	—	146	2	no	—
767	C₂×C₂²⋊C₄	—	146	2	no	—
768	C₂×C₂²⋊C₄	—	146	2	no	—
769	C₂×C₂²⋊C₄	—	146	2	no	—
770	C₂×C₄²	—	73	2	no	—
771	C₂×C₄²	—	73	1	no	—
772	C₂×C₄²	—	73	2	no	—
773	C₂×C₄²	—	73	2	no	—
774	C₂×C₄²	—	73	1	no	—
775	C₂×C₄²	—	73	1	no	—
776	C₂×C₄²	—	73	1	no	—
777	C₂×C₄²	—	73	1	no	—
778	C₂×C₄²	—	146	2	no	—
779	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
780	#107	—	73	2	no	—
781	#107	—	73	2	no	—
782	#107	—	73	2	no	—
783	#107	C₂²×D₇₃	1	2	yes	—
784	#106	—	73	1	no	—
785	#106	—	73	1	no	—
786	#106	—	73	2	no	—
787	#106	—	73	2	no	—
788	#106	C₂²×D₇₃	1	1	yes	characteristic
789	#106	C₂²×D₇₃	1	1	yes	characteristic
790	#103	—	73	2	no	—
791	#103	—	73	2	no	—
792	#103	—	73	2	no	—
793	#103	—	73	2	no	—
794	#103	—	73	2	no	—
795	#103	—	73	2	no	—
796	#103	C₂²×D₇₃	1	2	yes	—
797	#103	C₂²×D₇₃	1	2	yes	—
798	#102	—	73	2	no	—
799	#102	—	73	2	no	—
800	#102	—	73	2	no	—
801	#102	—	73	2	no	—
802	#102	—	73	2	no	—
803	#102	—	73	2	no	—
804	#102	C₂²×D₇₃	1	2	yes	—
805	#102	C₂²×D₇₃	1	2	yes	—
806	#97	—	73	1	no	—
807	#97	—	73	1	no	—
808	#97	—	73	1	no	—
809	#97	—	73	1	no	—
810	#97	—	73	1	no	—
811	#97	—	73	1	no	—
812	#97	C₂²×D₇₃	1	1	yes	characteristic
813	#97	C₂²×D₇₃	1	1	yes	characteristic
814	C₄×C₈	—	73	1	no	—
815	C₄×C₈	—	73	1	no	—
816	C₄×C₈	—	73	1	no	—
817	C₄×C₈	—	73	1	no	—
818	C₄×C₈	—	73	1	no	—
819	C₄×C₈	—	73	1	no	—
820	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
821	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
822	C₂⁴	—	73	1	no	—
823	C₂⁴	—	146	2	no	—
824	C₂×Q₈	—	73	2	no	—
825	C₂×Q₈	—	146	2	no	—
826	C₂×Q₈	—	146	4	no	—
827	C₂×Q₈	—	146	4	no	—
828	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	292	8	no	—
831	C₂×D₄	—	73	2	no	—
832	C₂×D₄	—	146	2	no	—
833	C₂×D₄	—	146	4	no	—
834	C₂×D₄	—	146	4	no	—
835	C₂×D₄	—	146	2	no	—
836	C₂×D₄	—	146	2	no	—
837	C₂×D₄	—	146	2	no	—
838	C₂×D₄	C₂³×D₇₃	1	2	yes	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	292	8	no	—
841	C₂²×C₄	—	292	4	no	—
842	C₂²×C₄	—	73	2	no	—
843	C₂²×C₄	—	73	2	no	—
844	C₂²×C₄	—	73	2	no	—
845	C₂²×C₄	—	73	1	no	—
846	C₂²×C₄	—	73	1	no	—
847	C₂²×C₄	—	73	2	no	—
848	C₂²×C₄	—	73	2	no	—
849	C₂²×C₄	—	73	1	no	—
850	C₂²×C₄	—	73	1	no	—
851	C₂²×C₄	—	73	1	no	—
852	C₂²×C₄	—	146	2	no	—
853	C₂²×C₄	—	146	2	no	—
854	C₂²×C₄	—	146	2	no	—
855	C₂²×C₄	—	146	2	no	—
856	C₂²×C₄	—	146	2	no	—
857	C₂²×C₄	—	146	2	no	—
858	C₂²×C₄	—	146	2	no	—
859	C₂²×C₄	—	146	2	no	—
860	C₂²×C₄	D₄×D₇₃	1	2	yes	—
861	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
862	Q₁₆	—	2	2	no	—
863	Q₁₆	—	146	4	no	—
864	Q₁₆	—	146	2	no	—
865	SD₁₆	—	2	4	no	—
866	SD₁₆	—	146	4	no	—
867	SD₁₆	—	146	4	no	—
868	SD₁₆	—	146	4	no	—
869	D₈	—	2	2	no	—
870	D₈	—	146	4	no	—
871	D₈	—	146	2	no	—
872	M₁₆	—	2	2	no	—
873	M₁₆	—	2	2	no	—
874	M₁₆	—	146	2	no	—
875	M₁₆	—	146	2	no	—
876	M₁₆	—	146	2	no	—
877	M₁₆	—	146	2	no	—
878	M₁₆	—	146	2	no	—
879	M₁₆	—	146	2	no	—
880	C₂×C₈	—	73	1	no	—
881	C₂×C₈	—	73	1	no	—
882	C₂×C₈	—	73	4	no	—
883	C₂×C₈	—	73	4	no	—
884	C₂×C₈	—	73	1	no	—
885	C₂×C₈	—	73	1	no	—
886	C₂×C₈	—	146	2	no	—
887	C₂×C₈	—	146	2	no	—
888	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	73	2	no	—
897	C₄⋊C₄	—	73	2	no	—
898	C₄⋊C₄	—	146	2	no	—
899	C₄⋊C₄	—	146	2	no	—
900	C₄⋊C₄	—	146	2	no	—
901	C₄⋊C₄	—	146	2	no	—
902	C₄⋊C₄	—	146	2	no	—
903	C₄⋊C₄	—	146	2	no	—
904	C₄⋊C₄	—	146	2	no	—
905	C₄⋊C₄	—	146	2	no	—
906	C₄⋊C₄	—	146	2	no	—
907	C₄⋊C₄	—	146	2	no	—
908	C₄⋊C₄	—	146	2	no	—
909	C₄⋊C₄	—	146	2	no	—
910	C₄⋊C₄	—	146	2	no	—
911	C₄⋊C₄	—	146	2	no	—
912	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
913	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	146	2	no	—
920	C₂²⋊C₄	—	146	2	no	—
921	C₂²⋊C₄	—	146	2	no	—
922	C₂²⋊C₄	—	146	2	no	—
923	C₂²⋊C₄	—	146	2	no	—
924	C₂²⋊C₄	—	146	2	no	—
925	C₂²⋊C₄	—	146	2	no	—
926	C₂²⋊C₄	—	146	2	no	—
927	C₂²⋊C₄	—	146	2	no	—
928	C₂²⋊C₄	—	146	2	no	—
929	C₂²⋊C₄	—	146	2	no	—
930	C₂²⋊C₄	—	146	2	no	—
931	C₂²⋊C₄	—	146	2	no	—
932	C₂²⋊C₄	—	146	2	no	—
933	C₂²⋊C₄	—	146	2	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	73	2	no	—
936	C₄²	—	73	2	no	—
937	C₄²	—	73	2	no	—
938	C₄²	—	73	2	no	—
939	C₄²	—	73	2	no	—
940	C₄²	—	73	1	no	—
941	C₄²	—	73	1	no	—
942	C₄²	—	146	2	no	—
943	C₄²	—	146	2	no	—
944	C₄²	—	146	2	no	—
945	C₄²	D₄×D₇₃	1	2	yes	—
946	C₄²	C₂³×D₇₃	1	1	yes	characteristic
947	C₄²	C₂³×D₇₃	1	1	yes	characteristic
948	C₂³	—	2	2	no	—
949	C₂³	—	292	4	no	—
950	C₂³	—	292	4	no	—
951	C₂³	—	292	4	no	—
952	C₂³	—	73	1	no	—
953	C₂³	—	73	1	no	—
954	C₂³	—	146	4	no	—
955	C₂³	—	146	2	no	—
956	C₂³	—	146	2	no	—
957	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
958	Q₈	—	2	2	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	292	4	no	—
961	Q₈	—	146	2	no	—
962	Q₈	—	146	2	no	—
963	D₄	—	2	2	no	—
964	D₄	—	2	2	no	—
965	D₄	—	4	4	no	—
966	D₄	—	292	4	no	—
967	D₄	—	292	4	no	—
968	D₄	—	292	4	no	—
969	D₄	—	292	4	no	—
970	D₄	—	146	2	no	—
971	D₄	—	146	2	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	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	292	4	no	—
980	C₂×C₄	—	292	2	no	—
981	C₂×C₄	—	292	2	no	—
982	C₂×C₄	—	292	4	no	—
983	C₂×C₄	—	292	4	no	—
984	C₂×C₄	—	292	4	no	—
985	C₂×C₄	—	292	4	no	—
986	C₂×C₄	—	292	4	no	—
987	C₂×C₄	—	292	2	no	—
988	C₂×C₄	—	73	1	no	—
989	C₂×C₄	—	73	2	no	—
990	C₂×C₄	—	73	2	no	—
991	C₂×C₄	—	73	2	no	—
992	C₂×C₄	—	73	2	no	—
993	C₂×C₄	—	73	1	no	—
994	C₂×C₄	—	146	2	no	—
995	C₂×C₄	—	146	4	no	—
996	C₂×C₄	—	146	4	no	—
997	C₂×C₄	—	146	2	no	—
998	C₂×C₄	—	146	2	no	—
999	C₂×C₄	—	146	2	no	—
1000	C₂×C₄	—	146	2	no	—
1001	C₂×C₄	—	146	2	no	—
1002	C₂×C₄	—	146	1	no	—
1003	C₂×C₄	—	146	1	no	—
1004	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1005	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1006	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1007	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1008	C₈	—	2	1	no	—
1009	C₈	—	2	1	no	—
1010	C₈	—	73	2	no	—
1011	C₈	—	73	2	no	—
1012	C₈	—	146	1	no	—
1013	C₈	—	146	1	no	—
1014	C₈	#41×D₇₃	1	2	yes	—
1015	C₈	#41×D₇₃	1	2	yes	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	292	4	no	—
1022	C₂²	—	292	2	no	—
1023	C₂²	—	292	2	no	—
1024	C₂²	—	292	2	no	—
1025	C₂²	—	584	8	no	—
1026	C₂²	—	73	4	no	—
1027	C₂²	—	73	2	no	—
1028	C₂²	—	146	2	no	—
1029	C₂²	—	146	1	no	—
1030	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	292	2	no	—
1038	C₄	—	292	2	no	—
1039	C₄	—	292	2	no	—
1040	C₄	—	73	2	no	—
1041	C₄	—	146	2	no	—
1042	C₄	—	146	2	no	—
1043	C₄	—	146	1	no	—
1044	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1045	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	2	no	—
1048	C₂	—	292	1	no	—
1049	C₂	—	584	2	no	—
1050	C₂	—	73	4	no	—
1051	C₂	#532×D₇₃	1	1	yes	characteristic
1052	C₂	#575×D₇₃	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3183	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#469×D₇₃	C₂
hypercenter	#3183	D₇₃
hypocenter	C₇₃	C₂×#3183
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3183

Complements

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

N	H ≅ G/N	type
1. #529×D₇₃	C₂	semidirect
2. #22620663	C₂	semidirect
3. #22620662	C₂	semidirect
4. #22620661	C₂	semidirect
5. #22620660	C₂	semidirect
6. #22620659	C₂	semidirect
7. #22620658	C₂	semidirect
8. #22620657	C₂	semidirect
9. #22620656	C₂	semidirect
10. #22620655	C₂	semidirect
11. #22620654	C₂	semidirect
12. #22620653	C₂	semidirect
13. #499×D₇₃	C₂	semidirect
14. #495×D₇₃	C₂	semidirect
15. #488×D₇₃	C₂	semidirect
16. #470×D₇₃	C₂	semidirect
18. #468×D₇₃	C₂	semidirect
19. #442×D₇₃	C₂	semidirect
20. #441×D₇₃	C₂	semidirect
21. #440×D₇₃	C₂	semidirect
22. C₄×M₁₆×D₇₃	C₂	semidirect
23. C₇₃×#3183	C₂	semidirect
29. #17989124	C₂²	semidirect
30. #17989123	C₂²	semidirect
31. #17989122	C₂²	semidirect
32. #17989121	C₂²	semidirect
34. #17989119	C₂²	semidirect
35. #17989118	C₂²	semidirect
37. #17989116	C₂²	semidirect
51. #17988989	C₂²	semidirect
52. #17988988	C₂²	semidirect
53. #17988987	C₂²	semidirect
54. #17988987	C₂²	semidirect
55. #17988986	C₂²	semidirect
56. #17988972	C₂²	semidirect
57. #17988971	C₂²	semidirect
58. #17988970	C₂²	semidirect
59. #17988969	C₂²	semidirect
60. #17988968	C₂²	semidirect
61. #17988944	C₂²	semidirect
62. #17988943	C₂²	semidirect
63. #17988943	C₂²	semidirect
64. #17988942	C₂²	semidirect
65. #17988941	C₂²	semidirect
66. #17988940	C₂²	semidirect
67. #17988940	C₂²	semidirect
68. #17988846	C₂²	semidirect
69. #17988845	C₂²	semidirect
70. #17988844	C₂²	semidirect
71. #17988843	C₂²	semidirect
72. #17988842	C₂²	semidirect
78. #17988836	C₂²	semidirect
79. #17988835	C₂²	semidirect
80. #17988834	C₂²	semidirect
81. #17988833	C₂²	semidirect
82. #17988832	C₂²	semidirect
83. #17988831	C₂²	semidirect
84. #17988830	C₂²	semidirect
85. #17988700	C₂²	semidirect
86. #17988699	C₂²	semidirect
87. #17988698	C₂²	semidirect
88. #17988697	C₂²	semidirect
89. #17988696	C₂²	semidirect
90. #17988695	C₂²	semidirect
91. #17988694	C₂²	semidirect
92. #17988693	C₂²	semidirect
93. #17988692	C₂²	semidirect
94. #17988691	C₂²	semidirect
95. #17988690	C₂²	semidirect
96. #17988689	C₂²	semidirect
97. #17988688	C₂²	semidirect
98. #17988687	C₂²	semidirect
99. #17988686	C₂²	semidirect
100. #17988685	C₂²	semidirect
101. #17988684	C₂²	semidirect
109. C₄×#11924012	C₂²	semidirect
110. #17988539	C₂²	semidirect
111. #17988539	C₂²	semidirect
112. M₁₆×Dic₇₃	C₂²	semidirect
113. M₁₆×Dic₇₃	C₂²	semidirect
114. C₄×#11924011	C₂²	semidirect
115. C₄×#11924011	C₂²	semidirect
120. #529×C₇₃	C₂²	semidirect
121. #499×C₇₃	C₂²	semidirect
122. #495×C₇₃	C₂²	semidirect
123. #488×C₇₃	C₂²	semidirect
124. #470×C₇₃	C₂²	semidirect
126. #468×C₇₃	C₂²	semidirect
127. #442×C₇₃	C₂²	semidirect
128. #441×C₇₃	C₂²	semidirect
129. #440×C₇₃	C₂²	semidirect
130. C₄×M₁₆×C₇₃	C₂²	semidirect
526. D₇₃	#3183	direct (N × H)
539. #3183	D₇₃	direct (N × H)
550. C₇₃	C₂×#3183	semidirect
567. #529	C₂×D₇₃	semidirect
584. #499	C₂×D₇₃	semidirect
590. #495	C₂×D₇₃	semidirect
598. #488	C₂×D₇₃	semidirect
604. #470	C₂×D₇₃	semidirect
618. #468	C₂×D₇₃	semidirect
624. #442	C₂×D₇₃	semidirect
630. #441	C₂×D₇₃	semidirect
638. #440	C₂×D₇₃	semidirect
653. C₄×M₁₆	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#529×D₇₃	2
#22620663	2
#22620662	2
#22620661	2
#22620660	2
#22620659	2
#22620658	2
#22620657	2
#22620656	2
#22620655	2
#22620654	2
#22620653	2
#499×D₇₃	2
#495×D₇₃	2
#488×D₇₃	2
#470×D₇₃	2
#469×D₇₃	2
#468×D₇₃	2
#442×D₇₃	2
#441×D₇₃	2
#440×D₇₃	2
C₄×M₁₆×D₇₃	2
C₇₃×#3183	2
C₂×#3183	73

Subgroups — #3183×D73 #33955930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3183×D₇₃ #33955930