Subgroups — #3222×D₇₃ #33957319

Order 18688.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1192 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	#535×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22621006	C₂	1	1	yes	maximal, characteristic, complemented
4	#22621005	C₂	1	1	yes	maximal, characteristic, complemented
5	#22621004	C₂	1	1	yes	maximal, characteristic, complemented
6	#22621003	C₂	1	1	yes	maximal, characteristic, complemented
7	#22621002	C₂	1	2	yes	maximal, complemented
8	#22621001	C₂	1	2	yes	maximal, complemented
9	#22621000	C₂	1	2	yes	maximal, complemented
10	#22620999	C₂	1	2	yes	maximal, complemented
11	#22620998	C₂	1	1	yes	maximal, characteristic, complemented
12	#22620997	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620996	C₂	1	1	yes	maximal, characteristic, complemented
14	#497×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#492×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#490×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#488×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#464×D₇₃	C₂	1	2	yes	maximal, complemented
19	#460×D₇₃	C₂	1	2	yes	maximal, complemented
20	#452×D₇₃	C₂	1	2	yes	maximal, complemented
21	#450×D₇₃	C₂	1	2	yes	maximal, complemented
22	#433×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×D₇₃	C₂²	1	1	yes	characteristic
25	C₂²×D₄×D₇₃	C₂²	1	1	yes	characteristic
26	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	complemented
27	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
28	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
29	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	complemented
30	#17989200	C₂²	1	1	yes	characteristic, complemented
31	#17989199	C₂²	1	1	yes	characteristic, complemented
32	#17989198	C₂²	1	1	yes	characteristic, complemented
33	#17989197	C₂²	1	2	yes	complemented
34	#17989196	—	2	2	no	—
35	#17989195	C₂²	1	2	yes	complemented
36	#17989194	—	2	2	no	—
37	#17989156	C₂²	1	1	yes	characteristic
38	#17989155	C₂²	1	1	yes	characteristic
39	#17989155	C₂²	1	1	yes	characteristic
40	#17989154	C₂²	1	1	yes	characteristic
41	#17989153	—	2	2	no	—
42	#17989152	—	2	2	no	—
43	#17989151	C₂²	1	1	yes	characteristic
44	#17989150	C₂²	1	1	yes	characteristic
45	#17989150	C₂²	1	1	yes	characteristic
46	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
47	#127×D₇₃	C₂²	1	1	yes	characteristic
48	#127×D₇₃	C₂²	1	1	yes	characteristic
49	#126×D₇₃	—	2	2	no	—
50	#125×D₇₃	—	2	2	no	—
51	#125×D₇₃	C₂²	1	1	yes	characteristic, complemented
52	#124×D₇₃	C₂²	1	1	yes	characteristic
53	#124×D₇₃	C₂²	1	1	yes	characteristic
54	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
55	#121×D₇₃	—	2	2	no	—
56	#120×D₇₃	—	2	2	no	—
57	C₄×Q₈×D₇₃	C₂²	1	2	yes	complemented
58	#117×D₇₃	C₂²	1	1	yes	characteristic
59	#17988982	C₂²	1	1	yes	characteristic, complemented
60	#17988981	C₂²	1	1	yes	characteristic, complemented
61	#17988980	C₂²	1	2	yes	complemented
62	#17988979	C₂²	1	1	yes	characteristic, complemented
63	#17988978	C₂²	1	2	yes	complemented
64	#17988961	C₂²	1	1	yes	characteristic, complemented
65	#17988960	C₂²	1	1	yes	characteristic, complemented
66	#17988959	C₂²	1	1	yes	characteristic, complemented
67	#17988958	C₂²	1	2	yes	complemented
68	#17988958	C₂²	1	2	yes	complemented
69	#17988953	C₂²	1	1	yes	characteristic, complemented
70	#17988952	C₂²	1	1	yes	characteristic, complemented
71	#17988951	C₂²	1	1	yes	characteristic, complemented
72	#17988950	C₂²	1	2	yes	complemented
73	#17988950	C₂²	1	2	yes	complemented
74	#17988944	C₂²	1	1	yes	characteristic, complemented
75	#17988943	C₂²	1	2	yes	complemented
76	#17988942	C₂²	1	1	yes	characteristic, complemented
77	#17988941	C₂²	1	1	yes	characteristic, complemented
78	#17988940	C₂²	1	2	yes	complemented
79	#17988812	C₂²	1	2	yes	complemented
80	#17988811	C₂²	1	2	yes	complemented
81	#17988810	C₂²	1	2	yes	complemented
82	#17988809	C₂²	1	2	yes	complemented
83	#17988808	C₂²	1	2	yes	complemented
84	#17988807	C₂²	1	2	yes	complemented
85	#17988806	C₂²	1	2	yes	complemented
86	#17988788	C₂²	1	2	yes	complemented
87	#17988787	C₂²	1	2	yes	complemented
88	#17988786	C₂²	1	2	yes	complemented
89	#17988786	C₂²	1	2	yes	complemented
90	#17988785	C₂²	1	2	yes	complemented
91	#17988785	C₂²	1	2	yes	complemented
92	#17988784	C₂²	1	2	yes	complemented
93	#17988752	C₂²	1	2	yes	complemented
94	#17988751	C₂²	1	2	yes	complemented
95	#17988750	C₂²	1	2	yes	complemented
96	#17988749	C₂²	1	2	yes	complemented
97	#17988748	C₂²	1	2	yes	complemented
98	#17988747	C₂²	1	2	yes	complemented
99	#17988746	C₂²	1	2	yes	complemented
100	#17988740	C₂²	1	2	yes	complemented
101	#17988739	C₂²	1	2	yes	complemented
102	#17988739	C₂²	1	2	yes	complemented
103	#17988738	C₂²	1	2	yes	complemented
104	#17988737	C₂²	1	2	yes	complemented
105	#17988736	C₂²	1	2	yes	complemented
106	#17988736	C₂²	1	2	yes	complemented
107	#17988649	C₂²	1	1	yes	characteristic, complemented
108	#17988648	C₂²	1	1	yes	characteristic, complemented
109	#17988647	C₂²	1	2	yes	complemented
110	#17988646	C₂²	1	1	yes	characteristic, complemented
111	#17988645	C₂²	1	2	yes	complemented
112	C₄⋊C₈×D₇₃	C₂²	1	2	yes	complemented
113	#103×D₇₃	C₂²	1	2	yes	complemented
114	#102×D₇₃	C₂²	1	2	yes	—
115	#102×D₇₃	C₂²	1	2	yes	—
116	#102×D₇₃	C₂²	1	2	yes	complemented
117	C₂²⋊C₈×D₇₃	C₂²	1	2	yes	—
118	#97×D₇₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
120	#541×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	#535×C₇₃	C₂²	1	1	yes	characteristic
122	#497×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#492×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#490×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#488×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#464×C₇₃	C₂²	1	2	yes	complemented
127	#460×C₇₃	C₂²	1	2	yes	complemented
128	#452×C₇₃	C₂²	1	2	yes	complemented
129	#450×C₇₃	C₂²	1	2	yes	complemented
130	#433×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂⁴×D₇₃	—	2	1	no	—
132	C₂×#11924029	C₂³	1	1	yes	characteristic
133	C₂×#11924028	—	2	1	no	—
134	C₂×#11924028	C₂³	1	1	yes	characteristic
135	C₂×#11924027	—	2	1	no	—
136	C₂×#11924027	C₂³	1	1	yes	characteristic
137	#41×D₇₃	—	4	4	no	—
138	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
139	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
140	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
141	C₂²×C₂²⋊D₇₃	—	2	1	no	—
142	C₂×D₄×D₇₃	—	2	1	no	—
143	C₂×D₄×D₇₃	—	2	1	no	—
144	C₂×D₄×D₇₃	—	2	1	no	—
145	C₂×D₄×D₇₃	—	2	2	no	—
146	C₂×D₄×D₇₃	—	2	2	no	—
147	C₂×D₄×D₇₃	—	4	4	no	—
148	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
149	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
150	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
151	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
152	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
153	C₂²×C₄×D₇₃	—	2	1	no	—
154	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
155	C₂×Dic₂₉₂	C₂³	1	2	yes	complemented
156	C₂×#11924018	C₂³	1	2	yes	complemented
157	C₂×#11924018	C₂³	1	2	yes	complemented
158	Q₁₆×D₇₃	—	4	4	no	—
159	C₂×#11924017	C₂³	1	2	yes	—
160	C₂×#11924017	C₂³	1	2	yes	—
161	C₂×#11924017	C₂³	1	2	yes	complemented
162	C₂×#11924016	C₂³	1	2	yes	—
163	C₂×#11924016	C₂³	1	2	yes	—
164	C₂×#11924016	C₂³	1	2	yes	complemented
165	C₂×#11924015	C₂³	1	2	yes	—
166	C₂×#11924015	C₂³	1	2	yes	—
167	C₂×#11924015	C₂³	1	2	yes	complemented
168	SD₁₆×D₇₃	—	4	4	no	—
169	SD₁₆×D₇₃	—	4	4	no	—
170	SD₁₆×D₇₃	—	4	4	no	—
171	C₂×C₈×D₇₃	C₂³	1	2	yes	—
172	C₂×C₈×D₇₃	C₂³	1	2	yes	—
173	#14556591	C₂³	1	1	yes	characteristic, complemented
174	#14556590	—	2	2	no	—
175	#14556589	C₂³	1	2	yes	complemented
176	#14556588	C₂³	1	1	yes	characteristic
177	#14556588	C₂³	1	1	yes	characteristic
178	#14556587	—	2	2	no	—
179	#14556587	—	2	2	no	—
180	#14556587	C₂³	1	1	yes	characteristic
181	#14556587	C₂³	1	1	yes	characteristic
182	#14556587	C₂³	1	1	yes	characteristic
183	#14556587	C₂³	1	1	yes	characteristic
184	#14556586	—	2	2	no	—
185	#14556586	—	2	2	no	—
186	#14556586	—	2	2	no	—
187	#14556585	—	2	2	no	—
188	#14556584	—	2	2	no	—
189	#14556584	—	2	2	no	—
190	#14556584	—	2	2	no	—
191	#14556583	—	2	2	no	—
192	#14556583	C₂³	1	1	yes	characteristic, complemented
193	#14556582	—	2	2	no	—
194	#14556582	—	2	2	no	—
195	#14556582	C₂³	1	2	yes	complemented
196	#14556581	—	2	2	no	—
197	#14556581	—	2	2	no	—
198	#14556581	—	2	2	no	—
199	#14556581	—	2	2	no	—
200	#14556581	—	2	2	no	—
201	#14556580	C₂³	1	1	yes	characteristic
202	#14556580	C₂³	1	1	yes	characteristic
203	#14556579	C₂³	1	1	yes	characteristic
204	#14556579	C₂³	1	1	yes	characteristic
205	#14556578	C₂³	1	1	yes	characteristic
206	#14556578	C₂³	1	1	yes	characteristic
207	#14556577	—	2	2	no	—
208	#14556577	—	2	2	no	—
209	#14556571	C₂³	1	2	yes	—
210	#14556570	C₂³	1	2	yes	—
211	#14556569	—	2	2	no	—
212	#14556568	—	2	2	no	—
213	#14556567	C₂³	1	2	yes	—
214	#14556566	—	2	2	no	—
215	#14556565	—	2	2	no	—
216	#14556564	—	2	2	no	—
217	#14556564	—	2	2	no	—
218	#14556563	—	2	2	no	—
219	#14556563	—	2	2	no	—
220	#14556562	—	2	2	no	—
221	#14556561	—	2	2	no	—
222	#14556561	—	2	2	no	—
223	#14556561	—	2	2	no	—
224	#14556560	—	2	2	no	—
225	#14556559	—	2	2	no	—
226	#14556559	—	2	2	no	—
227	#14556559	—	2	2	no	—
228	Q₈×Dic₇₃	C₂³	1	2	yes	complemented
229	C₄×Dic₁₄₆	—	2	2	no	—
230	C₄×Dic₁₄₆	C₂³	1	2	yes	complemented
231	#14556556	—	2	2	no	—
232	#14556556	C₂³	1	2	yes	complemented
233	#14556550	C₂³	1	1	yes	characteristic
234	#14556549	D₄	1	2	yes	—
235	#14556548	C₂³	1	1	yes	characteristic
236	#14556548	C₂³	1	1	yes	characteristic
237	#14556547	D₄	1	2	yes	—
238	C₄⋊C₄×D₇₃	—	2	2	no	—
239	C₄⋊C₄×D₇₃	—	2	2	no	—
240	C₄⋊C₄×D₇₃	—	2	2	no	—
241	C₄⋊C₄×D₇₃	—	2	2	no	—
242	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
243	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₂²⋊C₄×D₇₃	—	2	2	no	—
246	C₂²⋊C₄×D₇₃	—	2	2	no	—
247	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
248	C₄²×D₇₃	—	2	2	no	—
249	C₄²×D₇₃	C₂³	1	1	yes	characteristic
250	C₄²×D₇₃	C₂³	1	1	yes	characteristic
251	C₄⋊#10596831	C₂³	1	2	yes	complemented
252	#14556520	C₂³	1	2	yes	complemented
253	#14556520	C₂³	1	2	yes	complemented
254	#14556516	C₂³	1	2	yes	complemented
255	#14556515	C₂³	1	2	yes	complemented
256	#14556514	C₂³	1	2	yes	complemented
257	#14556513	C₂³	1	2	yes	—
258	#14556513	C₂³	1	2	yes	—
259	#14556513	C₂³	1	2	yes	complemented
260	#14556512	C₂³	1	2	yes	—
261	#14556512	C₂³	1	2	yes	—
262	#14556512	C₂³	1	2	yes	complemented
263	#14556511	C₂³	1	2	yes	—
264	#14556511	C₂³	1	2	yes	—
265	#14556511	C₂³	1	2	yes	complemented
266	C₂²⋊#10596831	C₂³	1	2	yes	—
267	#14556503	C₂³	1	2	yes	—
268	#14556503	C₂³	1	2	yes	—
269	#14556502	C₂³	1	1	yes	characteristic, complemented
270	#14556501	C₂³	1	2	yes	complemented
271	C₄×#10596831	C₂³	1	1	yes	characteristic, complemented
272	C₈×Dic₇₃	C₂³	1	2	yes	complemented
273	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
274	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	complemented
276	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
277	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
278	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	complemented
279	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic, complemented
280	#127×C₇₃	C₂³	1	1	yes	characteristic
281	#127×C₇₃	C₂³	1	1	yes	characteristic
282	#126×C₇₃	—	2	2	no	—
283	#125×C₇₃	—	2	2	no	—
284	#125×C₇₃	C₂³	1	1	yes	characteristic, complemented
285	#124×C₇₃	C₂³	1	1	yes	characteristic
286	#124×C₇₃	C₂³	1	1	yes	characteristic
287	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
288	#121×C₇₃	—	2	2	no	—
289	#120×C₇₃	—	2	2	no	—
290	C₄×Q₈×C₇₃	C₂³	1	2	yes	complemented
291	#117×C₇₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₇₃	C₂³	1	2	yes	complemented
293	#103×C₇₃	C₂³	1	2	yes	complemented
294	#102×C₇₃	C₂³	1	2	yes	—
295	#102×C₇₃	C₂³	1	2	yes	—
296	#102×C₇₃	C₂³	1	2	yes	complemented
297	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
298	#97×C₇₃	C₂³	1	1	yes	characteristic, complemented
299	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic, complemented
300	C₂³×D₇₃	—	2	1	no	—
301	C₂³×D₇₃	—	2	1	no	—
302	C₂³×D₇₃	—	2	1	no	—
303	C₂³×D₇₃	—	2	1	no	—
304	C₂³×D₇₃	—	2	1	no	—
305	C₂³×D₇₃	—	2	1	no	—
306	C₂³×D₇₃	—	4	4	no	—
307	C₂³×D₇₃	—	8	4	no	—
308	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
309	#11924029	—	4	2	no	—
310	#11924028	—	4	2	no	—
311	#11924028	—	4	4	no	—
312	#11924027	—	4	2	no	—
313	#11924027	—	4	4	no	—
314	C₂×Dic₁₄₆	—	2	2	no	—
315	C₂×Dic₁₄₆	—	2	1	no	—
316	C₂×Dic₁₄₆	C₂⁴	1	1	yes	characteristic
317	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
318	Q₈×D₇₃	—	2	4	no	—
319	Q₈×D₇₃	—	2	4	no	—
320	Q₈×D₇₃	—	2	4	no	—
321	C₂×D₂₉₂	—	2	1	no	—
322	C₂×D₂₉₂	—	2	1	no	—
323	C₂×D₂₉₂	—	2	2	no	—
324	C₂×D₂₉₂	—	2	2	no	—
325	C₂×D₂₉₂	—	4	2	no	—
326	C₂×D₂₉₂	C₂⁴	1	1	yes	characteristic
327	C₂×D₂₉₂	C₂⁴	1	1	yes	characteristic
328	C₂×D₂₉₂	C₂⁴	1	1	yes	characteristic
329	C₂×C₂²⋊D₇₃	—	2	1	no	—
330	C₂×C₂²⋊D₇₃	—	2	1	no	—
331	C₂×C₂²⋊D₇₃	—	2	1	no	—
332	C₂×C₂²⋊D₇₃	—	2	1	no	—
333	C₂×C₂²⋊D₇₃	—	2	1	no	—
334	C₂×C₂²⋊D₇₃	—	2	1	no	—
335	C₂×C₂²⋊D₇₃	—	2	1	no	—
336	C₂×C₂²⋊D₇₃	—	2	2	no	—
337	C₂×C₂²⋊D₇₃	—	2	2	no	—
338	C₂×C₂²⋊D₇₃	—	2	2	no	—
339	C₂×C₂²⋊D₇₃	—	2	2	no	—
340	C₂×C₂²⋊D₇₃	—	4	4	no	—
341	D₄×D₇₃	—	2	4	no	—
342	D₄×D₇₃	—	2	4	no	—
343	D₄×D₇₃	—	2	4	no	—
344	D₄×D₇₃	—	4	2	no	—
345	D₄×D₇₃	—	4	2	no	—
346	D₄×D₇₃	—	4	4	no	—
347	D₄×D₇₃	—	4	4	no	—
348	D₄×D₇₃	—	4	4	no	—
349	D₄×D₇₃	—	8	4	no	—
350	D₄×D₇₃	—	8	4	no	—
351	C₂²×Dic₇₃	—	2	1	no	—
352	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
353	C₂×C₄×D₇₃	—	2	4	no	—
354	C₂×C₄×D₇₃	—	2	2	no	—
355	C₂×C₄×D₇₃	—	2	2	no	—
356	C₂×C₄×D₇₃	—	2	1	no	—
357	C₂×C₄×D₇₃	—	2	1	no	—
358	C₂×C₄×D₇₃	—	2	1	no	—
359	C₂×C₄×D₇₃	—	4	4	no	—
360	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
361	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
362	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
363	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
364	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
366	Dic₂₉₂	—	4	2	no	—
367	#11924018	—	4	2	no	—
368	#11924018	—	4	2	no	—
369	#11924017	—	4	2	no	—
370	#11924017	—	4	2	no	—
371	#11924017	—	4	2	no	—
372	#11924016	—	4	2	no	—
373	#11924016	—	4	2	no	—
374	#11924016	—	4	2	no	—
375	#11924015	—	4	2	no	—
376	#11924015	—	4	2	no	—
377	#11924015	—	4	2	no	—
378	C₂×#10596831	C₂⁴	1	2	yes	—
379	C₂×#10596831	C₂⁴	1	2	yes	—
380	C₈×D₇₃	—	2	4	no	—
381	C₈×D₇₃	—	2	4	no	—
382	C₄⋊Dic₇₃	—	2	2	no	—
383	C₄⋊Dic₇₃	—	2	2	no	—
384	C₄⋊Dic₇₃	—	2	2	no	—
385	C₄⋊Dic₇₃	—	2	2	no	—
386	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
387	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
388	#11924007	—	2	2	no	—
389	#11924007	—	2	2	no	—
390	#11924007	—	2	2	no	—
391	#11924007	—	2	2	no	—
392	#11924007	—	2	2	no	—
393	#11924007	—	2	2	no	—
394	#11924007	—	2	2	no	—
395	#11924007	—	2	2	no	—
396	#11924007	—	2	2	no	—
397	#11924007	C₂×D₄	1	2	yes	—
398	#11924007	C₂×D₄	1	2	yes	—
399	C₂²⋊Dic₇₃	—	2	2	no	—
400	C₂²⋊Dic₇₃	—	2	2	no	—
401	C₂²⋊Dic₇₃	—	2	2	no	—
402	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
403	#11924005	—	2	2	no	—
404	#11924005	—	2	2	no	—
405	#11924005	—	2	2	no	—
406	#11924005	—	2	2	no	—
407	#11924005	—	2	2	no	—
408	#11924005	—	2	2	no	—
409	#11924005	C₂×D₄	1	2	yes	—
410	#11924005	C₂×D₄	1	2	yes	—
411	C₄×Dic₇₃	—	2	2	no	—
412	C₄×Dic₇₃	—	2	2	no	—
413	C₄×Dic₇₃	—	2	2	no	—
414	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
415	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
416	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
418	C₂⁴×C₇₃	—	2	1	no	—
419	#41×C₇₃	—	4	2	no	—
420	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
422	C₂×D₄×C₇₃	—	2	1	no	—
423	C₂×D₄×C₇₃	—	2	1	no	—
424	C₂×D₄×C₇₃	—	2	2	no	—
425	C₂×D₄×C₇₃	—	2	2	no	—
426	C₂×D₄×C₇₃	—	4	2	no	—
427	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
429	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₇₃	—	2	1	no	—
431	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
432	Q₁₆×C₇₃	—	4	2	no	—
433	SD₁₆×C₇₃	—	4	2	no	—
434	SD₁₆×C₇₃	—	4	2	no	—
435	SD₁₆×C₇₃	—	4	2	no	—
436	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
437	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₇₃	—	2	2	no	—
439	C₄⋊C₄×C₇₃	—	2	2	no	—
440	C₄⋊C₄×C₇₃	—	2	2	no	—
441	C₄⋊C₄×C₇₃	—	2	2	no	—
442	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
443	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
444	C₂²⋊C₄×C₇₃	—	2	2	no	—
445	C₂²⋊C₄×C₇₃	—	2	2	no	—
446	C₂²⋊C₄×C₇₃	—	2	2	no	—
447	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
448	C₄²×C₇₃	—	2	2	no	—
449	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
450	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
451	C₂³×C₇₃	—	2	1	no	—
452	C₂³×C₇₃	—	2	1	no	—
453	C₂³×C₇₃	—	2	1	no	—
454	C₂³×C₇₃	—	4	2	no	—
455	C₂³×C₇₃	—	8	2	no	—
456	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
457	C₂²×D₇₃	—	2	2	no	—
458	C₂²×D₇₃	—	2	4	no	—
459	C₂²×D₇₃	—	2	1	no	—
460	C₂²×D₇₃	—	2	1	no	—
461	C₂²×D₇₃	—	2	1	no	—
462	C₂²×D₇₃	—	4	2	no	—
463	C₂²×D₇₃	—	4	2	no	—
464	C₂²×D₇₃	—	4	2	no	—
465	C₂²×D₇₃	—	4	2	no	—
466	C₂²×D₇₃	—	4	2	no	—
467	C₂²×D₇₃	—	4	2	no	—
468	C₂²×D₇₃	—	4	4	no	—
469	C₂²×D₇₃	—	4	4	no	—
470	C₂²×D₇₃	—	4	4	no	—
471	C₂²×D₇₃	—	8	2	no	—
472	C₂²×D₇₃	—	8	2	no	—
473	C₂²×D₇₃	—	8	2	no	—
474	C₂²×D₇₃	—	8	16	no	—
475	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
476	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
477	Q₈×C₇₃	—	2	2	no	—
478	Q₈×C₇₃	—	2	2	no	—
479	Q₈×C₇₃	—	2	2	no	—
480	D₄×C₇₃	—	2	2	no	—
481	D₄×C₇₃	—	2	2	no	—
482	D₄×C₇₃	—	2	2	no	—
483	D₄×C₇₃	—	4	2	no	—
484	D₄×C₇₃	—	4	2	no	—
485	D₄×C₇₃	—	8	2	no	—
486	D₄×C₇₃	—	8	2	no	—
487	C₂×C₄×C₇₃	—	2	2	no	—
488	C₂×C₄×C₇₃	—	2	2	no	—
489	C₂×C₄×C₇₃	—	2	2	no	—
490	C₂×C₄×C₇₃	—	2	1	no	—
491	C₂×C₄×C₇₃	—	4	2	no	—
492	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
496	C₂²⋊D₇₃	—	4	2	no	—
497	C₂²⋊D₇₃	—	4	2	no	—
498	C₂²⋊D₇₃	—	4	2	no	—
499	C₂²⋊D₇₃	—	4	2	no	—
500	C₂²⋊D₇₃	—	4	2	no	—
501	C₂²⋊D₇₃	—	4	2	no	—
502	C₂²⋊D₇₃	—	4	2	no	—
503	C₂²⋊D₇₃	—	8	2	no	—
504	C₂²⋊D₇₃	—	8	2	no	—
505	C₂²⋊D₇₃	—	8	2	no	—
506	C₂²⋊D₇₃	—	8	2	no	—
507	C₂×Dic₇₃	—	2	2	no	—
508	C₂×Dic₇₃	—	2	2	no	—
509	C₂×Dic₇₃	—	2	2	no	—
510	C₂×Dic₇₃	—	2	1	no	—
511	C₂×Dic₇₃	—	4	2	no	—
512	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
513	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
514	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
516	D₂₉₂	—	2	2	no	—
517	D₂₉₂	—	2	2	no	—
518	D₂₉₂	—	2	2	no	—
519	D₂₉₂	—	4	2	no	—
520	D₂₉₂	—	4	2	no	—
521	D₂₉₂	—	8	2	no	—
522	D₂₉₂	—	8	2	no	—
523	C₄×D₇₃	—	2	2	no	—
524	C₄×D₇₃	—	2	4	no	—
525	C₄×D₇₃	—	2	4	no	—
526	C₄×D₇₃	—	2	2	no	—
527	C₄×D₇₃	—	2	2	no	—
528	C₄×D₇₃	—	4	2	no	—
529	C₄×D₇₃	—	4	2	no	—
530	C₄×D₇₃	—	4	2	no	—
531	C₄×D₇₃	—	4	4	no	—
532	C₄×D₇₃	—	4	4	no	—
533	C₄×D₇₃	H(5,𝔽₂)	1	4	yes	—
534	Dic₁₄₆	—	2	2	no	—
535	Dic₁₄₆	—	2	2	no	—
536	Dic₁₄₆	—	2	2	no	—
537	Dic₁₄₆	—	4	4	no	—
538	Dic₁₄₆	—	4	2	no	—
539	C₈×C₇₃	—	2	2	no	—
540	C₈×C₇₃	—	2	2	no	—
541	#10596831	—	2	2	no	—
542	#10596831	—	2	2	no	—
543	C₂²×C₇₃	—	2	1	no	—
544	C₂²×C₇₃	—	2	2	no	—
545	C₂²×C₇₃	—	4	1	no	—
546	C₂²×C₇₃	—	4	1	no	—
547	C₂²×C₇₃	—	4	1	no	—
548	C₂²×C₇₃	—	4	2	no	—
549	C₂²×C₇₃	—	4	2	no	—
550	C₂²×C₇₃	—	4	2	no	—
551	C₂²×C₇₃	—	8	4	no	—
552	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
553	C₂×D₇₃	—	2	1	no	—
554	C₂×D₇₃	—	2	2	no	—
555	C₂×D₇₃	—	4	4	no	—
556	C₂×D₇₃	—	4	1	no	—
557	C₂×D₇₃	—	4	1	no	—
558	C₂×D₇₃	—	4	1	no	—
559	C₂×D₇₃	—	4	2	no	—
560	C₂×D₇₃	—	4	2	no	—
561	C₂×D₇₃	—	4	2	no	—
562	C₂×D₇₃	—	8	4	no	—
563	C₂×D₇₃	—	8	4	no	—
564	C₂×D₇₃	—	8	4	no	—
565	C₂×D₇₃	—	8	4	no	—
566	C₂×D₇₃	—	8	4	no	—
567	C₂×D₇₃	—	8	4	no	—
568	C₂×D₇₃	#535	1	2	yes	—
569	C₂×D₇₃	#577	1	4	yes	—
570	C₄×C₇₃	—	2	1	no	—
571	C₄×C₇₃	—	2	2	no	—
572	C₄×C₇₃	—	2	2	no	—
573	C₄×C₇₃	—	4	1	no	—
574	C₄×C₇₃	—	4	2	no	—
575	C₄×C₇₃	—	4	2	no	—
576	C₄×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
577	Dic₇₃	—	2	1	no	—
578	Dic₇₃	—	2	2	no	—
579	Dic₇₃	—	2	2	no	—
580	Dic₇₃	—	4	1	no	—
581	Dic₇₃	—	4	2	no	—
582	Dic₇₃	—	4	2	no	—
583	Dic₇₃	#535	1	2	yes	—
584	C₂×#3222	—	73	1	no	maximal, Sylow
585	C₂×C₇₃	—	4	1	no	—
586	C₂×C₇₃	—	8	1	no	—
587	C₂×C₇₃	—	8	1	no	—
588	C₂×C₇₃	—	8	1	no	—
589	C₂×C₇₃	C₂×#535	1	1	yes	characteristic
590	C₂×C₇₃	C₂×#577	1	2	yes	—
591	D₇₃	—	4	1	no	—
592	D₇₃	—	8	1	no	—
593	D₇₃	—	8	1	no	—
594	D₇₃	—	8	1	no	—
595	D₇₃	#3222	1	4	yes	direct product factor
596	C₂×#541	—	73	1	no	—
597	C₂×#535	—	73	1	no	—
598	#3222	—	73	1	no	—
599	#3222	—	73	1	no	—
600	#3222	—	73	1	no	—
601	#3222	—	73	1	no	—
602	#3222	—	73	2	no	—
603	#3222	—	73	2	no	—
604	#3222	—	73	2	no	—
605	#3222	—	73	2	no	—
606	#3222	—	73	1	no	—
607	#3222	—	73	1	no	—
608	#3222	—	73	1	no	—
609	#3222	D₇₃	1	1	yes	characteristic, direct product factor
610	C₂×#497	—	73	1	no	—
611	C₂×#492	—	73	1	no	—
612	C₂×#490	—	73	1	no	—
613	C₂×#488	—	73	1	no	—
614	C₂×#464	—	73	2	no	—
615	C₂×#460	—	73	2	no	—
616	C₂×#452	—	73	2	no	—
617	C₂×#450	—	73	2	no	—
618	C₂×#433	—	73	1	no	—
619	C₇₃	C₂×#3222	1	1	yes	characteristic, complemented, Sylow
620	C₂²×#41	—	73	1	no	—
621	C₂³×D₄	—	73	1	no	—
622	C₂²×Q₁₆	—	73	2	no	—
623	C₂²×SD₁₆	—	73	2	no	—
624	C₂²×SD₁₆	—	73	2	no	—
625	C₂²×SD₁₆	—	73	2	no	—
626	#541	—	73	1	no	—
627	#541	—	73	1	no	—
628	#541	—	73	2	no	—
629	#541	—	73	2	no	—
630	#541	—	73	1	no	—
631	#541	—	146	2	no	—
632	#541	—	146	2	no	—
633	#541	C₂×D₇₃	1	1	yes	characteristic, complemented
634	#535	—	73	1	no	—
635	#535	—	73	1	no	—
636	#535	—	73	1	no	—
637	#535	—	73	1	no	—
638	#535	—	73	1	no	—
639	#535	—	73	1	no	—
640	#535	—	73	1	no	—
641	#535	—	146	2	no	—
642	#535	—	146	2	no	—
643	#535	C₂×D₇₃	1	1	yes	characteristic
644	C₂×C₄⋊Q₈	—	73	1	no	—
645	C₂×#127	—	73	1	no	—
646	C₂×#127	—	73	1	no	—
647	C₂×#126	—	146	2	no	—
648	C₂×#125	—	73	1	no	—
649	C₂×#125	—	146	2	no	—
650	C₂×#124	—	73	1	no	—
651	C₂×#124	—	73	1	no	—
652	C₂×C₂²⋊Q₈	—	73	2	no	—
653	C₂×#121	—	146	2	no	—
654	C₂×#120	—	146	2	no	—
655	C₂×C₄×Q₈	—	73	2	no	—
656	C₂×#117	—	73	1	no	—
657	#497	—	73	2	no	—
658	#497	—	73	2	no	—
659	#497	—	73	1	no	—
660	#497	—	73	1	no	—
661	#497	—	73	1	no	—
662	#497	C₂×D₇₃	1	1	yes	characteristic, complemented
663	#492	—	73	2	no	—
664	#492	—	73	2	no	—
665	#492	—	73	1	no	—
666	#492	—	73	1	no	—
667	#492	—	73	1	no	—
668	#492	C₂×D₇₃	1	1	yes	characteristic, complemented
669	#490	—	73	1	no	—
670	#490	—	73	1	no	—
671	#490	—	73	2	no	—
672	#490	—	73	2	no	—
673	#490	—	73	1	no	—
674	#490	C₂×D₇₃	1	1	yes	characteristic, complemented
675	#488	—	73	1	no	—
676	#488	—	73	1	no	—
677	#488	—	73	2	no	—
678	#488	—	73	2	no	—
679	#488	—	73	1	no	—
680	#488	C₂×D₇₃	1	1	yes	characteristic, complemented
681	#464	—	73	2	no	—
682	#464	—	73	2	no	—
683	#464	—	73	2	no	—
684	#464	—	73	2	no	—
685	#464	—	73	2	no	—
686	#464	—	73	2	no	—
687	#464	—	73	2	no	—
688	#464	C₂×D₇₃	1	2	yes	complemented
689	#460	—	73	2	no	—
690	#460	—	73	2	no	—
691	#460	—	73	2	no	—
692	#460	—	73	2	no	—
693	#460	—	73	2	no	—
694	#460	—	73	2	no	—
695	#460	—	73	2	no	—
696	#460	C₂×D₇₃	1	2	yes	complemented
697	#452	—	73	2	no	—
698	#452	—	73	2	no	—
699	#452	—	73	2	no	—
700	#452	—	73	2	no	—
701	#452	—	73	2	no	—
702	#452	—	73	2	no	—
703	#452	—	73	2	no	—
704	#452	C₂×D₇₃	1	2	yes	complemented
705	#450	—	73	2	no	—
706	#450	—	73	2	no	—
707	#450	—	73	2	no	—
708	#450	—	73	2	no	—
709	#450	—	73	2	no	—
710	#450	—	73	2	no	—
711	#450	—	73	2	no	—
712	#450	C₂×D₇₃	1	2	yes	complemented
713	#433	—	73	1	no	—
714	#433	—	73	2	no	—
715	#433	—	73	2	no	—
716	#433	—	73	1	no	—
717	#433	—	73	1	no	—
718	#433	C₂×D₇₃	1	1	yes	characteristic, complemented
719	C₂×C₄⋊C₈	—	73	2	no	—
720	C₂×#103	—	73	2	no	—
721	C₂×#102	—	73	2	no	—
722	C₂×#102	—	73	2	no	—
723	C₂×#102	—	73	2	no	—
724	C₂×C₂²⋊C₈	—	73	2	no	—
725	C₂×#97	—	73	1	no	—
726	C₂×C₄×C₈	—	73	1	no	—
727	C₂⁵	—	146	1	no	—
728	C₂×#41	—	292	4	no	—
729	C₂×#41	—	73	1	no	—
730	C₂×#41	—	73	1	no	—
731	C₂×#41	—	73	1	no	—
732	C₂×#41	—	146	1	no	—
733	C₂×#41	—	146	1	no	—
734	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
735	C₂²×Q₈	—	73	2	no	—
736	C₂²×Q₈	—	73	1	no	—
737	C₂²×D₄	—	292	4	no	—
738	C₂²×D₄	—	73	1	no	—
739	C₂²×D₄	—	73	1	no	—
740	C₂²×D₄	—	73	1	no	—
741	C₂²×D₄	—	73	1	no	—
742	C₂²×D₄	—	73	1	no	—
743	C₂²×D₄	—	73	1	no	—
744	C₂²×D₄	—	146	1	no	—
745	C₂²×D₄	—	146	1	no	—
746	C₂²×D₄	—	146	2	no	—
747	C₂²×D₄	—	146	2	no	—
748	C₂²×D₄	—	146	1	no	—
749	C₂²×D₄	—	146	1	no	—
750	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
751	C₂³×C₄	—	73	1	no	—
752	C₂³×C₄	—	146	1	no	—
753	C₂×Q₁₆	—	292	4	no	—
754	C₂×Q₁₆	—	73	2	no	—
755	C₂×Q₁₆	—	73	2	no	—
756	C₂×Q₁₆	—	73	2	no	—
757	C₂×Q₁₆	C₂²×D₇₃	1	2	yes	complemented
758	C₂×SD₁₆	—	292	4	no	—
759	C₂×SD₁₆	—	292	4	no	—
760	C₂×SD₁₆	—	292	4	no	—
761	C₂×SD₁₆	—	73	2	no	—
762	C₂×SD₁₆	—	73	2	no	—
763	C₂×SD₁₆	—	73	2	no	—
764	C₂×SD₁₆	—	73	2	no	—
765	C₂×SD₁₆	—	73	2	no	—
766	C₂×SD₁₆	—	73	2	no	—
767	C₂×SD₁₆	—	73	2	no	—
768	C₂×SD₁₆	—	73	2	no	—
769	C₂×SD₁₆	—	73	2	no	—
770	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
771	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
772	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	complemented
773	C₂²×C₈	—	73	2	no	—
774	C₂²×C₈	—	73	2	no	—
775	C₄⋊Q₈	—	73	2	no	—
776	C₄⋊Q₈	—	73	1	no	—
777	C₄⋊Q₈	—	146	2	no	—
778	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic, complemented
779	#127	—	73	1	no	—
780	#127	—	73	1	no	—
781	#127	—	73	1	no	—
782	#127	—	73	1	no	—
783	#127	—	73	1	no	—
784	#127	—	73	1	no	—
785	#127	—	146	2	no	—
786	#127	—	146	2	no	—
787	#127	C₂²×D₇₃	1	1	yes	characteristic
788	#127	C₂²×D₇₃	1	1	yes	characteristic
789	#126	—	2	2	no	—
790	#126	—	146	2	no	—
791	#126	—	146	2	no	—
792	#126	—	146	2	no	—
793	#126	—	146	2	no	—
794	#126	—	146	2	no	—
795	#126	—	146	2	no	—
796	#126	—	146	2	no	—
797	#125	—	2	2	no	—
798	#125	—	73	2	no	—
799	#125	—	73	1	no	—
800	#125	—	146	2	no	—
801	#125	—	146	2	no	—
802	#125	—	146	2	no	—
803	#125	—	146	2	no	—
804	#125	—	146	2	no	—
805	#125	—	146	2	no	—
806	#125	—	146	2	no	—
807	#125	—	146	2	no	—
808	#125	C₂²×D₇₃	1	1	yes	characteristic, complemented
809	#124	—	73	1	no	—
810	#124	—	73	1	no	—
811	#124	—	73	1	no	—
812	#124	—	73	1	no	—
813	#124	—	73	1	no	—
814	#124	—	73	1	no	—
815	#124	—	146	2	no	—
816	#124	—	146	2	no	—
817	#124	C₂²×D₇₃	1	1	yes	characteristic
818	#124	C₂²×D₇₃	1	1	yes	characteristic
819	C₂²⋊Q₈	—	73	2	no	—
820	C₂²⋊Q₈	—	73	2	no	—
821	C₂²⋊Q₈	—	73	2	no	—
822	C₂²⋊Q₈	—	146	2	no	—
823	C₂²⋊Q₈	—	146	2	no	—
824	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
825	#121	—	2	2	no	—
826	#121	—	146	2	no	—
827	#121	—	146	2	no	—
828	#121	—	146	2	no	—
829	#121	—	146	2	no	—
830	#121	—	146	2	no	—
831	#121	—	146	2	no	—
832	#121	—	146	2	no	—
833	#120	—	2	2	no	—
834	#120	—	146	2	no	—
835	#120	—	146	2	no	—
836	#120	—	146	2	no	—
837	#120	—	146	2	no	—
838	#120	—	146	2	no	—
839	#120	—	146	2	no	—
840	#120	—	146	2	no	—
841	C₄×Q₈	—	73	2	no	—
842	C₄×Q₈	—	73	2	no	—
843	C₄×Q₈	—	73	2	no	—
844	C₄×Q₈	—	146	2	no	—
845	C₄×Q₈	—	146	2	no	—
846	C₄×Q₈	C₂²×D₇₃	1	2	yes	complemented
847	#117	—	73	1	no	—
848	#117	—	73	2	no	—
849	#117	—	73	2	no	—
850	#117	—	73	1	no	—
851	#117	—	73	1	no	—
852	#117	C₂²×D₇₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	—	73	2	no	—
854	C₂×C₄⋊C₄	—	73	2	no	—
855	C₂×C₄⋊C₄	—	146	2	no	—
856	C₂×C₄⋊C₄	—	146	2	no	—
857	C₂×C₄⋊C₄	—	146	2	no	—
858	C₂×C₄⋊C₄	—	146	2	no	—
859	C₂×C₂²⋊C₄	—	73	2	no	—
860	C₂×C₂²⋊C₄	—	146	2	no	—
861	C₂×C₂²⋊C₄	—	146	2	no	—
862	C₂×C₂²⋊C₄	—	146	2	no	—
863	C₂×C₄²	—	73	1	no	—
864	C₂×C₄²	—	73	1	no	—
865	C₂×C₄²	—	146	2	no	—
866	C₄⋊C₈	—	73	2	no	—
867	C₄⋊C₈	—	73	2	no	—
868	C₄⋊C₈	—	73	2	no	—
869	C₄⋊C₈	C₂²×D₇₃	1	2	yes	complemented
870	#103	—	73	2	no	—
871	#103	—	73	2	no	—
872	#103	—	73	2	no	—
873	#103	C₂²×D₇₃	1	2	yes	complemented
874	#102	—	73	2	no	—
875	#102	—	73	2	no	—
876	#102	—	73	2	no	—
877	#102	—	73	2	no	—
878	#102	—	73	2	no	—
879	#102	—	73	2	no	—
880	#102	—	73	2	no	—
881	#102	—	73	2	no	—
882	#102	—	73	2	no	—
883	#102	C₂²×D₇₃	1	2	yes	—
884	#102	C₂²×D₇₃	1	2	yes	—
885	#102	C₂²×D₇₃	1	2	yes	complemented
886	C₂²⋊C₈	—	73	2	no	—
887	C₂²⋊C₈	—	73	2	no	—
888	C₂²⋊C₈	—	73	2	no	—
889	C₂²⋊C₈	C₂²×D₇₃	1	2	yes	—
890	#97	—	73	2	no	—
891	#97	—	73	1	no	—
892	#97	C₂²×D₇₃	1	1	yes	characteristic, complemented
893	C₄×C₈	—	73	2	no	—
894	C₄×C₈	—	73	1	no	—
895	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic, complemented
896	C₂⁴	—	2	1	no	—
897	C₂⁴	—	292	4	no	—
898	C₂⁴	—	584	4	no	—
899	C₂⁴	—	73	1	no	—
900	C₂⁴	—	146	1	no	—
901	C₂⁴	—	146	1	no	—
902	C₂⁴	—	146	1	no	—
903	C₂⁴	—	146	1	no	—
904	C₂⁴	—	146	1	no	—
905	C₂⁴	—	146	1	no	—
906	#41	—	4	2	no	—
907	#41	—	292	2	no	—
908	#41	—	292	4	no	—
909	#41	—	292	2	no	—
910	#41	—	292	4	no	—
911	#41	—	292	2	no	—
912	C₂×Q₈	—	73	1	no	—
913	C₂×Q₈	—	73	2	no	—
914	C₂×Q₈	—	146	2	no	—
915	C₂×Q₈	—	146	1	no	—
916	C₂×Q₈	—	146	4	no	—
917	C₂×Q₈	—	146	4	no	—
918	C₂×Q₈	—	146	4	no	—
919	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
920	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	292	2	no	—
927	C₂×D₄	—	292	4	no	—
928	C₂×D₄	—	292	2	no	—
929	C₂×D₄	—	292	2	no	—
930	C₂×D₄	—	292	4	no	—
931	C₂×D₄	—	292	4	no	—
932	C₂×D₄	—	292	4	no	—
933	C₂×D₄	—	584	4	no	—
934	C₂×D₄	—	584	4	no	—
935	C₂×D₄	—	73	1	no	—
936	C₂×D₄	—	73	1	no	—
937	C₂×D₄	—	73	1	no	—
938	C₂×D₄	—	146	1	no	—
939	C₂×D₄	—	146	4	no	—
940	C₂×D₄	—	146	4	no	—
941	C₂×D₄	—	146	4	no	—
942	C₂×D₄	—	146	1	no	—
943	C₂×D₄	—	146	1	no	—
944	C₂×D₄	—	146	1	no	—
945	C₂×D₄	—	146	1	no	—
946	C₂×D₄	—	146	1	no	—
947	C₂×D₄	—	146	2	no	—
948	C₂×D₄	—	146	2	no	—
949	C₂×D₄	—	146	2	no	—
950	C₂×D₄	—	146	2	no	—
951	C₂×D₄	—	146	1	no	—
952	C₂×D₄	—	146	1	no	—
953	C₂×D₄	—	146	1	no	—
954	C₂×D₄	—	146	2	no	—
955	C₂×D₄	—	146	2	no	—
956	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
957	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
958	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	292	4	no	—
961	C₂²×C₄	—	73	1	no	—
962	C₂²×C₄	—	73	1	no	—
963	C₂²×C₄	—	73	2	no	—
964	C₂²×C₄	—	73	2	no	—
965	C₂²×C₄	—	73	1	no	—
966	C₂²×C₄	—	73	1	no	—
967	C₂²×C₄	—	73	1	no	—
968	C₂²×C₄	—	146	1	no	—
969	C₂²×C₄	—	146	2	no	—
970	C₂²×C₄	—	146	2	no	—
971	C₂²×C₄	—	146	1	no	—
972	C₂²×C₄	—	146	4	no	—
973	C₂²×C₄	—	146	1	no	—
974	C₂²×C₄	—	146	1	no	—
975	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
976	Q₁₆	—	4	2	no	—
977	Q₁₆	—	292	2	no	—
978	Q₁₆	—	292	2	no	—
979	Q₁₆	—	292	2	no	—
980	SD₁₆	—	4	2	no	—
981	SD₁₆	—	4	2	no	—
982	SD₁₆	—	4	2	no	—
983	SD₁₆	—	292	2	no	—
984	SD₁₆	—	292	2	no	—
985	SD₁₆	—	292	2	no	—
986	SD₁₆	—	292	2	no	—
987	SD₁₆	—	292	2	no	—
988	SD₁₆	—	292	2	no	—
989	SD₁₆	—	292	2	no	—
990	SD₁₆	—	292	2	no	—
991	SD₁₆	—	292	2	no	—
992	C₂×C₈	—	73	2	no	—
993	C₂×C₈	—	73	2	no	—
994	C₂×C₈	—	146	4	no	—
995	C₂×C₈	—	146	4	no	—
996	C₂×C₈	C₂³×D₇₃	1	2	yes	—
997	C₂×C₈	C₂³×D₇₃	1	2	yes	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	73	2	no	—
1003	C₄⋊C₄	—	73	2	no	—
1004	C₄⋊C₄	—	73	2	no	—
1005	C₄⋊C₄	—	73	2	no	—
1006	C₄⋊C₄	—	146	2	no	—
1007	C₄⋊C₄	—	146	2	no	—
1008	C₄⋊C₄	—	146	2	no	—
1009	C₄⋊C₄	—	146	2	no	—
1010	C₄⋊C₄	—	146	2	no	—
1011	C₄⋊C₄	—	146	2	no	—
1012	C₄⋊C₄	—	146	2	no	—
1013	C₄⋊C₄	—	146	2	no	—
1014	C₄⋊C₄	—	146	2	no	—
1015	C₄⋊C₄	—	146	2	no	—
1016	C₄⋊C₄	—	146	2	no	—
1017	C₄⋊C₄	—	146	2	no	—
1018	C₄⋊C₄	—	146	2	no	—
1019	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
1020	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	73	2	no	—
1025	C₂²⋊C₄	—	73	2	no	—
1026	C₂²⋊C₄	—	73	2	no	—
1027	C₂²⋊C₄	—	146	2	no	—
1028	C₂²⋊C₄	—	146	2	no	—
1029	C₂²⋊C₄	—	146	2	no	—
1030	C₂²⋊C₄	—	146	2	no	—
1031	C₂²⋊C₄	—	146	2	no	—
1032	C₂²⋊C₄	—	146	2	no	—
1033	C₂²⋊C₄	—	146	2	no	—
1034	C₂²⋊C₄	—	146	2	no	—
1035	C₂²⋊C₄	—	146	2	no	—
1036	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	73	2	no	—
1039	C₄²	—	73	2	no	—
1040	C₄²	—	73	1	no	—
1041	C₄²	—	73	1	no	—
1042	C₄²	—	146	2	no	—
1043	C₄²	—	146	2	no	—
1044	C₄²	—	146	2	no	—
1045	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1046	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	292	2	no	—
1053	C₂³	—	292	2	no	—
1054	C₂³	—	292	2	no	—
1055	C₂³	—	292	2	no	—
1056	C₂³	—	292	4	no	—
1057	C₂³	—	292	4	no	—
1058	C₂³	—	292	4	no	—
1059	C₂³	—	292	2	no	—
1060	C₂³	—	292	2	no	—
1061	C₂³	—	584	2	no	—
1062	C₂³	—	584	2	no	—
1063	C₂³	—	584	2	no	—
1064	C₂³	—	584	16	no	—
1065	C₂³	—	73	1	no	—
1066	C₂³	—	73	1	no	—
1067	C₂³	—	146	2	no	—
1068	C₂³	—	146	4	no	—
1069	C₂³	—	146	1	no	—
1070	C₂³	—	146	1	no	—
1071	C₂³	—	146	1	no	—
1072	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	292	2	no	—
1077	Q₈	—	292	4	no	—
1078	Q₈	—	146	2	no	—
1079	Q₈	—	146	2	no	—
1080	Q₈	—	146	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	292	2	no	—
1089	D₄	—	292	2	no	—
1090	D₄	—	292	2	no	—
1091	D₄	—	292	2	no	—
1092	D₄	—	292	2	no	—
1093	D₄	—	292	2	no	—
1094	D₄	—	292	2	no	—
1095	D₄	—	292	2	no	—
1096	D₄	—	292	2	no	—
1097	D₄	—	584	2	no	—
1098	D₄	—	584	2	no	—
1099	D₄	—	584	2	no	—
1100	D₄	—	584	2	no	—
1101	D₄	—	584	2	no	—
1102	D₄	—	584	2	no	—
1103	D₄	—	146	2	no	—
1104	D₄	—	146	2	no	—
1105	D₄	—	146	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	292	2	no	—
1112	C₂×C₄	—	292	2	no	—
1113	C₂×C₄	—	292	4	no	—
1114	C₂×C₄	—	292	4	no	—
1115	C₂×C₄	—	292	2	no	—
1116	C₂×C₄	—	292	2	no	—
1117	C₂×C₄	—	73	1	no	—
1118	C₂×C₄	—	73	4	no	—
1119	C₂×C₄	—	73	2	no	—
1120	C₂×C₄	—	73	2	no	—
1121	C₂×C₄	—	73	1	no	—
1122	C₂×C₄	—	146	2	no	—
1123	C₂×C₄	—	146	2	no	—
1124	C₂×C₄	—	146	4	no	—
1125	C₂×C₄	—	146	4	no	—
1126	C₂×C₄	—	146	2	no	—
1127	C₂×C₄	—	146	2	no	—
1128	C₂×C₄	—	146	1	no	—
1129	C₂×C₄	—	146	2	no	—
1130	C₂×C₄	—	146	2	no	—
1131	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1132	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1133	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1134	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	146	2	no	—
1138	C₈	—	146	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	8	4	no	—
1148	C₂²	—	292	4	no	—
1149	C₂²	—	292	1	no	—
1150	C₂²	—	292	1	no	—
1151	C₂²	—	292	1	no	—
1152	C₂²	—	292	2	no	—
1153	C₂²	—	292	2	no	—
1154	C₂²	—	292	2	no	—
1155	C₂²	—	584	4	no	—
1156	C₂²	—	584	4	no	—
1157	C₂²	—	584	4	no	—
1158	C₂²	—	584	4	no	—
1159	C₂²	—	584	4	no	—
1160	C₂²	—	584	4	no	—
1161	C₂²	—	73	2	no	—
1162	C₂²	—	73	4	no	—
1163	C₂²	—	146	1	no	—
1164	C₂²	—	146	2	no	—
1165	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1166	C₄	—	2	1	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	292	1	no	—
1173	C₄	—	292	2	no	—
1174	C₄	—	292	2	no	—
1175	C₄	—	73	2	no	—
1176	C₄	—	146	1	no	—
1177	C₄	—	146	2	no	—
1178	C₄	—	146	2	no	—
1179	C₄	H(5,𝔽₂)×D₇₃	1	2	yes	—
1180	C₂	—	4	1	no	—
1181	C₂	—	8	1	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	1	no	—
1184	C₂	—	292	1	no	—
1185	C₂	—	584	1	no	—
1186	C₂	—	584	1	no	—
1187	C₂	—	584	1	no	—
1188	C₂	—	73	4	no	—
1189	C₂	#535×D₇₃	1	1	yes	characteristic
1190	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×#3222	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#535×D₇₃	C₂
hypercenter	#3222	D₇₃
hypocenter	C₇₃	C₂×#3222
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3222

Complements

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

N	H ≅ G/N	type
1. #541×D₇₃	C₂	semidirect
3. #22621006	C₂	semidirect
4. #22621005	C₂	semidirect
5. #22621004	C₂	semidirect
6. #22621003	C₂	semidirect
7. #22621002	C₂	semidirect
8. #22621001	C₂	semidirect
9. #22621000	C₂	semidirect
10. #22620999	C₂	semidirect
11. #22620998	C₂	semidirect
12. #22620997	C₂	semidirect
13. #22620996	C₂	semidirect
14. #497×D₇₃	C₂	semidirect
15. #492×D₇₃	C₂	semidirect
16. #490×D₇₃	C₂	semidirect
17. #488×D₇₃	C₂	semidirect
18. #464×D₇₃	C₂	semidirect
19. #460×D₇₃	C₂	semidirect
20. #452×D₇₃	C₂	semidirect
21. #450×D₇₃	C₂	semidirect
22. #433×D₇₃	C₂	semidirect
23. C₇₃×#3222	C₂	semidirect
26. C₂×Q₁₆×D₇₃	C₂²	semidirect
29. C₂×SD₁₆×D₇₃	C₂²	semidirect
30. #17989200	C₂²	semidirect
31. #17989199	C₂²	semidirect
32. #17989198	C₂²	semidirect
33. #17989197	C₂²	semidirect
35. #17989195	C₂²	semidirect
46. C₄⋊Q₈×D₇₃	C₂²	semidirect
51. #125×D₇₃	C₂²	semidirect
57. C₄×Q₈×D₇₃	C₂²	semidirect
59. #17988982	C₂²	semidirect
60. #17988981	C₂²	semidirect
61. #17988980	C₂²	semidirect
62. #17988979	C₂²	semidirect
63. #17988978	C₂²	semidirect
64. #17988961	C₂²	semidirect
65. #17988960	C₂²	semidirect
66. #17988959	C₂²	semidirect
67. #17988958	C₂²	semidirect
68. #17988958	C₂²	semidirect
69. #17988953	C₂²	semidirect
70. #17988952	C₂²	semidirect
71. #17988951	C₂²	semidirect
72. #17988950	C₂²	semidirect
73. #17988950	C₂²	semidirect
74. #17988944	C₂²	semidirect
75. #17988943	C₂²	semidirect
76. #17988942	C₂²	semidirect
77. #17988941	C₂²	semidirect
78. #17988940	C₂²	semidirect
79. #17988812	C₂²	semidirect
80. #17988811	C₂²	semidirect
81. #17988810	C₂²	semidirect
82. #17988809	C₂²	semidirect
83. #17988808	C₂²	semidirect
84. #17988807	C₂²	semidirect
85. #17988806	C₂²	semidirect
86. #17988788	C₂²	semidirect
87. #17988787	C₂²	semidirect
88. #17988786	C₂²	semidirect
89. #17988786	C₂²	semidirect
90. #17988785	C₂²	semidirect
91. #17988785	C₂²	semidirect
92. #17988784	C₂²	semidirect
93. #17988752	C₂²	semidirect
94. #17988751	C₂²	semidirect
95. #17988750	C₂²	semidirect
96. #17988749	C₂²	semidirect
97. #17988748	C₂²	semidirect
98. #17988747	C₂²	semidirect
99. #17988746	C₂²	semidirect
100. #17988740	C₂²	semidirect
101. #17988739	C₂²	semidirect
102. #17988739	C₂²	semidirect
103. #17988738	C₂²	semidirect
104. #17988737	C₂²	semidirect
105. #17988736	C₂²	semidirect
106. #17988736	C₂²	semidirect
107. #17988649	C₂²	semidirect
108. #17988648	C₂²	semidirect
109. #17988647	C₂²	semidirect
110. #17988646	C₂²	semidirect
111. #17988645	C₂²	semidirect
112. C₄⋊C₈×D₇₃	C₂²	semidirect
113. #103×D₇₃	C₂²	semidirect
116. #102×D₇₃	C₂²	semidirect
118. #97×D₇₃	C₂²	semidirect
119. C₄×C₈×D₇₃	C₂²	semidirect
120. #541×C₇₃	C₂²	semidirect
122. #497×C₇₃	C₂²	semidirect
123. #492×C₇₃	C₂²	semidirect
124. #490×C₇₃	C₂²	semidirect
125. #488×C₇₃	C₂²	semidirect
126. #464×C₇₃	C₂²	semidirect
127. #460×C₇₃	C₂²	semidirect
128. #452×C₇₃	C₂²	semidirect
129. #450×C₇₃	C₂²	semidirect
130. #433×C₇₃	C₂²	semidirect
155. C₂×Dic₂₉₂	C₂³	semidirect
156. C₂×#11924018	C₂³	semidirect
157. C₂×#11924018	C₂³	semidirect
161. C₂×#11924017	C₂³	semidirect
164. C₂×#11924016	C₂³	semidirect
167. C₂×#11924015	C₂³	semidirect
173. #14556591	C₂³	semidirect
175. #14556589	C₂³	semidirect
192. #14556583	C₂³	semidirect
195. #14556582	C₂³	semidirect
228. Q₈×Dic₇₃	C₂³	semidirect
230. C₄×Dic₁₄₆	C₂³	semidirect
232. #14556556	C₂³	semidirect
251. C₄⋊#10596831	C₂³	semidirect
252. #14556520	C₂³	semidirect
253. #14556520	C₂³	semidirect
254. #14556516	C₂³	semidirect
255. #14556515	C₂³	semidirect
256. #14556514	C₂³	semidirect
259. #14556513	C₂³	semidirect
262. #14556512	C₂³	semidirect
265. #14556511	C₂³	semidirect
269. #14556502	C₂³	semidirect
270. #14556501	C₂³	semidirect
271. C₄×#10596831	C₂³	semidirect
272. C₈×Dic₇₃	C₂³	semidirect
275. C₂×Q₁₆×C₇₃	C₂³	semidirect
278. C₂×SD₁₆×C₇₃	C₂³	semidirect
279. C₄⋊Q₈×C₇₃	C₂³	semidirect
284. #125×C₇₃	C₂³	semidirect
290. C₄×Q₈×C₇₃	C₂³	semidirect
292. C₄⋊C₈×C₇₃	C₂³	semidirect
293. #103×C₇₃	C₂³	semidirect
296. #102×C₇₃	C₂³	semidirect
298. #97×C₇₃	C₂³	semidirect
299. C₄×C₈×C₇₃	C₂³	semidirect
595. D₇₃	#3222	direct (N × H)
609. #3222	D₇₃	direct (N × H)
619. C₇₃	C₂×#3222	semidirect
633. #541	C₂×D₇₃	semidirect
662. #497	C₂×D₇₃	semidirect
668. #492	C₂×D₇₃	semidirect
674. #490	C₂×D₇₃	semidirect
680. #488	C₂×D₇₃	semidirect
688. #464	C₂×D₇₃	semidirect
696. #460	C₂×D₇₃	semidirect
704. #452	C₂×D₇₃	semidirect
712. #450	C₂×D₇₃	semidirect
718. #433	C₂×D₇₃	semidirect
757. C₂×Q₁₆	C₂²×D₇₃	semidirect
772. C₂×SD₁₆	C₂²×D₇₃	semidirect
778. C₄⋊Q₈	C₂²×D₇₃	semidirect
808. #125	C₂²×D₇₃	semidirect
846. C₄×Q₈	C₂²×D₇₃	semidirect
869. C₄⋊C₈	C₂²×D₇₃	semidirect
873. #103	C₂²×D₇₃	semidirect
885. #102	C₂²×D₇₃	semidirect
892. #97	C₂²×D₇₃	semidirect
895. C₄×C₈	C₂²×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
#535×D₇₃	2
#22621006	2
#22621005	2
#22621004	2
#22621003	2
#22621002	2
#22621001	2
#22621000	2
#22620999	2
#22620998	2
#22620997	2
#22620996	2
#497×D₇₃	2
#492×D₇₃	2
#490×D₇₃	2
#488×D₇₃	2
#464×D₇₃	2
#460×D₇₃	2
#452×D₇₃	2
#450×D₇₃	2
#433×D₇₃	2
C₇₃×#3222	2
C₂×#3222	73

Subgroups — #3222×D73 #33957319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3222×D₇₃ #33957319