Subgroups — #3174×D₇₃ #33955786

Order 18688.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#541×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#540×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22620562	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620561	C₂	1	1	yes	maximal, characteristic, complemented
5	#22620560	C₂	1	1	yes	maximal, characteristic, complemented
6	#22620559	C₂	1	1	yes	maximal, characteristic, complemented
7	#22620558	C₂	1	1	yes	maximal, characteristic, complemented
8	#22620557	C₂	1	2	yes	maximal, complemented
9	#22620556	C₂	1	1	yes	maximal, characteristic, complemented
10	#22620555	C₂	1	2	yes	maximal, complemented
11	#22620554	C₂	1	2	yes	maximal, complemented
12	#22620553	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620552	C₂	1	2	yes	maximal, complemented
14	#499×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#492×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#491×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#490×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#468×D₇₃	C₂	1	2	yes	maximal, complemented
19	#465×D₇₃	C₂	1	2	yes	maximal, complemented
20	#440×D₇₃	C₂	1	2	yes	maximal, complemented
21	C₄×SD₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
22	#405×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3174	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
25	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
26	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
28	#17989200	C₂²	1	1	yes	characteristic, complemented
29	#17989199	C₂²	1	1	yes	characteristic, complemented
30	#17989198	C₂²	1	1	yes	characteristic, complemented
31	#17989197	C₂²	1	2	yes	complemented
32	#17989196	—	2	2	no	—
33	#17989195	C₂²	1	2	yes	complemented
34	#17989194	—	2	2	no	—
35	#17989193	C₂²	1	1	yes	characteristic
36	#17989192	C₂²	1	1	yes	characteristic
37	#17989191	C₂²	1	1	yes	characteristic
38	#17989190	C₂²	1	2	yes	—
39	#17989189	—	2	2	no	—
40	#17989188	C₂²	1	2	yes	—
41	#17989187	—	2	2	no	—
42	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
43	#127×D₇₃	C₂²	1	1	yes	characteristic
44	#126×D₇₃	—	2	2	no	—
45	#125×D₇₃	—	2	2	no	—
46	#125×D₇₃	C₂²	1	1	yes	characteristic
47	#125×D₇₃	C₂²	1	1	yes	characteristic
48	#123×D₇₃	—	2	2	no	—
49	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
50	#121×D₇₃	—	2	2	no	—
51	#121×D₇₃	C₂²	1	2	yes	—
52	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
53	C₄×D₄×D₇₃	C₂²	1	2	yes	—
54	#117×D₇₃	C₂²	1	1	yes	characteristic
55	#17988989	C₂²	1	1	yes	characteristic, complemented
56	#17988988	C₂²	1	2	yes	complemented
57	#17988987	C₂²	1	2	yes	complemented
58	#17988986	C₂²	1	1	yes	characteristic, complemented
59	#17988986	C₂²	1	1	yes	characteristic, complemented
60	#17988961	C₂²	1	1	yes	characteristic, complemented
61	#17988960	C₂²	1	1	yes	characteristic, complemented
62	#17988959	C₂²	1	1	yes	characteristic, complemented
63	#17988958	C₂²	1	2	yes	complemented
64	#17988958	C₂²	1	2	yes	complemented
65	#17988957	C₂²	1	1	yes	characteristic, complemented
66	#17988956	C₂²	1	1	yes	characteristic, complemented
67	#17988955	C₂²	1	1	yes	characteristic, complemented
68	#17988954	C₂²	1	2	yes	complemented
69	#17988954	C₂²	1	2	yes	complemented
70	#17988953	C₂²	1	1	yes	characteristic, complemented
71	#17988952	C₂²	1	1	yes	characteristic, complemented
72	#17988951	C₂²	1	1	yes	characteristic, complemented
73	#17988950	C₂²	1	2	yes	complemented
74	#17988950	C₂²	1	2	yes	complemented
75	#17988836	C₂²	1	2	yes	complemented
76	#17988835	C₂²	1	2	yes	complemented
77	#17988834	C₂²	1	2	yes	complemented
78	#17988833	C₂²	1	2	yes	complemented
79	#17988832	C₂²	1	2	yes	complemented
80	#17988831	C₂²	1	2	yes	complemented
81	#17988830	C₂²	1	2	yes	complemented
82	#17988819	C₂²	1	2	yes	complemented
83	#17988818	C₂²	1	2	yes	complemented
84	#17988817	C₂²	1	2	yes	complemented
85	#17988816	C₂²	1	2	yes	complemented
86	#17988815	C₂²	1	2	yes	complemented
87	#17988814	C₂²	1	2	yes	complemented
88	#17988813	C₂²	1	2	yes	complemented
89	#17988690	C₂²	1	2	yes	complemented
90	#17988689	C₂²	1	2	yes	complemented
91	#17988688	C₂²	1	2	yes	complemented
92	#17988687	C₂²	1	2	yes	complemented
93	#17988686	C₂²	1	2	yes	complemented
94	#17988685	C₂²	1	2	yes	complemented
95	#17988684	C₂²	1	2	yes	complemented
96	#17988678	C₂²	1	2	yes	complemented
97	C₄×#11924017	C₂²	1	2	yes	complemented
98	SD₁₆×Dic₇₃	C₂²	1	2	yes	complemented
99	C₄×#11924015	C₂²	1	2	yes	complemented
100	#17988674	C₂²	1	2	yes	complemented
101	C₄×#11924016	C₂²	1	2	yes	complemented
102	#17988672	C₂²	1	2	yes	complemented
103	#107×D₇₃	C₂²	1	2	yes	—
104	#106×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	#541×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	#540×C₇₃	C₂²	1	1	yes	characteristic
122	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#492×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#491×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#490×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#468×C₇₃	C₂²	1	2	yes	complemented
127	#465×C₇₃	C₂²	1	2	yes	complemented
128	#440×C₇₃	C₂²	1	2	yes	complemented
129	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
130	#405×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	—	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×#11924017	C₂³	1	2	yes	—
138	C₂×#11924017	C₂³	1	2	yes	—
139	C₂×#11924016	C₂³	1	2	yes	—
140	C₂×#11924016	C₂³	1	2	yes	—
141	C₂×#11924015	C₂³	1	2	yes	—
142	C₂×#11924015	C₂³	1	2	yes	—
143	SD₁₆×D₇₃	—	2	8	no	—
144	SD₁₆×D₇₃	—	2	8	no	—
145	C₂×#11924012	C₂³	1	1	yes	characteristic
146	C₂×#11924011	C₂³	1	1	yes	characteristic
147	C₂×#11924011	C₂³	1	1	yes	characteristic
148	M₁₆×D₇₃	—	2	4	no	—
149	C₂²×#10596831	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₇₃	—	2	4	no	—
151	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
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	#14556591	C₂³	1	1	yes	characteristic
158	#14556590	—	2	2	no	—
159	#14556589	C₂³	1	2	yes	—
160	#14556588	C₂³	1	1	yes	characteristic
161	#14556587	—	2	2	no	—
162	#14556587	C₂³	1	2	yes	—
163	#14556586	—	2	2	no	—
164	#14556586	—	2	2	no	—
165	#14556586	—	2	2	no	—
166	#14556585	—	2	2	no	—
167	#14556584	—	2	2	no	—
168	#14556584	—	2	2	no	—
169	#14556584	—	2	2	no	—
170	#14556583	—	2	2	no	—
171	#14556583	C₂³	1	1	yes	characteristic
172	#14556583	C₂³	1	1	yes	characteristic
173	#14556582	—	2	2	no	—
174	#14556582	—	2	2	no	—
175	#14556582	C₂³	1	2	yes	—
176	#14556582	C₂³	1	2	yes	—
177	#14556581	—	2	2	no	—
178	#14556581	—	2	2	no	—
179	#14556581	—	2	2	no	—
180	#14556581	—	2	2	no	—
181	#14556581	—	2	2	no	—
182	#14556581	—	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	C₂³	1	2	yes	—
191	#14556570	C₂³	1	2	yes	—
192	#14556569	—	2	2	no	—
193	#14556568	—	2	2	no	—
194	#14556567	C₂³	1	2	yes	—
195	#14556566	—	2	2	no	—
196	#14556566	C₂³	1	2	yes	—
197	#14556565	—	2	2	no	—
198	#14556565	C₂³	1	2	yes	—
199	#14556564	—	2	2	no	—
200	#14556564	—	2	2	no	—
201	#14556564	—	2	2	no	—
202	#14556563	—	2	2	no	—
203	#14556563	—	2	2	no	—
204	#14556563	—	2	2	no	—
205	#14556562	—	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	2	yes	—
219	#14556548	C₂³	1	1	yes	characteristic
220	#14556548	C₂³	1	1	yes	characteristic
221	#14556547	D₄	1	2	yes	—
222	C₄⋊C₄×D₇₃	—	2	2	no	—
223	C₄⋊C₄×D₇₃	—	2	2	no	—
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	2	yes	—
228	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
229	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
230	C₂²⋊C₄×D₇₃	—	2	2	no	—
231	C₂²⋊C₄×D₇₃	—	2	2	no	—
232	C₂²⋊C₄×D₇₃	—	2	2	no	—
233	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
234	C₄²×D₇₃	—	2	2	no	—
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	2	yes	—
241	#14556522	C₂³	1	2	yes	—
242	#14556522	C₂³	1	2	yes	—
243	#14556516	C₂³	1	2	yes	—
244	#14556516	C₂³	1	2	yes	—
245	#14556515	C₂³	1	2	yes	—
246	#14556515	C₂³	1	2	yes	—
247	#14556514	C₂³	1	2	yes	—
248	#14556514	C₂³	1	2	yes	—
249	#14556513	C₂³	1	2	yes	—
250	#14556513	C₂³	1	2	yes	—
251	#14556512	C₂³	1	2	yes	—
252	#14556512	C₂³	1	2	yes	—
253	#14556511	C₂³	1	2	yes	—
254	#14556511	C₂³	1	2	yes	—
255	#14556502	C₂³	1	1	yes	characteristic
256	#14556502	C₂³	1	1	yes	characteristic
257	#14556501	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	C₄×#10596831	C₂³	1	1	yes	characteristic
262	C₄×#10596831	C₂³	1	1	yes	characteristic
263	C₈×Dic₇₃	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	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
268	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
269	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
272	#127×C₇₃	C₂³	1	1	yes	characteristic
273	#126×C₇₃	—	2	2	no	—
274	#125×C₇₃	—	2	2	no	—
275	#125×C₇₃	C₂³	1	1	yes	characteristic
276	#125×C₇₃	C₂³	1	1	yes	characteristic
277	#123×C₇₃	—	2	2	no	—
278	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
279	#121×C₇₃	—	2	2	no	—
280	#121×C₇₃	C₂³	1	2	yes	—
281	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
282	C₄×D₄×C₇₃	C₂³	1	2	yes	—
283	#117×C₇₃	C₂³	1	1	yes	characteristic
284	#107×C₇₃	C₂³	1	2	yes	—
285	#106×C₇₃	C₂³	1	2	yes	—
286	#103×C₇₃	C₂³	1	2	yes	—
287	#103×C₇₃	C₂³	1	2	yes	—
288	#102×C₇₃	C₂³	1	2	yes	—
289	#102×C₇₃	C₂³	1	2	yes	—
290	#97×C₇₃	C₂³	1	1	yes	characteristic
291	#97×C₇₃	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₂³×D₇₃	—	2	2	no	—
295	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
296	C₂×Dic₁₄₆	—	2	2	no	—
297	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
298	Q₈×D₇₃	—	2	4	no	—
299	Q₈×D₇₃	—	2	4	no	—
300	C₂×D₂₉₂	—	2	2	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	C₂×C₂²⋊D₇₃	—	2	2	no	—
307	C₂×C₂²⋊D₇₃	—	2	2	no	—
308	D₄×D₇₃	—	2	4	no	—
309	D₄×D₇₃	—	2	4	no	—
310	D₄×D₇₃	—	8	4	no	—
311	D₄×D₇₃	—	8	4	no	—
312	C₂²×Dic₇₃	—	2	2	no	—
313	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
320	C₂×C₄×D₇₃	—	2	2	no	—
321	C₂×C₄×D₇₃	—	8	4	no	—
322	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
323	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
324	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
325	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
326	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
327	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
328	#11924017	—	2	4	no	—
329	#11924017	—	2	4	no	—
330	#11924016	—	2	4	no	—
331	#11924016	—	2	4	no	—
332	#11924015	—	2	4	no	—
333	#11924015	—	2	4	no	—
334	#11924012	—	2	2	no	—
335	#11924011	—	2	2	no	—
336	#11924011	—	2	2	no	—
337	C₂×#10596831	—	2	2	no	—
338	C₂×#10596831	C₂⁴	1	1	yes	characteristic
339	C₂×#10596831	C₂⁴	1	1	yes	characteristic
340	C₂×#10596831	C₂⁴	1	1	yes	characteristic
341	C₂×#10596831	C₂⁴	1	1	yes	characteristic
342	C₈×D₇₃	—	2	2	no	—
343	C₈×D₇₃	—	2	2	no	—
344	C₈×D₇₃	—	2	2	no	—
345	C₈×D₇₃	—	2	2	no	—
346	C₈×D₇₃	#41	1	4	yes	—
347	C₈×D₇₃	#41	1	4	yes	—
348	C₄⋊Dic₇₃	—	2	2	no	—
349	C₄⋊Dic₇₃	—	2	2	no	—
350	C₄⋊Dic₇₃	—	2	2	no	—
351	C₄⋊Dic₇₃	—	2	2	no	—
352	C₄⋊Dic₇₃	—	2	2	no	—
353	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
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	#11924007	—	2	2	no	—
367	#11924007	—	2	2	no	—
368	#11924007	C₂×D₄	1	2	yes	—
369	#11924007	C₂×D₄	1	2	yes	—
370	C₂²⋊Dic₇₃	—	2	2	no	—
371	C₂²⋊Dic₇₃	—	2	2	no	—
372	C₂²⋊Dic₇₃	—	2	2	no	—
373	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
381	#11924005	C₂×D₄	1	2	yes	—
382	C₄×Dic₇₃	—	2	2	no	—
383	C₄×Dic₇₃	—	2	2	no	—
384	C₄×Dic₇₃	—	2	2	no	—
385	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
386	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
387	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
388	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
389	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
390	C₂×D₄×C₇₃	—	2	2	no	—
391	C₂×D₄×C₇₃	—	2	2	no	—
392	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₇₃	—	2	2	no	—
394	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
395	SD₁₆×C₇₃	—	2	4	no	—
396	SD₁₆×C₇₃	—	2	4	no	—
397	M₁₆×C₇₃	—	2	2	no	—
398	C₂×C₈×C₇₃	—	2	2	no	—
399	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₇₃	—	2	2	no	—
404	C₄⋊C₄×C₇₃	—	2	2	no	—
405	C₄⋊C₄×C₇₃	—	2	2	no	—
406	C₄⋊C₄×C₇₃	—	2	2	no	—
407	C₄⋊C₄×C₇₃	—	2	2	no	—
408	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
411	C₂²⋊C₄×C₇₃	—	2	2	no	—
412	C₂²⋊C₄×C₇₃	—	2	2	no	—
413	C₂²⋊C₄×C₇₃	—	2	2	no	—
414	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
415	C₄²×C₇₃	—	2	2	no	—
416	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₂³×C₇₃	—	2	2	no	—
419	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
420	C₂²×D₇₃	—	2	2	no	—
421	C₂²×D₇₃	—	2	4	no	—
422	C₂²×D₇₃	—	2	2	no	—
423	C₂²×D₇₃	—	4	4	no	—
424	C₂²×D₇₃	—	4	4	no	—
425	C₂²×D₇₃	—	4	4	no	—
426	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
427	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
428	Q₈×C₇₃	—	2	2	no	—
429	Q₈×C₇₃	—	2	2	no	—
430	D₄×C₇₃	—	2	2	no	—
431	D₄×C₇₃	—	2	2	no	—
432	D₄×C₇₃	—	8	2	no	—
433	D₄×C₇₃	—	8	2	no	—
434	C₂×C₄×C₇₃	—	2	1	no	—
435	C₂×C₄×C₇₃	—	2	1	no	—
436	C₂×C₄×C₇₃	—	2	2	no	—
437	C₂×C₄×C₇₃	—	2	2	no	—
438	C₂×C₄×C₇₃	—	2	2	no	—
439	C₂×C₄×C₇₃	—	8	2	no	—
440	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
444	C₂²⋊D₇₃	—	4	4	no	—
445	C₂²⋊D₇₃	—	8	2	no	—
446	C₂²⋊D₇₃	—	8	2	no	—
447	C₂²⋊D₇₃	—	8	2	no	—
448	C₂²⋊D₇₃	—	8	2	no	—
449	C₂×Dic₇₃	—	2	2	no	—
450	C₂×Dic₇₃	—	2	2	no	—
451	C₂×Dic₇₃	—	2	2	no	—
452	C₂×Dic₇₃	—	2	2	no	—
453	C₂×Dic₇₃	—	8	2	no	—
454	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
455	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
456	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
458	D₂₉₂	—	2	2	no	—
459	D₂₉₂	—	2	2	no	—
460	D₂₉₂	—	8	2	no	—
461	D₂₉₂	—	8	2	no	—
462	C₄×D₇₃	—	2	2	no	—
463	C₄×D₇₃	—	2	4	no	—
464	C₄×D₇₃	—	2	4	no	—
465	C₄×D₇₃	—	2	1	no	—
466	C₄×D₇₃	—	2	1	no	—
467	C₄×D₇₃	—	2	2	no	—
468	C₄×D₇₃	—	4	4	no	—
469	C₄×D₇₃	—	4	4	no	—
470	C₄×D₇₃	—	4	4	no	—
471	C₄×D₇₃	—	8	2	no	—
472	C₄×D₇₃	—	8	2	no	—
473	C₄×D₇₃	C₂×#41	1	2	yes	—
474	C₄×D₇₃	C₂×#41	1	2	yes	—
475	Dic₁₄₆	—	2	2	no	—
476	Dic₁₄₆	—	2	2	no	—
477	Dic₁₄₆	—	4	4	no	—
478	C₈×C₇₃	—	2	1	no	—
479	C₈×C₇₃	—	2	1	no	—
480	C₈×C₇₃	C₂×#41	1	2	yes	—
481	C₈×C₇₃	C₂×#41	1	2	yes	—
482	#10596831	—	2	1	no	—
483	#10596831	—	2	1	no	—
484	#10596831	C₂×#41	1	2	yes	—
485	#10596831	C₂×#41	1	2	yes	—
486	C₂²×C₇₃	—	2	1	no	—
487	C₂²×C₇₃	—	2	2	no	—
488	C₂²×C₇₃	—	4	2	no	—
489	C₂²×C₇₃	—	4	2	no	—
490	C₂²×C₇₃	—	4	2	no	—
491	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
492	C₂×D₇₃	—	2	1	no	—
493	C₂×D₇₃	—	2	2	no	—
494	C₂×D₇₃	—	4	4	no	—
495	C₂×D₇₃	—	4	2	no	—
496	C₂×D₇₃	—	4	2	no	—
497	C₂×D₇₃	—	4	2	no	—
498	C₂×D₇₃	—	8	8	no	—
499	C₂×D₇₃	#532	1	2	yes	—
500	C₂×D₇₃	#577	1	4	yes	—
501	C₄×C₇₃	—	2	1	no	—
502	C₄×C₇₃	—	2	2	no	—
503	C₄×C₇₃	—	2	2	no	—
504	C₄×C₇₃	—	4	2	no	—
505	C₄×C₇₃	—	4	2	no	—
506	C₄×C₇₃	—	4	2	no	—
507	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
508	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
509	Dic₇₃	—	2	1	no	—
510	Dic₇₃	—	2	2	no	—
511	Dic₇₃	—	2	2	no	—
512	Dic₇₃	—	4	2	no	—
513	Dic₇₃	—	4	2	no	—
514	Dic₇₃	—	4	2	no	—
515	Dic₇₃	#532	1	2	yes	—
516	C₂×#3174	—	73	1	no	maximal, Sylow
517	C₂×C₇₃	—	4	1	no	—
518	C₂×C₇₃	—	8	2	no	—
519	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
520	C₂×C₇₃	C₂×#577	1	2	yes	—
521	D₇₃	—	4	1	no	—
522	D₇₃	—	8	2	no	—
523	D₇₃	#3174	1	4	yes	direct product factor
524	C₂×#541	—	73	1	no	—
525	C₂×#540	—	73	1	no	—
526	#3174	—	73	1	no	—
527	#3174	—	73	1	no	—
528	#3174	—	73	1	no	—
529	#3174	—	73	1	no	—
530	#3174	—	73	2	no	—
531	#3174	—	73	2	no	—
532	#3174	—	73	2	no	—
533	#3174	—	73	2	no	—
534	#3174	—	73	1	no	—
535	#3174	—	73	1	no	—
536	#3174	—	73	1	no	—
537	#3174	D₇₃	1	1	yes	characteristic, direct product factor
538	C₂×#499	—	73	1	no	—
539	C₂×#492	—	73	1	no	—
540	C₂×#491	—	73	1	no	—
541	C₂×#490	—	73	1	no	—
542	C₂×#468	—	73	2	no	—
543	C₂×#465	—	73	2	no	—
544	C₂×#440	—	73	2	no	—
545	C₂×C₄×SD₁₆	—	73	2	no	—
546	C₂×#405	—	73	1	no	—
547	C₇₃	C₂×#3174	1	1	yes	characteristic, complemented, Sylow
548	C₂²×SD₁₆	—	73	2	no	—
549	C₂²×SD₁₆	—	73	2	no	—
550	C₂²×M₁₆	—	73	1	no	—
551	C₂³×C₈	—	73	1	no	—
552	#541	—	73	1	no	—
553	#541	—	73	1	no	—
554	#541	—	73	2	no	—
555	#541	—	73	2	no	—
556	#541	—	73	1	no	—
557	#541	—	146	2	no	—
558	#541	—	146	2	no	—
559	#541	C₂×D₇₃	1	1	yes	characteristic, complemented
560	#540	—	73	1	no	—
561	#540	—	73	1	no	—
562	#540	—	73	2	no	—
563	#540	—	73	2	no	—
564	#540	—	73	1	no	—
565	#540	—	146	2	no	—
566	#540	—	146	2	no	—
567	#540	C₂×D₇₃	1	1	yes	characteristic
568	C₂×C₄⋊Q₈	—	73	1	no	—
569	C₂×#127	—	73	1	no	—
570	C₂×#126	—	146	2	no	—
571	C₂×#125	—	73	1	no	—
572	C₂×#125	—	73	1	no	—
573	C₂×#125	—	146	2	no	—
574	C₂×#123	—	146	2	no	—
575	C₂×C₂²⋊Q₈	—	73	2	no	—
576	C₂×#121	—	73	2	no	—
577	C₂×#121	—	146	2	no	—
578	C₂×C₄×Q₈	—	73	2	no	—
579	C₂×C₄×D₄	—	73	2	no	—
580	C₂×#117	—	73	1	no	—
581	#499	—	73	1	no	—
582	#499	—	73	1	no	—
583	#499	—	73	2	no	—
584	#499	—	73	2	no	—
585	#499	—	73	1	no	—
586	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
587	#492	—	73	2	no	—
588	#492	—	73	2	no	—
589	#492	—	73	1	no	—
590	#492	—	73	1	no	—
591	#492	—	73	1	no	—
592	#492	C₂×D₇₃	1	1	yes	characteristic, complemented
593	#491	—	73	1	no	—
594	#491	—	73	1	no	—
595	#491	—	73	2	no	—
596	#491	—	73	2	no	—
597	#491	—	73	1	no	—
598	#491	C₂×D₇₃	1	1	yes	characteristic, complemented
599	#490	—	73	1	no	—
600	#490	—	73	1	no	—
601	#490	—	73	2	no	—
602	#490	—	73	2	no	—
603	#490	—	73	1	no	—
604	#490	C₂×D₇₃	1	1	yes	characteristic, complemented
605	#468	—	73	2	no	—
606	#468	—	73	2	no	—
607	#468	—	73	2	no	—
608	#468	—	73	2	no	—
609	#468	—	73	2	no	—
610	#468	—	73	2	no	—
611	#468	—	73	2	no	—
612	#468	C₂×D₇₃	1	2	yes	complemented
613	#465	—	73	2	no	—
614	#465	—	73	2	no	—
615	#465	—	73	2	no	—
616	#465	—	73	2	no	—
617	#465	—	73	2	no	—
618	#465	—	73	2	no	—
619	#465	—	73	2	no	—
620	#465	C₂×D₇₃	1	2	yes	complemented
621	#440	—	73	2	no	—
622	#440	—	73	2	no	—
623	#440	—	73	2	no	—
624	#440	—	73	2	no	—
625	#440	—	73	2	no	—
626	#440	—	73	2	no	—
627	#440	—	73	2	no	—
628	#440	C₂×D₇₃	1	2	yes	complemented
629	C₄×SD₁₆	—	73	2	no	—
630	C₄×SD₁₆	—	73	2	no	—
631	C₄×SD₁₆	—	73	2	no	—
632	C₄×SD₁₆	—	73	2	no	—
633	C₄×SD₁₆	—	73	2	no	—
634	C₄×SD₁₆	—	73	2	no	—
635	C₄×SD₁₆	—	73	2	no	—
636	C₄×SD₁₆	C₂×D₇₃	1	2	yes	complemented
637	C₂×#107	—	73	2	no	—
638	C₂×#106	—	73	2	no	—
639	C₂×#103	—	73	2	no	—
640	C₂×#103	—	73	2	no	—
641	C₂×#102	—	73	2	no	—
642	C₂×#102	—	73	2	no	—
643	#405	—	73	1	no	—
644	#405	—	73	1	no	—
645	#405	—	73	1	no	—
646	#405	—	73	1	no	—
647	#405	—	73	1	no	—
648	#405	—	73	1	no	—
649	#405	—	73	1	no	—
650	#405	C₂×D₇₃	1	1	yes	characteristic, complemented
651	C₂×#97	—	73	1	no	—
652	C₂×#97	—	73	1	no	—
653	C₂×C₄×C₈	—	73	1	no	—
654	C₂×C₄×C₈	—	73	1	no	—
655	C₂²×Q₈	—	73	2	no	—
656	C₂²×D₄	—	73	2	no	—
657	C₂²×D₄	—	146	2	no	—
658	C₂²×D₄	—	146	2	no	—
659	C₂³×C₄	—	73	1	no	—
660	C₂³×C₄	—	146	2	no	—
661	C₂×SD₁₆	—	73	2	no	—
662	C₂×SD₁₆	—	73	2	no	—
663	C₂×SD₁₆	—	73	2	no	—
664	C₂×SD₁₆	—	73	2	no	—
665	C₂×SD₁₆	—	73	2	no	—
666	C₂×SD₁₆	—	73	2	no	—
667	C₂×SD₁₆	—	146	8	no	—
668	C₂×SD₁₆	—	146	8	no	—
669	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
670	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
671	C₂×M₁₆	—	73	1	no	—
672	C₂×M₁₆	—	73	1	no	—
673	C₂×M₁₆	—	73	1	no	—
674	C₂×M₁₆	—	146	4	no	—
675	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
676	C₂²×C₈	—	73	1	no	—
677	C₂²×C₈	—	73	1	no	—
678	C₂²×C₈	—	73	1	no	—
679	C₂²×C₈	—	73	1	no	—
680	C₂²×C₈	—	73	1	no	—
681	C₂²×C₈	—	73	1	no	—
682	C₂²×C₈	—	73	1	no	—
683	C₂²×C₈	—	146	4	no	—
684	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
685	C₄⋊Q₈	—	73	2	no	—
686	C₄⋊Q₈	—	73	1	no	—
687	C₄⋊Q₈	—	146	2	no	—
688	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
689	#127	—	73	2	no	—
690	#127	—	73	1	no	—
691	#127	—	146	2	no	—
692	#127	C₂²×D₇₃	1	1	yes	characteristic
693	#126	—	2	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	#126	—	146	2	no	—
700	#126	—	146	2	no	—
701	#125	—	2	2	no	—
702	#125	—	73	2	no	—
703	#125	—	73	2	no	—
704	#125	—	73	1	no	—
705	#125	—	73	1	no	—
706	#125	—	146	2	no	—
707	#125	—	146	2	no	—
708	#125	—	146	2	no	—
709	#125	—	146	2	no	—
710	#125	—	146	2	no	—
711	#125	—	146	2	no	—
712	#125	—	146	2	no	—
713	#125	—	146	2	no	—
714	#125	—	146	2	no	—
715	#125	C₂²×D₇₃	1	1	yes	characteristic
716	#125	C₂²×D₇₃	1	1	yes	characteristic
717	#123	—	2	2	no	—
718	#123	—	146	2	no	—
719	#123	—	146	2	no	—
720	#123	—	146	2	no	—
721	#123	—	146	2	no	—
722	#123	—	146	2	no	—
723	#123	—	146	2	no	—
724	#123	—	146	2	no	—
725	C₂²⋊Q₈	—	73	2	no	—
726	C₂²⋊Q₈	—	73	2	no	—
727	C₂²⋊Q₈	—	73	2	no	—
728	C₂²⋊Q₈	—	146	2	no	—
729	C₂²⋊Q₈	—	146	2	no	—
730	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
731	#121	—	2	2	no	—
732	#121	—	73	2	no	—
733	#121	—	73	2	no	—
734	#121	—	73	2	no	—
735	#121	—	146	2	no	—
736	#121	—	146	2	no	—
737	#121	—	146	2	no	—
738	#121	—	146	2	no	—
739	#121	—	146	2	no	—
740	#121	—	146	2	no	—
741	#121	—	146	2	no	—
742	#121	—	146	2	no	—
743	#121	—	146	2	no	—
744	#121	C₂²×D₇₃	1	2	yes	—
745	C₄×Q₈	—	73	2	no	—
746	C₄×Q₈	—	73	2	no	—
747	C₄×Q₈	—	73	2	no	—
748	C₄×Q₈	—	146	2	no	—
749	C₄×Q₈	—	146	2	no	—
750	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
751	C₄×D₄	—	73	2	no	—
752	C₄×D₄	—	73	2	no	—
753	C₄×D₄	—	73	2	no	—
754	C₄×D₄	—	146	2	no	—
755	C₄×D₄	—	146	2	no	—
756	C₄×D₄	C₂²×D₇₃	1	2	yes	—
757	#117	—	73	1	no	—
758	#117	—	73	2	no	—
759	#117	—	73	2	no	—
760	#117	—	73	1	no	—
761	#117	—	73	1	no	—
762	#117	C₂²×D₇₃	1	1	yes	characteristic
763	C₂×C₄⋊C₄	—	73	2	no	—
764	C₂×C₄⋊C₄	—	73	2	no	—
765	C₂×C₄⋊C₄	—	73	2	no	—
766	C₂×C₄⋊C₄	—	146	2	no	—
767	C₂×C₄⋊C₄	—	146	2	no	—
768	C₂×C₄⋊C₄	—	146	2	no	—
769	C₂×C₄⋊C₄	—	146	2	no	—
770	C₂×C₄⋊C₄	—	146	2	no	—
771	C₂×C₂²⋊C₄	—	73	2	no	—
772	C₂×C₂²⋊C₄	—	146	2	no	—
773	C₂×C₂²⋊C₄	—	146	2	no	—
774	C₂×C₂²⋊C₄	—	146	2	no	—
775	C₂×C₄²	—	73	1	no	—
776	C₂×C₄²	—	73	1	no	—
777	C₂×C₄²	—	146	2	no	—
778	#107	—	73	2	no	—
779	#107	—	73	2	no	—
780	#107	—	73	2	no	—
781	#107	C₂²×D₇₃	1	2	yes	—
782	#106	—	73	2	no	—
783	#106	—	73	2	no	—
784	#106	—	73	2	no	—
785	#106	C₂²×D₇₃	1	2	yes	—
786	#103	—	73	2	no	—
787	#103	—	73	2	no	—
788	#103	—	73	2	no	—
789	#103	—	73	2	no	—
790	#103	—	73	2	no	—
791	#103	—	73	2	no	—
792	#103	C₂²×D₇₃	1	2	yes	—
793	#103	C₂²×D₇₃	1	2	yes	—
794	#102	—	73	2	no	—
795	#102	—	73	2	no	—
796	#102	—	73	2	no	—
797	#102	—	73	2	no	—
798	#102	—	73	2	no	—
799	#102	—	73	2	no	—
800	#102	C₂²×D₇₃	1	2	yes	—
801	#102	C₂²×D₇₃	1	2	yes	—
802	#97	—	73	1	no	—
803	#97	—	73	1	no	—
804	#97	—	73	1	no	—
805	#97	—	73	1	no	—
806	#97	—	73	1	no	—
807	#97	—	73	1	no	—
808	#97	C₂²×D₇₃	1	1	yes	characteristic
809	#97	C₂²×D₇₃	1	1	yes	characteristic
810	C₄×C₈	—	73	1	no	—
811	C₄×C₈	—	73	1	no	—
812	C₄×C₈	—	73	1	no	—
813	C₄×C₈	—	73	1	no	—
814	C₄×C₈	—	73	1	no	—
815	C₄×C₈	—	73	1	no	—
816	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
817	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
818	C₂⁴	—	73	1	no	—
819	C₂⁴	—	146	2	no	—
820	C₂×Q₈	—	73	2	no	—
821	C₂×Q₈	—	146	2	no	—
822	C₂×Q₈	—	146	4	no	—
823	C₂×Q₈	—	146	4	no	—
824	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	584	4	no	—
828	C₂×D₄	—	584	4	no	—
829	C₂×D₄	—	73	2	no	—
830	C₂×D₄	—	146	2	no	—
831	C₂×D₄	—	146	4	no	—
832	C₂×D₄	—	146	4	no	—
833	C₂×D₄	—	146	2	no	—
834	C₂×D₄	—	146	2	no	—
835	C₂×D₄	—	146	2	no	—
836	C₂×D₄	—	146	2	no	—
837	C₂×D₄	—	146	2	no	—
838	C₂×D₄	—	146	2	no	—
839	C₂×D₄	C₂³×D₇₃	1	2	yes	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	584	4	no	—
842	C₂²×C₄	—	73	1	no	—
843	C₂²×C₄	—	73	1	no	—
844	C₂²×C₄	—	73	2	no	—
845	C₂²×C₄	—	73	2	no	—
846	C₂²×C₄	—	73	1	no	—
847	C₂²×C₄	—	73	1	no	—
848	C₂²×C₄	—	73	1	no	—
849	C₂²×C₄	—	146	2	no	—
850	C₂²×C₄	—	146	2	no	—
851	C₂²×C₄	—	146	2	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	C₂³×D₇₃	1	1	yes	characteristic
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	2	4	no	—
860	SD₁₆	—	146	4	no	—
861	SD₁₆	—	146	4	no	—
862	SD₁₆	—	146	4	no	—
863	SD₁₆	—	146	4	no	—
864	SD₁₆	—	146	4	no	—
865	SD₁₆	—	146	4	no	—
866	M₁₆	—	2	2	no	—
867	M₁₆	—	146	2	no	—
868	M₁₆	—	146	2	no	—
869	M₁₆	—	146	2	no	—
870	C₂×C₈	—	2	2	no	—
871	C₂×C₈	—	73	1	no	—
872	C₂×C₈	—	73	1	no	—
873	C₂×C₈	—	73	4	no	—
874	C₂×C₈	—	73	4	no	—
875	C₂×C₈	—	73	1	no	—
876	C₂×C₈	—	73	1	no	—
877	C₂×C₈	—	146	2	no	—
878	C₂×C₈	—	146	2	no	—
879	C₂×C₈	—	146	2	no	—
880	C₂×C₈	—	146	2	no	—
881	C₂×C₈	—	146	2	no	—
882	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
883	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
884	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
885	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	73	2	no	—
892	C₄⋊C₄	—	73	2	no	—
893	C₄⋊C₄	—	73	2	no	—
894	C₄⋊C₄	—	73	2	no	—
895	C₄⋊C₄	—	73	2	no	—
896	C₄⋊C₄	—	146	2	no	—
897	C₄⋊C₄	—	146	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	—	146	2	no	—
913	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
914	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
915	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	73	2	no	—
920	C₂²⋊C₄	—	73	2	no	—
921	C₂²⋊C₄	—	73	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	D₄×D₇₃	1	2	yes	—
932	C₄²	—	2	2	no	—
933	C₄²	—	73	2	no	—
934	C₄²	—	73	2	no	—
935	C₄²	—	73	1	no	—
936	C₄²	—	73	1	no	—
937	C₄²	—	146	2	no	—
938	C₄²	—	146	2	no	—
939	C₄²	—	146	2	no	—
940	C₄²	C₂³×D₇₃	1	1	yes	characteristic
941	C₄²	C₂³×D₇₃	1	1	yes	characteristic
942	C₂³	—	2	2	no	—
943	C₂³	—	292	4	no	—
944	C₂³	—	292	4	no	—
945	C₂³	—	292	4	no	—
946	C₂³	—	73	1	no	—
947	C₂³	—	73	1	no	—
948	C₂³	—	146	2	no	—
949	C₂³	—	146	4	no	—
950	C₂³	—	146	2	no	—
951	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	292	4	no	—
955	Q₈	—	146	2	no	—
956	Q₈	—	146	2	no	—
957	D₄	—	2	2	no	—
958	D₄	—	2	2	no	—
959	D₄	—	8	2	no	—
960	D₄	—	8	2	no	—
961	D₄	—	292	4	no	—
962	D₄	—	584	2	no	—
963	D₄	—	584	2	no	—
964	D₄	—	584	2	no	—
965	D₄	—	584	2	no	—
966	D₄	—	584	2	no	—
967	D₄	—	584	2	no	—
968	D₄	—	146	2	no	—
969	D₄	—	146	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	292	4	no	—
977	C₂×C₄	—	292	4	no	—
978	C₂×C₄	—	292	4	no	—
979	C₂×C₄	—	584	2	no	—
980	C₂×C₄	—	584	2	no	—
981	C₂×C₄	—	584	2	no	—
982	C₂×C₄	—	73	1	no	—
983	C₂×C₄	—	73	2	no	—
984	C₂×C₄	—	73	2	no	—
985	C₂×C₄	—	73	2	no	—
986	C₂×C₄	—	73	2	no	—
987	C₂×C₄	—	73	1	no	—
988	C₂×C₄	—	146	2	no	—
989	C₂×C₄	—	146	4	no	—
990	C₂×C₄	—	146	2	no	—
991	C₂×C₄	—	146	4	no	—
992	C₂×C₄	—	146	2	no	—
993	C₂×C₄	—	146	2	no	—
994	C₂×C₄	—	146	2	no	—
995	C₂×C₄	—	146	2	no	—
996	C₂×C₄	—	146	1	no	—
997	C₂×C₄	—	146	1	no	—
998	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
999	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1000	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1001	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1002	C₈	—	2	1	no	—
1003	C₈	—	2	1	no	—
1004	C₈	—	73	2	no	—
1005	C₈	—	73	2	no	—
1006	C₈	—	146	1	no	—
1007	C₈	—	146	1	no	—
1008	C₈	#41×D₇₃	1	2	yes	—
1009	C₈	#41×D₇₃	1	2	yes	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	292	4	no	—
1016	C₂²	—	292	2	no	—
1017	C₂²	—	292	2	no	—
1018	C₂²	—	292	2	no	—
1019	C₂²	—	584	8	no	—
1020	C₂²	—	73	4	no	—
1021	C₂²	—	73	2	no	—
1022	C₂²	—	146	2	no	—
1023	C₂²	—	146	1	no	—
1024	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	2	no	—
1031	C₄	—	292	2	no	—
1032	C₄	—	292	2	no	—
1033	C₄	—	292	2	no	—
1034	C₄	—	73	2	no	—
1035	C₄	—	146	2	no	—
1036	C₄	—	146	2	no	—
1037	C₄	—	146	1	no	—
1038	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1039	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1040	C₂	—	4	1	no	—
1041	C₂	—	8	2	no	—
1042	C₂	—	292	1	no	—
1043	C₂	—	584	2	no	—
1044	C₂	—	73	4	no	—
1045	C₂	#532×D₇₃	1	1	yes	characteristic
1046	C₂	#577×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×#3174	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#540×D₇₃	C₂
hypercenter	#3174	D₇₃
hypocenter	C₇₃	C₂×#3174
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3174

Complements

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

N	H ≅ G/N	type
1. #541×D₇₃	C₂	semidirect
3. #22620562	C₂	semidirect
4. #22620561	C₂	semidirect
5. #22620560	C₂	semidirect
6. #22620559	C₂	semidirect
7. #22620558	C₂	semidirect
8. #22620557	C₂	semidirect
9. #22620556	C₂	semidirect
10. #22620555	C₂	semidirect
11. #22620554	C₂	semidirect
12. #22620553	C₂	semidirect
13. #22620552	C₂	semidirect
14. #499×D₇₃	C₂	semidirect
15. #492×D₇₃	C₂	semidirect
16. #491×D₇₃	C₂	semidirect
17. #490×D₇₃	C₂	semidirect
18. #468×D₇₃	C₂	semidirect
19. #465×D₇₃	C₂	semidirect
20. #440×D₇₃	C₂	semidirect
21. C₄×SD₁₆×D₇₃	C₂	semidirect
22. #405×D₇₃	C₂	semidirect
23. C₇₃×#3174	C₂	semidirect
28. #17989200	C₂²	semidirect
29. #17989199	C₂²	semidirect
30. #17989198	C₂²	semidirect
31. #17989197	C₂²	semidirect
33. #17989195	C₂²	semidirect
55. #17988989	C₂²	semidirect
56. #17988988	C₂²	semidirect
57. #17988987	C₂²	semidirect
58. #17988986	C₂²	semidirect
59. #17988986	C₂²	semidirect
60. #17988961	C₂²	semidirect
61. #17988960	C₂²	semidirect
62. #17988959	C₂²	semidirect
63. #17988958	C₂²	semidirect
64. #17988958	C₂²	semidirect
65. #17988957	C₂²	semidirect
66. #17988956	C₂²	semidirect
67. #17988955	C₂²	semidirect
68. #17988954	C₂²	semidirect
69. #17988954	C₂²	semidirect
70. #17988953	C₂²	semidirect
71. #17988952	C₂²	semidirect
72. #17988951	C₂²	semidirect
73. #17988950	C₂²	semidirect
74. #17988950	C₂²	semidirect
75. #17988836	C₂²	semidirect
76. #17988835	C₂²	semidirect
77. #17988834	C₂²	semidirect
78. #17988833	C₂²	semidirect
79. #17988832	C₂²	semidirect
80. #17988831	C₂²	semidirect
81. #17988830	C₂²	semidirect
82. #17988819	C₂²	semidirect
83. #17988818	C₂²	semidirect
84. #17988817	C₂²	semidirect
85. #17988816	C₂²	semidirect
86. #17988815	C₂²	semidirect
87. #17988814	C₂²	semidirect
88. #17988813	C₂²	semidirect
89. #17988690	C₂²	semidirect
90. #17988689	C₂²	semidirect
91. #17988688	C₂²	semidirect
92. #17988687	C₂²	semidirect
93. #17988686	C₂²	semidirect
94. #17988685	C₂²	semidirect
95. #17988684	C₂²	semidirect
96. #17988678	C₂²	semidirect
97. C₄×#11924017	C₂²	semidirect
98. SD₁₆×Dic₇₃	C₂²	semidirect
99. C₄×#11924015	C₂²	semidirect
100. #17988674	C₂²	semidirect
101. C₄×#11924016	C₂²	semidirect
102. #17988672	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. #541×C₇₃	C₂²	semidirect
122. #499×C₇₃	C₂²	semidirect
123. #492×C₇₃	C₂²	semidirect
124. #491×C₇₃	C₂²	semidirect
125. #490×C₇₃	C₂²	semidirect
126. #468×C₇₃	C₂²	semidirect
127. #465×C₇₃	C₂²	semidirect
128. #440×C₇₃	C₂²	semidirect
129. C₄×SD₁₆×C₇₃	C₂²	semidirect
130. #405×C₇₃	C₂²	semidirect
523. D₇₃	#3174	direct (N × H)
537. #3174	D₇₃	direct (N × H)
547. C₇₃	C₂×#3174	semidirect
559. #541	C₂×D₇₃	semidirect
586. #499	C₂×D₇₃	semidirect
592. #492	C₂×D₇₃	semidirect
598. #491	C₂×D₇₃	semidirect
604. #490	C₂×D₇₃	semidirect
612. #468	C₂×D₇₃	semidirect
620. #465	C₂×D₇₃	semidirect
628. #440	C₂×D₇₃	semidirect
636. C₄×SD₁₆	C₂×D₇₃	semidirect
650. #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
#541×D₇₃	2
#540×D₇₃	2
#22620562	2
#22620561	2
#22620560	2
#22620559	2
#22620558	2
#22620557	2
#22620556	2
#22620555	2
#22620554	2
#22620553	2
#22620552	2
#499×D₇₃	2
#492×D₇₃	2
#491×D₇₃	2
#490×D₇₃	2
#468×D₇₃	2
#465×D₇₃	2
#440×D₇₃	2
C₄×SD₁₆×D₇₃	2
#405×D₇₃	2
C₇₃×#3174	2
C₂×#3174	73

Subgroups — #3174×D73 #33955786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3174×D₇₃ #33955786