Subgroups — #33954994

Order 18688.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623829	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14556637	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620215	C₂	1	2	yes	maximal, complemented
4	#22620200	C₂	1	2	yes	maximal, complemented
5	#22620122	C₂	1	2	yes	maximal, complemented
6	#22620120	C₂	1	2	yes	maximal, complemented
7	#22620074	C₂	1	2	yes	maximal, complemented
8	#22620047	C₂	1	2	yes	maximal, complemented
9	#22619983	C₂	1	2	yes	maximal, complemented
10	#22619956	C₂	1	2	yes	maximal, complemented
11	#22619903	C₂	1	1	yes	maximal, characteristic, complemented
12	#22619892	C₂	1	1	yes	maximal, characteristic, complemented
13	#22619724	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619425	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#17988803	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619211	C₂	1	1	yes	maximal, characteristic, complemented
17	#22619202	C₂	1	1	yes	maximal, characteristic
18	#22618789	C₂	1	1	yes	maximal, characteristic, complemented
19	#22618782	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618777	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618766	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618596	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556637	C₂²	1	1	yes	characteristic
25	C₂×#14556621	C₂²	1	1	yes	characteristic
26	C₂×#14556616	C₂²	1	1	yes	characteristic
27	C₂²×#11924017	C₂²	1	1	yes	characteristic
28	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic
29	#17989322	—	2	1	no	—
30	#17989322	—	2	1	no	—
31	#17989310	—	2	1	no	—
32	#17989310	—	2	1	no	—
33	#17989264	—	2	2	no	—
34	#17989264	—	2	2	no	—
35	#17989211	C₂²	1	2	yes	complemented
36	#17989211	C₂²	1	2	yes	complemented
37	#17989163	C₂²	1	1	yes	characteristic
38	#17989156	C₂²	1	1	yes	characteristic
39	#17989122	C₂²	1	2	yes	complemented
40	#17989122	C₂²	1	2	yes	complemented
41	C₂×#14556579	C₂²	1	1	yes	characteristic, complemented
42	#17989070	C₂²	1	1	yes	characteristic
43	#17989069	C₂²	1	2	yes	complemented
44	#17989067	—	2	1	no	—
45	#17989067	C₂²	1	1	yes	characteristic
46	#17989064	C₂²	1	1	yes	characteristic, complemented
47	#17989061	—	2	1	no	—
48	#17989061	C₂²	1	1	yes	characteristic
49	#17989061	C₂²	1	1	yes	characteristic, complemented
50	#17989059	—	2	2	no	—
51	#17989059	C₂²	1	2	yes	complemented
52	C₄×#11924029	C₂²	1	2	yes	complemented
53	C₄×#11924028	—	2	1	no	—
54	C₄×#11924028	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₂₉₂	—	2	1	no	—
56	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
57	C₄×D₄×D₇₃	—	2	2	no	—
58	C₄×D₄×D₇₃	C₂²	1	2	yes	complemented
59	#17988931	C₂²	1	2	yes	complemented
60	#17988930	C₂²	1	2	yes	complemented
61	#17988924	C₂²	1	2	yes	complemented
62	#17988919	C₂²	1	2	yes	complemented
63	#17988914	C₂²	1	2	yes	complemented
64	#17988913	C₂²	1	2	yes	complemented
65	#17988907	C₂²	1	2	yes	complemented
66	#17988902	C₂²	1	2	yes	complemented
67	#17988884	C₂²	1	2	yes	complemented
68	#17988884	C₂²	1	2	yes	complemented
69	#17988874	C₂²	1	2	yes	complemented
70	#17988864	C₂²	1	2	yes	complemented
71	#17988809	C₂²	1	2	yes	complemented
72	#17988809	C₂²	1	2	yes	complemented
73	#17988803	C₂²	1	2	yes	complemented
74	#17988803	C₂²	1	2	yes	complemented
75	#17988803	C₂²	1	2	yes	complemented
76	#17988803	C₂²	1	2	yes	complemented
77	#17988802	C₂²	1	2	yes	complemented
78	#17988802	C₂²	1	2	yes	complemented
79	#17988752	C₂²	1	2	yes	complemented
80	#17988752	C₂²	1	2	yes	complemented
81	#17988739	C₂²	1	2	yes	complemented
82	#17988739	C₂²	1	2	yes	complemented
83	#17988735	C₂²	1	2	yes	—
84	#17988735	C₂²	1	2	yes	—
85	#17988722	C₂²	1	2	yes	—
86	#17988722	C₂²	1	2	yes	—
87	#17988698	C₂²	1	2	yes	complemented
88	#17988698	C₂²	1	2	yes	complemented
89	#17988696	C₂²	1	2	yes	complemented
90	#17988691	C₂²	1	2	yes	complemented
91	#17988690	C₂²	1	2	yes	complemented
92	#17988686	C₂²	1	2	yes	complemented
93	#17988686	C₂²	1	2	yes	complemented
94	#17988684	C₂²	1	2	yes	complemented
95	#17988679	C₂²	1	2	yes	complemented
96	#17988678	C₂²	1	2	yes	complemented
97	#17988674	C₂²	1	2	yes	complemented
98	#17988674	C₂²	1	2	yes	complemented
99	#17988672	C₂²	1	2	yes	complemented
100	#17988669	C₂²	1	2	yes	complemented
101	#17988669	C₂²	1	2	yes	complemented
102	#17988667	C₂²	1	2	yes	complemented
103	#17988647	C₂²	1	2	yes	complemented
104	#17988647	C₂²	1	2	yes	complemented
105	#17988643	C₂²	1	2	yes	complemented
106	#17988639	C₂²	1	2	yes	complemented
107	#17988630	C₂²	1	1	yes	characteristic, complemented
108	#17988630	C₂²	1	1	yes	characteristic, complemented
109	#17988611	C₂²	1	1	yes	characteristic, complemented
110	#17988595	C₂²	1	1	yes	characteristic, complemented
111	#17988591	C₂²	1	1	yes	characteristic
112	#17988591	C₂²	1	1	yes	characteristic
113	#17988591	C₂²	1	1	yes	characteristic, complemented
114	C₂×#14556516	C₂²	1	1	yes	characteristic, complemented
115	C₂×#14556513	C₂²	1	1	yes	characteristic, complemented
116	#17988553	C₂²	1	1	yes	characteristic
117	#17988553	C₂²	1	1	yes	characteristic
118	#17988542	C₂²	1	1	yes	characteristic, complemented
119	#17988542	C₂²	1	1	yes	characteristic, complemented
120	#533×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#478×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#478×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#477×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#476×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#475×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#474×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#416×C₇₃	C₂²	1	1	yes	characteristic
134	#416×C₇₃	C₂²	1	1	yes	characteristic
135	#14556637	—	2	4	no	—
136	#14556637	—	2	4	no	—
137	C₂×#11924029	C₂³	1	2	yes	—
138	C₂×#11924028	—	2	1	no	—
139	C₂×#11924028	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
141	C₂²×D₂₉₂	—	2	1	no	—
142	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
143	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
144	C₂×D₄×D₇₃	—	2	2	no	—
145	C₂×D₄×D₇₃	C₂³	1	2	yes	—
146	C₂²×C₄×D₇₃	—	2	2	no	—
147	C₂²×C₄×D₇₃	—	2	1	no	—
148	#14556621	—	2	4	no	—
149	#14556616	—	2	4	no	—
150	C₂×#11924018	C₂³	1	2	yes	—
151	C₂×#11924017	—	2	4	no	—
152	C₂×#11924017	C₂³	1	2	yes	—
153	C₂×#11924017	C₂³	1	2	yes	—
154	C₂×#11924016	C₂³	1	2	yes	—
155	C₂×#11924015	C₂³	1	2	yes	—
156	C₂×D₅₈₄	—	2	4	no	—
157	C₂×D₅₈₄	C₂³	1	2	yes	—
158	C₂×D₅₈₄	C₂³	1	2	yes	—
159	C₂×#11924013	C₂³	1	2	yes	—
160	C₂×#11924012	C₂³	1	1	yes	characteristic
161	C₂×#11924012	C₂³	1	1	yes	characteristic
162	#14556591	—	2	1	no	—
163	#14556588	—	2	1	no	—
164	#14556586	—	2	2	no	—
165	#14556586	—	2	2	no	—
166	#14556586	—	2	2	no	—
167	#14556586	—	2	2	no	—
168	#14556580	—	2	2	no	—
169	#14556580	—	2	2	no	—
170	#14556579	—	2	1	no	—
171	#14556579	—	2	1	no	—
172	#14556579	—	2	1	no	—
173	#14556579	—	2	1	no	—
174	#14556579	C₂³	1	2	yes	—
175	#14556579	C₂³	1	2	yes	—
176	#14556576	—	2	2	no	—
177	#14556576	—	2	2	no	—
178	#14556576	—	2	2	no	—
179	#14556576	—	2	2	no	—
180	#14556575	—	2	2	no	—
181	#14556571	C₂³	1	2	yes	—
182	#14556571	C₂³	1	2	yes	—
183	#14556567	—	2	2	no	—
184	#14556567	—	2	2	no	—
185	#14556566	C₂³	1	2	yes	—
186	#14556566	C₂³	1	2	yes	—
187	#14556561	—	2	2	no	—
188	Q₈×Dic₇₃	C₂³	1	2	yes	—
189	C₄×Dic₁₄₆	—	2	1	no	—
190	C₄×Dic₁₄₆	—	2	1	no	—
191	C₄×Dic₁₄₆	—	2	1	no	—
192	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
193	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
194	#14556556	C₂³	1	2	yes	—
195	#14556556	C₂³	1	2	yes	—
196	C₄×D₂₉₂	—	2	1	no	—
197	C₄×D₂₉₂	—	2	2	no	—
198	C₄×D₂₉₂	—	2	1	no	—
199	C₄×D₂₉₂	—	2	1	no	—
200	C₄×D₂₉₂	—	2	1	no	—
201	C₄×D₂₉₂	—	2	1	no	—
202	C₄×D₂₉₂	—	2	2	no	—
203	C₄×D₂₉₂	—	2	1	no	—
204	C₄×D₂₉₂	—	2	1	no	—
205	C₄×D₂₉₂	D₄	1	1	yes	characteristic
206	C₄×D₂₉₂	D₄	1	1	yes	characteristic
207	C₄×D₂₉₂	C₂³	1	2	yes	—
208	C₄×D₂₉₂	C₂³	1	2	yes	—
209	D₄×Dic₇₃	—	2	2	no	—
210	D₄×Dic₇₃	C₂³	1	2	yes	—
211	#14556553	—	2	2	no	—
212	#14556553	—	2	2	no	—
213	#14556553	—	2	2	no	—
214	#14556553	—	2	2	no	—
215	#14556553	C₂³	1	2	yes	—
216	#14556553	C₂³	1	2	yes	—
217	#14556553	C₂³	1	2	yes	—
218	#14556553	C₂³	1	2	yes	—
219	C₄×C₂²⋊D₇₃	—	2	2	no	—
220	C₄×C₂²⋊D₇₃	—	2	2	no	—
221	C₄×C₂²⋊D₇₃	D₄	1	2	yes	—
222	C₄×C₂²⋊D₇₃	D₄	1	2	yes	—
223	#14556551	—	2	2	no	—
224	#14556551	—	2	2	no	—
225	#14556551	—	2	2	no	—
226	#14556550	—	2	1	no	—
227	#14556550	C₂³	1	1	yes	characteristic
228	#14556549	—	2	2	no	—
229	#14556549	—	2	2	no	—
230	#14556549	—	2	2	no	—
231	#14556549	C₂³	1	2	yes	—
232	#14556548	—	2	2	no	—
233	#14556548	C₂³	1	2	yes	—
234	#14556547	—	2	2	no	—
235	C₂×C₄⋊Dic₇₃	—	2	1	no	—
236	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×D₇₃	—	2	2	no	—
238	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
239	C₂×#11924005	—	2	2	no	—
240	C₂×#11924005	—	2	1	no	—
241	C₂×#11924005	—	2	1	no	—
242	C₂×#11924005	—	2	1	no	—
243	C₂²⋊C₄×D₇₃	—	2	2	no	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₂²⋊C₄×D₇₃	—	2	2	no	—
246	C₂²⋊C₄×D₇₃	—	2	2	no	—
247	C₄²×D₇₃	—	2	2	no	—
248	C₄²×D₇₃	C₂³	1	2	yes	—
249	#14556524	C₂³	1	2	yes	—
250	#14556524	C₂³	1	2	yes	—
251	#14556522	C₂³	1	2	yes	—
252	#14556522	C₂³	1	2	yes	—
253	C₄⋊#10596831	C₂³	1	2	yes	—
254	C₄⋊#10596831	C₂³	1	2	yes	—
255	#14556516	C₂³	1	2	yes	—
256	#14556516	C₂³	1	2	yes	—
257	#14556514	C₂³	1	2	yes	—
258	#14556514	C₂³	1	2	yes	—
259	#14556513	C₂³	1	2	yes	—
260	#14556513	C₂³	1	2	yes	—
261	#14556511	C₂³	1	2	yes	—
262	#14556511	C₂³	1	2	yes	—
263	#14556511	C₂³	1	2	yes	—
264	#14556511	C₂³	1	2	yes	—
265	#14556511	C₂³	1	2	yes	—
266	#14556511	C₂³	1	2	yes	—
267	#14556503	C₂³	1	2	yes	—
268	#14556503	C₂³	1	2	yes	—
269	#14556503	C₂³	1	2	yes	—
270	#14556503	C₂³	1	2	yes	—
271	#14556501	C₂³	1	2	yes	—
272	#14556501	C₂³	1	2	yes	—
273	C₈×Dic₇₃	C₂³	1	2	yes	—
274	C₈×Dic₇₃	C₂³	1	2	yes	—
275	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
280	#125×C₇₃	C₂³	1	1	yes	characteristic
281	#125×C₇₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Q₈×C₇₃	—	2	1	no	—
283	C₂²⋊Q₈×C₇₃	—	2	1	no	—
284	C₄×Q₈×C₇₃	—	2	1	no	—
285	C₄×Q₈×C₇₃	—	2	1	no	—
286	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₇₃	—	2	1	no	—
289	C₄×D₄×C₇₃	—	2	1	no	—
290	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
292	#117×C₇₃	—	2	1	no	—
293	#117×C₇₃	C₂³	1	1	yes	characteristic
294	#117×C₇₃	C₂³	1	1	yes	characteristic
295	#117×C₇₃	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₇₃	—	2	1	no	—
297	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
298	#107×C₇₃	C₂³	1	1	yes	characteristic
299	#107×C₇₃	C₂³	1	1	yes	characteristic
300	#107×C₇₃	C₂³	1	1	yes	characteristic
301	#107×C₇₃	C₂³	1	1	yes	characteristic
302	#106×C₇₃	C₂³	1	1	yes	characteristic
303	#106×C₇₃	C₂³	1	1	yes	characteristic
304	#106×C₇₃	C₂³	1	1	yes	characteristic
305	#106×C₇₃	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
310	#103×C₇₃	C₂³	1	1	yes	characteristic
311	#103×C₇₃	C₂³	1	1	yes	characteristic
312	#103×C₇₃	C₂³	1	1	yes	characteristic
313	#103×C₇₃	C₂³	1	1	yes	characteristic
314	#102×C₇₃	C₂³	1	1	yes	characteristic
315	#102×C₇₃	C₂³	1	1	yes	characteristic
316	#102×C₇₃	C₂³	1	1	yes	characteristic
317	#102×C₇₃	C₂³	1	1	yes	characteristic
318	C₂³×D₇₃	—	2	1	no	—
319	C₂³×D₇₃	—	2	2	no	—
320	C₂³×D₇₃	—	2	1	no	—
321	#11924029	—	2	4	no	—
322	#11924029	—	2	4	no	—
323	#11924028	—	2	8	no	—
324	#11924028	—	2	2	no	—
325	#11924028	—	2	2	no	—
326	C₂×Dic₁₄₆	—	2	2	no	—
327	C₂×Dic₁₄₆	—	2	2	no	—
328	C₂×Dic₁₄₆	—	2	1	no	—
329	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
330	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
331	C₂×D₂₉₂	—	2	8	no	—
332	C₂×D₂₉₂	—	2	2	no	—
333	C₂×D₂₉₂	—	2	1	no	—
334	C₂×D₂₉₂	—	2	2	no	—
335	C₂×D₂₉₂	—	2	2	no	—
336	C₂×D₂₉₂	—	2	2	no	—
337	C₂×D₂₉₂	—	2	1	no	—
338	C₂×D₂₉₂	—	2	2	no	—
339	C₂×D₂₉₂	—	2	2	no	—
340	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
341	C₂×D₂₉₂	#41	1	4	yes	—
342	C₂×D₂₉₂	C₂⁴	1	2	yes	—
343	C₂×D₂₉₂	C₂⁴	1	2	yes	—
344	C₂×C₂²⋊D₇₃	—	2	2	no	—
345	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
346	D₄×D₇₃	—	2	16	no	—
347	D₄×D₇₃	—	2	4	no	—
348	D₄×D₇₃	—	2	4	no	—
349	C₂²×Dic₇₃	—	2	1	no	—
350	C₂²×Dic₇₃	—	2	1	no	—
351	C₂²×Dic₇₃	—	2	2	no	—
352	C₂×C₄×D₇₃	—	2	2	no	—
353	C₂×C₄×D₇₃	—	2	2	no	—
354	C₂×C₄×D₇₃	—	2	2	no	—
355	C₂×C₄×D₇₃	—	2	2	no	—
356	C₂×C₄×D₇₃	—	2	2	no	—
357	C₂×C₄×D₇₃	—	2	2	no	—
358	C₂×C₄×D₇₃	—	2	2	no	—
359	C₂×C₄×D₇₃	—	2	2	no	—
360	C₂×C₄×D₇₃	—	8	4	no	—
361	C₂×C₄×D₇₃	—	8	2	no	—
362	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
363	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
364	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
365	#11924018	—	2	4	no	—
366	#11924017	—	2	4	no	—
367	#11924017	—	2	4	no	—
368	#11924016	—	2	4	no	—
369	#11924015	—	2	4	no	—
370	D₅₈₄	—	2	4	no	—
371	D₅₈₄	—	2	4	no	—
372	#11924013	—	2	4	no	—
373	#11924012	—	2	2	no	—
374	#11924012	—	2	2	no	—
375	C₂×#10596831	C₂⁴	1	2	yes	—
376	C₂×#10596831	C₂⁴	1	2	yes	—
377	C₄⋊Dic₇₃	—	2	1	no	—
378	C₄⋊Dic₇₃	—	2	2	no	—
379	C₄⋊Dic₇₃	—	2	2	no	—
380	C₄⋊Dic₇₃	—	2	2	no	—
381	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
382	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
383	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
384	#11924007	—	2	2	no	—
385	#11924007	—	2	2	no	—
386	#11924007	—	2	2	no	—
387	#11924007	C₂×D₄	1	2	yes	—
388	#11924007	C₂×D₄	1	2	yes	—
389	C₂²⋊Dic₇₃	—	2	2	no	—
390	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
391	#11924005	—	2	2	no	—
392	#11924005	—	2	2	no	—
393	#11924005	—	2	2	no	—
394	#11924005	—	2	2	no	—
395	#11924005	—	2	2	no	—
396	#11924005	—	2	2	no	—
397	#11924005	—	2	2	no	—
398	#11924005	—	2	2	no	—
399	#11924005	—	2	2	no	—
400	#11924005	—	2	2	no	—
401	#11924005	—	2	2	no	—
402	#11924005	—	2	2	no	—
403	#11924005	—	2	2	no	—
404	#11924005	—	2	2	no	—
405	#11924005	—	2	2	no	—
406	#11924005	C₂×D₄	1	2	yes	—
407	#11924005	C₂×D₄	1	2	yes	—
408	C₄×Dic₇₃	—	2	2	no	—
409	C₄×Dic₇₃	—	2	2	no	—
410	C₄×Dic₇₃	—	2	2	no	—
411	C₄×Dic₇₃	—	2	2	no	—
412	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
413	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
414	C₄×Dic₇₃	C₂⁴	1	2	yes	—
415	#41×C₇₃	—	2	2	no	—
416	#41×C₇₃	#41	1	4	yes	—
417	C₂×Q₈×C₇₃	—	2	1	no	—
418	C₂×Q₈×C₇₃	—	2	1	no	—
419	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₂×D₄×C₇₃	—	2	1	no	—
421	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₇₃	—	2	1	no	—
423	C₂²×C₄×C₇₃	—	2	1	no	—
424	C₂²×C₄×C₇₃	—	2	1	no	—
425	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₇₃	—	2	2	no	—
429	C₂×C₈×C₇₃	—	2	2	no	—
430	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₇₃	—	2	1	no	—
435	C₄⋊C₄×C₇₃	—	2	1	no	—
436	C₄⋊C₄×C₇₃	—	2	1	no	—
437	C₄⋊C₄×C₇₃	—	2	1	no	—
438	C₄⋊C₄×C₇₃	—	2	1	no	—
439	C₄⋊C₄×C₇₃	—	2	1	no	—
440	C₄⋊C₄×C₇₃	—	2	1	no	—
441	C₄⋊C₄×C₇₃	—	2	1	no	—
442	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
448	C₂²⋊C₄×C₇₃	—	2	1	no	—
449	C₂²⋊C₄×C₇₃	—	2	1	no	—
450	C₂²⋊C₄×C₇₃	—	2	1	no	—
451	C₂²⋊C₄×C₇₃	—	2	1	no	—
452	C₂²⋊C₄×C₇₃	—	2	1	no	—
453	C₄²×C₇₃	—	2	1	no	—
454	C₄²×C₇₃	—	2	1	no	—
455	C₄²×C₇₃	—	2	1	no	—
456	C₄²×C₇₃	—	2	1	no	—
457	C₄²×C₇₃	—	2	1	no	—
458	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
461	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
462	C₂³×C₇₃	—	2	1	no	—
463	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂²×D₇₃	—	2	2	no	—
465	C₂²×D₇₃	—	2	8	no	—
466	C₂²×D₇₃	—	2	4	no	—
467	C₂²×D₇₃	—	2	2	no	—
468	C₂²×D₇₃	—	4	2	no	—
469	C₂²×D₇₃	—	8	2	no	—
470	C₂²×D₇₃	—	8	2	no	—
471	C₂²×D₇₃	—	8	1	no	—
472	C₂²×D₇₃	—	8	1	no	—
473	C₂²×D₇₃	—	8	1	no	—
474	C₂²×D₇₃	—	8	1	no	—
475	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
476	Q₈×C₇₃	—	2	1	no	—
477	Q₈×C₇₃	—	8	1	no	—
478	Q₈×C₇₃	—	8	1	no	—
479	Q₈×C₇₃	C₂×#41	1	2	yes	—
480	D₄×C₇₃	—	2	4	no	—
481	D₄×C₇₃	—	2	1	no	—
482	D₄×C₇₃	C₂×#41	1	2	yes	—
483	C₂×C₄×C₇₃	—	2	1	no	—
484	C₂×C₄×C₇₃	—	2	4	no	—
485	C₂×C₄×C₇₃	—	2	1	no	—
486	C₂×C₄×C₇₃	—	2	1	no	—
487	C₂×C₄×C₇₃	—	2	1	no	—
488	C₂×C₄×C₇₃	—	2	1	no	—
489	C₂×C₄×C₇₃	—	2	1	no	—
490	C₂×C₄×C₇₃	—	2	1	no	—
491	C₂×C₄×C₇₃	—	4	1	no	—
492	C₂×C₄×C₇₃	—	4	1	no	—
493	C₂×C₄×C₇₃	—	4	2	no	—
494	C₂×C₄×C₇₃	—	8	1	no	—
495	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
501	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
502	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
503	C₂²⋊D₇₃	—	2	8	no	—
504	C₂²⋊D₇₃	—	2	4	no	—
505	C₂×Dic₇₃	—	2	2	no	—
506	C₂×Dic₇₃	—	2	2	no	—
507	C₂×Dic₇₃	—	4	2	no	—
508	C₂×Dic₇₃	—	8	2	no	—
509	C₂×Dic₇₃	—	8	1	no	—
510	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
511	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
512	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
513	D₂₉₂	—	2	8	no	—
514	D₂₉₂	—	2	2	no	—
515	D₂₉₂	—	2	4	no	—
516	D₂₉₂	—	2	2	no	—
517	D₂₉₂	—	2	2	no	—
518	D₂₉₂	—	2	2	no	—
519	D₂₉₂	—	4	2	no	—
520	D₂₉₂	—	8	2	no	—
521	D₂₉₂	—	8	2	no	—
522	D₂₉₂	C₂×#41	1	4	yes	—
523	C₄×D₇₃	—	2	8	no	—
524	C₄×D₇₃	—	2	2	no	—
525	C₄×D₇₃	—	2	2	no	—
526	C₄×D₇₃	—	4	2	no	—
527	C₄×D₇₃	—	4	2	no	—
528	C₄×D₇₃	—	4	4	no	—
529	C₄×D₇₃	—	8	2	no	—
530	C₄×D₇₃	—	8	2	no	—
531	C₄×D₇₃	—	8	2	no	—
532	C₄×D₇₃	—	8	2	no	—
533	C₄×D₇₃	—	8	2	no	—
534	C₄×D₇₃	—	8	2	no	—
535	Dic₁₄₆	—	2	2	no	—
536	Dic₁₄₆	—	2	2	no	—
537	Dic₁₄₆	—	2	2	no	—
538	Dic₁₄₆	—	4	2	no	—
539	C₈×C₇₃	—	2	1	no	—
540	C₈×C₇₃	—	2	1	no	—
541	C₈×C₇₃	—	2	1	no	—
542	C₈×C₇₃	—	2	1	no	—
543	#10596831	—	2	2	no	—
544	#10596831	—	2	2	no	—
545	C₂²×C₇₃	—	2	1	no	—
546	C₂²×C₇₃	—	2	1	no	—
547	C₂²×C₇₃	—	2	2	no	—
548	C₂²×C₇₃	—	4	1	no	—
549	C₂²×C₇₃	—	4	1	no	—
550	C₂²×C₇₃	#525	1	2	yes	—
551	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
552	C₂×D₇₃	—	2	2	no	—
553	C₂×D₇₃	—	2	2	no	—
554	C₂×D₇₃	—	2	2	no	—
555	C₂×D₇₃	—	2	4	no	—
556	C₂×D₇₃	—	4	2	no	—
557	C₂×D₇₃	—	4	2	no	—
558	C₂×D₇₃	—	4	2	no	—
559	C₂×D₇₃	—	4	2	no	—
560	C₂×D₇₃	—	4	2	no	—
561	C₂×D₇₃	—	8	4	no	—
562	C₂×D₇₃	—	8	8	no	—
563	C₂×D₇₃	—	16	2	no	—
564	C₄×C₇₃	—	2	1	no	—
565	C₄×C₇₃	—	2	1	no	—
566	C₄×C₇₃	—	2	1	no	—
567	C₄×C₇₃	—	2	1	no	—
568	C₄×C₇₃	—	2	2	no	—
569	C₄×C₇₃	—	4	1	no	—
570	C₄×C₇₃	—	4	1	no	—
571	C₄×C₇₃	—	4	1	no	—
572	C₄×C₇₃	—	4	1	no	—
573	C₄×C₇₃	—	4	1	no	—
574	C₄×C₇₃	—	4	1	no	—
575	C₄×C₇₃	#525	1	2	yes	—
576	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
577	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
578	Dic₇₃	—	2	2	no	—
579	Dic₇₃	—	2	2	no	—
580	Dic₇₃	—	2	2	no	—
581	Dic₇₃	—	4	2	no	—
582	Dic₇₃	—	4	2	no	—
583	#60592	—	73	1	no	maximal, Sylow
584	C₂×C₇₃	—	2	2	no	—
585	C₂×C₇₃	—	4	2	no	—
586	C₂×C₇₃	C₂×#525	1	1	yes	characteristic
587	C₂×C₇₃	#3584	1	1	yes	characteristic
588	C₂×C₇₃	#3585	1	1	yes	characteristic
589	D₇₃	—	4	2	no	—
590	D₇₃	—	4	4	no	—
591	D₇₃	—	8	2	no	—
592	#3510	—	73	1	no	—
593	C₄×H(5,𝔽₂)	—	73	1	no	—
594	#3125	—	73	2	no	—
595	#3124	—	73	2	no	—
596	#3118	—	73	2	no	—
597	#3118	—	73	2	no	—
598	#3114	—	73	2	no	—
599	#3111	—	73	2	no	—
600	#3105	—	73	2	no	—
601	#3102	—	73	2	no	—
602	#3097	—	73	1	no	—
603	#3096	—	73	1	no	—
604	#3077	—	73	1	no	—
605	#3076	D₇₃	1	1	yes	characteristic, complemented
606	#3040	—	73	1	no	—
607	C₂×#463	—	73	1	no	—
608	#3009	—	73	1	no	—
609	#3008	—	73	1	no	—
610	#2949	—	73	1	no	—
611	#2948	—	73	1	no	—
612	#2947	—	73	1	no	—
613	#2946	—	73	1	no	—
614	#2925	—	73	1	no	—
615	C₇₃	#60592	1	1	yes	characteristic, complemented, Sylow
616	C₂×H(5,𝔽₂)	—	73	1	no	—
617	C₂×#137	—	73	1	no	—
618	C₂×AGL(1,ℤ/8)	—	73	1	no	—
619	C₂²×SD₁₆	—	73	1	no	—
620	C₂²×D₈	—	73	1	no	—
621	#559	—	146	1	no	—
622	#559	—	146	1	no	—
623	#556	—	146	1	no	—
624	#556	—	146	1	no	—
625	#551	—	146	2	no	—
626	#551	—	146	2	no	—
627	#542	—	73	2	no	—
628	#542	—	73	2	no	—
629	#536	—	73	1	no	—
630	#535	—	73	1	no	—
631	#533	C₂×D₇₃	1	1	yes	characteristic, complemented
632	#529	—	73	2	no	—
633	#529	—	73	2	no	—
634	C₂×#124	—	73	1	no	—
635	#520	—	73	1	no	—
636	#520	—	73	1	no	—
637	#520	—	73	2	no	—
638	#520	—	146	1	no	—
639	#519	—	73	1	no	—
640	#518	—	73	2	no	—
641	#518	—	73	1	no	—
642	#518	—	73	1	no	—
643	#518	—	146	1	no	—
644	#518	—	146	2	no	—
645	C₄×#41	—	73	1	no	—
646	C₄×#41	—	73	2	no	—
647	C₄×#41	—	146	1	no	—
648	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
649	C₂×C₄×D₄	—	73	2	no	—
650	C₂×C₄×D₄	—	73	1	no	—
651	C₂×C₄×D₄	—	146	1	no	—
652	C₂×C₄×D₄	—	146	2	no	—
653	#485	—	73	2	no	—
654	#485	—	73	2	no	—
655	#484	—	73	2	no	—
656	#483	—	73	2	no	—
657	#482	—	73	2	no	—
658	#482	—	73	2	no	—
659	#481	—	73	2	no	—
660	#480	—	73	2	no	—
661	#479	C₂×D₇₃	1	1	yes	characteristic, complemented
662	#479	C₂×D₇₃	1	1	yes	characteristic, complemented
663	#478	—	73	2	no	—
664	#478	—	73	2	no	—
665	#478	C₂×D₇₃	1	1	yes	characteristic, complemented
666	#478	C₂×D₇₃	1	1	yes	characteristic, complemented
667	#477	C₂×D₇₃	1	1	yes	characteristic, complemented
668	#476	—	73	2	no	—
669	#476	C₂×D₇₃	1	1	yes	characteristic, complemented
670	#475	C₂×D₇₃	1	1	yes	characteristic, complemented
671	#474	—	73	2	no	—
672	#474	C₂×D₇₃	1	1	yes	characteristic, complemented
673	#464	—	73	2	no	—
674	#464	—	73	2	no	—
675	#463	—	73	2	no	—
676	#463	—	73	2	no	—
677	#463	—	73	2	no	—
678	#463	—	73	2	no	—
679	#463	—	73	2	no	—
680	#463	—	73	2	no	—
681	#452	—	73	2	no	—
682	#452	—	73	2	no	—
683	#450	—	73	2	no	—
684	#450	—	73	2	no	—
685	#449	—	73	2	no	—
686	#449	—	73	2	no	—
687	#447	—	73	2	no	—
688	#447	—	73	2	no	—
689	#442	—	73	2	no	—
690	#442	—	73	2	no	—
691	#442	—	73	2	no	—
692	#441	—	73	2	no	—
693	#440	—	73	2	no	—
694	#440	—	73	2	no	—
695	#440	—	73	2	no	—
696	#440	—	73	2	no	—
697	C₄×Q₁₆	—	73	2	no	—
698	C₄×SD₁₆	—	73	2	no	—
699	C₄×SD₁₆	—	73	2	no	—
700	C₄×SD₁₆	—	73	2	no	—
701	C₄×SD₁₆	—	73	2	no	—
702	C₄×D₈	—	73	2	no	—
703	C₄×D₈	—	73	2	no	—
704	C₄×D₈	—	73	2	no	—
705	#433	—	73	2	no	—
706	#433	—	73	2	no	—
707	#432	—	73	2	no	—
708	#431	—	73	2	no	—
709	#428	—	73	1	no	—
710	#428	—	73	1	no	—
711	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
712	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
713	#423	—	73	1	no	—
714	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
715	#419	—	73	1	no	—
716	#418	—	73	1	no	—
717	#418	—	73	1	no	—
718	#418	—	73	1	no	—
719	#416	C₂×D₇₃	1	1	yes	characteristic
720	#416	C₂×D₇₃	1	1	yes	characteristic
721	C₂×#103	—	73	1	no	—
722	C₂×#102	—	73	1	no	—
723	#408	—	73	1	no	—
724	#408	—	73	1	no	—
725	#405	—	73	1	no	—
726	#405	—	73	1	no	—
727	H(5,𝔽₂)	—	146	4	no	—
728	H(5,𝔽₂)	—	146	4	no	—
729	C₂×#41	—	73	1	no	—
730	C₂×#41	—	73	2	no	—
731	C₂×#41	—	146	1	no	—
732	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
733	C₂²×Q₈	—	73	1	no	—
734	C₂²×D₄	—	73	2	no	—
735	C₂²×D₄	—	73	1	no	—
736	C₂²×D₄	—	73	1	no	—
737	C₂²×D₄	—	146	1	no	—
738	C₂²×D₄	—	146	2	no	—
739	C₂³×C₄	—	146	2	no	—
740	C₂³×C₄	—	146	1	no	—
741	#137	—	146	4	no	—
742	AGL(1,ℤ/8)	—	146	4	no	—
743	C₂×Q₁₆	—	73	2	no	—
744	C₂×SD₁₆	—	73	2	no	—
745	C₂×SD₁₆	—	73	2	no	—
746	C₂×SD₁₆	—	73	2	no	—
747	C₂×SD₁₆	—	73	2	no	—
748	C₂×SD₁₆	—	146	4	no	—
749	C₂×D₈	—	73	2	no	—
750	C₂×D₈	—	73	2	no	—
751	C₂×D₈	—	73	2	no	—
752	C₂×D₈	—	146	4	no	—
753	C₂×M₁₆	—	73	1	no	—
754	C₂×M₁₆	—	73	1	no	—
755	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
756	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
757	C₄⋊Q₈	—	146	1	no	—
758	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
760	#127	—	146	1	no	—
761	#126	—	146	2	no	—
762	#126	—	146	2	no	—
763	#126	—	146	2	no	—
764	#126	—	146	2	no	—
765	#125	C₂²×D₇₃	1	1	yes	characteristic
766	#125	C₂²×D₇₃	1	1	yes	characteristic
767	#124	—	73	2	no	—
768	#124	—	73	2	no	—
769	#124	—	146	1	no	—
770	#124	—	146	1	no	—
771	#124	—	146	2	no	—
772	#124	—	146	2	no	—
773	#124	—	146	1	no	—
774	#124	—	146	1	no	—
775	#123	—	146	2	no	—
776	#123	—	146	2	no	—
777	#123	—	146	2	no	—
778	#123	—	146	2	no	—
779	#123	—	146	2	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	73	2	no	—
783	C₂²⋊Q₈	—	73	2	no	—
784	C₂²⋊Q₈	—	146	2	no	—
785	C₂²⋊Q₈	—	146	2	no	—
786	#121	—	73	2	no	—
787	#121	—	73	2	no	—
788	#120	—	146	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	73	1	no	—
792	C₄×Q₈	—	73	1	no	—
793	C₄×Q₈	—	73	2	no	—
794	C₄×Q₈	—	73	2	no	—
795	C₄×Q₈	—	73	2	no	—
796	C₄×Q₈	—	146	1	no	—
797	C₄×Q₈	—	146	1	no	—
798	C₄×Q₈	—	146	1	no	—
799	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	73	2	no	—
804	C₄×D₄	—	73	2	no	—
805	C₄×D₄	—	73	2	no	—
806	C₄×D₄	—	73	2	no	—
807	C₄×D₄	—	73	2	no	—
808	C₄×D₄	—	73	2	no	—
809	C₄×D₄	—	73	2	no	—
810	C₄×D₄	—	73	1	no	—
811	C₄×D₄	—	73	1	no	—
812	C₄×D₄	—	73	2	no	—
813	C₄×D₄	—	73	2	no	—
814	C₄×D₄	—	146	2	no	—
815	C₄×D₄	—	146	1	no	—
816	C₄×D₄	—	146	1	no	—
817	C₄×D₄	—	146	1	no	—
818	C₄×D₄	—	146	1	no	—
819	C₄×D₄	—	146	2	no	—
820	C₄×D₄	—	146	1	no	—
821	C₄×D₄	—	146	2	no	—
822	C₄×D₄	—	146	2	no	—
823	C₄×D₄	—	146	2	no	—
824	C₄×D₄	—	146	2	no	—
825	C₄×D₄	—	146	2	no	—
826	C₄×D₄	—	146	2	no	—
827	C₄×D₄	—	146	2	no	—
828	C₄×D₄	—	146	2	no	—
829	C₄×D₄	—	146	2	no	—
830	C₄×D₄	—	146	2	no	—
831	C₄×D₄	—	146	1	no	—
832	C₄×D₄	—	146	1	no	—
833	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
835	#117	—	2	1	no	—
836	#117	—	73	1	no	—
837	#117	—	73	2	no	—
838	#117	—	73	2	no	—
839	#117	—	146	2	no	—
840	#117	—	146	2	no	—
841	#117	—	146	2	no	—
842	#117	—	146	2	no	—
843	#117	—	146	2	no	—
844	#117	—	146	1	no	—
845	#117	C₂²×D₇₃	1	1	yes	characteristic
846	#117	C₂²×D₇₃	1	1	yes	characteristic
847	#117	C₂²×D₇₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	—	73	1	no	—
849	C₂×C₄⋊C₄	—	73	2	no	—
850	C₂×C₄⋊C₄	—	146	2	no	—
851	C₂×C₄⋊C₄	—	146	1	no	—
852	C₂×C₂²⋊C₄	—	146	2	no	—
853	C₂×C₂²⋊C₄	—	146	2	no	—
854	C₂×C₂²⋊C₄	—	146	2	no	—
855	C₂×C₂²⋊C₄	—	146	2	no	—
856	C₂×C₂²⋊C₄	—	146	2	no	—
857	C₂×C₂²⋊C₄	—	146	1	no	—
858	C₂×C₂²⋊C₄	—	146	1	no	—
859	C₂×C₂²⋊C₄	—	146	1	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	73	2	no	—
862	C₂×C₄²	—	146	2	no	—
863	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
864	#107	—	73	2	no	—
865	#107	—	73	2	no	—
866	#107	C₂²×D₇₃	1	1	yes	characteristic
867	#107	C₂²×D₇₃	1	1	yes	characteristic
868	#107	C₂²×D₇₃	1	1	yes	characteristic
869	#107	C₂²×D₇₃	1	1	yes	characteristic
870	#106	—	73	2	no	—
871	#106	—	73	2	no	—
872	#106	C₂²×D₇₃	1	1	yes	characteristic
873	#106	C₂²×D₇₃	1	1	yes	characteristic
874	#106	C₂²×D₇₃	1	1	yes	characteristic
875	#106	C₂²×D₇₃	1	1	yes	characteristic
876	C₄⋊C₈	—	73	2	no	—
877	C₄⋊C₈	—	73	2	no	—
878	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
879	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
880	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
881	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
882	#103	—	73	2	no	—
883	#103	—	73	2	no	—
884	#103	—	73	2	no	—
885	#103	—	73	2	no	—
886	#103	C₂²×D₇₃	1	1	yes	characteristic
887	#103	C₂²×D₇₃	1	1	yes	characteristic
888	#103	C₂²×D₇₃	1	1	yes	characteristic
889	#103	C₂²×D₇₃	1	1	yes	characteristic
890	#102	—	73	2	no	—
891	#102	—	73	2	no	—
892	#102	—	73	2	no	—
893	#102	—	73	2	no	—
894	#102	—	73	2	no	—
895	#102	—	73	2	no	—
896	#102	—	73	2	no	—
897	#102	—	73	2	no	—
898	#102	C₂²×D₇₃	1	1	yes	characteristic
899	#102	C₂²×D₇₃	1	1	yes	characteristic
900	#102	C₂²×D₇₃	1	1	yes	characteristic
901	#102	C₂²×D₇₃	1	1	yes	characteristic
902	C₂²⋊C₈	—	73	2	no	—
903	C₂²⋊C₈	—	73	2	no	—
904	C₂²⋊C₈	—	73	2	no	—
905	C₂²⋊C₈	—	73	2	no	—
906	#97	—	73	2	no	—
907	#97	—	73	2	no	—
908	C₄×C₈	—	73	2	no	—
909	C₄×C₈	—	73	2	no	—
910	C₂⁴	—	146	2	no	—
911	C₂⁴	—	146	1	no	—
912	C₂⁴	—	146	1	no	—
913	#41	—	2	2	no	—
914	#41	—	146	8	no	—
915	#41	—	146	4	no	—
916	#41	—	146	4	no	—
917	#41	—	146	2	no	—
918	#41	—	146	2	no	—
919	#41	#11924029	1	4	yes	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	73	1	no	—
923	C₂×Q₈	—	73	2	no	—
924	C₂×Q₈	—	146	2	no	—
925	C₂×Q₈	—	146	2	no	—
926	C₂×Q₈	—	146	1	no	—
927	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	73	2	no	—
930	C₂×D₄	—	73	1	no	—
931	C₂×D₄	—	73	4	no	—
932	C₂×D₄	—	73	2	no	—
933	C₂×D₄	—	73	2	no	—
934	C₂×D₄	—	146	2	no	—
935	C₂×D₄	—	146	2	no	—
936	C₂×D₄	—	146	2	no	—
937	C₂×D₄	—	146	8	no	—
938	C₂×D₄	—	146	2	no	—
939	C₂×D₄	—	146	4	no	—
940	C₂×D₄	—	146	16	no	—
941	C₂×D₄	—	146	4	no	—
942	C₂×D₄	—	146	1	no	—
943	C₂×D₄	—	146	1	no	—
944	C₂×D₄	—	146	2	no	—
945	C₂×D₄	—	146	2	no	—
946	C₂×D₄	—	146	2	no	—
947	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	584	2	no	—
952	C₂²×C₄	—	584	4	no	—
953	C₂²×C₄	—	73	2	no	—
954	C₂²×C₄	—	73	2	no	—
955	C₂²×C₄	—	73	2	no	—
956	C₂²×C₄	—	146	2	no	—
957	C₂²×C₄	—	146	2	no	—
958	C₂²×C₄	—	146	2	no	—
959	C₂²×C₄	—	146	2	no	—
960	C₂²×C₄	—	146	2	no	—
961	C₂²×C₄	—	146	2	no	—
962	C₂²×C₄	—	146	1	no	—
963	C₂²×C₄	—	146	2	no	—
964	C₂²×C₄	—	146	2	no	—
965	C₂²×C₄	—	146	1	no	—
966	C₂²×C₄	—	146	2	no	—
967	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
968	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
969	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
970	Q₁₆	—	146	4	no	—
971	SD₁₆	—	146	4	no	—
972	SD₁₆	—	146	4	no	—
973	SD₁₆	—	146	4	no	—
974	SD₁₆	—	146	4	no	—
975	D₈	—	146	4	no	—
976	D₈	—	146	4	no	—
977	D₈	—	146	4	no	—
978	M₁₆	—	146	2	no	—
979	M₁₆	—	146	2	no	—
980	C₂×C₈	—	2	2	no	—
981	C₂×C₈	—	2	2	no	—
982	C₂×C₈	—	73	2	no	—
983	C₂×C₈	—	73	2	no	—
984	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
985	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
986	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
987	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	73	2	no	—
997	C₄⋊C₄	—	73	2	no	—
998	C₄⋊C₄	—	73	1	no	—
999	C₄⋊C₄	—	73	1	no	—
1000	C₄⋊C₄	—	73	2	no	—
1001	C₄⋊C₄	—	146	2	no	—
1002	C₄⋊C₄	—	146	2	no	—
1003	C₄⋊C₄	—	146	2	no	—
1004	C₄⋊C₄	—	146	2	no	—
1005	C₄⋊C₄	—	146	2	no	—
1006	C₄⋊C₄	—	146	2	no	—
1007	C₄⋊C₄	—	146	1	no	—
1008	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1011	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1012	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	73	2	no	—
1020	C₂²⋊C₄	—	73	2	no	—
1021	C₂²⋊C₄	—	73	2	no	—
1022	C₂²⋊C₄	—	146	2	no	—
1023	C₂²⋊C₄	—	146	2	no	—
1024	C₂²⋊C₄	—	146	2	no	—
1025	C₂²⋊C₄	—	146	2	no	—
1026	C₂²⋊C₄	—	146	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	—	146	2	no	—
1037	C₂²⋊C₄	—	146	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	73	2	no	—
1044	C₄²	—	73	2	no	—
1045	C₄²	—	73	2	no	—
1046	C₄²	—	146	2	no	—
1047	C₄²	—	146	2	no	—
1048	C₄²	—	146	2	no	—
1049	C₄²	—	146	2	no	—
1050	C₄²	D₄×D₇₃	1	1	yes	characteristic
1051	C₄²	D₄×D₇₃	1	1	yes	characteristic
1052	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1053	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	292	2	no	—
1056	C₂³	—	584	1	no	—
1057	C₂³	—	584	1	no	—
1058	C₂³	—	584	1	no	—
1059	C₂³	—	584	1	no	—
1060	C₂³	—	584	2	no	—
1061	C₂³	—	584	2	no	—
1062	C₂³	—	73	2	no	—
1063	C₂³	—	146	8	no	—
1064	C₂³	—	146	2	no	—
1065	C₂³	—	146	2	no	—
1066	C₂³	—	146	4	no	—
1067	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1068	Q₈	—	2	1	no	—
1069	Q₈	—	8	1	no	—
1070	Q₈	—	8	1	no	—
1071	Q₈	—	292	2	no	—
1072	Q₈	—	146	2	no	—
1073	Q₈	—	146	2	no	—
1074	Q₈	—	146	2	no	—
1075	Q₈	C₂×#11924029	1	2	yes	—
1076	D₄	—	2	4	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	292	2	no	—
1079	D₄	—	584	2	no	—
1080	D₄	—	584	2	no	—
1081	D₄	—	73	4	no	—
1082	D₄	—	146	8	no	—
1083	D₄	—	146	8	no	—
1084	D₄	—	146	4	no	—
1085	D₄	—	146	2	no	—
1086	D₄	—	146	2	no	—
1087	D₄	—	146	2	no	—
1088	D₄	—	146	4	no	—
1089	D₄	—	146	2	no	—
1090	D₄	C₂×#11924029	1	2	yes	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	292	4	no	—
1104	C₂×C₄	—	292	2	no	—
1105	C₂×C₄	—	292	2	no	—
1106	C₂×C₄	—	292	2	no	—
1107	C₂×C₄	—	584	2	no	—
1108	C₂×C₄	—	584	2	no	—
1109	C₂×C₄	—	584	2	no	—
1110	C₂×C₄	—	584	2	no	—
1111	C₂×C₄	—	584	2	no	—
1112	C₂×C₄	—	584	2	no	—
1113	C₂×C₄	—	584	1	no	—
1114	C₂×C₄	—	584	2	no	—
1115	C₂×C₄	—	73	2	no	—
1116	C₂×C₄	—	73	2	no	—
1117	C₂×C₄	—	73	2	no	—
1118	C₂×C₄	—	146	8	no	—
1119	C₂×C₄	—	146	2	no	—
1120	C₂×C₄	—	146	2	no	—
1121	C₂×C₄	—	146	2	no	—
1122	C₂×C₄	—	146	2	no	—
1123	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1124	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1125	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1126	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1127	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1128	C₂×C₄	#41×D₇₃	1	2	yes	—
1129	C₂×C₄	C₂×#11924029	1	2	yes	—
1130	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	146	2	no	—
1136	C₈	—	146	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	292	2	no	—
1143	C₂²	—	292	2	no	—
1144	C₂²	—	292	2	no	—
1145	C₂²	—	292	2	no	—
1146	C₂²	—	292	2	no	—
1147	C₂²	—	584	4	no	—
1148	C₂²	—	584	8	no	—
1149	C₂²	—	1168	2	no	—
1150	C₂²	—	146	2	no	—
1151	C₂²	—	146	2	no	—
1152	C₂²	—	146	4	no	—
1153	C₂²	—	146	2	no	—
1154	C₂²	#17989100	1	2	yes	—
1155	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	292	2	no	—
1168	C₄	—	292	2	no	—
1169	C₄	—	146	2	no	—
1170	C₄	—	146	2	no	—
1171	C₄	—	146	2	no	—
1172	C₄	#17989100	1	2	yes	—
1173	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1174	C₄	C₂²×#11924029	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	292	4	no	—
1178	C₂	—	292	2	no	—
1179	C₂	—	584	2	no	—
1180	C₂	C₂×#17989100	1	1	yes	characteristic
1181	C₂	#22624700	1	1	yes	characteristic
1182	C₂	#22624708	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×#3076	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#22619202	C₂
hypercenter	#3076	D₇₃
hypocenter	C₇₃	#60592
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #22623829	C₂	semidirect
2. C₄×#14556637	C₂	semidirect
3. #22620215	C₂	semidirect
4. #22620200	C₂	semidirect
5. #22620122	C₂	semidirect
6. #22620120	C₂	semidirect
7. #22620074	C₂	semidirect
8. #22620047	C₂	semidirect
9. #22619983	C₂	semidirect
10. #22619956	C₂	semidirect
11. #22619903	C₂	semidirect
12. #22619892	C₂	semidirect
13. #22619724	C₂	semidirect
14. #22619425	C₂	semidirect
15. C₂×#17988803	C₂	semidirect
16. #22619211	C₂	semidirect
18. #22618789	C₂	semidirect
19. #22618782	C₂	semidirect
20. #22618777	C₂	semidirect
21. #22618766	C₂	semidirect
22. #22618596	C₂	semidirect
23. C₇₃×#3076	C₂	semidirect
35. #17989211	C₂²	semidirect
36. #17989211	C₂²	semidirect
39. #17989122	C₂²	semidirect
40. #17989122	C₂²	semidirect
41. C₂×#14556579	C₂²	semidirect
43. #17989069	C₂²	semidirect
46. #17989064	C₂²	semidirect
49. #17989061	C₂²	semidirect
51. #17989059	C₂²	semidirect
52. C₄×#11924029	C₂²	semidirect
58. C₄×D₄×D₇₃	C₂²	semidirect
59. #17988931	C₂²	semidirect
60. #17988930	C₂²	semidirect
61. #17988924	C₂²	semidirect
62. #17988919	C₂²	semidirect
63. #17988914	C₂²	semidirect
64. #17988913	C₂²	semidirect
65. #17988907	C₂²	semidirect
66. #17988902	C₂²	semidirect
67. #17988884	C₂²	semidirect
68. #17988884	C₂²	semidirect
69. #17988874	C₂²	semidirect
70. #17988864	C₂²	semidirect
71. #17988809	C₂²	semidirect
72. #17988809	C₂²	semidirect
73. #17988803	C₂²	semidirect
74. #17988803	C₂²	semidirect
75. #17988803	C₂²	semidirect
76. #17988803	C₂²	semidirect
77. #17988802	C₂²	semidirect
78. #17988802	C₂²	semidirect
79. #17988752	C₂²	semidirect
80. #17988752	C₂²	semidirect
81. #17988739	C₂²	semidirect
82. #17988739	C₂²	semidirect
87. #17988698	C₂²	semidirect
88. #17988698	C₂²	semidirect
89. #17988696	C₂²	semidirect
90. #17988691	C₂²	semidirect
91. #17988690	C₂²	semidirect
92. #17988686	C₂²	semidirect
93. #17988686	C₂²	semidirect
94. #17988684	C₂²	semidirect
95. #17988679	C₂²	semidirect
96. #17988678	C₂²	semidirect
97. #17988674	C₂²	semidirect
98. #17988674	C₂²	semidirect
99. #17988672	C₂²	semidirect
100. #17988669	C₂²	semidirect
101. #17988669	C₂²	semidirect
102. #17988667	C₂²	semidirect
103. #17988647	C₂²	semidirect
104. #17988647	C₂²	semidirect
105. #17988643	C₂²	semidirect
106. #17988639	C₂²	semidirect
107. #17988630	C₂²	semidirect
108. #17988630	C₂²	semidirect
109. #17988611	C₂²	semidirect
110. #17988595	C₂²	semidirect
113. #17988591	C₂²	semidirect
114. C₂×#14556516	C₂²	semidirect
115. C₂×#14556513	C₂²	semidirect
118. #17988542	C₂²	semidirect
119. #17988542	C₂²	semidirect
120. #533×C₇₃	C₂²	semidirect
122. #479×C₇₃	C₂²	semidirect
123. #479×C₇₃	C₂²	semidirect
124. #478×C₇₃	C₂²	semidirect
125. #478×C₇₃	C₂²	semidirect
126. #477×C₇₃	C₂²	semidirect
127. #476×C₇₃	C₂²	semidirect
128. #475×C₇₃	C₂²	semidirect
129. #474×C₇₃	C₂²	semidirect
130. #427×C₇₃	C₂²	semidirect
131. #427×C₇₃	C₂²	semidirect
132. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
605. #3076	D₇₃	semidirect
615. C₇₃	#60592	semidirect
631. #533	C₂×D₇₃	semidirect
661. #479	C₂×D₇₃	semidirect
662. #479	C₂×D₇₃	semidirect
665. #478	C₂×D₇₃	semidirect
666. #478	C₂×D₇₃	semidirect
667. #477	C₂×D₇₃	semidirect
669. #476	C₂×D₇₃	semidirect
670. #475	C₂×D₇₃	semidirect
672. #474	C₂×D₇₃	semidirect
711. #427	C₂×D₇₃	semidirect
712. #427	C₂×D₇₃	semidirect
714. C₂×C₄⋊C₈	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623829	2
C₄×#14556637	2
#22620215	2
#22620200	2
#22620122	2
#22620120	2
#22620074	2
#22620047	2
#22619983	2
#22619956	2
#22619903	2
#22619892	2
#22619724	2
#22619425	2
C₂×#17988803	2
#22619211	2
#22619202	2
#22618789	2
#22618782	2
#22618777	2
#22618766	2
#22618596	2
C₇₃×#3076	2
#60592	73