Subgroups — C₆₇×#61095 #30740346

Order 17152.

2790 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
5	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3271	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
16	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
19	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
20	#577×C₆₇	—	2	16	no	—
21	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#135×C₆₇	C₂²	1	2	yes	—
27	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
29	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
31	#550×C₆₇	—	2	1	no	—
32	#550×C₆₇	C₂²	1	2	yes	—
33	#550×C₆₇	C₂²	1	2	yes	—
34	#550×C₆₇	C₂²	1	2	yes	complemented
35	D₄×Q₈×C₆₇	—	2	1	no	—
36	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
37	#548×C₆₇	—	2	2	no	—
38	#548×C₆₇	C₂²	1	4	yes	complemented
39	D₄²×C₆₇	—	2	2	no	—
40	D₄²×C₆₇	—	2	2	no	—
41	D₄²×C₆₇	C₂²	1	2	yes	—
42	D₄²×C₆₇	C₂²	1	2	yes	—
43	#537×C₆₇	—	2	2	no	—
44	#537×C₆₇	C₂²	1	2	yes	complemented
45	#535×C₆₇	—	2	2	no	—
46	#535×C₆₇	C₂²	1	2	yes	—
47	#532×C₆₇	—	2	1	no	—
48	#532×C₆₇	—	2	2	no	—
49	#532×C₆₇	C₂²	1	1	yes	characteristic
50	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×#127×C₆₇	—	2	1	no	—
52	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
53	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#496×C₆₇	C₂²	1	4	yes	complemented
56	#493×C₆₇	C₂²	1	2	yes	complemented
57	#492×C₆₇	C₂²	1	2	yes	complemented
58	#469×C₆₇	C₂²	1	4	yes	complemented
59	#468×C₆₇	C₂²	1	4	yes	complemented
60	#466×C₆₇	C₂²	1	4	yes	complemented
61	#465×C₆₇	C₂²	1	4	yes	complemented
62	#464×C₆₇	C₂²	1	2	yes	complemented
63	#463×C₆₇	C₂²	1	2	yes	complemented
64	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#460×C₆₇	C₂²	1	4	yes	complemented
67	#460×C₆₇	C₂²	1	2	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#450×C₆₇	C₂²	1	4	yes	complemented
73	#449×C₆₇	C₂²	1	4	yes	complemented
74	#449×C₆₇	C₂²	1	4	yes	complemented
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#448×C₆₇	C₂²	1	4	yes	complemented
77	#448×C₆₇	C₂²	1	4	yes	complemented
78	#447×C₆₇	C₂²	1	4	yes	complemented
79	#441×C₆₇	C₂²	1	2	yes	complemented
80	#440×C₆₇	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
83	#436×C₆₇	C₂²	1	2	yes	complemented
84	#435×C₆₇	C₂²	1	4	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#417×C₆₇	C₂²	1	1	yes	characteristic
90	#416×C₆₇	C₂²	1	2	yes	complemented
91	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
92	#408×C₆₇	C₂²	1	2	yes	complemented
93	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	2₋¹⁺⁴×C₆₇	—	2	8	no	—
95	2₋¹⁺⁴×C₆₇	—	4	4	no	—
96	H(5,𝔽₂)×C₆₇	—	2	8	no	—
97	H(5,𝔽₂)×C₆₇	—	4	4	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	4	no	—
100	C₂×#41×C₆₇	—	2	2	no	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	4	yes	—
103	C₂×#41×C₆₇	C₂³	1	4	yes	—
104	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
105	C₂×#41×C₆₇	C₂³	1	2	yes	—
106	C₂²×Q₈×C₆₇	—	2	2	no	—
107	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	—	2	2	no	—
110	C₂²×D₄×C₆₇	—	2	4	no	—
111	C₂²×D₄×C₆₇	—	2	2	no	—
112	C₂²×D₄×C₆₇	—	2	2	no	—
113	C₂²×D₄×C₆₇	—	2	1	no	—
114	C₂²×D₄×C₆₇	—	2	1	no	—
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
117	#137×C₆₇	—	2	16	no	—
118	#137×C₆₇	D₄	1	8	yes	complemented
119	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
120	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
121	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
122	#135×C₆₇	—	2	8	no	—
123	#135×C₆₇	—	2	16	no	—
124	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₇	—	2	8	no	—
127	C₂×SD₁₆×C₆₇	—	2	16	no	—
128	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
133	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
134	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×D₈×C₆₇	C₂³	1	2	yes	—
136	C₂×D₈×C₆₇	C₂³	1	4	yes	—
137	C₂×D₈×C₆₇	C₂³	1	4	yes	—
138	#131×C₆₇	—	2	8	no	—
139	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
140	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
143	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₆₇	—	2	2	no	—
145	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
146	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	#127×C₆₇	—	2	2	no	—
148	#127×C₆₇	—	2	2	no	—
149	#127×C₆₇	—	2	2	no	—
150	#127×C₆₇	—	2	2	no	—
151	#127×C₆₇	—	2	1	no	—
152	#127×C₆₇	—	2	1	no	—
153	#127×C₆₇	D₄	1	1	yes	characteristic
154	#127×C₆₇	C₂³	1	1	yes	characteristic
155	#127×C₆₇	C₂³	1	2	yes	—
156	#127×C₆₇	C₂³	1	2	yes	—
157	#124×C₆₇	—	2	2	no	—
158	#124×C₆₇	—	2	4	no	—
159	#124×C₆₇	D₄	1	2	yes	—
160	#124×C₆₇	C₂³	1	2	yes	—
161	C₂²⋊Q₈×C₆₇	—	2	2	no	—
162	C₂²⋊Q₈×C₆₇	—	2	4	no	—
163	C₂²⋊Q₈×C₆₇	—	2	4	no	—
164	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
165	#121×C₆₇	—	2	4	no	—
166	#121×C₆₇	—	2	4	no	—
167	#121×C₆₇	—	2	2	no	—
168	#121×C₆₇	—	2	1	no	—
169	#121×C₆₇	—	2	1	no	—
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	4	no	—
173	#121×C₆₇	—	2	4	no	—
174	#121×C₆₇	—	2	4	no	—
175	#121×C₆₇	D₄	1	2	yes	—
176	#121×C₆₇	D₄	1	2	yes	—
177	#121×C₆₇	C₂³	1	4	yes	—
178	#121×C₆₇	C₂³	1	4	yes	—
179	#121×C₆₇	C₂³	1	4	yes	—
180	#120×C₆₇	—	2	4	no	—
181	#120×C₆₇	—	2	4	no	—
182	#120×C₆₇	—	2	4	no	—
183	C₄×Q₈×C₆₇	—	2	1	no	—
184	C₄×Q₈×C₆₇	—	2	1	no	—
185	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
186	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
187	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
188	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₆₇	—	2	2	no	—
190	C₄×D₄×C₆₇	—	2	1	no	—
191	C₄×D₄×C₆₇	—	2	1	no	—
192	C₄×D₄×C₆₇	—	2	2	no	—
193	C₄×D₄×C₆₇	—	2	2	no	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	4	no	—
196	C₄×D₄×C₆₇	—	2	1	no	—
197	C₄×D₄×C₆₇	—	2	1	no	—
198	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	2	yes	—
202	#117×C₆₇	—	2	1	no	—
203	#117×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₇	—	2	1	no	—
207	C₂×C₄²×C₆₇	—	2	1	no	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	#107×C₆₇	C₂³	1	2	yes	—
210	#106×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#103×C₆₇	C₂³	1	2	yes	—
216	#103×C₆₇	C₂³	1	2	yes	—
217	#103×C₆₇	C₂³	1	2	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	2	yes	—
223	#102×C₆₇	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
226	#97×C₆₇	C₂³	1	2	yes	—
227	C₄×C₈×C₆₇	C₂³	1	2	yes	—
228	C₂⁴×C₆₇	—	2	4	no	—
229	C₂⁴×C₆₇	—	2	2	no	—
230	#41×C₆₇	—	2	4	no	—
231	#41×C₆₇	—	2	2	no	—
232	#41×C₆₇	—	2	4	no	—
233	#41×C₆₇	—	2	8	no	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	4	4	no	—
238	#41×C₆₇	—	4	4	no	—
239	#41×C₆₇	—	4	16	no	—
240	#41×C₆₇	—	4	8	no	—
241	#41×C₆₇	—	4	8	no	—
242	#41×C₆₇	C₂×D₄	1	4	yes	—
243	C₂×Q₈×C₆₇	—	2	1	no	—
244	C₂×Q₈×C₆₇	—	2	4	no	—
245	C₂×Q₈×C₆₇	—	2	2	no	—
246	C₂×Q₈×C₆₇	—	2	8	no	—
247	C₂×Q₈×C₆₇	—	4	4	no	—
248	C₂×Q₈×C₆₇	—	4	8	no	—
249	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
250	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
251	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
252	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
253	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₆₇	—	2	1	no	—
255	C₂×D₄×C₆₇	—	2	8	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	1	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	4	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	1	no	—
269	C₂×D₄×C₆₇	—	2	2	no	—
270	C₂×D₄×C₆₇	—	2	2	no	—
271	C₂×D₄×C₆₇	—	2	4	no	—
272	C₂×D₄×C₆₇	—	4	4	no	—
273	C₂×D₄×C₆₇	—	4	8	no	—
274	C₂×D₄×C₆₇	—	4	16	no	—
275	C₂×D₄×C₆₇	—	8	2	no	—
276	C₂×D₄×C₆₇	—	8	4	no	—
277	C₂×D₄×C₆₇	—	8	2	no	—
278	C₂×D₄×C₆₇	—	8	4	no	—
279	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
281	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
285	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	—	2	1	no	—
287	C₂²×C₄×C₆₇	—	2	1	no	—
288	C₂²×C₄×C₆₇	—	2	4	no	—
289	C₂²×C₄×C₆₇	—	2	1	no	—
290	C₂²×C₄×C₆₇	—	2	1	no	—
291	C₂²×C₄×C₆₇	—	2	1	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	4	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	Q₁₆×C₆₇	—	2	4	no	—
300	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
301	SD₁₆×C₆₇	—	2	8	no	—
302	SD₁₆×C₆₇	—	2	8	no	—
303	SD₁₆×C₆₇	—	2	4	no	—
304	SD₁₆×C₆₇	—	2	4	no	—
305	SD₁₆×C₆₇	—	2	8	no	—
306	SD₁₆×C₆₇	—	4	4	no	—
307	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
308	D₈×C₆₇	—	2	4	no	—
309	D₈×C₆₇	—	2	8	no	—
310	D₈×C₆₇	—	4	4	no	—
311	M₁₆×C₆₇	—	2	2	no	—
312	M₁₆×C₆₇	—	2	8	no	—
313	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
314	C₂×C₈×C₆₇	—	2	4	no	—
315	C₂×C₈×C₆₇	—	2	8	no	—
316	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
317	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
318	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
319	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	1	no	—
323	C₄⋊C₄×C₆₇	—	2	1	no	—
324	C₄⋊C₄×C₆₇	—	2	1	no	—
325	C₄⋊C₄×C₆₇	—	2	1	no	—
326	C₄⋊C₄×C₆₇	—	2	1	no	—
327	C₄⋊C₄×C₆₇	—	2	4	no	—
328	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²⋊C₄×C₆₇	—	2	1	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	1	no	—
336	C₂²⋊C₄×C₆₇	—	2	1	no	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	4	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
343	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
344	C₄²×C₆₇	—	2	1	no	—
345	C₄²×C₆₇	—	2	1	no	—
346	C₄²×C₆₇	—	2	1	no	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	—	2	2	no	—
349	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	4	no	—
356	C₂³×C₆₇	—	4	8	no	—
357	C₂³×C₆₇	—	4	4	no	—
358	C₂³×C₆₇	—	8	2	no	—
359	C₂³×C₆₇	—	8	2	no	—
360	C₂³×C₆₇	—	8	4	no	—
361	C₂³×C₆₇	—	8	4	no	—
362	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
363	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₆₇	—	2	4	no	—
365	Q₈×C₆₇	—	2	4	no	—
366	Q₈×C₆₇	—	2	2	no	—
367	Q₈×C₆₇	—	2	1	no	—
368	Q₈×C₆₇	—	2	2	no	—
369	Q₈×C₆₇	—	2	2	no	—
370	Q₈×C₆₇	—	4	8	no	—
371	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
372	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
373	D₄×C₆₇	—	2	4	no	—
374	D₄×C₆₇	—	2	8	no	—
375	D₄×C₆₇	—	2	4	no	—
376	D₄×C₆₇	—	2	4	no	—
377	D₄×C₆₇	—	2	2	no	—
378	D₄×C₆₇	—	2	4	no	—
379	D₄×C₆₇	—	2	1	no	—
380	D₄×C₆₇	—	2	2	no	—
381	D₄×C₆₇	—	2	4	no	—
382	D₄×C₆₇	—	4	2	no	—
383	D₄×C₆₇	—	4	8	no	—
384	D₄×C₆₇	—	4	8	no	—
385	D₄×C₆₇	—	4	8	no	—
386	D₄×C₆₇	—	4	4	no	—
387	D₄×C₆₇	—	4	4	no	—
388	D₄×C₆₇	—	4	4	no	—
389	D₄×C₆₇	—	4	2	no	—
390	D₄×C₆₇	—	4	4	no	—
391	D₄×C₆₇	—	8	1	no	—
392	D₄×C₆₇	—	8	2	no	—
393	D₄×C₆₇	—	8	2	no	—
394	D₄×C₆₇	—	8	4	no	—
395	D₄×C₆₇	—	8	4	no	—
396	D₄×C₆₇	—	8	4	no	—
397	D₄×C₆₇	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₆₇	—	2	4	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	4	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	4	no	—
404	C₂×C₄×C₆₇	—	2	4	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	4	1	no	—
410	C₂×C₄×C₆₇	—	4	8	no	—
411	C₂×C₄×C₆₇	—	4	8	no	—
412	C₂×C₄×C₆₇	—	4	8	no	—
413	C₂×C₄×C₆₇	—	4	2	no	—
414	C₂×C₄×C₆₇	—	4	4	no	—
415	C₂×C₄×C₆₇	—	4	2	no	—
416	C₂×C₄×C₆₇	—	8	1	no	—
417	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
421	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
425	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
426	C₈×C₆₇	—	2	2	no	—
427	C₈×C₆₇	—	2	2	no	—
428	C₈×C₆₇	—	2	2	no	—
429	C₈×C₆₇	C₂²×D₄	1	4	yes	—
430	C₂²×C₆₇	—	2	1	no	—
431	C₂²×C₆₇	—	2	1	no	—
432	C₂²×C₆₇	—	2	4	no	—
433	C₂²×C₆₇	—	2	4	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	4	no	—
436	C₂²×C₆₇	—	4	1	no	—
437	C₂²×C₆₇	—	4	1	no	—
438	C₂²×C₆₇	—	4	4	no	—
439	C₂²×C₆₇	—	4	2	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	4	no	—
442	C₂²×C₆₇	—	4	4	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	16	4	no	—
445	C₂²×C₆₇	—	16	8	no	—
446	C₂²×C₆₇	D₄²	1	2	yes	—
447	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₆₇	—	2	1	no	—
449	C₄×C₆₇	—	2	1	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	2	4	no	—
452	C₄×C₆₇	—	2	4	no	—
453	C₄×C₆₇	—	2	1	no	—
454	C₄×C₆₇	—	4	1	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	2	no	—
457	C₄×C₆₇	—	4	1	no	—
458	C₄×C₆₇	D₄²	1	2	yes	—
459	C₄×C₆₇	#577	1	2	yes	complemented
460	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	#61095	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂×C₆₇	—	2	2	no	—
464	C₂×C₆₇	—	4	4	no	—
465	C₂×C₆₇	—	4	2	no	—
466	C₂×C₆₇	—	8	2	no	—
467	C₂×C₆₇	—	8	4	no	—
468	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
469	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
470	C₂×C₆₇	#3585	1	1	yes	characteristic
471	C₂×#577	C₂×C₆₇	1	2	yes	complemented
472	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#3287	C₂×C₆₇	1	2	yes	complemented
475	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
476	#3278	C₂×C₆₇	1	2	yes	complemented
477	#3274	C₂×C₆₇	1	2	yes	complemented
478	#3271	C₂×C₆₇	1	4	yes	complemented
479	#3265	C₂×C₆₇	1	4	yes	complemented
480	#3151	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#3062	C₂×C₆₇	1	2	yes	complemented
482	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
483	C₂×#460	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#3012	C₂×C₆₇	1	2	yes	complemented
485	#3010	C₂×C₆₇	1	2	yes	complemented
486	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
488	C₆₇	#61095	1	1	yes	characteristic, direct product factor, Sylow
489	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
490	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
491	#577	—	2	16	no	—
492	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
494	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
495	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
496	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
497	C₂×#135	C₂²×C₆₇	1	2	yes	—
498	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
499	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
500	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
501	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
502	#550	—	2	1	no	—
503	#550	C₂²×C₆₇	1	2	yes	—
504	#550	C₂²×C₆₇	1	2	yes	—
505	#550	C₂²×C₆₇	1	2	yes	complemented
506	D₄×Q₈	—	2	1	no	—
507	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
508	#548	—	2	2	no	—
509	#548	C₂²×C₆₇	1	4	yes	complemented
510	D₄²	—	2	2	no	—
511	D₄²	—	2	2	no	—
512	D₄²	C₂²×C₆₇	1	2	yes	—
513	D₄²	C₂²×C₆₇	1	2	yes	—
514	#537	—	2	2	no	—
515	#537	C₂²×C₆₇	1	2	yes	complemented
516	#535	—	2	2	no	—
517	#535	C₂²×C₆₇	1	2	yes	—
518	#532	—	2	1	no	—
519	#532	—	2	2	no	—
520	#532	C₂²×C₆₇	1	1	yes	characteristic
521	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
522	C₂×#127	—	2	1	no	—
523	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
524	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
526	#496	C₂²×C₆₇	1	4	yes	complemented
527	#493	C₂²×C₆₇	1	2	yes	complemented
528	#492	C₂²×C₆₇	1	2	yes	complemented
529	#469	C₂²×C₆₇	1	4	yes	complemented
530	#468	C₂²×C₆₇	1	4	yes	complemented
531	#466	C₂²×C₆₇	1	4	yes	complemented
532	#465	C₂²×C₆₇	1	4	yes	complemented
533	#464	C₂²×C₆₇	1	2	yes	complemented
534	#463	C₂²×C₆₇	1	2	yes	complemented
535	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
536	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	#460	C₂²×C₆₇	1	4	yes	complemented
538	#460	C₂²×C₆₇	1	2	yes	complemented
539	#460	C₂²×C₆₇	1	2	yes	complemented
540	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	#452	C₂²×C₆₇	1	4	yes	complemented
543	#450	C₂²×C₆₇	1	4	yes	complemented
544	#449	C₂²×C₆₇	1	4	yes	complemented
545	#449	C₂²×C₆₇	1	4	yes	complemented
546	#449	C₂²×C₆₇	1	4	yes	complemented
547	#448	C₂²×C₆₇	1	4	yes	complemented
548	#448	C₂²×C₆₇	1	4	yes	complemented
549	#447	C₂²×C₆₇	1	4	yes	complemented
550	#441	C₂²×C₆₇	1	2	yes	complemented
551	#440	C₂²×C₆₇	1	2	yes	complemented
552	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
553	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
554	#436	C₂²×C₆₇	1	2	yes	complemented
555	#435	C₂²×C₆₇	1	4	yes	complemented
556	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
557	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
560	#417	C₂²×C₆₇	1	1	yes	characteristic
561	#416	C₂²×C₆₇	1	2	yes	complemented
562	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
563	#408	C₂²×C₆₇	1	2	yes	complemented
564	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	2₋¹⁺⁴	—	2	8	no	—
566	2₋¹⁺⁴	—	4	4	no	—
567	H(5,𝔽₂)	—	2	8	no	—
568	H(5,𝔽₂)	—	4	4	no	—
569	C₂×#41	—	2	2	no	—
570	C₂×#41	—	2	4	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	C₂³×C₆₇	1	2	yes	—
573	C₂×#41	C₂³×C₆₇	1	4	yes	—
574	C₂×#41	C₂³×C₆₇	1	4	yes	—
575	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×#41	C₂³×C₆₇	1	2	yes	—
577	C₂²×Q₈	—	2	2	no	—
578	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
579	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	4	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
587	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
588	#137	—	2	16	no	—
589	#137	D₄×C₆₇	1	8	yes	complemented
590	AGL(1,ℤ/8)	—	2	16	no	—
591	AGL(1,ℤ/8)	—	2	8	no	—
592	AGL(1,ℤ/8)	—	4	4	no	—
593	#135	—	2	8	no	—
594	#135	—	2	16	no	—
595	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
596	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
597	C₂×SD₁₆	—	2	8	no	—
598	C₂×SD₁₆	—	2	16	no	—
599	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
601	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
603	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
605	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
606	C₂×D₈	C₂³×C₆₇	1	2	yes	—
607	C₂×D₈	C₂³×C₆₇	1	4	yes	—
608	C₂×D₈	C₂³×C₆₇	1	4	yes	—
609	#131	—	2	8	no	—
610	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
611	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
613	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
614	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
618	#127	—	2	2	no	—
619	#127	—	2	2	no	—
620	#127	—	2	2	no	—
621	#127	—	2	2	no	—
622	#127	—	2	1	no	—
623	#127	—	2	1	no	—
624	#127	D₄×C₆₇	1	1	yes	characteristic
625	#127	C₂³×C₆₇	1	2	yes	—
626	#127	C₂³×C₆₇	1	2	yes	—
627	#127	C₂³×C₆₇	1	1	yes	characteristic
628	#124	—	2	2	no	—
629	#124	—	2	4	no	—
630	#124	D₄×C₆₇	1	2	yes	—
631	#124	C₂³×C₆₇	1	2	yes	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	4	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
636	#121	—	2	4	no	—
637	#121	—	2	4	no	—
638	#121	—	2	2	no	—
639	#121	—	2	1	no	—
640	#121	—	2	1	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	4	no	—
644	#121	—	2	4	no	—
645	#121	—	2	4	no	—
646	#121	D₄×C₆₇	1	2	yes	—
647	#121	D₄×C₆₇	1	2	yes	—
648	#121	C₂³×C₆₇	1	4	yes	—
649	#121	C₂³×C₆₇	1	4	yes	—
650	#121	C₂³×C₆₇	1	4	yes	—
651	#120	—	2	4	no	—
652	#120	—	2	4	no	—
653	#120	—	2	4	no	—
654	C₄×Q₈	—	2	1	no	—
655	C₄×Q₈	—	2	1	no	—
656	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
657	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
658	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
659	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	4	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₆₇	1	2	yes	—
672	C₄×D₄	C₂³×C₆₇	1	2	yes	—
673	#117	—	2	1	no	—
674	#117	C₂³×C₆₇	1	1	yes	characteristic
675	C₂×C₄⋊C₄	—	2	1	no	—
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
680	#107	C₂³×C₆₇	1	2	yes	—
681	#106	C₂³×C₆₇	1	2	yes	—
682	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
683	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
684	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
685	#103	C₂³×C₆₇	1	2	yes	—
686	#103	C₂³×C₆₇	1	2	yes	—
687	#103	C₂³×C₆₇	1	2	yes	—
688	#103	C₂³×C₆₇	1	2	yes	—
689	#103	C₂³×C₆₇	1	2	yes	—
690	#102	C₂³×C₆₇	1	4	yes	—
691	#102	C₂³×C₆₇	1	4	yes	—
692	#102	C₂³×C₆₇	1	2	yes	—
693	#102	C₂³×C₆₇	1	2	yes	—
694	#102	C₂³×C₆₇	1	2	yes	—
695	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
696	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
697	#97	C₂³×C₆₇	1	2	yes	—
698	C₄×C₈	C₂³×C₆₇	1	2	yes	—
699	C₂⁴	—	2	4	no	—
700	C₂⁴	—	2	2	no	—
701	#41	—	2	4	no	—
702	#41	—	2	2	no	—
703	#41	—	2	4	no	—
704	#41	—	2	8	no	—
705	#41	—	2	8	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	4	no	—
710	#41	—	4	16	no	—
711	#41	—	4	8	no	—
712	#41	—	4	8	no	—
713	#41	C₂×D₄×C₆₇	1	4	yes	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	4	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	8	no	—
718	C₂×Q₈	—	4	4	no	—
719	C₂×Q₈	—	4	8	no	—
720	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
721	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
722	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
723	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
724	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	8	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	8	no	—
745	C₂×D₄	—	4	16	no	—
746	C₂×D₄	—	8	2	no	—
747	C₂×D₄	—	8	4	no	—
748	C₂×D₄	—	8	2	no	—
749	C₂×D₄	—	8	4	no	—
750	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
751	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
752	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
753	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
754	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
756	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
769	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
770	Q₁₆	—	2	4	no	—
771	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
772	SD₁₆	—	2	8	no	—
773	SD₁₆	—	2	8	no	—
774	SD₁₆	—	2	4	no	—
775	SD₁₆	—	2	4	no	—
776	SD₁₆	—	2	8	no	—
777	SD₁₆	—	4	4	no	—
778	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
779	D₈	—	2	4	no	—
780	D₈	—	2	8	no	—
781	D₈	—	4	4	no	—
782	M₁₆	—	2	2	no	—
783	M₁₆	—	2	8	no	—
784	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
785	C₂×C₈	—	2	4	no	—
786	C₂×C₈	—	2	8	no	—
787	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
788	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
789	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
790	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
800	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
814	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	1	no	—
817	C₄²	—	2	1	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
821	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
822	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	4	8	no	—
828	C₂³	—	4	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	—	8	2	no	—
831	C₂³	—	8	4	no	—
832	C₂³	—	8	4	no	—
833	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
834	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
835	Q₈	—	2	4	no	—
836	Q₈	—	2	4	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	1	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	4	8	no	—
842	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
843	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	8	no	—
846	D₄	—	2	4	no	—
847	D₄	—	2	4	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	4	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	8	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	2	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	1	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	D₄	—	8	4	no	—
868	D₄	C₂²×D₄×C₆₇	1	2	yes	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	4	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	4	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	8	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	8	1	no	—
888	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
892	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
895	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
896	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
897	C₈	—	2	2	no	—
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	C₂²×D₄×C₆₇	1	4	yes	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	4	no	—
904	C₂²	—	2	4	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	4	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	4	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	4	no	—
915	C₂²	—	16	4	no	—
916	C₂²	—	16	8	no	—
917	C₂²	D₄²×C₆₇	1	2	yes	—
918	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	4	no	—
924	C₄	—	2	4	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	D₄²×C₆₇	1	2	yes	—
930	C₄	#577×C₆₇	1	2	yes	complemented
931	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
932	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
933	C₂	—	2	2	no	—
934	C₂	—	4	4	no	—
935	C₂	—	4	2	no	—
936	C₂	—	8	4	no	—
937	C₂	—	8	2	no	—
938	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
939	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
940	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₆₇×#3498	C₂	semidirect
3. C₆₇×#3497	C₂	semidirect
4. C₆₇×#3287	C₂	semidirect
5. D₄×SD₁₆×C₆₇	C₂	semidirect
6. C₆₇×#3278	C₂	semidirect
7. C₆₇×#3274	C₂	semidirect
8. C₆₇×#3271	C₂	semidirect
9. C₆₇×#3265	C₂	semidirect
10. C₆₇×#3151	C₂	semidirect
11. C₆₇×#3062	C₂	semidirect
12. C₆₇×#3035	C₂	semidirect
13. C₂×#460×C₆₇	C₂	semidirect
14. C₆₇×#3012	C₂	semidirect
15. C₆₇×#3010	C₂	semidirect
16. C₄×#137×C₆₇	C₂	semidirect
17. C₆₇×#2935	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
28. C₂²×SD₁₆×C₆₇	C₂²	semidirect
29. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂×#131×C₆₇	C₂²	semidirect
34. #550×C₆₇	C₂²	semidirect
36. D₄×Q₈×C₆₇	C₂²	semidirect
38. #548×C₆₇	C₂²	semidirect
44. #537×C₆₇	C₂²	semidirect
50. #532×C₆₇	C₂²	semidirect
54. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
55. #496×C₆₇	C₂²	semidirect
56. #493×C₆₇	C₂²	semidirect
57. #492×C₆₇	C₂²	semidirect
58. #469×C₆₇	C₂²	semidirect
59. #468×C₆₇	C₂²	semidirect
60. #466×C₆₇	C₂²	semidirect
61. #465×C₆₇	C₂²	semidirect
62. #464×C₆₇	C₂²	semidirect
63. #463×C₆₇	C₂²	semidirect
64. #462×C₆₇	C₂²	semidirect
65. #461×C₆₇	C₂²	semidirect
66. #460×C₆₇	C₂²	semidirect
67. #460×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #460×C₆₇	C₂²	semidirect
70. #459×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #449×C₆₇	C₂²	semidirect
74. #449×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #448×C₆₇	C₂²	semidirect
77. #448×C₆₇	C₂²	semidirect
78. #447×C₆₇	C₂²	semidirect
79. #441×C₆₇	C₂²	semidirect
80. #440×C₆₇	C₂²	semidirect
81. C₄×Q₁₆×C₆₇	C₂²	semidirect
82. C₄×SD₁₆×C₆₇	C₂²	semidirect
83. #436×C₆₇	C₂²	semidirect
84. #435×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. #428×C₆₇	C₂²	semidirect
87. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
88. #419×C₆₇	C₂²	semidirect
90. #416×C₆₇	C₂²	semidirect
91. C₂×#102×C₆₇	C₂²	semidirect
92. #408×C₆₇	C₂²	semidirect
93. C₄×M₁₆×C₆₇	C₂²	semidirect
118. #137×C₆₇	D₄	semidirect
250. C₂×Q₈×C₆₇	C₂×D₄	semidirect
300. Q₁₆×C₆₇	C₂×D₄	semidirect
307. SD₁₆×C₆₇	C₂×D₄	semidirect
313. M₁₆×C₆₇	C₂×D₄	semidirect
459. C₄×C₆₇	#577	semidirect
462. #61095	C₆₇	direct (N × H)
471. C₂×#577	C₂×C₆₇	semidirect
472. #3498	C₂×C₆₇	semidirect
473. #3497	C₂×C₆₇	semidirect
474. #3287	C₂×C₆₇	semidirect
475. D₄×SD₁₆	C₂×C₆₇	semidirect
476. #3278	C₂×C₆₇	semidirect
477. #3274	C₂×C₆₇	semidirect
478. #3271	C₂×C₆₇	semidirect
479. #3265	C₂×C₆₇	semidirect
480. #3151	C₂×C₆₇	semidirect
481. #3062	C₂×C₆₇	semidirect
482. #3035	C₂×C₆₇	semidirect
483. C₂×#460	C₂×C₆₇	semidirect
484. #3012	C₂×C₆₇	semidirect
485. #3010	C₂×C₆₇	semidirect
486. C₄×#137	C₂×C₆₇	semidirect
487. #2935	C₂×C₆₇	semidirect
488. C₆₇	#61095	direct (N × H)
489. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
493. C₂×#137	C₂²×C₆₇	semidirect
494. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
495. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
496. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
498. C₂×#135	C₂²×C₆₇	semidirect
499. C₂²×SD₁₆	C₂²×C₆₇	semidirect
500. C₂²×SD₁₆	C₂²×C₆₇	semidirect
501. C₂×#131	C₂²×C₆₇	semidirect
505. #550	C₂²×C₆₇	semidirect
507. D₄×Q₈	C₂²×C₆₇	semidirect
509. #548	C₂²×C₆₇	semidirect
515. #537	C₂²×C₆₇	semidirect
521. #532	C₂²×C₆₇	semidirect
525. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
526. #496	C₂²×C₆₇	semidirect
527. #493	C₂²×C₆₇	semidirect
528. #492	C₂²×C₆₇	semidirect
529. #469	C₂²×C₆₇	semidirect
530. #468	C₂²×C₆₇	semidirect
531. #466	C₂²×C₆₇	semidirect
532. #465	C₂²×C₆₇	semidirect
533. #464	C₂²×C₆₇	semidirect
534. #463	C₂²×C₆₇	semidirect
535. #462	C₂²×C₆₇	semidirect
536. #461	C₂²×C₆₇	semidirect
537. #460	C₂²×C₆₇	semidirect
538. #460	C₂²×C₆₇	semidirect
539. #460	C₂²×C₆₇	semidirect
540. #460	C₂²×C₆₇	semidirect
541. #459	C₂²×C₆₇	semidirect
542. #452	C₂²×C₆₇	semidirect
543. #450	C₂²×C₆₇	semidirect
544. #449	C₂²×C₆₇	semidirect
545. #449	C₂²×C₆₇	semidirect
546. #449	C₂²×C₆₇	semidirect
547. #448	C₂²×C₆₇	semidirect
548. #448	C₂²×C₆₇	semidirect
549. #447	C₂²×C₆₇	semidirect
550. #441	C₂²×C₆₇	semidirect
551. #440	C₂²×C₆₇	semidirect
552. C₄×Q₁₆	C₂²×C₆₇	semidirect
553. C₄×SD₁₆	C₂²×C₆₇	semidirect
554. #436	C₂²×C₆₇	semidirect
555. #435	C₂²×C₆₇	semidirect
556. C₈×D₄	C₂²×C₆₇	semidirect
557. #428	C₂²×C₆₇	semidirect
558. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
559. #419	C₂²×C₆₇	semidirect
561. #416	C₂²×C₆₇	semidirect
562. C₂×#102	C₂²×C₆₇	semidirect
563. #408	C₂²×C₆₇	semidirect
564. C₄×M₁₆	C₂²×C₆₇	semidirect
589. #137	D₄×C₆₇	semidirect
721. C₂×Q₈	C₂×D₄×C₆₇	semidirect
771. Q₁₆	C₂×D₄×C₆₇	semidirect
778. SD₁₆	C₂×D₄×C₆₇	semidirect
784. M₁₆	C₂×D₄×C₆₇	semidirect
930. C₄	#577×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₆₇×#3498	2
C₆₇×#3497	2
C₆₇×#3287	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3278	2
C₆₇×#3274	2
C₆₇×#3271	2
C₆₇×#3265	2
C₆₇×#3151	2
C₆₇×#3062	2
C₆₇×#3035	2
C₂×#460×C₆₇	2
C₆₇×#3012	2
C₆₇×#3010	2
C₄×#137×C₆₇	2
C₆₇×#2935	2
#61095	67

Subgroups — C67×#61095 #30740346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61095 #30740346