Subgroups — #3175×D₇₃ #33955798

Order 18688.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#542×D₇₃	C₂	1	2	yes	maximal, complemented
2	#22620573	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620572	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620571	C₂	1	1	yes	maximal, characteristic, complemented
5	#22620570	C₂	1	1	yes	maximal, characteristic, complemented
6	#22620569	C₂	1	2	yes	maximal, complemented
7	#22620568	C₂	1	2	yes	maximal, complemented
8	#22620567	C₂	1	1	yes	maximal, characteristic, complemented
9	#22620566	C₂	1	1	yes	maximal, characteristic, complemented
10	#22620565	C₂	1	2	yes	maximal, complemented
11	#22620564	C₂	1	2	yes	maximal, complemented
12	#22620563	C₂	1	1	yes	maximal, characteristic, complemented
13	#500×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#489×D₇₃	C₂	1	2	yes	maximal, complemented
16	#468×D₇₃	C₂	1	2	yes	maximal, complemented
17	#467×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#466×D₇₃	C₂	1	1	yes	maximal, characteristic
19	#440×D₇₃	C₂	1	2	yes	maximal, complemented
20	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#405×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3175	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	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	#17989211	C₂²	1	2	yes	complemented
30	#17989210	C₂²	1	2	yes	complemented
31	#17989209	C₂²	1	2	yes	complemented
32	#17989208	C₂²	1	2	yes	complemented
33	#17989207	—	2	2	no	—
34	#17989206	C₂²	1	2	yes	complemented
35	#17989205	—	2	2	no	—
36	#17989204	C₂²	1	2	yes	complemented
37	#17989203	—	2	2	no	—
38	#17989202	C₂²	1	2	yes	complemented
39	#17989201	—	2	2	no	—
40	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
41	#126×D₇₃	—	2	2	no	—
42	#124×D₇₃	—	2	2	no	—
43	#124×D₇₃	C₂²	1	2	yes	—
44	#123×D₇₃	—	2	2	no	—
45	C₂²⋊Q₈×D₇₃	—	2	2	no	—
46	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
47	#121×D₇₃	C₂²	1	2	yes	—
48	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
49	C₄×D₄×D₇₃	C₂²	1	2	yes	—
50	#117×D₇₃	C₂²	1	1	yes	characteristic
51	#17988992	C₂²	1	1	yes	characteristic, complemented
52	#17988991	C₂²	1	1	yes	characteristic, complemented
53	#17988991	C₂²	1	2	yes	complemented
54	#17988991	C₂²	1	1	yes	characteristic, complemented
55	#17988990	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	#17988949	C₂²	1	2	yes	complemented
62	#17988948	C₂²	1	2	yes	complemented
63	#17988948	C₂²	1	2	yes	complemented
64	#17988947	C₂²	1	2	yes	complemented
65	#17988946	C₂²	1	2	yes	complemented
66	#17988945	C₂²	1	2	yes	complemented
67	#17988945	C₂²	1	2	yes	complemented
68	#17988836	C₂²	1	2	yes	complemented
69	#17988835	C₂²	1	2	yes	complemented
70	#17988834	C₂²	1	2	yes	complemented
71	#17988833	C₂²	1	2	yes	complemented
72	#17988832	C₂²	1	2	yes	complemented
73	#17988831	C₂²	1	2	yes	complemented
74	#17988830	C₂²	1	2	yes	complemented
75	#17988829	C₂²	1	1	yes	characteristic, complemented
76	#17988828	C₂²	1	1	yes	characteristic, complemented
77	#17988827	C₂²	1	2	yes	complemented
78	#17988826	C₂²	1	2	yes	complemented
79	#17988825	C₂²	1	1	yes	characteristic, complemented
80	#17988824	C₂²	1	1	yes	characteristic
81	#17988823	C₂²	1	1	yes	characteristic
82	#17988822	C₂²	1	2	yes	—
83	#17988821	C₂²	1	2	yes	—
84	#17988820	C₂²	1	1	yes	characteristic
85	#17988690	C₂²	1	2	yes	complemented
86	#17988689	C₂²	1	2	yes	complemented
87	#17988688	C₂²	1	2	yes	complemented
88	#17988687	C₂²	1	2	yes	complemented
89	#17988686	C₂²	1	2	yes	complemented
90	#17988685	C₂²	1	2	yes	complemented
91	#17988684	C₂²	1	2	yes	complemented
92	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
93	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
94	#17988681	C₂²	1	1	yes	characteristic, complemented
95	C₄×#11924018	C₂²	1	2	yes	complemented
96	#17988679	C₂²	1	2	yes	complemented
97	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
98	D₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
99	#17988669	C₂²	1	1	yes	characteristic, complemented
100	C₄×#11924013	C₂²	1	2	yes	complemented
101	#17988667	C₂²	1	2	yes	complemented
102	#107×D₇₃	C₂²	1	1	yes	characteristic
103	#107×D₇₃	C₂²	1	1	yes	characteristic
104	#107×D₇₃	C₂²	1	2	yes	—
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	#17988545	C₂²	1	1	yes	characteristic, complemented
110	#17988544	C₂²	1	1	yes	characteristic, complemented
111	#17988544	C₂²	1	1	yes	characteristic, complemented
112	#17988543	C₂²	1	1	yes	characteristic, complemented
113	#17988542	C₂²	1	1	yes	characteristic, complemented
114	#17988541	C₂²	1	1	yes	characteristic, complemented
115	#17988541	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	#542×C₇₃	C₂²	1	2	yes	complemented
121	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#495×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#489×C₇₃	C₂²	1	2	yes	complemented
124	#468×C₇₃	C₂²	1	2	yes	complemented
125	#467×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#466×C₇₃	C₂²	1	1	yes	characteristic
127	#440×C₇₃	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#405×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₇₃	—	2	2	no	—
132	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
133	C₂×D₄×D₇₃	—	2	2	no	—
134	C₂×D₄×D₇₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₇₃	—	2	2	no	—
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×#11924011	C₂³	1	1	yes	characteristic
149	C₂×#11924011	C₂³	1	1	yes	characteristic
150	M₁₆×D₇₃	—	2	4	no	—
151	C₂²×#10596831	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₇₃	—	2	4	no	—
153	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
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	#14556591	C₂³	1	2	yes	—
160	#14556590	—	2	2	no	—
161	#14556590	C₂³	1	2	yes	—
162	#14556590	C₂³	1	2	yes	—
163	#14556589	—	2	2	no	—
164	#14556586	—	2	2	no	—
165	#14556586	—	2	2	no	—
166	#14556586	—	2	2	no	—
167	#14556585	—	2	2	no	—
168	#14556584	—	2	2	no	—
169	#14556584	—	2	2	no	—
170	#14556584	—	2	2	no	—
171	#14556580	—	2	2	no	—
172	#14556580	C₂³	1	2	yes	—
173	#14556579	—	2	2	no	—
174	#14556579	C₂³	1	2	yes	—
175	#14556578	—	2	2	no	—
176	#14556578	C₂³	1	2	yes	—
177	#14556577	—	2	2	no	—
178	#14556577	—	2	2	no	—
179	#14556577	—	2	2	no	—
180	#14556577	—	2	2	no	—
181	#14556577	—	2	2	no	—
182	#14556577	—	2	2	no	—
183	#14556576	—	2	2	no	—
184	#14556576	—	2	2	no	—
185	#14556575	—	2	2	no	—
186	#14556574	—	2	2	no	—
187	#14556573	—	2	2	no	—
188	#14556573	—	2	2	no	—
189	#14556572	—	2	2	no	—
190	#14556571	—	2	2	no	—
191	#14556571	C₂³	1	2	yes	—
192	#14556570	—	2	2	no	—
193	#14556570	C₂³	1	2	yes	—
194	#14556569	—	2	2	no	—
195	#14556569	—	2	2	no	—
196	#14556569	—	2	2	no	—
197	#14556568	—	2	2	no	—
198	#14556568	—	2	2	no	—
199	#14556568	—	2	2	no	—
200	#14556567	—	2	2	no	—
201	#14556567	C₂³	1	2	yes	—
202	#14556566	C₂³	1	2	yes	—
203	#14556565	C₂³	1	2	yes	—
204	#14556564	—	2	2	no	—
205	#14556563	—	2	2	no	—
206	#14556562	C₂³	1	2	yes	—
207	Q₈×Dic₇₃	C₂³	1	2	yes	—
208	C₄×Dic₁₄₆	—	2	2	no	—
209	C₄×Dic₁₄₆	C₂³	1	2	yes	—
210	#14556556	—	2	2	no	—
211	#14556556	C₂³	1	2	yes	—
212	C₄×D₂₉₂	C₂³	1	2	yes	—
213	D₄×Dic₇₃	C₂³	1	2	yes	—
214	#14556553	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₇₃	—	2	2	no	—
216	#14556551	—	2	2	no	—
217	#14556550	C₂³	1	1	yes	characteristic
218	#14556549	D₄	1	1	yes	characteristic
219	#14556549	D₄	1	1	yes	characteristic
220	#14556548	C₂³	1	1	yes	characteristic
221	#14556548	C₂³	1	1	yes	characteristic
222	#14556547	D₄	1	1	yes	characteristic
223	#14556547	D₄	1	1	yes	characteristic
224	C₄⋊C₄×D₇₃	—	2	2	no	—
225	C₄⋊C₄×D₇₃	—	2	2	no	—
226	C₄⋊C₄×D₇₃	—	2	2	no	—
227	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
228	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
229	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
230	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
231	C₂²⋊C₄×D₇₃	—	2	2	no	—
232	C₂²⋊C₄×D₇₃	—	2	2	no	—
233	C₂²⋊C₄×D₇₃	—	2	2	no	—
234	C₂²⋊C₄×D₇₃	—	2	2	no	—
235	C₂²⋊C₄×D₇₃	—	2	2	no	—
236	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
237	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
238	C₄²×D₇₃	—	2	2	no	—
239	C₄²×D₇₃	C₂³	1	1	yes	characteristic
240	C₄²×D₇₃	C₂³	1	1	yes	characteristic
241	#14556525	C₂³	1	1	yes	characteristic
242	#14556525	C₂³	1	1	yes	characteristic
243	#14556525	C₂³	1	2	yes	—
244	#14556524	C₂³	1	2	yes	—
245	#14556524	C₂³	1	2	yes	—
246	#14556524	C₂³	1	2	yes	—
247	#14556524	C₂³	1	2	yes	—
248	#14556516	C₂³	1	2	yes	—
249	#14556516	C₂³	1	2	yes	—
250	#14556515	C₂³	1	2	yes	—
251	#14556515	C₂³	1	2	yes	—
252	#14556514	C₂³	1	2	yes	—
253	#14556514	C₂³	1	2	yes	—
254	#14556513	C₂³	1	2	yes	—
255	#14556513	C₂³	1	2	yes	—
256	#14556512	C₂³	1	2	yes	—
257	#14556512	C₂³	1	2	yes	—
258	#14556511	C₂³	1	2	yes	—
259	#14556511	C₂³	1	2	yes	—
260	#14556502	C₂³	1	1	yes	characteristic
261	#14556502	C₂³	1	1	yes	characteristic
262	#14556501	C₂³	1	1	yes	characteristic
263	#14556501	C₂³	1	1	yes	characteristic
264	#14556501	C₂³	1	1	yes	characteristic
265	#14556501	C₂³	1	1	yes	characteristic
266	C₄×#10596831	C₂³	1	1	yes	characteristic
267	C₄×#10596831	C₂³	1	1	yes	characteristic
268	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
270	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
271	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
274	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
278	#126×C₇₃	—	2	2	no	—
279	#124×C₇₃	—	2	2	no	—
280	#124×C₇₃	C₂³	1	2	yes	—
281	#123×C₇₃	—	2	2	no	—
282	C₂²⋊Q₈×C₇₃	—	2	2	no	—
283	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
284	#121×C₇₃	C₂³	1	2	yes	—
285	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
286	C₄×D₄×C₇₃	C₂³	1	2	yes	—
287	#117×C₇₃	C₂³	1	1	yes	characteristic
288	#107×C₇₃	C₂³	1	1	yes	characteristic
289	#107×C₇₃	C₂³	1	1	yes	characteristic
290	#107×C₇₃	C₂³	1	2	yes	—
291	#103×C₇₃	C₂³	1	2	yes	—
292	#103×C₇₃	C₂³	1	2	yes	—
293	#102×C₇₃	C₂³	1	2	yes	—
294	#102×C₇₃	C₂³	1	2	yes	—
295	#97×C₇₃	C₂³	1	1	yes	characteristic
296	#97×C₇₃	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
299	C₂³×D₇₃	—	2	2	no	—
300	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
301	C₂×Dic₁₄₆	—	2	2	no	—
302	C₂×Dic₁₄₆	—	2	2	no	—
303	C₂×Dic₁₄₆	—	2	2	no	—
304	C₂×Dic₁₄₆	—	2	2	no	—
305	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
306	Q₈×D₇₃	—	2	4	no	—
307	Q₈×D₇₃	—	2	4	no	—
308	Q₈×D₇₃	—	8	4	no	—
309	C₂×D₂₉₂	—	2	2	no	—
310	C₂×D₂₉₂	C₂⁴	1	2	yes	—
311	C₂×C₂²⋊D₇₃	—	2	2	no	—
312	C₂×C₂²⋊D₇₃	—	2	2	no	—
313	C₂×C₂²⋊D₇₃	—	2	2	no	—
314	D₄×D₇₃	—	2	4	no	—
315	D₄×D₇₃	—	2	4	no	—
316	D₄×D₇₃	—	8	4	no	—
317	C₂²×Dic₇₃	—	2	2	no	—
318	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
319	C₂×C₄×D₇₃	—	2	2	no	—
320	C₂×C₄×D₇₃	—	2	2	no	—
321	C₂×C₄×D₇₃	—	2	2	no	—
322	C₂×C₄×D₇₃	—	2	2	no	—
323	C₂×C₄×D₇₃	—	2	2	no	—
324	C₂×C₄×D₇₃	—	2	2	no	—
325	C₂×C₄×D₇₃	—	2	2	no	—
326	C₂×C₄×D₇₃	—	8	4	no	—
327	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
335	Dic₂₉₂	—	2	2	no	—
336	#11924018	—	2	4	no	—
337	#11924017	—	2	4	no	—
338	#11924016	—	2	4	no	—
339	#11924015	—	2	4	no	—
340	D₅₈₄	—	2	2	no	—
341	#11924013	—	2	4	no	—
342	#11924012	—	2	2	no	—
343	#11924011	—	2	2	no	—
344	#11924011	—	2	2	no	—
345	C₂×#10596831	—	2	2	no	—
346	C₂×#10596831	C₂⁴	1	1	yes	characteristic
347	C₂×#10596831	C₂⁴	1	1	yes	characteristic
348	C₂×#10596831	C₂⁴	1	1	yes	characteristic
349	C₂×#10596831	C₂⁴	1	1	yes	characteristic
350	C₈×D₇₃	—	2	2	no	—
351	C₈×D₇₃	—	2	2	no	—
352	C₈×D₇₃	—	2	2	no	—
353	C₈×D₇₃	—	2	2	no	—
354	C₈×D₇₃	#41	1	4	yes	—
355	C₈×D₇₃	#41	1	4	yes	—
356	C₄⋊Dic₇₃	—	2	2	no	—
357	C₄⋊Dic₇₃	—	2	2	no	—
358	C₄⋊Dic₇₃	—	2	2	no	—
359	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
362	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
365	#11924007	—	2	2	no	—
366	#11924007	—	2	2	no	—
367	#11924007	—	2	2	no	—
368	#11924007	—	2	2	no	—
369	#11924007	—	2	2	no	—
370	#11924007	—	2	2	no	—
371	#11924007	C₂×D₄	1	1	yes	characteristic
372	#11924007	C₂×D₄	1	1	yes	characteristic
373	#11924007	C₂×D₄	1	1	yes	characteristic
374	#11924007	C₂×D₄	1	1	yes	characteristic
375	C₂²⋊Dic₇₃	—	2	2	no	—
376	C₂²⋊Dic₇₃	—	2	2	no	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	—	2	2	no	—
379	C₂²⋊Dic₇₃	—	2	2	no	—
380	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
381	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
382	#11924005	—	2	2	no	—
383	#11924005	—	2	2	no	—
384	#11924005	—	2	2	no	—
385	#11924005	—	2	2	no	—
386	#11924005	—	2	2	no	—
387	#11924005	—	2	2	no	—
388	#11924005	—	2	2	no	—
389	#11924005	—	2	2	no	—
390	#11924005	—	2	2	no	—
391	#11924005	—	2	2	no	—
392	#11924005	C₂×D₄	1	1	yes	characteristic
393	#11924005	C₂×D₄	1	1	yes	characteristic
394	#11924005	C₂×D₄	1	1	yes	characteristic
395	#11924005	C₂×D₄	1	1	yes	characteristic
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	—	2	2	no	—
398	C₄×Dic₇₃	—	2	2	no	—
399	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
401	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
402	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
403	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
404	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×Q₈×C₇₃	—	2	2	no	—
406	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
407	C₂×D₄×C₇₃	—	2	2	no	—
408	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₇₃	—	2	2	no	—
410	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
411	Q₁₆×C₇₃	—	2	2	no	—
412	SD₁₆×C₇₃	—	2	4	no	—
413	D₈×C₇₃	—	2	2	no	—
414	M₁₆×C₇₃	—	2	2	no	—
415	C₂×C₈×C₇₃	—	2	2	no	—
416	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₃	—	2	2	no	—
421	C₄⋊C₄×C₇₃	—	2	2	no	—
422	C₄⋊C₄×C₇₃	—	2	2	no	—
423	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
427	C₂²⋊C₄×C₇₃	—	2	2	no	—
428	C₂²⋊C₄×C₇₃	—	2	2	no	—
429	C₂²⋊C₄×C₇₃	—	2	2	no	—
430	C₂²⋊C₄×C₇₃	—	2	2	no	—
431	C₂²⋊C₄×C₇₃	—	2	2	no	—
432	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
433	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₇₃	—	2	2	no	—
435	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
437	C₂³×C₇₃	—	2	2	no	—
438	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₇₃	—	2	2	no	—
440	C₂²×D₇₃	—	2	2	no	—
441	C₂²×D₇₃	—	2	2	no	—
442	C₂²×D₇₃	—	2	2	no	—
443	C₂²×D₇₃	—	4	4	no	—
444	C₂²×D₇₃	—	4	4	no	—
445	C₂²×D₇₃	—	4	4	no	—
446	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
447	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₇₃	—	2	2	no	—
449	Q₈×C₇₃	—	2	2	no	—
450	Q₈×C₇₃	—	8	2	no	—
451	D₄×C₇₃	—	2	2	no	—
452	D₄×C₇₃	—	2	2	no	—
453	D₄×C₇₃	—	8	2	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	—	2	2	no	—
457	C₂×C₄×C₇₃	—	2	2	no	—
458	C₂×C₄×C₇₃	—	2	2	no	—
459	C₂×C₄×C₇₃	—	8	2	no	—
460	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
466	C₂²⋊D₇₃	—	4	4	no	—
467	C₂²⋊D₇₃	—	8	2	no	—
468	C₂²⋊D₇₃	—	8	2	no	—
469	C₂×Dic₇₃	—	2	2	no	—
470	C₂×Dic₇₃	—	2	2	no	—
471	C₂×Dic₇₃	—	2	2	no	—
472	C₂×Dic₇₃	—	2	2	no	—
473	C₂×Dic₇₃	—	8	2	no	—
474	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
480	D₂₉₂	—	2	2	no	—
481	D₂₉₂	—	2	2	no	—
482	D₂₉₂	—	8	2	no	—
483	C₄×D₇₃	—	2	2	no	—
484	C₄×D₇₃	—	2	2	no	—
485	C₄×D₇₃	—	2	2	no	—
486	C₄×D₇₃	—	2	2	no	—
487	C₄×D₇₃	—	2	2	no	—
488	C₄×D₇₃	—	2	1	no	—
489	C₄×D₇₃	—	2	1	no	—
490	C₄×D₇₃	—	2	2	no	—
491	C₄×D₇₃	—	4	4	no	—
492	C₄×D₇₃	—	4	4	no	—
493	C₄×D₇₃	—	4	4	no	—
494	C₄×D₇₃	—	8	2	no	—
495	C₄×D₇₃	—	8	2	no	—
496	C₄×D₇₃	C₂×#41	1	2	yes	—
497	C₄×D₇₃	C₂×#41	1	2	yes	—
498	Dic₁₄₆	—	2	2	no	—
499	Dic₁₄₆	—	2	2	no	—
500	Dic₁₄₆	—	4	4	no	—
501	Dic₁₄₆	—	8	2	no	—
502	Dic₁₄₆	—	8	2	no	—
503	Dic₁₄₆	—	8	2	no	—
504	C₈×C₇₃	—	2	1	no	—
505	C₈×C₇₃	—	2	1	no	—
506	C₈×C₇₃	C₂×#41	1	2	yes	—
507	C₈×C₇₃	C₂×#41	1	2	yes	—
508	#10596831	—	2	1	no	—
509	#10596831	—	2	1	no	—
510	#10596831	C₂×#41	1	2	yes	—
511	#10596831	C₂×#41	1	2	yes	—
512	C₂²×C₇₃	—	2	1	no	—
513	C₂²×C₇₃	—	2	1	no	—
514	C₂²×C₇₃	—	2	1	no	—
515	C₂²×C₇₃	—	4	2	no	—
516	C₂²×C₇₃	—	4	2	no	—
517	C₂²×C₇₃	—	4	2	no	—
518	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
519	C₂×D₇₃	—	2	1	no	—
520	C₂×D₇₃	—	2	1	no	—
521	C₂×D₇₃	—	2	1	no	—
522	C₂×D₇₃	—	4	4	no	—
523	C₂×D₇₃	—	4	2	no	—
524	C₂×D₇₃	—	4	2	no	—
525	C₂×D₇₃	—	4	2	no	—
526	C₂×D₇₃	—	8	8	no	—
527	C₂×D₇₃	#532	1	2	yes	—
528	C₂×D₇₃	#576	1	2	yes	—
529	C₂×D₇₃	#578	1	2	yes	—
530	C₄×C₇₃	—	2	1	no	—
531	C₄×C₇₃	—	2	1	no	—
532	C₄×C₇₃	—	2	1	no	—
533	C₄×C₇₃	—	2	1	no	—
534	C₄×C₇₃	—	2	1	no	—
535	C₄×C₇₃	—	4	2	no	—
536	C₄×C₇₃	—	4	2	no	—
537	C₄×C₇₃	—	4	2	no	—
538	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
539	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
540	Dic₇₃	—	2	1	no	—
541	Dic₇₃	—	2	1	no	—
542	Dic₇₃	—	2	1	no	—
543	Dic₇₃	—	2	1	no	—
544	Dic₇₃	—	2	1	no	—
545	Dic₇₃	—	4	2	no	—
546	Dic₇₃	—	4	2	no	—
547	Dic₇₃	—	4	2	no	—
548	Dic₇₃	#532	1	2	yes	—
549	C₂×#3175	—	73	1	no	maximal, Sylow
550	C₂×C₇₃	—	4	1	no	—
551	C₂×C₇₃	—	8	2	no	—
552	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
553	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
554	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
555	D₇₃	—	4	1	no	—
556	D₇₃	—	8	2	no	—
557	D₇₃	#3175	1	4	yes	direct product factor
558	C₂×#542	—	73	2	no	—
559	#3175	—	73	1	no	—
560	#3175	—	73	1	no	—
561	#3175	—	73	2	no	—
562	#3175	—	73	2	no	—
563	#3175	—	73	1	no	—
564	#3175	—	73	1	no	—
565	#3175	—	73	2	no	—
566	#3175	—	73	1	no	—
567	#3175	—	73	1	no	—
568	#3175	—	73	1	no	—
569	#3175	—	73	2	no	—
570	#3175	D₇₃	1	1	yes	characteristic, direct product factor
571	C₂×#500	—	73	1	no	—
572	C₂×#495	—	73	1	no	—
573	C₂×#489	—	73	2	no	—
574	C₂×#468	—	73	2	no	—
575	C₂×#467	—	73	1	no	—
576	C₂×#466	—	73	1	no	—
577	C₂×#440	—	73	2	no	—
578	C₂×C₄×Q₁₆	—	73	1	no	—
579	C₂×C₄×D₈	—	73	1	no	—
580	C₂×#405	—	73	1	no	—
581	C₇₃	C₂×#3175	1	1	yes	characteristic, complemented, Sylow
582	C₂²×Q₁₆	—	73	1	no	—
583	C₂²×SD₁₆	—	73	2	no	—
584	C₂²×D₈	—	73	1	no	—
585	C₂²×M₁₆	—	73	1	no	—
586	C₂³×C₈	—	73	1	no	—
587	#542	—	73	2	no	—
588	#542	—	73	2	no	—
589	#542	—	73	2	no	—
590	#542	—	73	2	no	—
591	#542	—	73	2	no	—
592	#542	—	73	2	no	—
593	#542	—	73	2	no	—
594	#542	—	146	2	no	—
595	#542	—	146	2	no	—
596	#542	—	146	2	no	—
597	#542	—	146	2	no	—
598	#542	C₂×D₇₃	1	2	yes	complemented
599	C₂×C₄⋊Q₈	—	73	2	no	—
600	C₂×#126	—	146	2	no	—
601	C₂×#124	—	73	2	no	—
602	C₂×#124	—	146	2	no	—
603	C₂×#123	—	146	2	no	—
604	C₂×C₂²⋊Q₈	—	73	2	no	—
605	C₂×C₂²⋊Q₈	—	146	2	no	—
606	C₂×#121	—	73	2	no	—
607	C₂×C₄×Q₈	—	73	2	no	—
608	C₂×C₄×D₄	—	73	2	no	—
609	C₂×#117	—	73	1	no	—
610	#500	—	73	2	no	—
611	#500	—	73	1	no	—
612	#500	—	73	1	no	—
613	#500	—	73	2	no	—
614	#500	—	73	1	no	—
615	#500	C₂×D₇₃	1	1	yes	characteristic, complemented
616	#495	—	73	1	no	—
617	#495	—	73	2	no	—
618	#495	—	73	1	no	—
619	#495	—	73	2	no	—
620	#495	—	73	1	no	—
621	#495	C₂×D₇₃	1	1	yes	characteristic, complemented
622	#489	—	73	2	no	—
623	#489	—	73	2	no	—
624	#489	—	73	2	no	—
625	#489	—	73	2	no	—
626	#489	—	73	2	no	—
627	#489	—	73	2	no	—
628	#489	—	73	2	no	—
629	#489	C₂×D₇₃	1	2	yes	complemented
630	#468	—	73	2	no	—
631	#468	—	73	2	no	—
632	#468	—	73	2	no	—
633	#468	—	73	2	no	—
634	#468	—	73	2	no	—
635	#468	—	73	2	no	—
636	#468	—	73	2	no	—
637	#468	C₂×D₇₃	1	2	yes	complemented
638	#467	—	73	1	no	—
639	#467	—	73	1	no	—
640	#467	—	73	2	no	—
641	#467	—	73	1	no	—
642	#467	—	73	2	no	—
643	#467	C₂×D₇₃	1	1	yes	characteristic, complemented
644	#466	—	73	1	no	—
645	#466	—	73	1	no	—
646	#466	—	73	2	no	—
647	#466	—	73	1	no	—
648	#466	—	73	2	no	—
649	#466	C₂×D₇₃	1	1	yes	characteristic
650	#440	—	73	2	no	—
651	#440	—	73	2	no	—
652	#440	—	73	2	no	—
653	#440	—	73	2	no	—
654	#440	—	73	2	no	—
655	#440	—	73	2	no	—
656	#440	—	73	2	no	—
657	#440	C₂×D₇₃	1	2	yes	complemented
658	C₄×Q₁₆	—	73	1	no	—
659	C₄×Q₁₆	—	73	2	no	—
660	C₄×Q₁₆	—	73	1	no	—
661	C₄×Q₁₆	—	73	2	no	—
662	C₄×Q₁₆	—	73	1	no	—
663	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
664	C₄×D₈	—	73	1	no	—
665	C₄×D₈	—	73	2	no	—
666	C₄×D₈	—	73	1	no	—
667	C₄×D₈	—	73	2	no	—
668	C₄×D₈	—	73	1	no	—
669	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
670	C₂×#107	—	73	1	no	—
671	C₂×#107	—	73	1	no	—
672	C₂×#107	—	73	2	no	—
673	C₂×#103	—	73	2	no	—
674	C₂×#103	—	73	2	no	—
675	C₂×#102	—	73	2	no	—
676	C₂×#102	—	73	2	no	—
677	#405	—	73	1	no	—
678	#405	—	73	1	no	—
679	#405	—	73	1	no	—
680	#405	—	73	1	no	—
681	#405	—	73	1	no	—
682	#405	—	73	1	no	—
683	#405	—	73	1	no	—
684	#405	C₂×D₇₃	1	1	yes	characteristic, complemented
685	C₂×#97	—	73	1	no	—
686	C₂×#97	—	73	1	no	—
687	C₂×C₄×C₈	—	73	1	no	—
688	C₂×C₄×C₈	—	73	1	no	—
689	C₂²×Q₈	—	73	2	no	—
690	C₂²×Q₈	—	146	2	no	—
691	C₂²×D₄	—	73	2	no	—
692	C₂²×D₄	—	146	2	no	—
693	C₂³×C₄	—	73	1	no	—
694	C₂³×C₄	—	146	2	no	—
695	C₂×Q₁₆	—	73	2	no	—
696	C₂×Q₁₆	—	73	1	no	—
697	C₂×Q₁₆	—	146	4	no	—
698	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
699	C₂×SD₁₆	—	73	2	no	—
700	C₂×SD₁₆	—	73	2	no	—
701	C₂×SD₁₆	—	73	2	no	—
702	C₂×SD₁₆	—	146	8	no	—
703	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
704	C₂×D₈	—	73	2	no	—
705	C₂×D₈	—	73	1	no	—
706	C₂×D₈	—	146	4	no	—
707	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
708	C₂×M₁₆	—	73	1	no	—
709	C₂×M₁₆	—	73	1	no	—
710	C₂×M₁₆	—	73	1	no	—
711	C₂×M₁₆	—	146	4	no	—
712	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
713	C₂²×C₈	—	73	1	no	—
714	C₂²×C₈	—	73	1	no	—
715	C₂²×C₈	—	73	1	no	—
716	C₂²×C₈	—	73	1	no	—
717	C₂²×C₈	—	73	1	no	—
718	C₂²×C₈	—	73	1	no	—
719	C₂²×C₈	—	73	1	no	—
720	C₂²×C₈	—	146	4	no	—
721	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
722	C₄⋊Q₈	—	73	2	no	—
723	C₄⋊Q₈	—	73	2	no	—
724	C₄⋊Q₈	—	73	2	no	—
725	C₄⋊Q₈	—	146	2	no	—
726	C₄⋊Q₈	—	146	2	no	—
727	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
728	#126	—	2	2	no	—
729	#126	—	146	2	no	—
730	#126	—	146	2	no	—
731	#126	—	146	2	no	—
732	#126	—	146	2	no	—
733	#126	—	146	2	no	—
734	#126	—	146	2	no	—
735	#126	—	146	2	no	—
736	#124	—	2	2	no	—
737	#124	—	73	2	no	—
738	#124	—	73	2	no	—
739	#124	—	73	2	no	—
740	#124	—	146	2	no	—
741	#124	—	146	2	no	—
742	#124	—	146	2	no	—
743	#124	—	146	2	no	—
744	#124	—	146	2	no	—
745	#124	—	146	2	no	—
746	#124	—	146	2	no	—
747	#124	—	146	2	no	—
748	#124	—	146	2	no	—
749	#124	C₂²×D₇₃	1	2	yes	—
750	#123	—	2	2	no	—
751	#123	—	146	2	no	—
752	#123	—	146	2	no	—
753	#123	—	146	2	no	—
754	#123	—	146	2	no	—
755	#123	—	146	2	no	—
756	#123	—	146	2	no	—
757	#123	—	146	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	73	2	no	—
760	C₂²⋊Q₈	—	73	2	no	—
761	C₂²⋊Q₈	—	73	2	no	—
762	C₂²⋊Q₈	—	146	2	no	—
763	C₂²⋊Q₈	—	146	2	no	—
764	C₂²⋊Q₈	—	146	2	no	—
765	C₂²⋊Q₈	—	146	2	no	—
766	C₂²⋊Q₈	—	146	2	no	—
767	C₂²⋊Q₈	—	146	2	no	—
768	C₂²⋊Q₈	—	146	2	no	—
769	C₂²⋊Q₈	—	146	2	no	—
770	C₂²⋊Q₈	—	146	2	no	—
771	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
772	#121	—	73	2	no	—
773	#121	—	73	2	no	—
774	#121	—	73	2	no	—
775	#121	—	146	2	no	—
776	#121	—	146	2	no	—
777	#121	C₂²×D₇₃	1	2	yes	—
778	C₄×Q₈	—	73	2	no	—
779	C₄×Q₈	—	73	2	no	—
780	C₄×Q₈	—	73	2	no	—
781	C₄×Q₈	—	146	2	no	—
782	C₄×Q₈	—	146	2	no	—
783	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
784	C₄×D₄	—	73	2	no	—
785	C₄×D₄	—	73	2	no	—
786	C₄×D₄	—	73	2	no	—
787	C₄×D₄	—	146	2	no	—
788	C₄×D₄	—	146	2	no	—
789	C₄×D₄	C₂²×D₇₃	1	2	yes	—
790	#117	—	73	1	no	—
791	#117	—	73	1	no	—
792	#117	—	73	1	no	—
793	#117	—	73	1	no	—
794	#117	—	73	1	no	—
795	#117	—	73	1	no	—
796	#117	—	73	1	no	—
797	#117	C₂²×D₇₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	—	73	1	no	—
799	C₂×C₄⋊C₄	—	73	1	no	—
800	C₂×C₄⋊C₄	—	73	2	no	—
801	C₂×C₄⋊C₄	—	73	2	no	—
802	C₂×C₄⋊C₄	—	146	2	no	—
803	C₂×C₄⋊C₄	—	146	2	no	—
804	C₂×C₄⋊C₄	—	146	2	no	—
805	C₂×C₂²⋊C₄	—	73	1	no	—
806	C₂×C₂²⋊C₄	—	73	1	no	—
807	C₂×C₂²⋊C₄	—	146	2	no	—
808	C₂×C₂²⋊C₄	—	146	2	no	—
809	C₂×C₂²⋊C₄	—	146	2	no	—
810	C₂×C₂²⋊C₄	—	146	2	no	—
811	C₂×C₂²⋊C₄	—	146	2	no	—
812	C₂×C₄²	—	73	1	no	—
813	C₂×C₄²	—	73	1	no	—
814	C₂×C₄²	—	146	2	no	—
815	#107	—	73	1	no	—
816	#107	—	73	1	no	—
817	#107	—	73	2	no	—
818	#107	—	73	2	no	—
819	#107	—	73	2	no	—
820	#107	—	73	2	no	—
821	#107	—	73	2	no	—
822	#107	C₂²×D₇₃	1	1	yes	characteristic
823	#107	C₂²×D₇₃	1	1	yes	characteristic
824	#107	C₂²×D₇₃	1	2	yes	—
825	#103	—	73	2	no	—
826	#103	—	73	2	no	—
827	#103	—	73	2	no	—
828	#103	—	73	2	no	—
829	#103	—	73	2	no	—
830	#103	—	73	2	no	—
831	#103	C₂²×D₇₃	1	2	yes	—
832	#103	C₂²×D₇₃	1	2	yes	—
833	#102	—	73	2	no	—
834	#102	—	73	2	no	—
835	#102	—	73	2	no	—
836	#102	—	73	2	no	—
837	#102	—	73	2	no	—
838	#102	—	73	2	no	—
839	#102	C₂²×D₇₃	1	2	yes	—
840	#102	C₂²×D₇₃	1	2	yes	—
841	#97	—	73	1	no	—
842	#97	—	73	1	no	—
843	#97	—	73	1	no	—
844	#97	—	73	1	no	—
845	#97	—	73	1	no	—
846	#97	—	73	1	no	—
847	#97	C₂²×D₇₃	1	1	yes	characteristic
848	#97	C₂²×D₇₃	1	1	yes	characteristic
849	C₄×C₈	—	73	1	no	—
850	C₄×C₈	—	73	1	no	—
851	C₄×C₈	—	73	1	no	—
852	C₄×C₈	—	73	1	no	—
853	C₄×C₈	—	73	1	no	—
854	C₄×C₈	—	73	1	no	—
855	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
856	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
857	C₂⁴	—	73	1	no	—
858	C₂⁴	—	146	2	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	584	4	no	—
861	C₂×Q₈	—	73	2	no	—
862	C₂×Q₈	—	146	2	no	—
863	C₂×Q₈	—	146	2	no	—
864	C₂×Q₈	—	146	2	no	—
865	C₂×Q₈	—	146	4	no	—
866	C₂×Q₈	—	146	4	no	—
867	C₂×Q₈	—	146	2	no	—
868	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	584	4	no	—
871	C₂×D₄	—	73	2	no	—
872	C₂×D₄	—	146	2	no	—
873	C₂×D₄	—	146	4	no	—
874	C₂×D₄	—	146	4	no	—
875	C₂×D₄	—	146	2	no	—
876	C₂×D₄	—	146	2	no	—
877	C₂×D₄	—	146	2	no	—
878	C₂×D₄	C₂³×D₇₃	1	2	yes	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	584	4	no	—
881	C₂²×C₄	—	73	1	no	—
882	C₂²×C₄	—	73	1	no	—
883	C₂²×C₄	—	73	1	no	—
884	C₂²×C₄	—	73	1	no	—
885	C₂²×C₄	—	73	1	no	—
886	C₂²×C₄	—	73	1	no	—
887	C₂²×C₄	—	73	1	no	—
888	C₂²×C₄	—	73	1	no	—
889	C₂²×C₄	—	73	1	no	—
890	C₂²×C₄	—	146	2	no	—
891	C₂²×C₄	—	146	2	no	—
892	C₂²×C₄	—	146	2	no	—
893	C₂²×C₄	—	146	2	no	—
894	C₂²×C₄	—	146	2	no	—
895	C₂²×C₄	—	146	2	no	—
896	C₂²×C₄	—	146	2	no	—
897	C₂²×C₄	—	146	2	no	—
898	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
899	Q₁₆	—	2	2	no	—
900	Q₁₆	—	146	4	no	—
901	Q₁₆	—	146	2	no	—
902	SD₁₆	—	2	4	no	—
903	SD₁₆	—	146	4	no	—
904	SD₁₆	—	146	4	no	—
905	SD₁₆	—	146	4	no	—
906	D₈	—	2	2	no	—
907	D₈	—	146	4	no	—
908	D₈	—	146	2	no	—
909	M₁₆	—	2	2	no	—
910	M₁₆	—	146	2	no	—
911	M₁₆	—	146	2	no	—
912	M₁₆	—	146	2	no	—
913	C₂×C₈	—	2	2	no	—
914	C₂×C₈	—	73	1	no	—
915	C₂×C₈	—	73	1	no	—
916	C₂×C₈	—	73	4	no	—
917	C₂×C₈	—	73	4	no	—
918	C₂×C₈	—	73	1	no	—
919	C₂×C₈	—	73	1	no	—
920	C₂×C₈	—	146	2	no	—
921	C₂×C₈	—	146	2	no	—
922	C₂×C₈	—	146	2	no	—
923	C₂×C₈	—	146	2	no	—
924	C₂×C₈	—	146	2	no	—
925	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
926	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
927	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
928	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	73	1	no	—
933	C₄⋊C₄	—	73	1	no	—
934	C₄⋊C₄	—	73	1	no	—
935	C₄⋊C₄	—	73	1	no	—
936	C₄⋊C₄	—	73	1	no	—
937	C₄⋊C₄	—	73	1	no	—
938	C₄⋊C₄	—	73	2	no	—
939	C₄⋊C₄	—	73	2	no	—
940	C₄⋊C₄	—	146	2	no	—
941	C₄⋊C₄	—	146	2	no	—
942	C₄⋊C₄	—	146	2	no	—
943	C₄⋊C₄	—	146	2	no	—
944	C₄⋊C₄	—	146	2	no	—
945	C₄⋊C₄	—	146	2	no	—
946	C₄⋊C₄	—	146	2	no	—
947	C₄⋊C₄	—	146	2	no	—
948	C₄⋊C₄	—	146	2	no	—
949	C₄⋊C₄	—	146	2	no	—
950	C₄⋊C₄	—	146	2	no	—
951	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
952	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
954	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	73	1	no	—
961	C₂²⋊C₄	—	73	1	no	—
962	C₂²⋊C₄	—	73	1	no	—
963	C₂²⋊C₄	—	73	1	no	—
964	C₂²⋊C₄	—	73	1	no	—
965	C₂²⋊C₄	—	73	1	no	—
966	C₂²⋊C₄	—	146	2	no	—
967	C₂²⋊C₄	—	146	2	no	—
968	C₂²⋊C₄	—	146	2	no	—
969	C₂²⋊C₄	—	146	2	no	—
970	C₂²⋊C₄	—	146	2	no	—
971	C₂²⋊C₄	—	146	2	no	—
972	C₂²⋊C₄	—	146	2	no	—
973	C₂²⋊C₄	—	146	2	no	—
974	C₂²⋊C₄	—	146	2	no	—
975	C₂²⋊C₄	—	146	2	no	—
976	C₂²⋊C₄	—	146	2	no	—
977	C₂²⋊C₄	—	146	2	no	—
978	C₂²⋊C₄	—	146	2	no	—
979	C₂²⋊C₄	—	146	2	no	—
980	C₂²⋊C₄	—	146	2	no	—
981	C₂²⋊C₄	D₄×D₇₃	1	1	yes	characteristic
982	C₂²⋊C₄	D₄×D₇₃	1	1	yes	characteristic
983	C₄²	—	2	2	no	—
984	C₄²	—	73	1	no	—
985	C₄²	—	73	1	no	—
986	C₄²	—	73	1	no	—
987	C₄²	—	73	1	no	—
988	C₄²	—	73	1	no	—
989	C₄²	—	73	1	no	—
990	C₄²	—	146	2	no	—
991	C₄²	—	146	2	no	—
992	C₄²	—	146	2	no	—
993	C₄²	C₂³×D₇₃	1	1	yes	characteristic
994	C₄²	C₂³×D₇₃	1	1	yes	characteristic
995	C₂³	—	2	2	no	—
996	C₂³	—	292	4	no	—
997	C₂³	—	292	4	no	—
998	C₂³	—	292	4	no	—
999	C₂³	—	73	1	no	—
1000	C₂³	—	73	1	no	—
1001	C₂³	—	146	2	no	—
1002	C₂³	—	146	2	no	—
1003	C₂³	—	146	2	no	—
1004	C₂³	—	146	2	no	—
1005	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	8	2	no	—
1009	Q₈	—	292	4	no	—
1010	Q₈	—	584	2	no	—
1011	Q₈	—	584	2	no	—
1012	Q₈	—	584	2	no	—
1013	Q₈	—	146	2	no	—
1014	Q₈	—	146	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	—	292	4	no	—
1019	D₄	—	584	2	no	—
1020	D₄	—	584	2	no	—
1021	D₄	—	584	2	no	—
1022	D₄	—	146	2	no	—
1023	D₄	—	146	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	292	4	no	—
1031	C₂×C₄	—	292	4	no	—
1032	C₂×C₄	—	292	4	no	—
1033	C₂×C₄	—	584	2	no	—
1034	C₂×C₄	—	584	2	no	—
1035	C₂×C₄	—	584	2	no	—
1036	C₂×C₄	—	73	1	no	—
1037	C₂×C₄	—	73	2	no	—
1038	C₂×C₄	—	73	2	no	—
1039	C₂×C₄	—	73	1	no	—
1040	C₂×C₄	—	73	1	no	—
1041	C₂×C₄	—	73	1	no	—
1042	C₂×C₄	—	73	1	no	—
1043	C₂×C₄	—	73	1	no	—
1044	C₂×C₄	—	146	2	no	—
1045	C₂×C₄	—	146	2	no	—
1046	C₂×C₄	—	146	2	no	—
1047	C₂×C₄	—	146	2	no	—
1048	C₂×C₄	—	146	2	no	—
1049	C₂×C₄	—	146	2	no	—
1050	C₂×C₄	—	146	2	no	—
1051	C₂×C₄	—	146	2	no	—
1052	C₂×C₄	—	146	2	no	—
1053	C₂×C₄	—	146	2	no	—
1054	C₂×C₄	—	146	1	no	—
1055	C₂×C₄	—	146	1	no	—
1056	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1057	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1058	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1059	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1060	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1061	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	73	2	no	—
1065	C₈	—	73	2	no	—
1066	C₈	—	146	1	no	—
1067	C₈	—	146	1	no	—
1068	C₈	#41×D₇₃	1	2	yes	—
1069	C₈	#41×D₇₃	1	2	yes	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	292	4	no	—
1077	C₂²	—	292	2	no	—
1078	C₂²	—	292	2	no	—
1079	C₂²	—	292	2	no	—
1080	C₂²	—	584	8	no	—
1081	C₂²	—	73	2	no	—
1082	C₂²	—	73	2	no	—
1083	C₂²	—	73	2	no	—
1084	C₂²	—	146	1	no	—
1085	C₂²	—	146	1	no	—
1086	C₂²	—	146	1	no	—
1087	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	292	2	no	—
1097	C₄	—	292	2	no	—
1098	C₄	—	292	2	no	—
1099	C₄	—	73	2	no	—
1100	C₄	—	146	1	no	—
1101	C₄	—	146	1	no	—
1102	C₄	—	146	1	no	—
1103	C₄	—	146	1	no	—
1104	C₄	—	146	1	no	—
1105	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1106	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1107	C₂	—	4	1	no	—
1108	C₂	—	8	2	no	—
1109	C₂	—	292	1	no	—
1110	C₂	—	584	2	no	—
1111	C₂	—	73	4	no	—
1112	C₂	#532×D₇₃	1	1	yes	characteristic
1113	C₂	#576×D₇₃	1	1	yes	characteristic
1114	C₂	#578×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3175	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#466×D₇₃	C₂
hypercenter	#3175	D₇₃
hypocenter	C₇₃	C₂×#3175
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #542×D₇₃	C₂	semidirect
2. #22620573	C₂	semidirect
3. #22620572	C₂	semidirect
4. #22620571	C₂	semidirect
5. #22620570	C₂	semidirect
6. #22620569	C₂	semidirect
7. #22620568	C₂	semidirect
8. #22620567	C₂	semidirect
9. #22620566	C₂	semidirect
10. #22620565	C₂	semidirect
11. #22620564	C₂	semidirect
12. #22620563	C₂	semidirect
13. #500×D₇₃	C₂	semidirect
14. #495×D₇₃	C₂	semidirect
15. #489×D₇₃	C₂	semidirect
16. #468×D₇₃	C₂	semidirect
17. #467×D₇₃	C₂	semidirect
19. #440×D₇₃	C₂	semidirect
20. C₄×Q₁₆×D₇₃	C₂	semidirect
21. C₄×D₈×D₇₃	C₂	semidirect
22. #405×D₇₃	C₂	semidirect
23. C₇₃×#3175	C₂	semidirect
29. #17989211	C₂²	semidirect
30. #17989210	C₂²	semidirect
31. #17989209	C₂²	semidirect
32. #17989208	C₂²	semidirect
34. #17989206	C₂²	semidirect
36. #17989204	C₂²	semidirect
38. #17989202	C₂²	semidirect
51. #17988992	C₂²	semidirect
52. #17988991	C₂²	semidirect
53. #17988991	C₂²	semidirect
54. #17988991	C₂²	semidirect
55. #17988990	C₂²	semidirect
56. #17988972	C₂²	semidirect
57. #17988971	C₂²	semidirect
58. #17988970	C₂²	semidirect
59. #17988969	C₂²	semidirect
60. #17988968	C₂²	semidirect
61. #17988949	C₂²	semidirect
62. #17988948	C₂²	semidirect
63. #17988948	C₂²	semidirect
64. #17988947	C₂²	semidirect
65. #17988946	C₂²	semidirect
66. #17988945	C₂²	semidirect
67. #17988945	C₂²	semidirect
68. #17988836	C₂²	semidirect
69. #17988835	C₂²	semidirect
70. #17988834	C₂²	semidirect
71. #17988833	C₂²	semidirect
72. #17988832	C₂²	semidirect
73. #17988831	C₂²	semidirect
74. #17988830	C₂²	semidirect
75. #17988829	C₂²	semidirect
76. #17988828	C₂²	semidirect
77. #17988827	C₂²	semidirect
78. #17988826	C₂²	semidirect
79. #17988825	C₂²	semidirect
85. #17988690	C₂²	semidirect
86. #17988689	C₂²	semidirect
87. #17988688	C₂²	semidirect
88. #17988687	C₂²	semidirect
89. #17988686	C₂²	semidirect
90. #17988685	C₂²	semidirect
91. #17988684	C₂²	semidirect
92. C₄×Dic₂₉₂	C₂²	semidirect
93. Q₁₆×Dic₇₃	C₂²	semidirect
94. #17988681	C₂²	semidirect
95. C₄×#11924018	C₂²	semidirect
96. #17988679	C₂²	semidirect
97. C₄×D₅₈₄	C₂²	semidirect
98. D₈×Dic₇₃	C₂²	semidirect
99. #17988669	C₂²	semidirect
100. C₄×#11924013	C₂²	semidirect
101. #17988667	C₂²	semidirect
109. #17988545	C₂²	semidirect
110. #17988544	C₂²	semidirect
111. #17988544	C₂²	semidirect
112. #17988543	C₂²	semidirect
113. #17988542	C₂²	semidirect
114. #17988541	C₂²	semidirect
115. #17988541	C₂²	semidirect
120. #542×C₇₃	C₂²	semidirect
121. #500×C₇₃	C₂²	semidirect
122. #495×C₇₃	C₂²	semidirect
123. #489×C₇₃	C₂²	semidirect
124. #468×C₇₃	C₂²	semidirect
125. #467×C₇₃	C₂²	semidirect
127. #440×C₇₃	C₂²	semidirect
128. C₄×Q₁₆×C₇₃	C₂²	semidirect
129. C₄×D₈×C₇₃	C₂²	semidirect
130. #405×C₇₃	C₂²	semidirect
557. D₇₃	#3175	direct (N × H)
570. #3175	D₇₃	direct (N × H)
581. C₇₃	C₂×#3175	semidirect
598. #542	C₂×D₇₃	semidirect
615. #500	C₂×D₇₃	semidirect
621. #495	C₂×D₇₃	semidirect
629. #489	C₂×D₇₃	semidirect
637. #468	C₂×D₇₃	semidirect
643. #467	C₂×D₇₃	semidirect
657. #440	C₂×D₇₃	semidirect
663. C₄×Q₁₆	C₂×D₇₃	semidirect
669. C₄×D₈	C₂×D₇₃	semidirect
684. #405	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#542×D₇₃	2
#22620573	2
#22620572	2
#22620571	2
#22620570	2
#22620569	2
#22620568	2
#22620567	2
#22620566	2
#22620565	2
#22620564	2
#22620563	2
#500×D₇₃	2
#495×D₇₃	2
#489×D₇₃	2
#468×D₇₃	2
#467×D₇₃	2
#466×D₇₃	2
#440×D₇₃	2
C₄×Q₁₆×D₇₃	2
C₄×D₈×D₇₃	2
#405×D₇₃	2
C₇₃×#3175	2
C₂×#3175	73

Subgroups — #3175×D73 #33955798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3175×D₇₃ #33955798