Subgroups — #6344466

Order 512.

1481 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60295	C₂	1	1	yes	maximal, characteristic
2	#60292	C₂	1	1	yes	maximal, characteristic
3	#60280	C₂	1	1	yes	maximal, characteristic
4	#17841	C₂	1	1	yes	maximal, characteristic, complemented
5	#17841	C₂	1	1	yes	maximal, characteristic, complemented
6	#17839	C₂	1	1	yes	maximal, characteristic, complemented
7	#17839	C₂	1	1	yes	maximal, characteristic, complemented
8	#17837	C₂	1	1	yes	maximal, characteristic, complemented
9	#17836	C₂	1	1	yes	maximal, characteristic, complemented
10	#17835	C₂	1	1	yes	maximal, characteristic, complemented
11	#17834	C₂	1	1	yes	maximal, characteristic, complemented
12	#17833	C₂	1	2	yes	maximal, complemented
13	#17831	C₂	1	2	yes	maximal, complemented
14	#17829	C₂	1	2	yes	maximal, complemented
15	#17827	C₂	1	2	yes	maximal, complemented
16	#17825	C₂	1	2	yes	maximal, complemented
17	#17824	C₂	1	2	yes	maximal, complemented
18	#17819	C₂	1	1	yes	maximal, characteristic, complemented
19	#17815	C₂	1	1	yes	maximal, characteristic, complemented
20	#17812	C₂	1	2	yes	maximal, complemented
21	#17811	C₂	1	2	yes	maximal, complemented
22	#17806	C₂	1	1	yes	maximal, characteristic, complemented
23	#17803	C₂	1	1	yes	maximal, characteristic, complemented
24	#3444	C₂²	1	1	yes	characteristic
25	#2994	C₄	1	4	yes	—
26	#2994	C₄	1	2	yes	—
27	#2994	C₄	1	2	yes	—
28	#2991	C₂²	1	1	yes	characteristic
29	#2991	C₂²	1	1	yes	characteristic
30	#2991	C₂²	1	1	yes	characteristic
31	#2991	C₂²	1	1	yes	characteristic
32	#2990	C₂²	1	1	yes	characteristic
33	#2990	C₂²	1	1	yes	characteristic
34	#2990	C₂²	1	1	yes	characteristic
35	#2990	C₂²	1	1	yes	characteristic
36	#2989	C₂²	1	2	yes	—
37	#2989	C₂²	1	2	yes	—
38	#2989	C₂²	1	2	yes	—
39	#2988	C₂²	1	2	yes	—
40	#2986	—	2	1	no	—
41	#2986	C₄	1	2	yes	—
42	#2985	—	2	1	no	—
43	#2981	—	2	1	no	—
44	#2979	—	2	1	no	—
45	#2979	C₄	1	2	yes	—
46	#2978	—	2	2	no	—
47	#2977	C₄	1	4	yes	—
48	#2976	—	2	2	no	—
49	#2969	—	2	2	no	—
50	#2969	—	2	1	no	—
51	#2969	—	2	1	no	—
52	#2967	—	2	2	no	—
53	#2966	—	2	1	no	—
54	#2966	—	2	1	no	—
55	#2965	C₂²	1	2	yes	—
56	#2965	C₂²	1	1	yes	characteristic
57	#2965	C₂²	1	1	yes	characteristic
58	C₈×#41	C₂²	1	2	yes	—
59	C₈×#41	C₂²	1	1	yes	characteristic
60	C₈×#41	C₂²	1	1	yes	characteristic
61	#2925	C₂²	1	2	yes	—
62	#2925	C₂²	1	2	yes	—
63	#2925	C₂²	1	2	yes	—
64	#2925	C₂²	1	2	yes	—
65	#2922	C₂²	1	2	yes	—
66	#2922	C₂²	1	2	yes	—
67	#2920	C₂²	1	1	yes	characteristic
68	#2920	C₂²	1	1	yes	characteristic
69	#2920	C₂²	1	1	yes	characteristic
70	C₂×#431	C₂²	1	1	yes	characteristic
71	C₂×#431	C₂²	1	1	yes	characteristic
72	C₂×#431	C₂²	1	1	yes	characteristic
73	#1574	C₂²	1	1	yes	characteristic
74	#1574	C₂²	1	1	yes	characteristic
75	#1574	C₂²	1	1	yes	characteristic
76	#1574	C₂²	1	1	yes	characteristic
77	#1574	C₂²	1	2	yes	—
78	#1574	C₂²	1	2	yes	—
79	#1574	C₂²	1	1	yes	characteristic
80	#1574	C₂²	1	1	yes	characteristic
81	#1574	C₂²	1	1	yes	characteristic
82	#1574	C₂²	1	1	yes	characteristic
83	#1574	C₂²	1	2	yes	complemented
84	#1574	C₂²	1	2	yes	complemented
85	#1574	C₂²	1	2	yes	complemented
86	#1574	C₂²	1	2	yes	complemented
87	#1573	C₂²	1	2	yes	—
88	#1573	C₂²	1	2	yes	—
89	#1573	C₂²	1	2	yes	complemented
90	#1573	C₂²	1	2	yes	complemented
91	#1573	C₂²	1	2	yes	complemented
92	#1573	C₂²	1	2	yes	complemented
93	#1572	C₂²	1	1	yes	characteristic
94	#1572	C₂²	1	1	yes	characteristic
95	#1572	C₂²	1	1	yes	characteristic
96	#1572	C₂²	1	1	yes	characteristic
97	#1572	C₂²	1	2	yes	—
98	#1572	C₂²	1	2	yes	—
99	#1572	C₂²	1	2	yes	—
100	#1572	C₂²	1	2	yes	—
101	#1572	C₂²	1	2	yes	complemented
102	#1572	C₂²	1	2	yes	complemented
103	#1572	C₂²	1	2	yes	complemented
104	#1572	C₂²	1	2	yes	complemented
105	#1571	C₂²	1	1	yes	characteristic
106	#1571	C₂²	1	1	yes	characteristic
107	#1571	C₂²	1	2	yes	complemented
108	#1571	C₂²	1	2	yes	complemented
109	#1570	C₂²	1	1	yes	characteristic
110	#1570	C₂²	1	1	yes	characteristic
111	#1570	C₂²	1	2	yes	complemented
112	#1570	C₂²	1	2	yes	complemented
113	#1569	C₂²	1	2	yes	complemented
114	#1569	C₂²	1	2	yes	complemented
115	#1569	C₂²	1	2	yes	complemented
116	#1569	C₂²	1	2	yes	complemented
117	#1568	C₂²	1	2	yes	—
118	#1568	C₂²	1	2	yes	—
119	#1568	C₂²	1	2	yes	complemented
120	#1568	C₂²	1	2	yes	complemented
121	#1567	C₂²	1	1	yes	characteristic
122	#1567	C₂²	1	1	yes	characteristic
123	#1567	C₂²	1	2	yes	complemented
124	#1566	C₂²	1	1	yes	characteristic
125	#1566	C₂²	1	1	yes	characteristic
126	#1566	C₂²	1	2	yes	complemented
127	#1565	C₂²	1	2	yes	complemented
128	#1565	C₂²	1	2	yes	complemented
129	#1565	C₂²	1	2	yes	complemented
130	#1565	C₂²	1	2	yes	complemented
131	#1564	C₂²	1	1	yes	characteristic
132	#1564	C₂²	1	1	yes	characteristic
133	#1564	C₂²	1	1	yes	characteristic
134	#1564	C₂²	1	1	yes	characteristic
135	#1564	C₂²	1	2	yes	—
136	#1564	C₂²	1	2	yes	—
137	#1564	C₂²	1	2	yes	complemented
138	#1564	C₂²	1	2	yes	complemented
139	C₂×#335	C₂²	1	2	yes	complemented
140	C₂×#334	C₂²	1	2	yes	complemented
141	#533	C₂×C₄	1	1	yes	characteristic
142	#533	D₄	1	1	yes	characteristic
143	#533	Q₈	1	1	yes	characteristic
144	#532	C₂×C₄	1	1	yes	characteristic
145	#532	D₄	1	1	yes	characteristic
146	#532	Q₈	1	1	yes	characteristic
147	#529	C₂×C₄	1	2	yes	—
148	#529	C₂×C₄	1	1	yes	characteristic
149	#529	C₂×C₄	1	1	yes	characteristic
150	#529	D₄	1	1	yes	characteristic
151	#529	D₄	1	1	yes	characteristic
152	#529	D₄	1	2	yes	—
153	#529	Q₈	1	2	yes	—
154	#529	Q₈	1	2	yes	—
155	#525	C₂×C₄	1	2	yes	—
156	#525	D₄	1	2	yes	—
157	#525	Q₈	1	1	yes	characteristic
158	#525	Q₈	1	1	yes	characteristic
159	C₄×#41	C₂³	1	2	yes	—
160	C₄×#41	C₂³	1	2	yes	—
161	C₄×#41	C₂³	1	1	yes	characteristic
162	C₄×#41	C₂³	1	1	yes	characteristic
163	C₂²×C₄²	C₂³	1	1	yes	characteristic
164	#446	—	2	1	no	—
165	#446	—	2	1	no	—
166	#446	—	2	2	no	—
167	#446	—	2	2	no	—
168	#446	—	2	1	no	—
169	#446	—	2	1	no	—
170	#446	—	2	2	no	—
171	#446	C₂×C₄	1	4	yes	—
172	#446	C₂×C₄	1	2	yes	—
173	#446	C₂×C₄	1	2	yes	—
174	C₈×Q₈	—	2	1	no	—
175	C₈×Q₈	—	2	1	no	—
176	C₈×Q₈	—	2	1	no	—
177	C₈×Q₈	—	2	1	no	—
178	C₈×Q₈	—	2	2	no	—
179	C₈×Q₈	C₂×C₄	1	4	yes	—
180	C₈×Q₈	C₂×C₄	1	2	yes	—
181	C₈×Q₈	C₂×C₄	1	2	yes	—
182	#436	—	2	1	no	—
183	#436	—	2	1	no	—
184	#436	—	2	2	no	—
185	#436	—	2	2	no	—
186	#436	—	2	2	no	—
187	#436	—	2	2	no	—
188	#436	—	2	2	no	—
189	#436	—	2	2	no	—
190	#436	—	2	2	no	—
191	#436	—	2	1	no	—
192	#436	—	2	1	no	—
193	#436	C₂×C₄	1	4	yes	—
194	#436	C₂×C₄	1	2	yes	—
195	#436	C₂×C₄	1	2	yes	—
196	#435	—	2	2	no	—
197	#435	—	2	2	no	—
198	#435	—	2	2	no	—
199	#435	—	2	2	no	—
200	#435	—	2	2	no	—
201	#435	—	2	2	no	—
202	#435	—	2	2	no	—
203	#435	—	2	2	no	—
204	#435	—	2	2	no	—
205	#435	—	2	2	no	—
206	#435	C₂×C₄	1	4	yes	—
207	#435	C₂×C₄	1	4	yes	—
208	#435	C₂×C₄	1	4	yes	—
209	#435	C₂×C₄	1	4	yes	—
210	C₈×D₄	—	2	2	no	—
211	C₈×D₄	—	2	2	no	—
212	C₈×D₄	—	2	1	no	—
213	C₈×D₄	—	2	1	no	—
214	C₈×D₄	—	2	2	no	—
215	C₈×D₄	—	2	1	no	—
216	C₈×D₄	—	2	1	no	—
217	C₈×D₄	C₂×C₄	1	4	yes	—
218	C₈×D₄	C₂×C₄	1	4	yes	—
219	C₈×D₄	C₂×C₄	1	4	yes	—
220	C₈×D₄	C₂×C₄	1	4	yes	—
221	C₈×D₄	C₂×C₄	1	4	yes	—
222	C₈×D₄	C₂×C₄	1	2	yes	—
223	C₈×D₄	C₂×C₄	1	2	yes	—
224	#433	—	2	2	no	—
225	#433	—	2	2	no	—
226	#433	—	2	2	no	—
227	#433	—	2	2	no	—
228	#433	—	2	2	no	—
229	#433	—	2	2	no	—
230	#433	—	2	2	no	—
231	#433	—	2	2	no	—
232	#433	C₂×C₄	1	4	yes	—
233	#433	C₂×C₄	1	4	yes	—
234	#433	C₂×C₄	1	4	yes	—
235	#433	C₂×C₄	1	4	yes	—
236	#432	—	2	1	no	—
237	#432	—	2	1	no	—
238	#432	—	2	1	no	—
239	#432	C₂³	1	1	yes	characteristic
240	#432	C₂³	1	2	yes	—
241	#432	C₂³	1	1	yes	characteristic
242	#432	C₂³	1	2	yes	—
243	#432	C₂³	1	2	yes	—
244	#432	C₂³	1	2	yes	—
245	#432	C₂³	1	2	yes	—
246	#432	C₂³	1	2	yes	—
247	#431	—	2	1	no	—
248	#431	—	2	1	no	—
249	#431	—	2	1	no	—
250	#431	—	2	1	no	—
251	#431	—	2	1	no	—
252	#431	C₂×C₄	1	2	yes	—
253	#431	C₂×C₄	1	2	yes	—
254	#431	C₂×C₄	1	2	yes	—
255	#431	C₂×C₄	1	2	yes	—
256	#431	C₂³	1	1	yes	characteristic
257	#431	C₂³	1	1	yes	characteristic
258	#431	C₂³	1	2	yes	—
259	#431	C₂³	1	1	yes	characteristic
260	#431	C₂³	1	1	yes	characteristic
261	#431	C₂³	1	1	yes	characteristic
262	#431	C₂³	1	1	yes	characteristic
263	#431	C₂³	1	2	yes	—
264	#431	C₂³	1	2	yes	—
265	#431	C₂³	1	2	yes	—
266	#431	C₂³	1	2	yes	—
267	#431	C₂³	1	2	yes	—
268	#431	C₂³	1	1	yes	characteristic
269	#431	C₂³	1	2	yes	—
270	#431	C₂³	1	1	yes	characteristic
271	#431	C₂³	1	2	yes	—
272	#431	C₂³	1	1	yes	characteristic
273	#431	C₂³	1	1	yes	characteristic
274	#431	C₂³	1	2	yes	—
275	#431	C₂³	1	2	yes	—
276	#431	C₂³	1	2	yes	—
277	#431	C₂³	1	1	yes	characteristic
278	#431	C₂³	1	1	yes	characteristic
279	#424	C₂×C₄	1	4	yes	—
280	#424	C₂×C₄	1	4	yes	—
281	#423	C₂³	1	1	yes	characteristic
282	#423	C₂³	1	1	yes	characteristic
283	#423	C₂³	1	1	yes	characteristic
284	#423	C₂³	1	1	yes	characteristic
285	#423	C₂³	1	2	yes	—
286	#423	C₂³	1	2	yes	—
287	#423	C₂³	1	2	yes	—
288	#423	C₂³	1	2	yes	—
289	#423	C₂³	1	1	yes	characteristic
290	#423	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
292	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
293	C₂×C₄⋊C₈	C₂³	1	2	yes	—
294	C₂×C₄⋊C₈	C₂³	1	2	yes	—
295	C₂×C₄⋊C₈	C₂³	1	2	yes	—
296	C₂×C₄⋊C₈	C₂³	1	2	yes	—
297	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
299	#408	—	2	2	no	—
300	#408	—	2	2	no	—
301	#408	—	2	2	no	—
302	#408	—	2	2	no	—
303	#408	C₂×C₄	1	4	yes	—
304	#408	C₂×C₄	1	4	yes	—
305	#407	—	2	1	no	—
306	#407	—	2	1	no	—
307	#407	—	2	1	no	—
308	C₂×C₂²⋊C₈	—	2	1	no	—
309	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
311	#405	—	2	2	no	—
312	#405	—	2	2	no	—
313	#405	—	2	2	no	—
314	#405	—	2	2	no	—
315	C₄×M₁₆	—	2	1	no	—
316	C₄×M₁₆	—	2	1	no	—
317	C₄×M₁₆	—	2	1	no	—
318	C₄×M₁₆	C₂³	1	2	yes	—
319	C₄×M₁₆	C₂³	1	2	yes	—
320	C₂×C₄×C₈	—	2	1	no	—
321	C₂×C₄×C₈	C₂³	1	2	yes	—
322	C₂×C₄×C₈	C₂³	1	2	yes	—
323	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂³	1	2	yes	—
326	#335	C₂³	1	1	yes	characteristic
327	#335	C₂³	1	2	yes	—
328	#335	C₂³	1	2	yes	—
329	#335	C₂³	1	2	yes	—
330	#335	C₂³	1	1	yes	characteristic
331	#335	C₂³	1	1	yes	characteristic
332	#335	C₂³	1	1	yes	characteristic
333	#335	C₂³	1	2	yes	—
334	#335	C₂³	1	1	yes	characteristic
335	#335	C₂³	1	2	yes	—
336	#335	C₂³	1	1	yes	characteristic
337	#335	C₂³	1	1	yes	characteristic
338	#335	C₂³	1	1	yes	characteristic
339	#335	C₂³	1	2	yes	—
340	#335	C₂³	1	2	yes	—
341	#335	C₂³	1	2	yes	—
342	#335	C₂³	1	2	yes	—
343	#335	C₂³	1	2	yes	—
344	#335	C₂³	1	2	yes	—
345	#335	C₂³	1	2	yes	—
346	#334	C₂³	1	1	yes	characteristic
347	#334	C₂³	1	2	yes	—
348	#334	C₂³	1	2	yes	—
349	#334	C₂³	1	2	yes	—
350	#334	C₂³	1	1	yes	characteristic
351	#334	C₂³	1	1	yes	characteristic
352	#334	C₂³	1	1	yes	characteristic
353	#334	C₂³	1	2	yes	—
354	#334	C₂³	1	1	yes	characteristic
355	#334	C₂³	1	2	yes	—
356	#334	C₂³	1	1	yes	characteristic
357	#334	C₂³	1	1	yes	characteristic
358	#334	C₂³	1	1	yes	characteristic
359	#334	C₂³	1	2	yes	—
360	#334	C₂³	1	2	yes	—
361	#334	C₂³	1	2	yes	—
362	#334	C₂³	1	2	yes	—
363	#334	C₂³	1	2	yes	—
364	#334	C₂³	1	2	yes	—
365	#334	C₂³	1	2	yes	—
366	C₂×#41	C₂²×C₄	1	2	yes	—
367	C₂×#41	C₂×D₄	1	2	yes	—
368	C₂×#41	C₂×Q₈	1	1	yes	characteristic
369	C₂×#41	C₂×Q₈	1	1	yes	characteristic
370	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
371	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
372	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	C₂²×C₄	1	4	yes	—
384	C₂×M₁₆	C₂²×C₄	1	4	yes	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	2	2	no	—
391	C₂²×C₈	C₂²×C₄	1	2	yes	—
392	C₂²×C₈	C₂²×C₄	1	2	yes	—
393	C₂²×C₈	C₂²×C₄	1	4	yes	—
394	C₂²×C₈	C₂²×C₄	1	4	yes	—
395	C₂²×C₈	C₂²×C₄	1	4	yes	—
396	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
397	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
398	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
399	#127	C₄⋊C₄	1	1	yes	characteristic
400	#126	C₄⋊C₄	1	2	yes	—
401	#126	C₄⋊C₄	1	2	yes	—
402	#126	C₄⋊C₄	1	2	yes	—
403	#126	C₄⋊C₄	1	2	yes	—
404	#125	C₄⋊C₄	1	1	yes	characteristic
405	#125	C₄⋊C₄	1	1	yes	characteristic
406	#125	C₄⋊C₄	1	2	yes	—
407	#125	C₄⋊C₄	1	2	yes	—
408	#124	C₄⋊C₄	1	1	yes	characteristic
409	#124	C₄⋊C₄	1	1	yes	characteristic
410	#124	C₄⋊C₄	1	2	yes	—
411	#124	C₄⋊C₄	1	2	yes	—
412	#123	C₄⋊C₄	1	2	yes	—
413	#123	C₄⋊C₄	1	2	yes	—
414	#123	C₄⋊C₄	1	2	yes	—
415	#123	C₄⋊C₄	1	2	yes	—
416	#123	C₄⋊C₄	1	2	yes	—
417	#123	C₄⋊C₄	1	2	yes	—
418	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
419	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
420	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
421	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
422	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
423	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
424	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
425	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
426	#121	C₄⋊C₄	1	2	yes	—
427	#121	C₄⋊C₄	1	2	yes	—
428	#121	C₄⋊C₄	1	2	yes	—
429	#121	C₄⋊C₄	1	2	yes	—
430	#121	C₄⋊C₄	1	1	yes	characteristic
431	#121	C₄⋊C₄	1	1	yes	characteristic
432	#121	C₄⋊C₄	1	1	yes	characteristic
433	#121	C₄⋊C₄	1	1	yes	characteristic
434	#120	C₄⋊C₄	1	2	yes	—
435	#120	C₄⋊C₄	1	2	yes	—
436	C₄×Q₈	C₂²×C₄	1	2	yes	—
437	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
438	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
439	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
440	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
441	C₄×Q₈	C₂×D₄	1	2	yes	—
442	C₄×Q₈	C₂×Q₈	1	2	yes	—
443	C₄×Q₈	C₂×Q₈	1	2	yes	—
444	C₄×D₄	C₂²×C₄	1	2	yes	—
445	C₄×D₄	C₂²×C₄	1	2	yes	—
446	C₄×D₄	C₂²×C₄	1	2	yes	—
447	C₄×D₄	C₂²×C₄	1	2	yes	—
448	C₄×D₄	C₂²×C₄	1	2	yes	—
449	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
450	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
451	C₄×D₄	C₂×D₄	1	2	yes	—
452	C₄×D₄	C₂×D₄	1	2	yes	—
453	C₄×D₄	C₂×D₄	1	2	yes	—
454	C₄×D₄	C₂×D₄	1	2	yes	—
455	C₄×D₄	C₂×D₄	1	1	yes	characteristic
456	C₄×D₄	C₂×D₄	1	1	yes	characteristic
457	C₄×D₄	C₂×D₄	1	2	yes	—
458	C₄×D₄	C₂×Q₈	1	2	yes	—
459	C₄×D₄	C₂×Q₈	1	2	yes	—
460	C₄×D₄	C₂×Q₈	1	2	yes	—
461	C₄×D₄	C₂×Q₈	1	2	yes	—
462	C₄×D₄	C₂×Q₈	1	2	yes	—
463	C₄×D₄	C₂×Q₈	1	2	yes	—
464	#117	C₂²×C₄	1	2	yes	—
465	#117	C₂²×C₄	1	2	yes	—
466	#117	C₂²×C₄	1	2	yes	—
467	#117	C₂×D₄	1	2	yes	—
468	#117	C₂×D₄	1	2	yes	—
469	#117	C₂×D₄	1	2	yes	—
470	#117	C₂×Q₈	1	1	yes	characteristic
471	#117	C₂×Q₈	1	1	yes	characteristic
472	#117	C₂×Q₈	1	2	yes	—
473	#117	C₂×Q₈	1	2	yes	—
474	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
475	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
476	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
477	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
478	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
479	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
480	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
481	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
482	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
483	C₂×C₄²	C₂⁴	1	2	yes	—
484	C₂×C₄²	C₂⁴	1	2	yes	—
485	C₂×C₄²	C₂⁴	1	1	yes	characteristic
486	C₂×C₄²	C₂⁴	1	1	yes	characteristic
487	C₂×C₄²	C₂⁴	1	1	yes	characteristic
488	C₄⋊C₈	—	2	1	no	—
489	C₄⋊C₈	—	2	1	no	—
490	C₄⋊C₈	—	2	2	no	—
491	C₄⋊C₈	—	2	2	no	—
492	C₄⋊C₈	—	2	2	no	—
493	C₄⋊C₈	—	2	2	no	—
494	C₄⋊C₈	—	2	1	no	—
495	C₄⋊C₈	—	2	1	no	—
496	C₄⋊C₈	—	2	1	no	—
497	C₄⋊C₈	—	2	1	no	—
498	C₄⋊C₈	—	2	1	no	—
499	C₄⋊C₈	—	2	1	no	—
500	C₄⋊C₈	—	2	2	no	—
501	C₄⋊C₈	—	2	2	no	—
502	C₄⋊C₈	—	2	2	no	—
503	C₄⋊C₈	—	2	2	no	—
504	C₄⋊C₈	C₂²×C₄	1	2	yes	—
505	C₄⋊C₈	C₂²×C₄	1	2	yes	—
506	C₄⋊C₈	C₂²×C₄	1	4	yes	—
507	C₄⋊C₈	C₂²×C₄	1	2	yes	—
508	C₄⋊C₈	C₂²×C₄	1	2	yes	—
509	C₄⋊C₈	C₂²×C₄	1	2	yes	—
510	C₄⋊C₈	C₂²×C₄	1	2	yes	—
511	C₄⋊C₈	C₂²×C₄	1	4	yes	—
512	C₄⋊C₈	C₂²×C₄	1	4	yes	—
513	C₄⋊C₈	C₂²×C₄	1	4	yes	—
514	C₄⋊C₈	C₂²×C₄	1	4	yes	—
515	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
516	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
517	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
518	C₄⋊C₈	C₂⁴	1	2	yes	—
519	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
520	C₄⋊C₈	C₂⁴	1	2	yes	—
521	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
522	C₄⋊C₈	C₂⁴	1	2	yes	—
523	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
524	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
525	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
526	C₄⋊C₈	C₂⁴	1	2	yes	—
527	C₂²⋊C₈	—	2	1	no	—
528	C₂²⋊C₈	—	2	1	no	—
529	C₂²⋊C₈	—	2	1	no	—
530	C₂²⋊C₈	—	2	1	no	—
531	C₂²⋊C₈	—	2	2	no	—
532	C₂²⋊C₈	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	C₂²⋊C₈	—	2	2	no	—
535	C₂²⋊C₈	—	2	2	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	—	2	1	no	—
538	C₂²⋊C₈	—	2	1	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	C₂²⋊C₈	—	2	2	no	—
543	C₂²⋊C₈	—	2	2	no	—
544	C₂²⋊C₈	—	2	2	no	—
545	C₂²⋊C₈	—	2	2	no	—
546	C₂²⋊C₈	—	2	2	no	—
547	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
548	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
549	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
550	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
551	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
552	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
553	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
554	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
555	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
556	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
557	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
558	#97	—	2	2	no	—
559	#97	—	2	1	no	—
560	#97	—	2	1	no	—
561	#97	—	2	2	no	—
562	#97	—	2	2	no	—
563	#97	—	2	2	no	—
564	#97	—	2	2	no	—
565	#97	—	2	2	no	—
566	#97	C₂²×C₄	1	4	yes	—
567	#97	C₂²×C₄	1	4	yes	—
568	C₄×C₈	—	2	1	no	—
569	C₄×C₈	—	2	1	no	—
570	C₄×C₈	—	2	1	no	—
571	C₄×C₈	—	2	1	no	—
572	C₄×C₈	—	2	2	no	—
573	C₄×C₈	—	2	1	no	—
574	C₄×C₈	—	2	2	no	—
575	C₄×C₈	—	2	1	no	—
576	C₄×C₈	—	2	2	no	—
577	C₄×C₈	—	2	2	no	—
578	C₄×C₈	—	2	2	no	—
579	C₄×C₈	—	2	2	no	—
580	C₄×C₈	C₂²×C₄	1	2	yes	—
581	C₄×C₈	C₂²×C₄	1	2	yes	—
582	C₄×C₈	C₂²×C₄	1	4	yes	—
583	C₄×C₈	C₂²×C₄	1	4	yes	—
584	C₄×C₈	C₂²×C₄	1	4	yes	—
585	C₄×C₈	C₂⁴	1	1	yes	characteristic
586	C₄×C₈	C₂⁴	1	2	yes	—
587	C₄×C₈	C₂⁴	1	1	yes	characteristic
588	C₄×C₈	C₂⁴	1	2	yes	—
589	C₄×C₈	C₂⁴	1	1	yes	characteristic
590	C₄×C₈	C₂⁴	1	1	yes	characteristic
591	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
592	#41	—	4	4	no	—
593	#41	—	4	2	no	—
594	#41	—	4	2	no	—
595	#41	—	4	2	no	—
596	#41	—	4	2	no	—
597	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
598	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
599	C₂×Q₈	C₂×C₄⋊C₄	1	2	yes	—
600	C₂×Q₈	C₂×C₄⋊C₄	1	2	yes	—
601	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
602	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
603	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
604	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
605	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
606	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
607	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
608	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
609	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
610	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
617	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
619	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
620	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
621	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
622	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
623	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
624	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
625	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
626	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
627	C₂²×C₄	C₂³×C₄	1	2	yes	—
628	C₂²×C₄	C₂³×C₄	1	2	yes	—
629	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
630	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
631	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
632	C₂²×C₄	C₂²×D₄	1	2	yes	—
633	C₂²×C₄	C₂²×D₄	1	2	yes	—
634	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
635	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
636	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
637	C₂²×C₄	C₂²×Q₈	1	2	yes	—
638	C₂²×C₄	C₂²×Q₈	1	2	yes	—
639	M₁₆	—	4	4	no	—
640	M₁₆	—	4	4	no	—
641	M₁₆	—	8	1	no	—
642	M₁₆	—	8	1	no	—
643	M₁₆	—	8	1	no	—
644	M₁₆	—	8	1	no	—
645	M₁₆	—	8	1	no	—
646	M₁₆	—	8	2	no	—
647	M₁₆	—	8	2	no	—
648	M₁₆	—	8	2	no	—
649	M₁₆	—	8	2	no	—
650	M₁₆	—	8	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	2	no	—
659	C₂×C₈	—	2	2	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	—	4	4	no	—
665	C₂×C₈	—	4	2	no	—
666	C₂×C₈	—	4	2	no	—
667	C₂×C₈	—	4	4	no	—
668	C₂×C₈	—	8	1	no	—
669	C₂×C₈	—	8	2	no	—
670	C₂×C₈	—	8	2	no	—
671	C₂×C₈	—	8	2	no	—
672	C₂×C₈	—	8	2	no	—
673	C₂×C₈	—	8	1	no	—
674	C₂×C₈	C₂³×C₄	1	2	yes	—
675	C₂×C₈	C₂³×C₄	1	4	yes	—
676	C₂×C₈	C₂³×C₄	1	2	yes	—
677	C₂×C₈	C₂³×C₄	1	2	yes	—
678	C₂×C₈	C₂³×C₄	1	2	yes	—
679	C₂×C₈	C₂³×C₄	1	4	yes	—
680	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
681	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
682	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
683	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
684	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
685	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
686	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
687	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
688	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
689	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
690	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
691	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
692	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
693	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
694	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
695	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
696	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
697	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
698	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
699	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
700	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
701	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
702	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
703	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
704	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
705	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
706	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
707	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
708	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
709	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
710	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
711	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
712	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
713	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
714	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
715	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
716	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
717	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
718	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
719	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
720	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
721	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
722	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
723	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
724	C₄²	C₂³×C₄	1	1	yes	characteristic
725	C₄²	C₂³×C₄	1	1	yes	characteristic
726	C₄²	C₂³×C₄	1	2	yes	—
727	C₄²	C₂³×C₄	1	2	yes	—
728	C₄²	C₂³×C₄	1	1	yes	characteristic
729	C₄²	C₂²×D₄	1	1	yes	characteristic
730	C₄²	C₂²×D₄	1	1	yes	characteristic
731	C₄²	C₂²×D₄	1	1	yes	characteristic
732	C₄²	C₂²×D₄	1	2	yes	—
733	C₄²	C₂²×D₄	1	2	yes	—
734	C₄²	C₂²×Q₈	1	1	yes	characteristic
735	C₄²	C₂²×Q₈	1	1	yes	characteristic
736	C₄²	C₂²×Q₈	1	1	yes	characteristic
737	C₄²	C₂²×Q₈	1	2	yes	—
738	C₄²	C₂²×Q₈	1	2	yes	—
739	C₄²	C₂⁵	1	1	yes	characteristic
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
744	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
745	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
746	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
747	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	4	2	no	—
751	Q₈	—	4	2	no	—
752	D₄	—	2	2	no	—
753	D₄	—	2	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	2	no	—
757	D₄	—	4	2	no	—
758	D₄	—	4	2	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
792	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
793	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
794	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
795	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
797	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
799	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
800	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
801	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
802	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
803	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
804	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
805	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
806	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
807	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
808	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
809	C₈	—	2	2	no	—
810	C₈	—	2	4	no	—
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	4	no	—
815	C₈	—	4	1	no	—
816	C₈	—	4	1	no	—
817	C₈	—	4	1	no	—
818	C₈	—	4	2	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	2	no	—
821	C₈	—	4	1	no	—
822	C₈	—	4	1	no	—
823	C₈	—	4	2	no	—
824	C₈	—	4	1	no	—
825	C₈	—	4	2	no	—
826	C₈	—	4	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	8	2	no	—
843	C₂²	C₂³×C₄⋊C₄	1	1	yes	characteristic
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	#2916	1	2	yes	—
860	C₄	#3573	1	2	yes	—
861	C₄	#3584	1	1	yes	characteristic
862	C₄	#3584	1	1	yes	characteristic
863	C₂	—	4	2	no	—
864	C₂	—	4	2	no	—
865	C₂	—	4	1	no	—
866	C₂	—	4	1	no	—
867	C₂	—	4	1	no	—
868	C₂	#60100	1	1	yes	characteristic
869	C₂	#60108	1	1	yes	characteristic
870	C₂	C₂×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂³×C₄⋊C₄
prime radical	#3444	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #3444 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #17841	C₂	semidirect
5. #17841	C₂	semidirect
6. #17839	C₂	semidirect
7. #17839	C₂	semidirect
8. #17837	C₂	semidirect
9. #17836	C₂	semidirect
10. #17835	C₂	semidirect
11. #17834	C₂	semidirect
12. #17833	C₂	semidirect
13. #17831	C₂	semidirect
14. #17829	C₂	semidirect
15. #17827	C₂	semidirect
16. #17825	C₂	semidirect
17. #17824	C₂	semidirect
18. #17819	C₂	semidirect
19. #17815	C₂	semidirect
20. #17812	C₂	semidirect
21. #17811	C₂	semidirect
22. #17806	C₂	semidirect
23. #17803	C₂	semidirect
83. #1574	C₂²	semidirect
84. #1574	C₂²	semidirect
85. #1574	C₂²	semidirect
86. #1574	C₂²	semidirect
89. #1573	C₂²	semidirect
90. #1573	C₂²	semidirect
91. #1573	C₂²	semidirect
92. #1573	C₂²	semidirect
101. #1572	C₂²	semidirect
102. #1572	C₂²	semidirect
103. #1572	C₂²	semidirect
104. #1572	C₂²	semidirect
107. #1571	C₂²	semidirect
108. #1571	C₂²	semidirect
111. #1570	C₂²	semidirect
112. #1570	C₂²	semidirect
113. #1569	C₂²	semidirect
114. #1569	C₂²	semidirect
115. #1569	C₂²	semidirect
116. #1569	C₂²	semidirect
119. #1568	C₂²	semidirect
120. #1568	C₂²	semidirect
123. #1567	C₂²	semidirect
126. #1566	C₂²	semidirect
127. #1565	C₂²	semidirect
128. #1565	C₂²	semidirect
129. #1565	C₂²	semidirect
130. #1565	C₂²	semidirect
137. #1564	C₂²	semidirect
138. #1564	C₂²	semidirect
139. C₂×#335	C₂²	semidirect
140. C₂×#334	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#60295	2
#60292	2
#60280	2
#17841	2
#17839	2
#17837	2
#17836	2
#17835	2
#17834	2
#17833	2
#17831	2
#17829	2
#17827	2
#17825	2
#17824	2
#17819	2
#17815	2
#17812	2
#17811	2
#17806	2
#17803	2