Subgroups — C₆₇×#60562 #30739813

Order 17152.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3116	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3110	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3107	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3104	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3101	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3095	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3079	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3039	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3007	C₂	1	2	yes	maximal
13	C₄×#137×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#137×C₆₇	C₂²	1	4	yes	—
17	#533×C₆₇	—	2	1	no	—
18	#533×C₆₇	—	2	1	no	—
19	#533×C₆₇	—	2	1	no	—
20	#533×C₆₇	—	2	1	no	—
21	#533×C₆₇	C₂²	1	2	yes	—
22	#533×C₆₇	C₂²	1	2	yes	—
23	#533×C₆₇	C₂²	1	2	yes	complemented
24	#533×C₆₇	C₂²	1	2	yes	complemented
25	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#125×C₆₇	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₄×#41×C₆₇	—	2	1	no	—
31	C₄×#41×C₆₇	—	2	1	no	—
32	C₄×#41×C₆₇	—	2	1	no	—
33	C₄×#41×C₆₇	—	2	1	no	—
34	C₄×#41×C₆₇	C₂²	1	2	yes	—
35	C₄×#41×C₆₇	C₂²	1	2	yes	—
36	C₄×#41×C₆₇	C₂²	1	2	yes	—
37	C₄×#41×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
39	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₆₇	—	2	1	no	—
43	C₂×C₄×D₄×C₆₇	—	2	1	no	—
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#117×C₆₇	—	2	1	no	—
47	C₂×#117×C₆₇	—	2	1	no	—
48	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₆₇	—	2	1	no	—
50	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
51	#485×C₆₇	C₂²	1	8	yes	complemented
52	#484×C₆₇	C₂²	1	4	yes	—
53	#483×C₆₇	C₂²	1	4	yes	—
54	#477×C₆₇	C₂²	1	4	yes	complemented
55	#476×C₆₇	C₂²	1	4	yes	complemented
56	#475×C₆₇	C₂²	1	4	yes	complemented
57	#474×C₆₇	C₂²	1	4	yes	complemented
58	#462×C₆₇	C₂²	1	4	yes	complemented
59	#462×C₆₇	C₂²	1	4	yes	complemented
60	#461×C₆₇	C₂²	1	4	yes	complemented
61	#461×C₆₇	C₂²	1	4	yes	complemented
62	#452×C₆₇	C₂²	1	8	yes	—
63	#451×C₆₇	C₂²	1	4	yes	—
64	#450×C₆₇	C₂²	1	4	yes	—
65	#441×C₆₇	C₂²	1	8	yes	complemented
66	#440×C₆₇	C₂²	1	8	yes	complemented
67	C₄×Q₁₆×C₆₇	C₂²	1	8	yes	complemented
68	C₄×SD₁₆×C₆₇	C₂²	1	8	yes	complemented
69	#432×C₆₇	C₂²	1	2	yes	—
70	#432×C₆₇	C₂²	1	2	yes	complemented
71	#431×C₆₇	C₂²	1	2	yes	—
72	#431×C₆₇	C₂²	1	2	yes	complemented
73	#428×C₆₇	C₂²	1	4	yes	complemented
74	#423×C₆₇	C₂²	1	2	yes	complemented
75	#419×C₆₇	C₂²	1	4	yes	complemented
76	#417×C₆₇	C₂²	1	4	yes	—
77	#407×C₆₇	C₂²	1	2	yes	—
78	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
79	C₂×#41×C₆₇	—	2	8	no	—
80	C₂×#41×C₆₇	—	2	1	no	—
81	C₂×#41×C₆₇	—	2	1	no	—
82	C₂×#41×C₆₇	C₂³	1	2	yes	—
83	C₂×#41×C₆₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₆₇	—	2	1	no	—
85	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₆₇	—	2	1	no	—
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	C₂³×C₄×C₆₇	—	2	1	no	—
91	C₂³×C₄×C₆₇	—	2	1	no	—
92	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	#137×C₆₇	—	2	16	no	—
96	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	—
97	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	—
98	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
99	C₄⋊Q₈×C₆₇	—	2	1	no	—
100	C₄⋊Q₈×C₆₇	—	2	1	no	—
101	C₄⋊Q₈×C₆₇	—	2	1	no	—
102	C₄⋊Q₈×C₆₇	—	2	1	no	—
103	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
107	#125×C₆₇	—	2	2	no	—
108	#125×C₆₇	—	2	2	no	—
109	#125×C₆₇	—	2	2	no	—
110	#125×C₆₇	—	2	2	no	—
111	C₂²⋊Q₈×C₆₇	—	2	2	no	—
112	C₂²⋊Q₈×C₆₇	—	2	2	no	—
113	C₂²⋊Q₈×C₆₇	—	2	2	no	—
114	C₂²⋊Q₈×C₆₇	—	2	2	no	—
115	C₂²⋊Q₈×C₆₇	—	2	2	no	—
116	C₂²⋊Q₈×C₆₇	—	2	2	no	—
117	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
118	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
119	C₄×Q₈×C₆₇	—	2	2	no	—
120	C₄×Q₈×C₆₇	—	2	2	no	—
121	C₄×Q₈×C₆₇	—	2	2	no	—
122	C₄×Q₈×C₆₇	—	2	2	no	—
123	C₄×Q₈×C₆₇	—	2	1	no	—
124	C₄×Q₈×C₆₇	—	2	1	no	—
125	C₄×Q₈×C₆₇	—	2	1	no	—
126	C₄×Q₈×C₆₇	—	2	1	no	—
127	C₄×Q₈×C₆₇	—	2	2	no	—
128	C₄×Q₈×C₆₇	—	2	2	no	—
129	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
130	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
131	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
132	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
133	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
134	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
135	C₄×D₄×C₆₇	—	2	2	no	—
136	C₄×D₄×C₆₇	—	2	2	no	—
137	C₄×D₄×C₆₇	—	2	2	no	—
138	C₄×D₄×C₆₇	—	2	2	no	—
139	C₄×D₄×C₆₇	—	2	2	no	—
140	C₄×D₄×C₆₇	—	2	2	no	—
141	C₄×D₄×C₆₇	—	2	2	no	—
142	C₄×D₄×C₆₇	—	2	2	no	—
143	C₄×D₄×C₆₇	—	2	1	no	—
144	C₄×D₄×C₆₇	—	2	1	no	—
145	C₄×D₄×C₆₇	—	2	1	no	—
146	C₄×D₄×C₆₇	—	2	1	no	—
147	C₄×D₄×C₆₇	C₂³	1	2	yes	—
148	C₄×D₄×C₆₇	C₂³	1	2	yes	—
149	C₄×D₄×C₆₇	C₂³	1	2	yes	—
150	C₄×D₄×C₆₇	C₂³	1	2	yes	—
151	#117×C₆₇	—	2	2	no	—
152	#117×C₆₇	—	2	2	no	—
153	#117×C₆₇	—	2	2	no	—
154	#117×C₆₇	—	2	2	no	—
155	#117×C₆₇	—	2	1	no	—
156	#117×C₆₇	—	2	1	no	—
157	#117×C₆₇	—	2	2	no	—
158	#117×C₆₇	—	2	2	no	—
159	#117×C₆₇	—	2	2	no	—
160	#117×C₆₇	—	2	2	no	—
161	#117×C₆₇	C₂³	1	2	yes	—
162	#117×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
164	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
165	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
166	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
174	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
177	C₂×C₄²×C₆₇	—	2	1	no	—
178	C₂×C₄²×C₆₇	—	2	1	no	—
179	C₂×C₄²×C₆₇	—	2	1	no	—
180	C₂×C₄²×C₆₇	—	2	2	no	—
181	C₂×C₄²×C₆₇	—	2	2	no	—
182	C₂×C₄²×C₆₇	—	2	2	no	—
183	C₂×C₄²×C₆₇	—	2	2	no	—
184	C₂×C₄²×C₆₇	—	2	2	no	—
185	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	#107×C₆₇	C₂³	1	8	yes	—
198	#106×C₆₇	C₂³	1	8	yes	—
199	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
200	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	8	yes	—
202	#103×C₆₇	C₂³	1	8	yes	—
203	#103×C₆₇	C₂³	1	8	yes	—
204	#102×C₆₇	C₂³	1	8	yes	—
205	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
207	#97×C₆₇	C₂³	1	4	yes	—
208	C₄×C₈×C₆₇	C₂³	1	4	yes	—
209	C₂⁴×C₆₇	—	2	1	no	—
210	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
211	#41×C₆₇	—	2	8	no	—
212	#41×C₆₇	—	2	8	no	—
213	#41×C₆₇	—	2	4	no	—
214	#41×C₆₇	—	2	4	no	—
215	#41×C₆₇	—	2	4	no	—
216	#41×C₆₇	#41	1	8	yes	—
217	C₂×Q₈×C₆₇	—	2	4	no	—
218	C₂×Q₈×C₆₇	—	2	1	no	—
219	C₂×Q₈×C₆₇	—	2	2	no	—
220	C₂×Q₈×C₆₇	—	2	2	no	—
221	C₂×Q₈×C₆₇	—	2	2	no	—
222	C₂×Q₈×C₆₇	—	2	8	no	—
223	C₂×Q₈×C₆₇	—	4	4	no	—
224	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
225	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₇	—	2	8	no	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	2	2	no	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₇	—	2	8	no	—
233	C₂²×C₄×C₆₇	—	2	1	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	4	2	no	—
247	C₂²×C₄×C₆₇	—	4	4	no	—
248	C₂²×C₄×C₆₇	—	4	4	no	—
249	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₆₇	—	2	16	no	—
268	SD₁₆×C₆₇	—	2	16	no	—
269	M₁₆×C₆₇	—	2	8	no	—
270	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	2	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	—	2	2	no	—
300	C₄²×C₆₇	—	2	2	no	—
301	C₄²×C₆₇	—	2	2	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	2	no	—
304	C₄²×C₆₇	—	2	4	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	—	2	4	no	—
307	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂³×C₆₇	—	2	4	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	4	1	no	—
328	C₂³×C₆₇	—	4	2	no	—
329	C₂³×C₆₇	—	4	2	no	—
330	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₆₇	—	2	4	no	—
334	Q₈×C₆₇	—	2	2	no	—
335	Q₈×C₆₇	—	2	8	no	—
336	Q₈×C₆₇	—	4	4	no	—
337	Q₈×C₆₇	—	4	4	no	—
338	Q₈×C₆₇	—	4	4	no	—
339	Q₈×C₆₇	C₂×#41	1	4	yes	—
340	D₄×C₆₇	—	2	8	no	—
341	D₄×C₆₇	—	2	4	no	—
342	D₄×C₆₇	—	2	8	no	—
343	D₄×C₆₇	—	2	2	no	—
344	D₄×C₆₇	C₂×#41	1	4	yes	—
345	C₂×C₄×C₆₇	—	2	4	no	—
346	C₂×C₄×C₆₇	—	2	8	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	8	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	4	no	—
365	C₂×C₄×C₆₇	—	2	4	no	—
366	C₂×C₄×C₆₇	—	4	1	no	—
367	C₂×C₄×C₆₇	—	4	1	no	—
368	C₂×C₄×C₆₇	—	4	1	no	—
369	C₂×C₄×C₆₇	—	4	4	no	—
370	C₂×C₄×C₆₇	—	4	2	no	—
371	C₂×C₄×C₆₇	—	4	4	no	—
372	C₂×C₄×C₆₇	—	4	4	no	—
373	C₂×C₄×C₆₇	—	4	2	no	—
374	C₂×C₄×C₆₇	—	4	4	no	—
375	C₂×C₄×C₆₇	—	4	4	no	—
376	C₂×C₄×C₆₇	—	4	4	no	—
377	C₂×C₄×C₆₇	#137	1	4	yes	complemented
378	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
390	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
391	C₈×C₆₇	—	2	8	no	—
392	C₂²×C₆₇	—	2	1	no	—
393	C₂²×C₆₇	—	2	1	no	—
394	C₂²×C₆₇	—	2	1	no	—
395	C₂²×C₆₇	—	2	1	no	—
396	C₂²×C₆₇	—	2	1	no	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	1	no	—
399	C₂²×C₆₇	—	2	1	no	—
400	C₂²×C₆₇	—	4	4	no	—
401	C₂²×C₆₇	—	4	8	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	#525	1	2	yes	—
405	C₂²×C₆₇	C₂×#137	1	2	yes	—
406	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₆₇	—	2	1	no	—
408	C₄×C₆₇	—	2	4	no	—
409	C₄×C₆₇	—	2	1	no	—
410	C₄×C₆₇	—	2	1	no	—
411	C₄×C₆₇	—	2	1	no	—
412	C₄×C₆₇	—	2	1	no	—
413	C₄×C₆₇	—	2	1	no	—
414	C₄×C₆₇	—	2	1	no	—
415	C₄×C₆₇	—	4	4	no	—
416	C₄×C₆₇	—	4	2	no	—
417	C₄×C₆₇	—	4	2	no	—
418	C₄×C₆₇	—	4	4	no	—
419	C₄×C₆₇	#525	1	2	yes	—
420	C₄×C₆₇	C₂×#137	1	2	yes	—
421	C₄×C₆₇	C₂×#137	1	2	yes	—
422	C₄×C₆₇	#575	1	2	yes	—
423	C₄×C₆₇	C₂²×#41	1	2	yes	—
424	#60562	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂×C₆₇	—	2	2	no	—
426	C₂×C₆₇	—	2	2	no	—
427	C₂×C₆₇	—	4	1	no	—
428	C₂×C₆₇	—	4	4	no	—
429	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
430	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
431	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
432	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
433	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic
434	#3116	C₂×C₆₇	1	4	yes	complemented
435	#3113	C₂×C₆₇	1	2	yes	complemented
436	#3110	C₂×C₆₇	1	2	yes	complemented
437	#3107	C₂×C₆₇	1	4	yes	complemented
438	#3104	C₂×C₆₇	1	2	yes	complemented
439	#3101	C₂×C₆₇	1	2	yes	complemented
440	#3095	C₂×C₆₇	1	2	yes	complemented
441	#3079	C₂×C₆₇	1	2	yes	complemented
442	#3039	C₂×C₆₇	1	2	yes	complemented
443	#3007	C₂×C₆₇	1	2	yes	—
444	C₄×#137	C₂×C₆₇	1	4	yes	complemented
445	#2920	C₂×C₆₇	1	1	yes	characteristic, complemented
446	C₆₇	#60562	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×#137	C₂²×C₆₇	1	4	yes	—
449	#533	—	2	1	no	—
450	#533	—	2	1	no	—
451	#533	—	2	1	no	—
452	#533	—	2	1	no	—
453	#533	C₂²×C₆₇	1	2	yes	—
454	#533	C₂²×C₆₇	1	2	yes	—
455	#533	C₂²×C₆₇	1	2	yes	complemented
456	#533	C₂²×C₆₇	1	2	yes	complemented
457	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
458	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	C₂×#125	—	2	1	no	—
460	C₂×C₂²⋊Q₈	—	2	1	no	—
461	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
462	C₄×#41	—	2	1	no	—
463	C₄×#41	—	2	1	no	—
464	C₄×#41	—	2	1	no	—
465	C₄×#41	—	2	1	no	—
466	C₄×#41	C₂²×C₆₇	1	2	yes	—
467	C₄×#41	C₂²×C₆₇	1	2	yes	—
468	C₄×#41	C₂²×C₆₇	1	2	yes	—
469	C₄×#41	C₂²×C₆₇	1	2	yes	—
470	C₂×C₄×Q₈	—	2	1	no	—
471	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
474	C₂×C₄×D₄	—	2	1	no	—
475	C₂×C₄×D₄	—	2	1	no	—
476	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×#117	—	2	1	no	—
479	C₂×#117	—	2	1	no	—
480	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
481	C₂²×C₄²	—	2	1	no	—
482	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
483	#485	C₂²×C₆₇	1	8	yes	complemented
484	#484	C₂²×C₆₇	1	4	yes	—
485	#483	C₂²×C₆₇	1	4	yes	—
486	#477	C₂²×C₆₇	1	4	yes	complemented
487	#476	C₂²×C₆₇	1	4	yes	complemented
488	#475	C₂²×C₆₇	1	4	yes	complemented
489	#474	C₂²×C₆₇	1	4	yes	complemented
490	#462	C₂²×C₆₇	1	4	yes	complemented
491	#462	C₂²×C₆₇	1	4	yes	complemented
492	#461	C₂²×C₆₇	1	4	yes	complemented
493	#461	C₂²×C₆₇	1	4	yes	complemented
494	#452	C₂²×C₆₇	1	8	yes	—
495	#451	C₂²×C₆₇	1	4	yes	—
496	#450	C₂²×C₆₇	1	4	yes	—
497	#441	C₂²×C₆₇	1	8	yes	complemented
498	#440	C₂²×C₆₇	1	8	yes	complemented
499	C₄×Q₁₆	C₂²×C₆₇	1	8	yes	complemented
500	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
501	#432	C₂²×C₆₇	1	2	yes	—
502	#432	C₂²×C₆₇	1	2	yes	complemented
503	#431	C₂²×C₆₇	1	2	yes	—
504	#431	C₂²×C₆₇	1	2	yes	complemented
505	#428	C₂²×C₆₇	1	4	yes	complemented
506	#423	C₂²×C₆₇	1	2	yes	complemented
507	#419	C₂²×C₆₇	1	4	yes	complemented
508	#417	C₂²×C₆₇	1	4	yes	—
509	#407	C₂²×C₆₇	1	2	yes	—
510	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
511	C₂×#41	—	2	8	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	2	1	no	—
514	C₂×#41	C₂³×C₆₇	1	2	yes	—
515	C₂×#41	C₂³×C₆₇	1	2	yes	—
516	C₂²×Q₈	—	2	1	no	—
517	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
525	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
527	#137	—	2	16	no	—
528	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	—
529	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	—
530	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
538	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
550	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
562	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
563	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
564	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
565	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
566	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	C₂³×C₆₇	1	2	yes	—
580	C₄×D₄	C₂³×C₆₇	1	2	yes	—
581	C₄×D₄	C₂³×C₆₇	1	2	yes	—
582	C₄×D₄	C₂³×C₆₇	1	2	yes	—
583	#117	—	2	2	no	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	1	no	—
588	#117	—	2	1	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	C₂³×C₆₇	1	2	yes	—
594	#117	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	—	2	2	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₄²	—	2	1	no	—
610	C₂×C₄²	—	2	2	no	—
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	—	2	2	no	—
614	C₂×C₄²	—	2	2	no	—
615	C₂×C₄²	—	2	2	no	—
616	C₂×C₄²	—	2	2	no	—
617	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
618	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
619	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
620	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
621	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
622	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
629	#107	C₂³×C₆₇	1	8	yes	—
630	#106	C₂³×C₆₇	1	8	yes	—
631	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
632	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
633	#103	C₂³×C₆₇	1	8	yes	—
634	#103	C₂³×C₆₇	1	8	yes	—
635	#103	C₂³×C₆₇	1	8	yes	—
636	#102	C₂³×C₆₇	1	8	yes	—
637	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
638	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
639	#97	C₂³×C₆₇	1	4	yes	—
640	C₄×C₈	C₂³×C₆₇	1	4	yes	—
641	C₂⁴	—	2	1	no	—
642	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
643	#41	—	2	8	no	—
644	#41	—	2	8	no	—
645	#41	—	2	4	no	—
646	#41	—	2	4	no	—
647	#41	—	2	4	no	—
648	#41	#41×C₆₇	1	8	yes	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	8	no	—
655	C₂×Q₈	—	4	4	no	—
656	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
657	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
658	C₂×D₄	—	2	8	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
664	C₂²×C₄	—	2	8	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	4	no	—
680	C₂²×C₄	—	4	4	no	—
681	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	Q₁₆	—	2	16	no	—
700	SD₁₆	—	2	16	no	—
701	M₁₆	—	2	8	no	—
702	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
721	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
741	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
751	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
755	C₂³	—	2	4	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
763	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
764	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
765	Q₈	—	2	4	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	8	no	—
768	Q₈	—	4	4	no	—
769	Q₈	—	4	4	no	—
770	Q₈	—	4	4	no	—
771	Q₈	C₂×#41×C₆₇	1	4	yes	—
772	D₄	—	2	8	no	—
773	D₄	—	2	4	no	—
774	D₄	—	2	8	no	—
775	D₄	—	2	2	no	—
776	D₄	C₂×#41×C₆₇	1	4	yes	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	8	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	8	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	#137×C₆₇	1	4	yes	complemented
810	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
821	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
822	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
823	C₈	—	2	8	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	8	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	#525×C₆₇	1	2	yes	—
837	C₂²	C₂×#137×C₆₇	1	2	yes	—
838	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	4	no	—
851	C₄	#525×C₆₇	1	2	yes	—
852	C₄	C₂×#137×C₆₇	1	2	yes	—
853	C₄	C₂×#137×C₆₇	1	2	yes	—
854	C₄	#575×C₆₇	1	2	yes	—
855	C₄	C₂²×#41×C₆₇	1	2	yes	—
856	C₂	—	2	2	no	—
857	C₂	—	2	2	no	—
858	C₂	—	4	1	no	—
859	C₂	—	4	4	no	—
860	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
861	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
862	C₂	C₂×#575×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₆₇	C₂	semidirect
3. C₆₇×#3116	C₂	semidirect
4. C₆₇×#3113	C₂	semidirect
5. C₆₇×#3110	C₂	semidirect
6. C₆₇×#3107	C₂	semidirect
7. C₆₇×#3104	C₂	semidirect
8. C₆₇×#3101	C₂	semidirect
9. C₆₇×#3095	C₂	semidirect
10. C₆₇×#3079	C₂	semidirect
11. C₆₇×#3039	C₂	semidirect
13. C₄×#137×C₆₇	C₂	semidirect
14. C₆₇×#2920	C₂	semidirect
23. #533×C₆₇	C₂²	semidirect
24. #533×C₆₇	C₂²	semidirect
25. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
26. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
41. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
51. #485×C₆₇	C₂²	semidirect
54. #477×C₆₇	C₂²	semidirect
55. #476×C₆₇	C₂²	semidirect
56. #475×C₆₇	C₂²	semidirect
57. #474×C₆₇	C₂²	semidirect
58. #462×C₆₇	C₂²	semidirect
59. #462×C₆₇	C₂²	semidirect
60. #461×C₆₇	C₂²	semidirect
61. #461×C₆₇	C₂²	semidirect
65. #441×C₆₇	C₂²	semidirect
66. #440×C₆₇	C₂²	semidirect
67. C₄×Q₁₆×C₆₇	C₂²	semidirect
68. C₄×SD₁₆×C₆₇	C₂²	semidirect
70. #432×C₆₇	C₂²	semidirect
72. #431×C₆₇	C₂²	semidirect
73. #428×C₆₇	C₂²	semidirect
74. #423×C₆₇	C₂²	semidirect
75. #419×C₆₇	C₂²	semidirect
78. C₄×M₁₆×C₆₇	C₂²	semidirect
377. C₂×C₄×C₆₇	#137	semidirect
424. #60562	C₆₇	direct (N × H)
432. C₂×#533	C₂×C₆₇	semidirect
434. #3116	C₂×C₆₇	semidirect
435. #3113	C₂×C₆₇	semidirect
436. #3110	C₂×C₆₇	semidirect
437. #3107	C₂×C₆₇	semidirect
438. #3104	C₂×C₆₇	semidirect
439. #3101	C₂×C₆₇	semidirect
440. #3095	C₂×C₆₇	semidirect
441. #3079	C₂×C₆₇	semidirect
442. #3039	C₂×C₆₇	semidirect
444. C₄×#137	C₂×C₆₇	semidirect
445. #2920	C₂×C₆₇	semidirect
446. C₆₇	#60562	direct (N × H)
455. #533	C₂²×C₆₇	semidirect
456. #533	C₂²×C₆₇	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
458. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
473. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
483. #485	C₂²×C₆₇	semidirect
486. #477	C₂²×C₆₇	semidirect
487. #476	C₂²×C₆₇	semidirect
488. #475	C₂²×C₆₇	semidirect
489. #474	C₂²×C₆₇	semidirect
490. #462	C₂²×C₆₇	semidirect
491. #462	C₂²×C₆₇	semidirect
492. #461	C₂²×C₆₇	semidirect
493. #461	C₂²×C₆₇	semidirect
497. #441	C₂²×C₆₇	semidirect
498. #440	C₂²×C₆₇	semidirect
499. C₄×Q₁₆	C₂²×C₆₇	semidirect
500. C₄×SD₁₆	C₂²×C₆₇	semidirect
502. #432	C₂²×C₆₇	semidirect
504. #431	C₂²×C₆₇	semidirect
505. #428	C₂²×C₆₇	semidirect
506. #423	C₂²×C₆₇	semidirect
507. #419	C₂²×C₆₇	semidirect
510. C₄×M₁₆	C₂²×C₆₇	semidirect
809. C₂×C₄	#137×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#3116	2
C₆₇×#3113	2
C₆₇×#3110	2
C₆₇×#3107	2
C₆₇×#3104	2
C₆₇×#3101	2
C₆₇×#3095	2
C₆₇×#3079	2
C₆₇×#3039	2
C₆₇×#3007	2
C₄×#137×C₆₇	2
C₆₇×#2920	2
#60562	67

Subgroups — C67×#60562 #30739813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60562 #30739813